ejpam: A Pathfinder

This is a computer-generated pathfinder created against the Distant Reader study called ejpam.

Each Distant Reader study carrel is composed of many individual items. Each item is bibliographically described with author, title, date, summary, and keyword values. Below is a list of the items' most signficant keywords as well as lists of the items themselves. Purpusing the content of this pathfinder provides the student, researcher, or scholar with one way to get their heads around the scope of the carrel. The keywords include:

Model; Method; Fractional; Pure; Math; Graph; Fuzzy; Open; Appl; Dominating; Solution; Equation; System; Time; Function; Space; Equations; Sets; Distribution; Functions; Point; Data; Matrix; Order; Hop; Problem; Differential; Metric; Numerical; Ideal; Solutions; Polynomials; Theorem; Group; Flow; I=1; Vertex; Stability; Neutrosophic; Spaces; Transform; Optimization; Ring; Fluid; Algorithm; Disease; Σ1σ2; Algebra; Rate; Numbers; Τ1τ2; Decision; Log; Class; Table; Analysis; Series; Operator; Vertices; Index; Temperature; J=1; Sequence; Prime; Values; Edge; Let; Energy; Integral; Finite; Resolving; Parameter; Value; Convex; Codes; Module; N=0; Mod; Inverse; Subgroup; Linear; Operators; Systems; Population; Performance; Gradient; Type; Scheme; Velocity; Cost; Curve; Network; Submodule; Distance; Labeling; Step; Manifold; Learning; Regression; Methods; Lim; Semigroup; Quasi; Variables; Supra; Forcing; Graphs; Theory; Product; Lie; Ternary; Inequality; Sup; Hyper; Boundary; Domination; Mathematics; Quantum; Definition; Test; Cover; Skew; Inequalities; Concentration; K=1; Category; N=1; Self; Vector; Left; Cyclic; Family; Process; Estimator; Pre; Sin; Fractal; Cos; Structure; Neighborhood; Sp)-open; K=0; Problems; Indices; Matrices; Interval; Weight; Element; Lemma; Act; Representation; Prey; Banach; Example; Projective; Block; Mapping; Blow; Algebras; Locating; Subalgebra; Pythagorean; Entropy; Γ(β; Contraction; J)−; J(r; Semi; Semigroups; Likelihood; Binary; Points; Monoid; Hausdorff; Water; Complex; G(t; Pseudo; Property; Cone; Option; Density; Exp; Resp; Poisson; Filter; Max; Triangle; Wall; Approximation; Symmetry; I=0; Sultan; Eisenstein; Contra; -open; P(x; Code; Map; Multi; Base; Finsler; ∥∥∥∥; N→∞; Secret; Form; Hierarchy; S−1; L−1; Proposition; Respect; Waste; Conjecture; U(x; Triangular; Key; Spline; Lattice; I∈i; Cauchy; Coloring; Δp(λ; G(x; Basis; P)-open; Min; Der; Sum; Sheffer; A(x; Quaternions; Φ(x; U(t; Lines; Monomorphisms; Equivalent; Addition; Expansion; Hyperring; Ρ(x; F(z; D(xn; State; Bounds; Case; Hypervector; R(s; Q(x; Micro; Deg; Γ∗tpw; ∥∥∥∥∥∥; Regular; Paper; Law; Dokdo; Rainbow; Mosquitoes; Independent; Stk; Clique; Generator; Degenerate; Y;u; Primal; N+1; D(x; Liquid; Z=0; Iup; R+1; ⟨0.5; Q(ξ; Observations; Crossing; Quaternion; Secη+; |z|; J(m; Randić; G(r; -closed; Wijsman; O32; Q)s; Εn10; Hurewicz; Simplicial; Mpq; R(x; Extension; S(s; ∆2,8; Cl∗e; Αgrw; Semimodule; Encoding; Nzi; 1)b; B]t; A]p; Chaudhary; Diframe; D(a; Σ(z; Eif; Hh(x; Aru; 2,2,t; I(x; Covering; Divergence; E)∗s; Tubings; Tmax; Controllability; L2(u; D2(x; F1(t; Page; Grand; Hks; R−,k; Τ−1; Mcshane; K(x; L+1; Ẋ1; U,∆m; Êxt; Φ(t)dt; Kfd; P10; X3k+2; X(n; A+1; Brk; N≥0; T)bp]1−; 2imπ; L(e; D(q; Levels; S(λ; ˜̃g; X}(λ; Meet; Γkgr(g; Integrable; J(t)g; B)-open; Intf; Ee1; Hyperplanes; Sβcli; Δs(λ; N∈z; Ν+1; Gbasp; Γ(1+(s+1)γ; Aλ2; Yj(ε; Primes; 2n−1; Qge; Division; Mds; Hs1; Dpd; Rh(k; Kim; Α(τ1; Dense; U12; Pchs; |ℶ2|+; Ωswd(z; Id−r; Ρ̌0; G(k; Irregularity; 1+ε; B1−ξ; |n2; Functional; Eccentricity; |b|; Cohomology; Gµ-paracompact; Ζhgk; F(ζ; C[a; S)-f; ˜̃m; Θ(i; 0.6; Exp−1; Ω(γ; Möbius; ℵa(s)e; Ð=0; S(ξ; Αw(g; S̃ℓ; Tpf; I→1; Srl; Ρ̃γ; F2℘; Sla; Γ(κ; Diag; A1+κ̄; Ti−1; Alt(n; L(sdg; Aczel; S(α1; -regular; Fix; Γs(g; Qω1; Gmcϱ; Λ,ℓ; Ln+1; Grill; Extropy; Δ(p; Is⋆g; Λ,µ; Integrals

Depending on how this pathfinder was created, many of the bibliographic sections will include elaborations on the meaning(s) of the given keywords. These elaborations were generated by feeding the items' summaries to a large langauge model and asking the model to address the question, "What is X?", where "X" is the keyword. The result will be a few sentences of elaboration. Be forewarned. The elaborations are often plausible, but they should not be take as truth. Instead, they should be taken as points for consideration.

Model

Analysis of Thermoelastic Response in a Fiber Reinforced Thin Annular Disc with Three-Phase-Lag Effect by Kar, Avijit; Kanoria, M. (2011) - Email addresses: akmathemati s�yahoo. τr r = C11 ∂ u ∂ r + C12 u r −β11T, (1) τθθ = C12 ∂ u ∂ r + C11 u r − β22T (2) and the generalized heat conduction equation in the three-phase-lag model [27] is K∗∇2T +τ∗ν∇2 Ṫ + KτT∇2 T̈ = � 1+τq ∂ ∂ t + 1 2 τ2 q ∂ 2 ∂ t2 � × � ρCe T̈ + T0 ∂ 2 ∂ t2 � β11 ∂ u ∂ r + β22 u r �� , (3) where τi j (i, j = r,θ) is the stress tensor, T is the temperature increase over the reference temperature T0, C11 and C12 are elastic constants, β11 and β22 are thermal modulii, K is the coefficient of thermal conductivity along radial direction, K∗ is the additional material constant along radial direction, ρ is the mass density, Ce is the specific heat of the solid at constant strain, τT and τq are the the phase-lag of temperature gradient and the phase-lag of heat flux respectively. Keywords: j(r; lag; model; phase; thermo; � �
Predictive Subset Selection using Regression Trees and RBF Neural Networks Hybridized with the Genetic Algorithm by Akbilgic, Oguz; Bozdogan, Hamparsum (2011) - Least Squares Estimation Given a network (or model) in (1) consisting of m RBFs with centers ¦ c j ©m j=1 and radii¦ r j ©m j=1 and a training set with p patterns, �� x i, yi � p i=1 , the optimal network weights can be found by minimizing the sum of squared errors: SSE = p∑ i=1 � f (x i)− yi �2 (8) and is given by ŵ = � H ′ H �−1 H ′ y (9) the so called normal equation. Hi j = h j(x i), and y = � y1, y2, . . . Keywords: bozdogan; information; model; rbf; regression; selection; subset; � −; � �
Decomposition of Symmetry Model into Three Models for Cumulative Probabilities in Square Contingency Tables by Tahata, Kouji; Yamamoto, Kouji; Tomizawa, Sadao (2017) - A simple diagonals-parameter symmetry and quasi-symmetry model. Linear diagonals-parameter symmetry and quasi-symmetry models for cumulative probabilities in square contingency tables with ordered categories. Keywords: model
Misspecified Multivariate Regression Models Using the Genetic Algorithm and Information Complexity as the Fitness Function by Bozdogan, Hamparsum; Howe, J. Andrew (2012) - Theoretical results are then applied to multivariate regression models in subset selection of the best predictors in the presence of model misspecification by using the novel genetic algorithm (GA), with our extended ICOM P as the fitness function. For example, if the crossover point is 2, we have �� 1 1 1 0 1 1 0 0 1 0 Keywords: bozdogan; covariance; criteria; howe; icom; information; log; math; matrix; misspecification; model; multivariate; pure; regression
Performance of Information Complexity Criteria in Structural Equation Models with Applications by Deniz Howe, Eylem; Bozdogan, Hamparsum; Kiroglu, Gulay (2012) - = s 2 log   1 n t r(Σ̂) + 1 2n  t r(Σ̂2) + (t r(Σ̂))2 + 2 p+q∑ j=1 � σ̂ j j �2   s   − 1 2 (p+ q+ 2) log ��Σ̂ ��+ 1 2 � (p+ q) + 1 2 � p+ q �� p+ q+ 1 �� log(n) (31) + 1 4 � p+ q �� p+ q− 1 � log(2), where s = dim(F̂−1) = rank(F̂−1) A common problem in structural equation modeling is that of model selection. Keywords: aic; bozdogan; criteria; icom; information; log; model; p(i; sem
On Multivariate Time Series Model Selection Involving Many Candidate VAR Models by Zhao, Xindong; Qian, Guoqi (2014) - However, difficulty may arise in VAR model selection when the number of the candidate models is extremely large. Rather we focus on the aforementioned computing issue of VAR model selection that is largely ignored in literature but needs to be addressed when there are very many candidate models available for selection. Keywords: candidate; coefficients; model; model selection; order; qian; sample; selection; subset; var; var model
Binary Classification for Hydraulic Fracturing Operations in Oil & GasWells via Tree Based Logistic RBF Networks by Akbilgic, Oguz (2017) - We have also tested our model on classification problems with more than two classes and again our results were encouraging in terms of classification accuracy. [4] is one of the tree-based statistical tech- niques for prediction and classification problems depending on the type of target variables, either continuous or categorical. Keywords: classification; data; layer; logistic; model; rbf; regression
Robust control system for Spacecraft Motion Trajectory by Zarina, Samigulina Ildusovna; Olga, Shiryeva Ivanovna; Galina, Samigulina Ahmetovna; Hassen, Fourati Ben Mahmoud (2014) - Then, the problem of model reference adaptive control system can be seen as a regulation problem for the spacecraft system displaced from its equilibrium state (defined by AM = AS , BM = BS) using the adjusted parameters fA and fB (see Figure 1). Optimal Mathematical Model of SMT Let consider the mathematical model of SMT which is described by the nonlinear differen- tial equations system based on the boundary conditions [7]:      ṗ (t) = 2 � p (t) �(3/2) (Q (t) + 1)−1 aφ Q̇ (t) = � −p (t) �(−3/2) (Q (t) + Keywords: adaptive; control; model; reference; samigulina; smt; spacecraft; system
Analyzing Periodic Solutions of an ODE Suspension Bridge Model using Difference Equations and Polynomial Methods by Basu, Sukanya (2014) - It was also missing three key aspects, namely, (a) bounds on the number of real equilibria and real periodic solutions, (b) existence conditions for the real equilibria and periodic solutions, and (c) global attractivity results for these solutions including basins of attraction and precise bifurcation values for the parameters λ and µ. In this paper, the author will set up a rigorous mathematical foundation for the McKenna- Moore suspension bridge model (1) by first discretizing it and then employing analytical and geometrical methods from the theory of difference equations (see [2–4, 9–12, 15]) to analyze equilibria and periodic solutions of the resulting difference equation. Since periodic solutions of discrete 2D-systems occur in pairs, one can conclude that there exist at most three pairs of real nontrivial periodic solutions of equation (12) for 0< Keywords: bridge; equation; equilibria; model; solutions
The Optimal Orchestration of Packaging for Sustainability by Onay, Onur; Cetin, Eyup (2016) - The models determine package usage ratios which minimize the packaging wastes when packaging amount is at maximum level in the envi- ronment. The model applied to packaging amount of 2011. Keywords: model; packaging
Measuring Set Latent Variables Through Exploratory Factor Analysis with Principal Components Extraction and Validation with AMOS Software by GarcÃa-SantillÃ¡n, Arturo (2017) - To get objectives SO2 and SO3, we should use the approach of two steps for SEM; measurement of model and structural model. Math, 10 (2) (2017), 167-198 179 Furthermore, the estimation of model parameters is performed in order to determine which one best fit has maximum likelihood; weighted least squares and generalized least squares. 2.1. Keywords: analysis; anxiety; appl; attitude; data; escalera; eur; factors; fit; garcía; index; mathematics; matrix; model; pure; santillán; variables; variance
Granger Causality by Hendry, David F. (2017) - Math, 10 (1) (2017), 12-29 15 Unfortunately, such a confusion abounds in the empirical literature, with studies often claiming evidence for Granger causality from bivariate models. [17] highlight the role of Granger causality in the distributions of some encompassing test statistics when ‘completing’ models are needed to link the variables in the two models under consideration. Keywords: causality; changes; exogeneity; granger; hendry; model; non; oxford; time; variables; x2,t
Sir Clive W.J. Granger's Contributions to Forecasting by Clements, Michael P. (2017) - The fixed-weight combination forecasts are not feasible, as they are calculated based on the full set of forecast errors, and as noted above, [5] suggest time-varying weight schemes. It covers forecast combination in section 2, improving forecast practice in section 3, forecast evaluation in section 4, and forecasting white noise in section 5. Keywords: clements; combination; economic; error; forecast; forecasting; granger; journal; linear; loss; model; time
Sir Clive W.J. Granger's Contributions to Nonlinear Time Series and Econometrics by Terasvirta, Timo (2017) - In this work the focus is on his contributions to nonlinear time series models and modelling. In fact, this definition incorporates many models that are normally thought of as nonlinear time series models such as smooth transition, threshold autoregressive or Markov-switching autoregressive models. Keywords: clive; cointegration; granger; j. granger; journal; model; nonlinear; process; pure; series; teräsvirta; test; time; timo; white
Sir Clive W.J. Granger Model Selection by Castle, Jennifer L. (2017) - Model selection, model averaging and thick modelling Commencing from an information set, model selection can be interpreted as pooling the available information set and selecting possible model specifications therefrom. This paper proposes to integrate thick modelling into the general-to-specific model selection literature, yielding the benefits of selecting a set of well-specified encompassing models while taking seriously Granger’s critique of model selection. Keywords: averaging; castle; forecasts; granger; gum; hendry; ldgp; model; model selection; modelling; selection; set; terminal; thick; variables
Solving the Ivancevic Pricing Model Using the He's Frecuency Amplitude Formulation by GonzÃ¡lez-Gaxiola, Oswaldo; Edeki, S. O.; Ugbebor, O. O.; de Ch'avez, J. Ruiz (2017) - Thus, the Ivancevic option pricing model (IOPM) is a nonlinear adaptive- wave alternative for the classical Black-Scholes option pricing model; it represents a controlled Brownian motion (BM) in an adaptive setting with relation to nonlinear Schrödinger equation. Math, 10 (4) (2017), 631-637 633 Henceforth, such nonlinear adaptive model is referred to as Ivancevic option pricing model as follows: Keywords: frequency; model; nonlinear; option; pricing; scholes
A New Mathematical Model of Heat Equations And its Application on the Agriculture Soil by Allahem, Ali; Boulaaras, Salah; Zennir, Khaled; Haiour, Mohamed (2018) - Temperature diffusion equation The objective of this work is precisely to propose a one-dimensional numerical predic- tion model based on the finite element approximation for the evolution of the temperature field in a homogeneous soil. The model was treated through this research that enable to know the degree of soil temperature homogeneous without recourse to tools of measuring physical expensive. Keywords: finite; model; n−1∑; soil; temperature; uhn; uhn+1
Novel Approaches on Sovereign Credit Ratings by Onal, Nisa Ozge; Karacuha, Ertugrul (2018) - With the increase of international financial and economic integration, country credit ratings have become one of the most important elements that direct the global capital flow. 2010 Mathematics Subject Classifications: 92B20, 62-07, 62F10 Key Words and Phrases: Artificial neural networks, Adaptive filters, Normalized least mean square algorithm, Sovereign credit ratings, Stock market prediction 1. Introduction Sovereign credit rating is determined using quantitative and qualitative features devel- oped by the CRAs, taking into account the economic and political risks of the countries. Keywords: countries; cras; credit; data; journal; mape; market; model; nlms; ratings; results; stock; values
Existence and Uniqueness Solution Under Non-Lipschiz Condition of the Mixed Fractional Heston's Model by Njamen Njomen, Didier Alain; Djeutcha, Eric; Fono, Louis-Aime (2019) - Using the successive ap- proximation method, the existence and uniqueness theorems of solutions to the following non-Lipschitz SDEs driven by mfBm are proved: X(t) = x0 + ∫ t 0 µ(s,X(s))ds+ ∫ t 0 σ1(s,X(s))dBs + ∫ t 0 σ2(s,X(s))dBHs , (3) where t ∈ [0, T ], x0 = ξ ∈ Rn is a random variable, 0 ≤ T < ∞, the process B represent a m-dimensional standard Ft-Brownian motion and the process BH represent a d-dimensional Ft-adapted fractional Brownian motion with the Hurst index H ∈ ( 3 4 , 1) defined in a same com- plete probability space (Ω,F ,P), and µ(t,X(t))[0, T ] × R → R,σ1(t,X(t)) : [Dϕ s u(s)]2dsdt < ∞ and for each sequence of partition (πn, n ∈ N) such that |πn| → 0 as n→ 0 n−1∑ i=0 E ∫ t (n) i+1 t (n) i ∫ t (n) j+1 t (n) j ∣∣∣Dϕ s u π(t (n) i )uπ(t (n) j )−Dϕ s u(t)Dϕ t u(s) ∣∣∣ dsdt and E[‖uπ − u‖2ϕ]2 tend to 0 as n→ 0, where πn = t (n) 0 < t (n) 1 < . . . Keywords: american; brownian; mfh; model; option; price
Optimal Control of a Time Delayed HIV-1 Infection Model by Ali, Nigar; Chohan, Muhammad Ikhlaq; Zaman, Gul (2019) - Key Words and Phrases: HIV-1 model, Optimal control, Recombinant virus, Pontryagin’s maximum principle, Objective functional. Proof : To prove the existence of optimal control, we will follow [? ]. Keywords: cells; control; density; hiv; model; treatment; virus
Mathematical Analysis of an Immune-structured Chikungunya Transmission Model by Famane, Kambire; ElisÃ©e, Gouba; Sadou, Tao; Some, Blaise (2019) - − dII, we obtain the inequality dNH dt ≤ (bH − dH − d2HNH)NH . Math, 12 (4) (2019), 1533-1552 1542 lim t→+∞ NV (t) = bV − dV d2V . Keywords: humans; model
Developing Optimal Policies to Fight Pandemics and COVID-19 Combat in the United States by Cetin, Eyup; Kiremitci, Serap; Kiremitci, Baris (2020) - Here we develop and propose two optimization models to maximize the total protection from any epidemic, pandemic or bioterror attacks; the first one is personal protection model or protocol and the other one is mass protection model that is in- spired by the well-known weapon-target assignment problem of operations research. In this work, we propose two mathematical programming models for fighting any pan- demic at micro and macro levels, respectively; the first one is personal protection model or protocol and the other one is mass protection model for a country. Keywords: agents; coronavirus; cost; covid-19; kiremitci; mass; model; number; pandemic; person; protection; segments; target; tools; total; url
Scenario Tree and Adaptive Decision Making on Optimal Type and Timing for Intervention and Social-economic Activity Changes to Manage the COVID-19 Pandemic by Nah, Kyeongah; Chen, Shengyuan; Xiao, Yanyu; Tang, Biao; Bragazzi, Nicola; Heffernan, Jane; Asgary, Ali; Ogden, Nicholas; Wu, Jianhong (2020) - Taking into account the uncertainties in contact rates during different re-opening phases, we find the optimal timing for the upcoming re-opening phase that maximizes the relaxation of social contacts under uncertainties, while not overwhelming the health system capacity before the arrival of effective therapeutics or vaccines. However, they can be informed by, for example, mathematical modelling studies of historical measures of COVID-19 public health mitigation strategies during different closure stages – bounds of contact rates in the future may be reasonably established in terms of the economic sec- tor and social, economic and health considerations, from which ranges in the timing and magnitude of peak demand of ICU units can be inferred. Keywords: canada; cases; contact; covid-19; escalation; health; icu; model; oct; ontario; opening; phase; rate; scenarios; transmission
The Component Weighted Median Absolute Deviations Problem by Novoselac, Vedran (2020) - This is the situation when w = w(p) starts to be included into the sum (3), which immediately generates the interval Is for the second case (II) in Theorem 2, i.e. Is = 〈w−s ,+∞〉, so that F (z;w) = z(ν+s +1) = z(p), w ∈ Is, and singleton case when F (z;w−s ) , z(dm+1 2 e)}, (5) it holds that ν−i = maxL, w ∈ Ii, where an interval Ii presents the solution of the observed inequality (5) for the corresponding ν−i . Keywords: function; model
A Delayed Vaccination Model for Rotavirus Infection by Adongo, Florence A.; Lawrence, Onyango Omondi; Bonyo, Job; Lawi, G. O.; Elisha, Ogada A. (2020) - a8 = βI∗ a9 = βS∗ + (1− ε)V ∗(t− τ)− (δ + κ+ µ) To find the characteristic equation of the linearized system (1) at steady states, we compute the eigenvalues of the following matrix∣∣∣∣∣∣ λ− a1 a2 a3 a4 λ− [a5e −λτ + a6] a7 a8 a5e −λτ λ− a9 ∣∣∣∣∣∣ = 0 this gives λ3 +M2λ 2 +M1λ+M0 + (N2λ 2 +N1λ+N0)e−λτ = 0, (2) where M2 = −(a1 + a6 + a9) M1 = (a6a9 + a1a6 + a1a9 − a2a4 − a3a8) M0 = (−a1a6a9 − a2a4a9 − a2a7a8 + a3a6a8) N2 = −a5 N1 = (a5a9 − a5a7 + a1a5) N0 = (a1a5a7 − a1a5a9 + a3a4a5 + a3a5a8). Figure (3) shows that the endemic equilibrium E∗(35.7321, 45.5913, 6.3217) Figure 2: Simulation of system (1) shows the global stability of the disease-free equilibrium when Rv = 0.7692 is locally asymptotically stable when τ ∈ Keywords: disease; equilibrium; model; onyango; rotavirus; time
A Blood Bank Location Model: A Multiobjective Approach by Cetin, Eyup; Sarul, L. Sinem (2009) - The objectives, which are handled via binary nonlinear goal programming, are minimizitation of total fixed cost of location blood banks, total traveled distance between the blood banks and hospitals and an inequality index as a fairness mechanism for the distances. There are some crucial factors for blood bank location, namely, transaction demands (or shipments) Keywords: banks; blood; care; goal; health; hospitals; location; model; programming
Analysis of Agricultural Performance in Burkina Faso Using Data Envelopment Analysis by YougbarÃ©, Jacob Wendpanga (2021) - Our specific objectives are: • to enable measures and analyses of agricultural production efficiencies; • to enable the determination of efficient units that can be used as a reference; • to enable the identification of sources of production inefficiency; • to enable decision-makers and partners to guide investments taking into account reference units and inefficiencies in agriculture sector in Burkina Faso. DEA technical efficiency The performance of the DMU d is fully (100%) efficient (CCR ) Keywords: data; dea; dmu; efficiency; input; model; output; performance; production
Modeling the Historical Temperature in the Province of Laguna Using Ornstein-Uhlenbeck Process by Quindala, Kemuel III; Cuaresma, Diane Carmeliza; Mamplata, Jonathan (2021) - This indicates that increasing in minimum temperature is higher than that of maximum temperature. It has been known that oxygen solubility decreases as temperature increases [19]. Keywords: climate; increase; laguna; maximum; minimum; model; temperature
The ARMA-APARCH-EVT Models Based on HAC in Dependence Modeling and Risk Assessment of a Financial Portfolio by Moutari, Natatou Dodo; Hassane, Abba Mallam; Diakarya, Barro; Bisso, Saley (2021) - −0.03 | Mean: −0.0134 G A R C H m od el : a pA R C H ● ● normal Density sstd (0,1) Fitted Density ● ● ● ● ● ● ● ● ● ●●●● ●● ● ● ● ● ● ●● ●●●● ● ●●● ● ● ● ●● ● ● ● ●● ● ●●●● ● ● ● ●●●●●●● ● ●● ● ● ● ● ● ● ● ●● ● ●● ● ●● ● ● ● ●● ●● ●● ● ● ●●●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ●● ●● ●●●● ● ●● ● ●● ● ● ● ● ●●●●●●●● ● ●● ● ● ● ●● ●●●●●● ● ●● ●● ● ●● ●● ●●●●● ● ● ●●●● ● ●●● ● ● ●● ● ●●● ● ● ●● ● ● ● ● ● ●● ●● ● ●● ● ●●●● ● ●● ● ● ● ●●●● ● ● ● ● ● ●●● ● ● ● ● ● ● ●●● ●● ● ● ● ● ● ● ● ●● ●● ●●●● ● ●● ● ●●● ●●● ● ● ●●●● ●●●●●●●● ● ●● ● ● ● ● ● ● ●● ● ● ●●●●● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ●●●● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●●● ● ● ●● ● ● ● ● ● ●●● ● ●● ● ● ●● ●● ●● ● ●●● ● ● ● ●● ● ● ● ● ●●●● ● ●●● ●● ● ● ● ●● ●● ● ● ● ●● ● ● ● ● ● ● ●●●● ●● ● ● ● ● ●● ● ● ●● ●● ● ●● ●●●● ● ● ● ● ● ● ● ● ● ●●● ● ● ●● ● ●●●● ● ● ● 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H m od el : a pA R C H Figure 4: The top row shows empirical density graphs of standardized residuals and the quantile-quantile-sstd plot of the SP 500 series. Estimation of HAC model parameters We use the means of the pairwise versions of Kendall’s tau and the relationship θ ∼ τ to estimate the different parameters of the HAC. Keywords: aparch; archimedean; arma; copulas; dependence; hac; model; modeling; risk; structure; var; ● ●
Bifurcation Analysis of a Mathematical Model for the Covid-19 Infection among Pregnant and Non-Pregnant Women by Tsetimi, Jonathan; Ossaiugbo, Marcus Ifeanyi; Atonuje, Augustine (2022) - β Modification parameter accounting for increased susceptibility to covid-19 infection by pregnant women µ Natural death rate ς Disease-induced death rate ε Rate at which infectious non-pregnant women move into the hospitalised class α Rate at which infectious pregnant women move into the class of hospitalised individuals η Recovery rate of non-pregnant infectious individuals γ Recovery rate of infectious pregnant women ϕ The effects of the effective contact rate, delivery rate, transmission coefficient of the class of infectious pregnant women and modification parameter accounting for in- creased susceptibility to covid-19 infection by pregnant women over the population of infectious individuals shall also be considered. Keywords: class; covid-19; disease; infection; model; number; rate; women
Computer Virus Fractional Order Model with Effects of Internal and External Storage Media by Farman, Muhammad ; Akgül, Ali ; Shanak, Hussein; Asad, Jihad; Ahmad, Aqeel (2022) - We have following system of differential equations dS dt = b1 + γ2L+ γ3B + ηR− µS − γ1S − β1LS − β2BS − θS, dL dt = b2 + β1LS + β2BS + θS − γ1L− γ2L− µL− αL, dB dt = b3 + αL− µB − γ1B − γ3B, dR dt = b4 + γ1S + γ1L+ γ1B − ηR− µR. (5) We can express the above system in ABC fractional order form as: ABC 0D α t S(t) = b1 + γ2L+ γ3B + ηR− µS − γ1S − β1LS − β2BS − θS, ABC 0D α t L(t) = b2 + β1LS + β2BS + θS − γ1L− γ2L− µL− αL, ABC 0D α t B(t) = b3 + αL− µB − γ1B − γ3B, ABC 0D α t R(t) + α Γ(σ)×ABC(σ) m∑ k=o ( h(tk, yk) h ∫ tk+1 tk (τ − tk−1)(tn+1 − τ)σ−1dτ − h(tk−1, yk−1) Keywords: 1)eα; abc; b(α)αγ(α+; computer; fractional; model; system; virus
Mathematical Analysis and Simulation of an Age-Structured Model with Two-Patch and an Uncontrolled Migration: Application to Tuberculosis by Badjo Kimba, Abdoul Wahid; Moustapha, Dijbo; Saley, Bisso (2022) - [λ1(t, a) + ψ1(a) + b(a) − µ1(a)i1(t, a) − µ2(a)i2(t, a) + ρ11]s1(t, a) + ρ21s2(t, a)( ∂ ∂t + ∂ ∂a ) l1(t, a) = λ1(t, a)[(1 − ϕ1)s1(t, a) + σ1j1(t, a) + δ1v1(t, a)] −(k1 + b(a) − µ1(a)i1(t, a) − µ2(a)i2(t, a) + ρ12)l1(t, a) + ρ22l2(t, a)( ∂ ∂t + ∂ ∂a ) i1(t, a) = −(r1 + µ1(a) + b(a) − µ1(a)i1(t, a) − µ2(a)i2(t, a) + ρ13)i1(t, a) + ρ23i2(t, a) +ϕ1λ1(t, a)s1(t, a) + k1l1(t, a)( ∂ ∂t + ∂ ∂a ) j1(t, a) = r1i1(t, a) − (σ1λ1(t, a) + b(a) − µ1(a)i1(t, a) − µ2(a)i2(t, a) + ρ14)j1(t, a) + ρ24j2(t, a)( ∂ ∂t + ∂ ∂a ) v1(t, a) = ψ1(a)s1(t, a) + ρ25v2(t, a) − (b(a) + ρ15 + δ1λ1(t, a) − µ1(a)i1(t, a) − µ2(a)i2(t, a))v1(t, a)( ∂ ∂t + ∂ ∂a ) s2(t, a) = α2b2(a) − [λ2(t, a) + ψ2(a) + b(a) − µ1(a)i1(t, a) − µ2(a)i2(t, a) + ρ21]s2(t, a) + ρ11s1(t, a)( ∂ ∂t + ∂ ∂a ) l2(t, a) = λ2(t, a)[(1 − ϕ2)s2(t, a) + σ2j2(t, a) + δ2v2(t, a)) −(k2 + b(a) − µ1(a)i1(t, a) − µ2(a)i2(t, a) + ρ22)l2(t, a) + ρ12l1(t, a)( ∂ ∂t + ∂ ∂a ) i2(t, a) = −(r2 + µ2(a) + b(a) − µ1(a)i1(t, a) − µ2(a)i2(t, a) + ρ23)i2(t, a) + ρ13i1(t, a) +ϕ2λ2(t, a)s2(t, a) + k2l2(t, a)( ∂ ∂t + ∂ ∂a ) j2(t, a) = r2i2(t, a) − (σ2λ2(t, a) + b(a) − µ1(a)i1(t, a) − µ2(a)i2(t, a) + ρ24)j2(t, a) + ρ14j1(t, a)( ∂ ∂t + ∂ ∂a ) v2(t, a) = ψ2(a)s2(t, a) + ρ15v1(t, a) − (b(a) + ρ25 + δ2λ2(t, a) − µ1(a)i1(t, a) − µ2(a)i2(t, a))v2(t, a) (5) with boundary conditions si(t, 0) = Λi; vi(t, 0) = li(t, 0) = ii(t, 0) = ji(t, 0) Keywords: age; b(a; disease; model; tuberculosis; − ∫
Using Kriging Technique to Interpolate and Forecasting Temperatures Spatio-Temporal Data by Dhaher, Ghanim; Shexo, Ahmed (2023) - Dynamic semi-parameter factor model uses for temperature data covering a large area of Mosul city in Iraq and evaluating its performance rather than Baghdad city. To obtain the number of dynamic semi parameter factor model, we use the value, ”Value” which can be clear as the shown difference of the model and written as follows: v1 = T∑ t=1 I∑ i=1 { Z(t,i) −mo (xt,i)− L∑ l=1 Ẑ(t,l) · Keywords: city; data; factor; function; kriging; model; mosul; temperature; variogram
Predictive Subset VAR Modeling Using the Genetic Algorithm and Information Complexity by Howe, Andrew; Bozdogan, Hamparsum (2010) - [14] and Penm and Terrell [18] recommend subset VAR models which are basically saturated VAR(q∗) models, where q∗ < order of full saturated model. While one simulation took at most 15 minutes, obtaining results across many simulations is recommended, due to the fact that there are 9.808×1055 possible REFERENCES 404 subset VAR models. Keywords: appl; bozdogan; data; eur; howe; icom; math; matrix; model; pure; subset; var
Optimal Control of COVID-19 Model with Partial Comorbid Subpopulations and Two Isolation Treatments in Indonesia by Rois, Muhammad Abdurrahman; Fatmawati; Alfiniyah, Cicik (2023) - Math, 16 (1) (2023), 523-537 525 Figure 1: COVID-19 Model with Partial Comorbidity Sub-populations and Two Isolation Treatments dEN dt = α (β1SIN + β2SIC) N − δ1EN − µEN , dEC dt = (1− α) (β1SIN + β2SIC) N − δ2EC − µEC , dIN dt = δ1EN − h1IN − r1IN − d1IN − µIN , (1) dIC dt = δ2EC − h2IC − r2IC − d2IC − µIC , dHT dt = θh1IN + δh2IC − r3HT − d3HT − µHT , dHN dt = (1− θ)h1IN + (1− δ)h2IC − r4HN − d4HN − µHN , dR dt = r1IN + r2IC + r3HT + r4HN − µR. Based on Indonesian data, it can be concluded that the MAPE (Mean Absolute Per- centage Error) for model validation that we present in Figure 2 using the lsqcurvefit com- mand is 0.028579. IC − r4HN − d4HN − µHN ) + τ8 (r1IN + r2IC + r3HT + r4HN − µR) . Keywords: comorbidity; control; covid-19; model
A Host-parasitoid Dynamics with Allee and Refuge effects by Kulahcioglu, Burcin; Ufuktepe, Unal; Kalampakas, Antonios (2023) - Math, 16 (2) (2023), 736-750 747 Figure 12: Numerical simulation of the stability of the (0,0) fixed point. We examined fixed point stability and bifurcations and investigated global and local fixed point stability. Keywords: figure; host; model; parasitoid; point
Dynamical Behaviors of Four Dimensional Prey-Predator Model by Farhan, A. G.; Khalaf , Nihad Sh. ; Aldhlki , Talat J. (2023) - − µiyi − (ρ2 − ρ1) 2 y 1 y2 − x1x2yi x1 + x2 (αi + βi−εi) ) A. G. Farhan, N. Sh. Simple calculations yield that the characteristic equation of the matrixJ (P5) is: ( Γ̌ε1x̌1 − ρ2y2 − µ1 − λ )( λ3 − trM̌ λ2 + 3∑ i=1 M̌ii λ−detM̌ ) Keywords: equilibrium; i=1; model; point; prey; system
Using the Modified Artificial Bee Colony Algorithm to Find the Non-Archimedean Epsilon for Evaluating the Efficiency in DEA by Zeidani, Sara; Asady, Babak ; Rostamy - Malkhalifeh, Mohsen; Lotfi, Taher (2023) - DMU z∗ v1 v2 u1 |z − z∗| 1 1.00133 0.77618 0.11291 1.00133 0.00133 2 1.00131 0.11292 0.77616 1.00131 0.00131 3 0.77904 0.11407 0.54572 0.77904 0.00126 4 0.77901 0.54564 0.11409 0.77901 0.00123 5 0.33460 0.11114 0.11123 0.33460 0.00127 Table 5: The results of MABC algorithm on CCR model (2) for ratio 4:1 (employed/onlooker)). Math, 16 (3) (2023), 1608-1623 1615 Table 6: The results MABC algorithm on CCR model (2) for ratio 3:1. Keywords: abc; algorithm; ccr; dmu; efficiency; mabc; model; results; table
A simulation Model of COVID-19 Epidemic Based on Vaccination and Treatment by Alshammari, Fahdah; Mustafa, Alaa; Omer, Ehssan; Omer, Fatima (2023) - Sies epidemic model for novel covid-19 by conformable fractional derivative. Vaccination rate The study aims to determine the effectiveness of vaccination in removing susceptible individuals from infection risk. Keywords: covid-19; epidemic; model; number; rate; vaccination
Mathematical Modelling and Numerical Simulation of Hepatitis B Viral Infection: The Case of Burkina Faso by Kiemtore , Adama; Sawadogo, Wenddabo Olivier; Aquel, Fatima; Alaa, Hamza; Somda, Kounpielime Sosthène (2024) - Where F1(s1, s2, s3, ei, ec, i, c, r) = λ− iλi − cλc − (µ+ p1)s1 − b1,1eis1 − b1,2ecs1 − b1,3is1 − b1,4cs1 F2(s1, s2, s3, ei, ec, i, c, r) = p1s1 − (µ+ p2)s2 − b2,1eis2 − b2,2ecs2 − b2,3is2 − b2,4cs2 F3(s1, s2, s3, ei, ec, i, c, r) = p2s2 − µs3 − b3,1eis3 − b3,2ecs3 − b3,3is3 − b3,4cs3 F4(s1, s2, s3, ei, ec, i, c, r) = α1s1(b1,1ei + b1,2ec + b1,3i+ b1,4c) + α2s2(b2,1ei + b2,2ec + b2,3i+ b2,4c)+ + α3s3(b3,1ei + b3,2ec + b3,3i+ b3,4c) As at the endemic equilibrium point dN dt = 0, then one obtains Λ = µII ∗ + µCC ∗ + µN∗ (30) From (28), (29), (30), and by assuming that N −N∗ ≥ 0, I − I∗ ≥ 0, C − C∗ ≥ 0, one has dV dt = ( 1− N∗ N ) (µII ∗ + µCC ∗ + µN∗ − µII − µCC − µN) dV dt = − ( N −N∗ N ) Keywords: burkina; faso; global; hbv; hepatitis; individuals; infected; model
Bayesian Regression Analysis using Median Rank Set Sampling by Nawajah, Inad; Kanj, Hassan; Kotb, Yehia; Hoxha, Julian; Alakkoumi, Mouhammad ; Jebreen, Kamel (2024) - Math, 17 (1) (2024), 180-200 197 Table 3: The efficiency of Bayesian regression parameters using MRSS concerning MRSS with different m. efficiency (θ̂1, θ̂2)= MSE(θ̂1)/MSE(θ̂2) efficiency (β̂0, ˆβ0M ) efficiency (β̂1, ˆβ1M ) efficiency (σ̂2, σ̂2 M ) m=3 1.29 1.76 1.01 m=5 1.78 2.88 1.98 m=7 2.21 3.07 2.34 7. In order to develop effective estimators of regression model parameters, the Bayesian regression estimators were examined in this study utilizing a median ranked set sample. Keywords: bayesian; linear; model; mrss; parameters; regression; sampling; set
Analyzing the Impact of Control Strategies on VisceralLeishmaniasis: A Mathematical Modeling Perspective by EL Gumaa, Fathelrhman ; A. Abdoon, Mohamed ; Qazza, Ahmad ; Saadeh, Rania; Ali Arishi, Mohammed ; M. Degoot, Abdoelnaser (2024) - We investigated the impact of different values of the parameters on the cumulative number of human VL cases, as elaborated in Section 4. We analyse the impact of interventions using percentages and consider that the number of reported human VL cases is only a portion of the total community infections. Keywords: cases; control; disease; human; leishmaniasis; model; population; rate; saadeh; sudan
Analysis and Applications of the Chaotic Hyperbolic Memristor Model with Fractional Order Derivative by Ahmed, Ghada (2024) - Introduction The history of non-integer order systems in science and technology,which has been heavily influenced by fractional derivatives, has had a significant impact on the emer- gence of chaotic systems [37].Fractional derivatives are used to explain and resolve inte- gral equations as well as ordinary and partial differential equations as an extension of classical derivatives. The conse- quences of the modified Chua’s system explored by Tom et al. using fractional derivatives are only one example of the various current contributions of fractional derivatives in the field of fractional index chaotic systems[18].Recently, chaos dynamics control has been more well-liked due to a new trend of studying chaotic systems utilizing various mathe- matical and physical models, such as the Chen system with fractional order investigated by Chunguang and Guanrong[29].The study of chaotic regimes and the creation of low-power systems with rapid processing units both heavily rely on digital/analogue electronics and fractional index systems. Keywords: abdoon; dynamics; fractional; model; mohamed; numerical; order; system
Law of Iterated Logarithm and Strong Consistency in Poisson Regression Model Selection by Qian, Guoqi (2010) - Thirdly, conditions (C.3) to (C.6) together with (C.2) indicate ξn p log log n→ 0, δn p log n log log n→ 0, δn log n p log log n→ 0 and ξn log n p log log n→ 0 respectively. Accordingly, we have ∂ ℓ ∂ β |β=β0 = n ∑ k=1 (yk −µ0k)xk = X t n(Yn−µ0) = O( p n log log n) Keywords: a.s; log; log log; model; selection
Mathematical Analysis and Numerical Simulation on Free-Living Leptospira: A Mathematical Modeling Perspective by Artiono, Rudianto; Prawoto, Budi Priyo ; Savitri, Dian ; Maulana, Dimas Avian ; Izzati Hamdan, Nur ; Abdul Latif, Nurul Syaza ; Hadi, Normi Abdul (2024) - Table 1: Summary of parameter’s description Parameter Description ΛHu the rate at which the human population is being recruited ΛHo the rate at which animal host populations are being recruited ΛV the rate at which animal vector populations are being recruited µHu the rate of death in the human population µHo the rate of death of animal host population µV the rate of death of animal vector population µL the rate of death of free-living leptospira in the environment θHu the transmission rate of humans from the recovered population to the susceptible population θHo the transmission rate of the animal host from the recovered population to the susceptible population γHu the transmission rate from the septicemic phase to the immune phase σHu the transmission rate of humans from the exposed population to the recovered population Rudianto Artiono et al. / Eur. Math, 17 (3) (2024), 1637-1658 1642 Table 2: Summary of parameter’s description Parameter Description δHu mortality rate caused by sickness in the human population δHo mortality rate caused by sickness of animal host population αHu the recovery rate of the human population αHo the recovery rate of animal host population βHu1 the infection rate of the human population by free-living lep- tospires in the environment βHu2 the infection rate of the human population by infected animal host population βHu3 the infection rate of the human population by infected animal vector population βV infection rate of animal host population by free-living leptospira in the environment L0 infection rate of animal vector population by free-living leptospira in the environment ε saturation constant of leptospires bacteria κHu a reduction in the growth rate of leptospires bacteria, given the rise in cases κHo the excretion rate of leptospira from the human population into the environment κV the excretion rate of leptospira from animal-host populations into the environment 3. Keywords: animal; animal host; disease; equilibrium; host; human; leptospira; leptospirosis; model; population; rate; vector; µhu
Two-Warehouse Inventory Model: Interval Valued Costs, Advanced Payment, Stock-Dependent Demand, and Partial Backlogging by Ahmed, Ashfar ; Kummari, Krishna ; Bandaru, Ravikumar ; Shukla, Rahul (2024) - A great deal of inventory costs are typically unpredictable because of the unpredictabil- ity of a competitive market. Below is a summary of the major contributions: • Inventory costs like ordering cost, holding cost, purchasing cost, shortage cost, de- terioration cost and capital cost are interval valued. Keywords: cost; inventory; model; time
A Structural Equation Modeling of the Impact of Teacher Self-Efficacy on Teachers' Teaching Practice in Saudi Arabia: Evidence from TALIS 2018 by Almutairi, Ameerah; Altaf, Bothinah (2024) - He found that there is a significant relationship between teacher efficacy and teacher teaching practices. The confirmatory factor analysis and the structural equation modeling were implemented using Analysis of Moment Structures (AMOS 26) software to confirm the EFA and to model the relationship between teacher efficacy and teacher teaching practices respectively. Keywords: classroom; data; education; efficacy; equation; management; model; modeling; practice; relationship; research; self; sem; students; t t; talis; teacher; teacher self; teaching
Using Modified Fractional Euler Formula for Solving the Fractional Smoking Model by Khader, Mohamed (2024) - https://doi.org/10.29020/nybg.ejpam.v17i4.5366 Email address: mmkhader@imamu.edu.sa (M. M. Khader) https://www.ejpam.com 2676 M. M. Khader / Eur. Keywords: fractional; math; method; model; numerical; smoking
Efficient Numerical Solutions for Breast Cancer Model by Assiri, Tagreed (2024) - Additionally, it possesses diverse uses in resolving chaotic systems with fractional orders. Comparison the solution obtained by proposed method and RK4M. REFERENCES 2717 7. Conclusions and remarks This study aims to utilize an efficient and accurate method to gain numerical solutions for the CF-fractional BC mathematical system. Keywords: appl; cancer; fractional; math; model; numerical; system
On the Solution of the Fractional-Order PneumoniaModel Using Numerical Computational Methods by Alalyani, Ahmad (2024) - Therefore, (λ+ µ)(λ+ µ+ η) = 0, (3) or ∣∣∣∣ λ− δωθS0 N +Z1 δθS0 N δω(1−θ)S0 N +π λ− δ(1−θ)S0 N +Z2 ∣∣∣∣ = 0. From Eq. (3), we have λ1 = −(λ+ µ), λ2 = −(λ+ µ+ η), or λ2 + c1λ+ c2 = 0, where c1 = −δωθS0 N + Z1 − δ(1− θ)S0 N + Z2, c2 = −πδθS0 N − δωθZ2S0 N − δ(1− θ)Z1S0 N + Z1Z2, c2 = − − µ− λ −f2 −f3 η f1θ f2θ − Z1 − λ f3θ 0 f1(1− θ) f2(1− θ) + π f3(1− θ)− Z2 Keywords: alalyani; appl; differential; eur; fractional; math; mathematical; method; model; n+1; numerical; order; pneumonia; pure; solution
Statistical Insights into Stochastic Glucose-InsulinDynamics: Modeling Insulin Degradation with the Michaelis-Menten Function by Alzahrani, Salem Mubarak (2025) - To address this limitation, stochastic models incorporating randomness have been introduced, offering a more realistic representation of glucose-insulin dynamics in diabetic patients To address this limitation, stochastic models have been introduced, incorpo- rating random perturbations that reflect the unpredictable fluctuations in glucose and insulin levels observed in diabetic patients. Keywords: alzahrani; diabetes; dynamics; glucose; iin; insulin; mean; model; noise; stochastic; time
Numerical Treatment for the Caputo-Fabrizio Fractional Smoking Model using an Efficient Numerical Technique by Adel, M.; Khader, M. M.; Mohammed, Najla (2024) - Additionally, it possesses diverse uses in resolving chaotic systems with fractional orders. DOI: https://doi.org/10.29020/nybg.ejpam.v17i4.5442 Email addresses: m.adel@iu.edu.sa or adel@sci.cu.edu.eg (M. Adel), mmkhader@imamu.edu.sa (M. M. Khader), namohammed@uqu.edu.sa (N. A. Mohammed) https://www.ejpam.com 3277 Keywords: fractional; m. m.; model; numerical; smoking
Designing an Efficient Numerical Method for Solving the Blood Ethanol Concentration System and Ebola Virus Models by Khader, Mohamed M. ; Babatin, M. M. (2024) - DOI: https://doi.org/10.29020/nybg.ejpam.v17i4.5447 Email addresses: mmkhader@imamu.edu.sa (M. M. Khader), mmbabatin@imamu.edu.sa (M. M. Babatin) https://www.ejpam.com 3167 (CC BY-NC 4.0) M. M. Khader, M. M. Babatin / Eur. Keywords: fractional; m. m.; model; numerical; order; scheme; system
A Novel Forced Scrambling Model Under Time-Scaled Surveys for Estimation of Population Variance by Azeem, Muhammad; Salam, Abdul ; Hussain, Sundus (2025) - Math, 18 (1) (2025), 5449 5 of 19 In traditional sample surveys, a simple variance estimator of a sensitive variable using the model (R1) is given by: s2Y (GS) = s2Z − (p1 + p2)(1− p1 − p2)(z̄ − F )2 − p2σ 2 T z̄ 2 p1 + p2(σ2 T + 1) . (11) In traditional sample surveys, a ratio-type estimator of Y is: RGS = s2Z − (p1 + p2)(1− p1 − p2)(z̄ − F )2 − p2σ 2 T z̄ 2 p1 + p2(σ2 T + 1) σ2 X s2X . Keywords: estimator; model; response; surveys; time; variance
Periodic Solutions and Bifurcations in a Long-Timescale Oceanic Carbon Cycle Model by Alraddadi, Ibrahim (2024) - We use MAPLE to compute the l1 and l2 in the normal form at Hopf bifurcation point where l0 = 0. We use MAPLE to compute the l1 and l2 in the normal form at Hopf bifurcation point where l0 = 0. Keywords: bautin; bifurcation; carbon; cycle; equilibrium; form; model; point; rothman
Numerical Investigation of the Dynamical Behavior of Hepatitis B Virus via Caputo-Fabrizio Fractional Derivative by Ahmad, Imtiaz; Jan, Rashid; Razak, Normy Norfiza Abdul; Khan, Aziz; Abdeljawad, Thabet (2025) - = M(α) α ∫ t a k′(x)e[− t−x α ]dx, M(0) = M(∞) = 2(1− ς) (2− ς)U(ς) { αV1 − (ϵ+ µ)V2 } + 2ς (2− ς)U(ς) ∫ t 0 { αV1 − (ϵ+ µ)V2 } dy, A(t)−A(0) = 2(1− ς) (2− ς)U(ς) { λS − (δ + σ + µ)A } + 2ς (2− ς)U(ς) ∫ t 0 { λS − (δ + σ + µ)A } dy, C(t)− C(0) Keywords: ahmad; appl; fractional; hepatitis; infection; math; model; pure; system; time; ς)u(ς
Using the Modified Decomposition Method Associated with Mohand Transforms for a Numerical Simulation of the Mathematical Model for Breast Cancer by Khader, Mohamed; Tedjani, Ali H. (2025) - [13] M. M. Khader, N. H. Sweilam, A. M. S. Mahdy, and N. K. A. Moniem. https://doi.org/10.29020/nybg.ejpam.v18i1.5529 Email addresses: mmkhader@imamu.edu.sa (M. M. Khader), Ahtedjani@imamu.edu.sa (A. H. Tedjani) https://www.ejpam.com 1 Keywords: breast; cancer; model; numerical; solution
Nonlinear Dynamics of a Zoonotic Disease with Control Interventions through Fractional Derivative by Jan, Rashid; Boulaaras, Salah; Alharbi, Asma ; Abdul Razak, Normy Norfiza (2024) - Math, 17 (4) (2024), 3781-3800 3785 with the above assumptions is given by dSh dt = Ξh − βh(Ih + Ia)Sh + νhRh − µhSh, dIh dt = βh(Ih + Ia)Sh − ϵ1τ1(1 − p1)Ih − (γh + αh + µh)Ih, dRh dt = ϵ1τ1(1 − p1)Ih + γhIh − (νh + µh)Rh, dSa dt = Ξa − βa(Ih + Ia)Sa + νaRa − µaSa, dIa dt = βa(Ih + Ia)Sa Dϑ t Ih = βh(Ih + Ia)Sh − ϵ1τ1(1 − p1)Ih − (γh + αh + µh)Ih, LC 0 Dϑ t Rh = ϵ1τ1(1 − p1)Ih + γhIh − (νh + µh)Rh, LC 0 Keywords: campylobacteriosis; dynamics; infection; model; resistance; solution; γ(ϑ
Stability Analysis of Parkinson's Disease Model with Multiple Delay Differential Equations using Laplace Transform Method by Veerabathiran, G. ; Jagan Kumar, G. ; Donganont, Siriluk (2025) - [3] focus on the Pantograph DDE, a fundamental model in delay differential equations. The reviewed literature underscores the versatility and efficacy of the Laplace trans- form method in solving a wide range of delay differential equations. Keywords: ddes; delay; differential; disease; equations; laplace; medication; model; parkinson; stability; transform
Dynamics of Deposit and Loan Volumes Model with Non-Performing Loan and Deposit Withdrawal Factors by Damayanti, Onik Febria; Darti, Isnani; Suryanto, Agus (2025) - Math, 18 (1) (2025), 5643 6 of 24 −(β1 + β2)L1L2 − h1L 2 1 − h2L 2 2 ≤ (γ − w)D − γD2 k + (c1µ1 − c1 − σ1 − n1)L1 + (c2µ2 − c2 − σ2 − n2)L2. − c1 − σ1 − n1)L1 +(ξ + c2µ2 − c2 − σ2 − n2)L2. by taking ξ < min{c1(1− µ1) + σ1 + n1, c2(1− µ2) + σ2 + n2}, then we get dV dt + ξV ≤ (γ + ξ − w)D − γD2 k ≤ k(γ + ξ − w)2 4γ , dV dt ≤ k(γ + ξ − w)2 4γ − ξV. Clearly, the solution to a first order differential inequality satisfies V (t) ≤ k(γ + ξ − w)2 4ξγ + ( V (0)− k(γ + ξ − w)2 4ξγ ) e−ξt. Keywords: bank; darti; deposit; equilibrium; loan; model; point; rate; suryanto; volume
Modeling the Response of the Immune System to HIV-tumor Interaction via a Fractional Framework by Jan, Rashid; Alsulami, Mansoor ; Abdul Razak, Normy Norfiza (2025) - This streamlined formulation enhances the understanding of HIV dynamics. variations in immune system dynamics. Keywords: cells; dynamics; hiv; immune; model; response; system; time; tumor
Enhancing Reliability of Series-Parallel Systems: A Novel Mathematical Model for Redundancy Allocation by Surapati, Ramadevi; Akiri, Sridhar; Velampudi, Srinivasa Rao; Nagarjuna, Vasili B V ; Swethan, Potluri S. S.; Kapu, Bhavani (2025) - This research examines the influence of several constraints, namely weight, volume, dimensions, and spatial limitations on enhancing system reliability, specifically regarding spare components for standard oil burners, including nozzle tubes and electrode brackets. [17], developed a mathematical framework aimed at improving system reliability under linear constraints. Keywords: analysis; component; constraints; efficiency; method; model; parallel; phase; problem; programming; reliability; rβj; rβpj; series; system; table
Existence and Sensitivity Analysis of a Caputo-Fabirizo Fractional Order Vector-Borne Disease model by Shah , Zahir ; Ullah, Nekmat ; Jan, Rashid; Alshehri, Mansoor H. ; Vrinceanu, Narcisa; Antonescu, Elisabeta; Farhan, Muhammad (2025) - Fractional order epidemic model for the dynamics of novel covid-19. The importance of fractional epidemic models lies in their ability to generalize tradi- tional approaches, offering greater flexibility in modeling various disease scenarios Keywords: borne; caputo; disease; dynamics; fractional; model; order; pure; u 0; vector; γ(p
Numerical Analysis of Dissipative and Magnetized Reiner-Philippoff Nanofluid with Activation Energy and Cattaneo-Christov Double Diffusion Model by Adel, M.; Khader, M. M.; Alradaddi, I.; Alaidrous, A.; Mohammed, N. A.; Ismail, G. M. (2025) - [22] N. J. Vidyarani, M. M. Mahesh, Praveena, D. G. Prakasha, M. R. Krishanamurthy, K. G. Kumar, D. Abduvalieva, and M. I. Khan. DOI: https://doi.org/10.29020/nybg.ejpam.v18i1.5700 Email addresses: m.adel@iu.edu.sa and adel@sci.cu.edu.eg (M. Adel), mmkhader@imamu.edu.sa (M. M. Khader), ialraddadi@iu.edu.sa (I. Alradaddi), aaaidrous@uqu.edu.sa (A. Alaidrous), namohammed@uqu.edu.sa (N. A. Mohammed), gismail@iu.edu.sa (G. M. Ismail) https://www.ejpam.com 1 Keywords: concentration; flow; fluid; heat; model; number; parameter; philippoff; reiner; thermal; transfer
Exploring Fractional-Order Models in Computational Finance via an Efficient Hybrid Approach by Ahmad, Imtiaz; Jan, Rashid; Abdul Razak, Normy Norfiza ; Khan, Aziz; Abdeljawad, Thabet (2025) - (CC BY-NC 4.0) Imtiaz Ahmad et al. / Eur. American Imtiaz Ahmad et al. / Eur. Keywords: ahmad; appl; eur; figure; imtiaz; math; method; model; numerical; option; p(a; pure; solution; time; η =
A Fractional Model of Abalone Growth Using Adomian Decomposition Method by Wahi, Nadihah; Susanto, Marliadi; Kilicman, Adem (2025) - Fractional growth model of abalone length. Exponential growth model also provide approximation the growth of carcinoma and melanoma properly [3]. Keywords: abalone; differential; equation; fractional; growth; method; model; order
Chaotic and Quasi-Periodic Behaviors in Ferromagnetic Materials: A Dynamical Analysis Utilizing the Truncated Mittag-Leffler Function by Khater, Mostafa (2025) - Dynamics of propagation patterns: An analytical investigation into fractional systems. Despite the substantial advancements in fractional ferromagnetic models, a compre- hensive comprehension of the magnetization dynamics and phase transitions within the FCHFA system remains incomplete. Keywords: derivative; dynamics; fractional; khater; magnetization; method; model; solutions; system; wave
A Mathematical Model for the Dengue Fever Epidemic with Vaccination and Treatment by Alnoor, Fatima; Wahbi, Hajir ; Saadi, Fatma; Daoub, Rabeea M.A. (2025) - The studies on dengue fever vaccination look at various factors, including F.Alnoor et al. / Eur. However, only a handful of published studies concentrate on treating dengue disease, relying solely on ordinary differential equations [17]. Keywords: dengue; disease; fever; mathematical; model; transmission; treatment; vaccination
An Efficient Adaptive Time-stepping Method for the Modeling of Epidemic Dynamics by Kim, Junseok (2025) - Consequently, there is a growing need for computational methods that can automatically adjust time steps while maintaining efficiency. When selecting adaptive time steps, it is possible for tn+1 to exceed the specified final time T . Keywords: epidemic; method; model; size; step; time
A Two-Warehouse Inventory Model for Green Technology Investment: Deteriorating Items with Selling Price and Carbon Emissions by Ahmed, Ashfar ; Kummari, Krishna ; Shukla, Rahul (2025) - Additionally, several researchers have developed inventory models that simulate CO2 emissions, as documented in [11–22]. Various researchers have explored different carbon tax strategies for specific products in inventory models to mitigate emissions. Keywords: carbon; cost; demand; emissions; green; inventory; model; ϕ1 −; − ϕ2p
A Mathematical Model of COVID-19 Using Piecewise Derivative of Fractional Order by Naz, Shabana; Sarwar, Muhammad; Shah, Kamal; Fatima, Nahid; Abdeljawad, Thabet (2025) - t1 0 ϕ(t)dt, with t ∈ ∇1, 1 Γ(ε) ∫ t t1 (t− φ)ε−1ϕ(φ)dφ, with t ∈ ∇2. =  dϕ(t) dt , with t ∈ ∇1, CDε 0+ϕ(t), with t ∈ ∇2, such that PCDε 0+ represents ordinary differentiation in ∇1 and the Caputo differentiation on ∇2. Keywords: appl; eur; fractional; math; model; pure; ∣∣∣∣
Optimized Energy Forecasting Using Hidden Markov Model and Transformed Fuzzy Relational Matrices Enhanced by Genetic Algorithm and Particle Swarm Optimization by Kavitha, G.; Kalpana, K. (2025) - Traditional energy forecasting models often struggle to handle the nonlinear, un- certain, and dynamic nature of energy markets, resulting in sub-optimal predictions and inefficiencies in energy distribution. [10] to en- hance predictive performance and include market integration in energy price forecasting. Keywords: algorithm; energy; forecasting; market; markov; mcp; model; optimization; particle; swarm; time
Mathematical Insights into Zoonotic Disease Spread: Application of the Milstein Method by Saber, Sayed ; Alahmari, Abdullah (2025) - Previous Shortcomings in Existing Models Several limitations exist in previous zoonotic disease models. The findings of this study are directly applicable to zoonotic disease control in the Al-Baha region but can also be adapted to similar wildlife-related transmission scenarios worldwide. Keywords: a. a.; baboons; control; disease; dynamics; food; human; interactions; model; saber; stochastic; strategies; study; time; transmission
Impact of Fractal-Fractional Dynamics on Pneumonia Transmission Modeling by Saber, Sayed ; Alahmari, Abdullah (2025) - Fractional models exhibit smoother transitions and prolonged infection durations compared to classical integer-order models. Fractional models allow greater flexibility in capturing real-world disease dynamics, incorporating memory effects and population heterogeneity. Keywords: b∗(ϱ1; fractal; fractional; model; order; pneumonia; saber; ϱ1)t; ϱ1ϱ2; ϱ2−1; ϵϱ2−1(t−
Impact of Singular and Non-Singular Kernels on Crossover Monkeypox Mathematical Model by Sweilam, Nasser; Al−Mekhlafi, S. M. ; Ahmed, Aya; Mohamed, Doaa; Abo-Eldahab, Emad (2025) - − β1Sh Nh β1Ir+β2Ih Nh −α1 − α2 − µh β2Sh Dα,β t Sh = Λα h − (βα 1 Ir + βα 2 Ih)Sh Nh − µα hSh + ϕαQh, FFAB 0 Keywords: appl; caputo; eur; fractional; math; model; order; pure; s=0; sweilam; t α=0.90,α(t)=0.94−0.01; µh +; β t; −s+
Mathematical SEIR Model of the Lumpy Skin Disease Using Caputo-Fabrizio Fractional-Order by Ramaswamy, Rajagopalan ; Mani, Gunaseelan; Mohanraj, Radhakrishnan ; Mohanraj, Radhakrishnan ; Ege, Ozgur (2025) - Experimental infection of game animals with lumpy skin disease virus (prototype strain neethling). Charac- terization of lumpy skin disease virus isolated from a giraffe in vietnam. Keywords: 2(1−; a)m(a; cattle; disease; eur; fractional; model; pure; skin; virus
Enhancing Classification Performance through Rough Set Theory Feature Selection: A Comparative Study across Multiple Datasets by T, Ashika; G, Hannah Grace (2025) - After evaluating the RST based models, a comparison was made between the results of the original ML models and those utilizing RST based feature selection. This selection pro- vides a robust foundation for evaluating the effectiveness of classification models both with and without RST based feature selection. Keywords: accuracy; attributes; classification; dataset; feature; feature selection; grace; model; performance; pure; rst; selection; svm
A Logistic Growth Epidemiological SEIR Model with Computational and Qualitative Results by Kamran; Maqsood, Sana; Thinakaran, Rajermani ; Khan, Hasib; Alzabut, Jehad (2025) - Math, 18 (2) (2025), 5944 18 of 32 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t 0 2 4 6 8 10 12 14 u (t ) =0.5 =0.6 =0.7 =0.8 =0.9 =1 (a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t 0 5 10 15 20 25 30 35 40 u (t ) =0.5 =0.6 =0.7 =0.8 =0.9 =1 (b) Figure 8: (a) The approximate solutions of problem 2 using FRK4 method with u0 = 1, k = 1, h = 0.1 for different fractional orders β. (b) The approximate solutions of problem 2 using FRK4 method with u0 = 1, k = 1, h = 0.01 for different fractional orders β. Keywords: exact; figure; fractional; frk4; frk4 method; h =; method; model; numerical; order; problem; solution
The analytic hierarchy and analytic network measurement processes: Applications to decisions under Risk by Saaty, Thomas L. (2007) - If desired, include a criterion in each hierarchy called “other” or “the unknown” for which appropriate priority values may be derived from paired comparisons. To perform marginal analysis, we first ordered the alternatives by increasing cost priorities and then formed the benefit-to-cost ratios corresponding to the smallest cost, followed by the ratios of the differences of successive benefits to costs. Keywords: alternatives; appl; benefits; costs; criteria; criterion; decision; elements; eur; figure; hierarchy; j. pure; judgments; market; math; matrix; model; priorities; priority; pure; relative; respect; risks; saaty; supermatrix; t. saaty; table; values
Mathematical Modeling with Two Strains to Investigate Evolution of COVID-19 from Computational and Theoretical Perspectives by Riaz, Muhammad; Ali, Zeeshan; Ud Din, Rahim; Ahmad, Sadique ; Abodayeh, Kamaleldin ; Sarwar, Muhammad (2025) - On nonlinear dynamics of COVID-19 disease model corre- sponding to nonsingular fractional order derivative. Math, 18 (2) (2025), 6001 13 of 27 Parameters Sensitivity Index Parameters Sensitivity Index f(b) 1 f(γ1) 0.8737 f(K) 1 f(γ2) 0.6978 f(h1) −0.00124 f(c1) −0.00103 f(h2) −0.00124 f(c2) −0.0015 f(d0) 0.9674 f(η) −0.1044 f(ϕ) −0.9895 Table 1: Sensitivity indices of R0 with respect to model parameters . Keywords: covid-19; disease; dynamics; fractional; infection; model; numerical; order; rate; strain
Numerical Analysis of Deterministic and Stochastic Model of COVID-19 Co-infection with Influenza by Ud din, Rahim; Shoaib Arif, Muhammad (2025) - Endemic equilibrium point (EEP), and disease free equilibrium points (DFEP) are calculated for deterministic model. For numerical simulation, the non-standard finite difference (NSFD) scheme is used for deterministic model. Keywords: arif; covid-19; din; infection; influenza; model; numerical
Unraveling Symmetry Properties in a Three-Dimensional Nonlinear Evolution Model via the Lie Group Method by Hussain, Akhtar; Usman, M.; Zidan, Ahmed M.; Herrera, Jorge (2025) - = 1 2 (ψxx − 2ψ3)x + 3 2 ( − 1 4 ∂−1 x ψyy + ψψy ) , ψt = −1 4 (ψxx − 2ψ3)x − 3 4 ( 1 4 ∂−1 x ψyy + ψx∂ −1 x ψy ) , ψt = 2(ψxx − 2ψ3)x − 3 4 ( ∂−1 x ψyy − 2ψx∂ −1 x ψy − 6ψψy ) , (1) where ∂−1 x is the inverse of ∂x with ∂−1 x ∂x = ∂x∂ −1 x = 1, and (∂−1 x g)(x) = ∫ =− avzux + avuxz. Keywords: lie; model; symmetry
Integrated Sustainable Inventory and Remanufacturing Optimization in a Circular Economy: A Two-Echelon Supply Chain Approach Under Carbon Regulations by R. , Suvetha; K., Rangarajan; P, Rajadurai; M., Kaviyarasu ; Mohammad , Alqahtani (2025) - Inventory systems, in particular, are at the forefront of these efforts, where the interplay between deteriorating items, circular economy (CE) principles, and carbon emissions policies necessitates innovative approaches. As a result, inventory models that address carbon emissions policy, item deteriora- tion, imperfect quality and CE indicators are the primary focus of the research study. Keywords: appl; carbon; cost; demand; emissions; et al; eur; inventory; manufacturing; math; model; profit; pure; retailer; supply; time
Modeling Virus Mutation Dynamics Using Piecewise Fractional Derivatives by ., Eiman; Shah, Kamal; Sarwar, Muhammad; Abdeljawad, Thabet (2025) - Precise estimates of virus mutation rates are crucial to our understanding of how viruses evolve and their defence. The concerned study aims to detect the crossover behavior of the dynamics of virus mutation. Keywords: abc(ξ; fractional; model; mutation; post; pre; virus; γ(ξ
Anti-Diagonals-Parameter Symmetry Model for Square Contingency Tables with Ordinal Classifications by Ando, Shuji (2025) - Four kinds of symmetry models and their decompositions in a square contingency table with ordered categories. Analysis of the grip strength data using anti-diagonal symmetry models. Keywords: adps; diagonal; model; table
Sustainable Data Analysis: Developing a Novel Probability Mass Function with Mathematical and Inferential Foundations by Eliwa, Mohamed; Alqueer, Lama ; Alseilo, Hussah (2025) - This flexibility allows the model to accommodate a wide range of data distributions. Additionally, this distribution is appro- priate for modeling positively skewed data, providing flexibility in representing different shapes of data distributions. Keywords: data; dgzexgc; discrete; distribution; eliwa; model
Advanced Fractional Reaction-Diffusion Modeling for Spatio-Temporal Dynamics of Poliovirus Transmission with Disability Outcomes and Vaccination Impacts by Guedri, Kamel ; Zarin, Rahat; M. Makhdoum, Basim ; A. Niyazi, Hatoon (2025) - These characteristics make FOMs a powerful framework for incorporating memory and hereditary properties into infectious disease models, surpass- ing the capabilities of integer-order models, which lack non-local interactions and memory effects. Global stability of infectious disease models using Lyapunov functions. Keywords: appl; d α; disease; dynamics; eur; fractional; guedri; math; model; population; pure; α t
Dynamics of Competitive Stochastic Predator-Prey Model with Holling Type II under Small Random Immigration by Mohammed, Mogtaba ; Alebraheem, Jawdat; Tayel , Ismail ; Muhamad Hifzhudin (2025) - Stability analysis of prey predator model with holling ii functional343 response and threshold harvesting for the predator. Dynamics of a predator–prey model with the effect of oscillation321 of immigration of the prey. Keywords: immigration; model; population; predator; prey; stochastic
Gender-Specific Modeling for Lassa Virus Transmission with Hearing Loss Disability Risk and Control Strategies by Guedri, Kamel; Ramzan, Yasir; Bilal, Muhammad Mudassar; Niyazi, Hatoon Abdullah; Awan, Aziz Ullah; Makhdoum, Basim M. (2025) - β2Ms H + (τ2 − τ5)θ1h3 − (τ3 − τ4)h2 β2Ms H dτ3 dt = τ3µ+ (τ3 − τ4) α2Ri M + (τ3 − τ4) β2Fi H − (τ3 − τ4)h2 β2Fi H dτ4 dt = −Z2 + τ4µ+ τ4δ2 + (τ4 − τ5)ρ2 + (τ1 − τ2) β1Fs H + (τ4 − τ5)θ1h3 dτ5 Based on these findings, cost-effective intervention techniques are developed, including targeted health campaigns, mobile technologies for early detection, structural pest-proofing, and rodent population control by trapping and rodenticides. Keywords: control; fever; humans; infection; lassa; male; model; population; rate; rodents; sensitivity; virus
Optimal Control Strategies Applied to a Mathematical Model of Meningitis by Mohammed, Sahar; Ahmed, Hasim; Bashier, Eihab; Patidar, Kailash (2025) - Optimal control strategies have been applied for various mathematical models of epi- demic diseases, for example one can refer to [14–22]. In this paper, we deal with the problem of optimal control for the transmission dynam- ics of the meningococcal meningitis. Keywords: control; d u; days; meningitis; model; time; treatment; vaccination
Understanding Transmission Dynamics of HIV/AIDS with Sensitivity Analysis and Optimal Control Strategies by M. Fatah, Saiwan ; H. A. Khoshnaw, Sarbaz; N. Mustafa, Arkan (2025) - = γmIm − ΩmDm dTf dt = ρfDf −ΨfTf dTm dt = ρmDm −ΨmTm dUf dt = θfIf − ΦfUf dUm dt = θmIm − ΦmUm dAf dt = λfUf + ωfTf − ζAf dAm dt = λmUm + ωmTm − ζAm (3) Im dDf dt = γfIf − (µ+ η + ρf )Df dDm dt = γmIm − (µ+ η + ρm)Dm dTf dt = ρfDf − (µ+ η + ωf ) Keywords: aids; control; hiv; khoshnaw; math; model; transmission; treatment; η +
A Novel Discrete Probability Distribution with Theoretical and Inferential Insights: Cutting-Edge Approaches to Sustainable Dispersion Data Modeling by Eliwa, Mohamed; Alghanem, Weed; Alenizi, Manahel (2025) - Model ↓ Parameter → γ τ θ MLE Std-er MLE Std-er MLE Std-er DGzHLo 0.959 0.019 0.037 0.026 0.550 0.004 DGzEx 0.587 0.023 0.588 0.041 0.039 0.002 DEx 0.965 0.009 − − − − DGEx-II 0.956 0.013 1.491 0.535 − − DR 0.999 2.58× 10−4 − − − − DIR 1.8× 10−7 0.055 − − − − DIW 2.2× 10−4 7.75× 10−4 0.875 0.164 − − DLo 0.012 0.039 104.506 84.409 − − DB-XII 0.975 0.051 13.367 27.785 − − DPa 0.720 0.061 This characteristic makes the PMF particularly beneficial for sustainable dispersion data, where it can accommodate different forms of data distributions, ensuring accurate modeling of real-world phenomena across multiple domains. Keywords: data; dgzhlo; discrete; distribution; eliwa; model
A Mathematical Model for COVID-19 and Tuberculosis Coinfection with the Effect of a Quarantine Measure by Puebla, Julito; Macalalag, Jay Michael; Pajaron, Kaye (2025) - Sensitivity Analysis of COVID-19 Sub-model In this subsection, sensitivity analysis of the parameters in the COVID-19 sub-model is performed. − αtβtITEC − (rc + δe + µ)EC dIC dt = rcEC − (δc + µ+ µ1)IC dQC dt = δeEC + δcIC + γctQCT − (γc + µ+ µ4)QC dECT dt = αtβtITEC + αcβc(EC + Keywords: covid-19; disease; equilibrium; individuals; infection; model; r0c; rate; sub; tuberculosis
Hyers-Ulam Stability and Control of Fractional Glucose-Insulin Systems by Saber, Sayed ; Dridi, Brahim ; Alahmari, Abdullah ; Messaoudi, Mohammed (2025) - ST [ − d1 ǔi + d2 ǔiv̌i + d3 v̌ 2 i + d4 v̌ 3 i + d5 w̌i + d6 w̌ 2 i + d7 w̌ 3 i + d20 ] (s) ] − ǔj − ST−1 [1− α̌+ α̌s N(α̌) Chaos in fractional-order glu- cose–insulin models with variable derivatives: Insights from the laplace–adomian de- composition method and generalized euler techniques. Keywords: caputo; diabetes; fractional; glucose; insulin; model; n(α̌; order; saber; stability; system
A Hybrid Exponential Runge-Kutta Scheme for Stochastic SIQR Disease Modeling by Arif, Muhammad Shoaib; Abodayeh, Kamaleldin ; Nawaz , Yasir (2025) - A two-stage mixture of exponential integrator and Runge-Kutta scheme is proposed for solving stochastic epidemic disease models. This underscores its capability as an effective instrument for simulating complex stochastic epidemic models incorporating spatial effects and non-linear dynam- ics. Keywords: epidemic; method; model; rate; scheme; α3 =; γ1 =
Mathematical Modeling of SEIRV Epidemic Model with Delay and Optimal Control of Holling type II by Irum, Shumaila ; Zeb, Anwar; Ahmed A. Mohsen; Alharthi, Thoraya N. ; Ilyas Khan; Oqilat, Osama ; Wei Sin Koh (2025) - 3. Epidemic Model SEIRV-Formulation with optimal control In this section, we examine control strategy of model model presented in [11]. Now, we first find the kernels of control model. Keywords: control; disease; figure; math; model; pure; system
A Hybrid Approach for Approximating a Smoking Epidemic Model via Caputo’s Derivative, a Novel Integral Transform, and Artificial NeuralNetworks by Belgacem, Rachid; Bokhari, Ahmed; Benali, Abdelkader ; Alraddadi, Ibrahim ; Ahmad, Hijaz ; Abdelfattah, Waleed Mohammed (2025) - When V (t) = tx−1 in formula of TN G transform 5, then: TN G [ tx−1 ] = Γ(x)M(s)Kx−1 (s) Bx (s) . Applying TN G transform and according to properties 1 and 2, we have: TN G [ RLIα 0,tV (t) ] = TN G [ 1 Γ(α) tα−1 ? Keywords: appl; b(s; fractional; math; model; tn g; transform
A Hybrid Finite Difference Approach for Solving Fuzzy Stochastic $SIR-\beta$ Model with Diffusion and Incidence Rate by Arif, Muhammad Shoaib; Abodayeh, Kamaleldin ; Nawaz , Yasir (2025) - System parameters are variable, oscillating around a mean value, which constrains the capacity of these models to represent reality compared to stochastic models accurately [25]. Figure 1: Comparison of proposed and Euler-Maruyama method for stochastic model using d1 = d2 = d3 = d4 = 0.1, µ = 0.1, θ = 0.1, γ = 0.4, c1 = 0.1, Λ = 0.1, β1 = 0.1, α = 0.1, m = 0.1. Keywords: appl; fuzzy; math; method; model; nsfd; numerical; population; rate; scheme; stochastic; time; transmission
Coronary Artery Segmentation in CTA Images: Evaluating Automated Segmentation of Coronary Arteries Using U-Net Variants and Vesselness Enhancement by Alirr, Omar Ibrahim (2025) - The proposed method not only improves the accuracy and efficiency of coronary artery segmentation, but also plays a crucial role in the timely diagnosis and effective treatment of cardiovascular dis- eases. Lei et al. used this idea for medical image segmentation and used attention-based deep learning networks to create an automated technique for coronary artery segmentation Keywords: arteries; artery; attention; cta; fold; image; learning; model; net; performance; precision; resu; results; segmentation
Green Synthesis of Silver Nanoparticles with \textit{Musa Acuminata} Flower Extraction: A Fractional Approach by Dhanalakshmi, R.; N, Jeeva; Dharmalingam, K.M.; Kekana, M.C. (2025) - The integration of green chemistry and nanotechnology has led to the development of green nanotechnology, which aims to minimize the environ- mental impact of nanoparticle synthesis. This method not only provides a more efficient way to solve the model but also aids in understanding the interactions between the various compartments involved in nanoparticle synthesis. Keywords: agnps; appl; eur; extract; fractional; green; model; nanoparticles; pure; silver; synthesis
K-th Moving, Weighted and Exponential Moving Average for Time Series Forecasting Models by Tsokos, Chris P. (2010) - 7. Solve the estimates of original time series by using (2). The model for one day ahead forecasting time series of the closing price of stock A is given by x t = x t−1− 0.033ǫt−1− 0.11ǫt−2. Keywords: average; model; moving; series; time
Stability and Sensitivity Analysis of Cyberattack Propagation Models in Computer Networks by Ahmad, Sadique; Ahmad, Naveed; Shah, Ismail (2025) - The model classifies network nodes into different states: susceptible (S), exposed (E), infected (I), controlled (C), recovered (R), protected (P), disabled (D), and attackers (A). The model organizes network nodes into separate states which include susceptible, exposed, infected, controlled (botnet), recovered, protected, disabled and at- tacking entities. Keywords: ahmad; equilibrium; model; network; nodes; shah
Hamiltonian and Neural Network-Based Framework for Modeling Conjunctivitis Transmission with Medical Intervention by Abbas, Nadeem; Shatanawi, Wasfi; Zanib, Syeda Alishwa (2025) - For model system (2.1-2.6), the basic reproduction number R0 is provided by R0 = ρ (1− ψ)κ δ (ρ+ φ) (φ+ λ1 + λ2)φ (3.18) Proof. In this study, we address several gaps identified in the existing literature by proposing a modified mathematical model that in- corporates key real-world dynamics of conjunctivitis transmission. Keywords: abbas; appl; conjunctivitis; control; eur; math; model; pure; rate; shatanawi; zanib
Mathematical Modeling of SARS-CoV-2 Epidemics Using Fractional Calculus and Optimal Interventions by Abbas, Nadeem; Shatanawi, Wasfi; Zanib, Syeda Alishwa (2025) - For the optimal control (a∗2, a ∗ 2, a ∗ 3) and corresponding state solution (S,E,U,Q, P,H,C, F, V,R) that minimize J over U of the corresponding system of equation (2.4) having the adjoint variable ξ1, ...., ξ10 such that, dξ1 dt = (ξ1 − ξ2)ϕE + (ξ1 − ξ9)a1 − aξ1, (3.62) dξ2 dt = (ξ1 − ξ2)ϕS + (ξ9 − ξ2)γV + (ξ2 − ξ3)λ1U − (ξ2 − ξ4)λ2Q+ ξ2(µ+ d1)−X1, (3.63) dξ3 dt = (ξ2 − ξ3)λ1E + (ξ3 − ξ10)α1 + (ξ3 − ξ5)α2 + ξ3(µ+ d2)−X2, (3.64) dξ4 dt = (ξ2 − ξ4)λ2E + (ξ4 − ξ5)b1 + (ξ4 − ξ1)b2 + (ξ4 − ξ9)b3 + ξ4(µ+ d3)−X3, (3.65) dξ5 dt = (ξ5 − ξ6)φ1 + (ξ5 − ξ7)φ2 + (ξ5 − ξ8)φ3 + ξ5(µ+ d4)−X4, (3.66) dξ6 dt = (ξ6 − ξ10)a2 + (ξ6 − ξ7)m2 + (ξ6 − ξ8)m3 + ξ6(µ+ d5)−X5, (3.67) dξ7 dt = (ξ7 − ξ6)η + ξ7(µ+ d6)−X6, (3.68) dξ8 dt = (ξ8 − ξ10)a3 + (ξ8 − ξ6)σ2 + ξ8(µ+ d7)−X7, (3.69) dξ9 dt = (ξ9 − ξ2)γE + ξ9(µ)− ξ9a, (3.70) dξ10 dt = ξ10 (µ+ τ)− ξ1τ. (3.71) ξi(T ) = 0, for i = 1, 2, 3....10 having conditions, a∗1 = max{0,min(1,(ξ1 − ξ9)S 2Y1 )}, a∗2 = max{0,min(1, (ξ6 − ξ10)H 2Y2 )}, a∗3 = max{0,min(1, (ξ8 − ξ10)F 2Y3 )}, (3.72) N. Abbas, W. Shatanawi, S. A. Zanib / Eur. =0.1 =0.3 =0.5 =0.7 =0.9 0 20 40 60 80 100 Days (Time) 10 15 20 25 30 Qu ar an tin ed (Q ) =0.1 =0.3 =0.5 =0.7 =0.9 0 20 40 60 80 100 Days (Time) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 Cl in ica lly P os iti ve (P ) =0.1 =0.3 =0.5 =0.7 =0.9 0 20 40 60 80 100 Days (Time) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Ho sp ita liz ed (H ) =0.1 =0.3 =0.5 =0.7 =0.9 0 20 40 60 80 100 Days (Time) 1.5 1.6 1.7 1.8 1.9 2.0 As ym pt om at ic (F ) =0.1 =0.3 =0.5 =0.7 =0.9 0 20 40 60 80 100 Days (Time) 0.70 0.75 0.80 0.85 0.90 0.95 1.00 IC U (C ) =0.1 =0.3 =0.5 =0.7 =0.9 0 20 40 60 80 100 Days (Time) 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 Va cc in at ed (V ) =0.1 =0.3 =0.5 =0.7 =0.9 0 20 40 60 80 100 Days (Time) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Re co ve re d (R ) =0.1 =0.3 =0.5 =0.7 =0.9 Figure 9: Dynamic convergence of conformable fractional model solutions to classical solutions as ς → 1. Shading represents solution variance across ς ∈ Keywords: abbas; appl; control; covid-19; days; disease; eur; math; model; pure; shatanawi; time; zanib
Adaptive Hyperheuristic Framework for Hyperparameter Tuning: A Q-Learning-Based Heuristic Selection Approach with Simulated Annealing Acceptance Criteria by Danach, Kassem ; Aly, Wael Hosny Fouad (2025) - Proposed Contribution Despite significant advancements in hyperparameter tuning methods, many existing approaches still suffer from critical limitations. Hyperparameter tuning is a crucial step in optimizing machine learning models, di- rectly impacting their performance and generalization capabilities. Keywords: aly; convergence; danach; framework; heuristic; hyperheuristic; hyperparameter; learning; machine; methods; model; optimization; performance; search; selection; tuning
Modeling of Eye Infection Transmitting by Conjunctivitis Adenovirus: Deterministic and Stochastic Approach by Ud din, Rahim; Ahmad, Naveed; Ahmad, Sadique; Pongsumpun, Puntani (2025) - |M1(S, t)|2 = ∣∣∣∣b− KSI 1 + βI − d0S ∣∣∣∣2 , ≤ ∣∣∣∣b− KSI 1 + βI − d0S ∣∣∣∣2 , ≤ |S|2 ∣∣∣∣b− KI 1 + βI − d0 ∣∣∣∣2 , ≤ (|S|2 + 1) ∣∣∣∣b− KI 1 + βI − d0 ∣∣∣∣2 , ≤ (|S|2 + 1) sup t∈[0,T ] ∣∣∣∣b− KI 1 + βI − d0 ∣∣∣∣2 , ≤ K1(|S|2 + 1) R. ud Din et al. / Eur. Math, 18 (4) (2025), 6364 15 of 23 for K1 = sup t∈[0,T ] ∣∣∣∣b− KI 1 + βI − d0 ∣∣∣∣2 . Keywords: conjunctivitis; din; model; pure
Stochastic Modelling of Seasonal Influenza Dynamics: Integrating Random Perturbations and Behavioural Factors by Saadeh, Rania; Shokeralla, Alshaikh A. ; Al-Kuleab, Naseam ; Hamad, Walid S. ; Ali, Mawada ; Abdoon, Mohamed A. ; Guma, Fathelrhman El (2025) - − lnS − lnH − lnR+ S + E +I +H + V +R = (w5 + 1) (S + E + I +H + V +R) −(w1w5 + 1) lnS − w2w5 lnE − w3w5 ln I −w4w5 lnV − lnH − lnR Where w5 is positive constant. Environmental randomicity is an important factor in the occurrence and progression of epidemics, and there is a greater attention to stochastic models containing randomicity. Keywords: + h; + r; + δ21; i(t; influenza; model; r6 +; saadeh; stochastic; weeks; ρ(v +
Length-Biased Discretized Fréchet-Weibull Probability Distribution: Mathematical Theory, Simulation Analysis, and Goodness-of-Fit Evaluation Using Real-Life Data by Das, Diksha ; Abouelenein, Mohamed ; Das, Bhanita ; Eliwa, Mohamed (2025) - Let YL denote the length-biased version of the random variable Y ∼ DFW(α, β,m, k), named as LBDFW model, then its pmf is given by PL[YL = y] = y × P Hence, LBDFW model has an increasing failure rate distribution. 3.2. Keywords: das; data; distribution; function; lbdfw; length; model; q(y
Stepwise Variable Selection for Loglinear Mixture in Record Linkage by Zhu, Rong; Zhang, Jin; Zhang, Da; Yan, Guohua (2010) - 2000 Mathematics Subject Classifications: 62F07, 62F10, 62J99, 62P25 Key Words and Phrases: record linkage, loglinear mixture models, EM algorithm, model selection, alternatively climbing pathways ∗Corresponding author. These questions lead to the model selection for loglinear mixture models in record linkage. Keywords: comparison; data; interactions; linkage; loglinear; mixture; model; pairs; record; zhang
Anti-Linear-Diagonals-Parameter Symmetry Model and Orthogonal Decomposition of Anti-Symmetry for Square Contingency Tables with Ordinal Classifications by Ando, Shuji (2025) - Accordingly, we are interested in applying the AS, ACS, ADPS, and ALDPS models to the dataset in Table 3. Four kinds of symmetry models and their decompositions in a square contingency table with ordered categories. Keywords: aldps; anti; diagonal; model; symmetry; table
Analysis of a Smoking Dynamics Model with Age-Dependent Incidence Function by Samia Bushnaq; Sameera Bano; Zeb, Anwar (2025) - Thus we can bound dV dt by dV dt ≤ −(σ + µ)(E − E∗)2 − (I − I∗)2(γ + µ) + 1 2ϵ(λS − λ∗S∗)2 +σ 2 (E − E∗)2 + σ 2 (I − I∗)2, =⇒ dV dt ≤ −( σ 2 + µ)(E − E∗)2 − (γ + µ− σ 2 )(I − I∗)2 Qualitative behavior of giving up smoking models. Keywords: model; smoking; β(a
Exploring the Effectiveness of an Optimal Control Model for Marijuana Consumption by Ullah, Atta; Sakidin, Hamzah; Gul, Shehza; N. Alharthi, Thoraya; S. Metwally, Diaa ; Hamed, Yaman; Shah, Kamal; Sambas, Aceng (2025) - This comparison provides a clear measure of how optimal control techniques enhance the model’s ability to reduce marijuana use more effectively than the existing basic model. 2020 Mathematics Subject Classifications: 92D25, 92D30, 93B30, 93C95, 91A80 Key Words and Phrases: Basic mathematical model, basic reproduction number, sensitivity analysis, optimal control model, marijuana consumption ∗Corresponding author. The overall distribution of weights aligns with commonly adopted practices in related optimal control models [50, 75]. Keywords: appl; class; control; eur; individuals; marijuana; math; model; non; pure; rate; smokers; time; u ∗; ullah; use; users
Optimal Control Strategies in a Nonlinear Smoking Cessation Model by Sameera Bano; Siddiqui, Shifa; Zeb, Anwar; Alharthi, Thoraya N. ; Ilyas Khan; Oqilat, Osama ; Wei Sin Koh (2025) - = ( a0 B1 )2 [(b1 − b4)a1 − (b̄1 − b̄4)ā1] 2, ≤ B4[(a1 − ā1) 2 + (b1 − b̄1) 2 + (b4 − b̄4) 2]. For third eigen value, we have λ3 = βζP ∗(1 + 2νS∗)r1 − r1r2r3 − r2r3βS ∗(1 + νS∗), S. Bano et al. / Eur. Keywords: appl; bano; control; delay; equilibrium; eur; math; model; pure; rate; smokers; smoking; system
Improving Wheelchair Mobility through Enhanced Kalman Filtering by Aly, Wael Hosny Fouad; Samashvili, Nino; Riman, Chadi (2025) - [13], where a differential scheme using space-time block cod- ing was introduced to minimize decoding overhead—an optimization trade-off relevant to embedded wheelchair control systems. Math, 18 (3) (2025), 6495 20 of 28 Figure 7: REFEKFPF reference model navigation in the terrain in 87 sec on uneven surfaces and 95 sec on very rough terrain. Keywords: aly; ekfwc; error; f. aly; filter; indoor; kalman; model; navigation; outdoor; riman; speed; step; surface; system; terrain; velocity; wheelchair
A Fractional Smoking Transmission Model Utilizing the Caputo-Fabrizio Operator: A Comprehensive Analysis and Simulation by Bhosale, Supriya ; Lande, Chhaya Kiran; Jafari, Hossein; Raut, Dnyaneshwar (2025) - Several additional researchers have contributed to the literature by developing smoking models formulated in both fractional and integer orders, enriching the understanding of behavioral dynam- ics and intervention strategies.[13] Many researchers studied smoking model using various Numerical techniques like LADM (Laplace-Adomian Decomposition method) Keywords: fractional; model; q(1−; smoking; z=0; η +
Numerical and Statistical Sensitivity Analysis of Deterministic and Stochastic SVEITR Model for Measles Infection. by Madiha Mohi U Din; Sana Ullah ; Kan, Shema; Naveed Ahmad; Sadique Ahmad; Elaffendi, Mohammed A. (2025) - Vj+1 = Vj + h ( c2Sj − c1Vj − µ0Vj ) , Ej+1 = Ej + h ( kSjIj M − αEj − r1Ej − µ0Ej ) , Ij+1 = Ij + h ( αEj − θ)Ij − (d1 + µ0)Ij ) , Tj+1 = Tj + h ( θIj − r2Tj − (d2 + µ0)Tj ) , Rj+1 = Rj + h ( r2Tj + r1Ej − µ0Rj ) . = αx3 − θx4 − (d1 + µ0)x4 = αx3 − (θ − d1 + µ0)x4 = αx3 − k3x4, h5(x) = θx4 − r2x5 − (d2 + µ0)x5 = θx4 − (r2 + d2 + µ0)x5 = θx4 − k4x5. Keywords: appl; compartment; disease; eur; math; measles; model; mohiudin; pure; system; vaccination
Stability Analysis and Numerical Simulation of Fractional-Order Models for Wolbachia Transmission in Aedes Aegypti Mosquitoes with Seasonal Effects by Yar, Mohammad; Shumaila Javeed; Khan, Tanveer Abbas (2025) - This factor thus demonstrates how the ratio of aquatic-stage mosquitoes that are WI affects the likelihood of WI mosquitoes displacing WU mosquitoes when WU males mate with WI females. However, and except for the biological implications of using insecticides, applying insecticides and destroying breeding sites have been an effective method in reducing mosquito populations. Keywords: fractional; fw̄; model; mosquitoes; wolbachia
Hybrid Power Market Forecasting Using an3 Interval-Valued Hidden Markov and Fuzzy Relational4 Particle Swarm Optimization Model by Kalpana, K. ; Kavitha, G. (2025) - Overall, the iHMMF-RPSO framework delivers an accurate, interpretable, and compu- tationally efficient solution for electricity market forecasting, validated on real IEX market data across both Day-Ahead Market (DAM) and Real-Time Market (RTM) scenarios. Application in Time-Series Modeling and Energy Markets In electricity market forecasting, Hidden Markov Models (HMMs) are well-suited for capturing temporal dependencies and regime-switching behavior in prices and volumes. Keywords: appl; eur; forecasting; frpso; ihmm; kalpana; kavitha; market; markov; math; mcp; model; optimization; particle; price; pso; pure; time
Machine Learning-Enhanced Simulation of Multi-Vector Email Malware Spread in Organizational Networks by Ahmad, Sadique ; A.Elaffendi, Mohammed; Ahmad, Naveed; Shah, Ismail (2025) - By replacing traditional signature-based detection with our adap- tive approach, security teams can achieve substantial improvements in threat detection while reducing false positives, our validation studies demonstrated a 28% reduction in false alerts while maintaining high detection rates. The system (1) extends classical epidemiological frameworks with three key innovations specific to organizational email threats: Exposed State (E) captures the incubation period I. Shah et al. / Eur. Keywords: analysis; appl; detection; email; eur; malware; math; model; pure; shah; threat
Stability and Optimal Control Analysis of an SEIQR Epidemic Model with Saturated Incidence Rate by Gul, Noshi; Shah, Ismail ; Ahmad, Saeed; Ullah, Ihsan; De la Sen, Manuel (2025) - The estimation of parameters, the development and testing of hypotheses that aid in disease prediction and disease control are some of the fundamental characteristics of mathematical models. The results of the investigation have shown how crucial the incidence rate is to understanding the nature of epidemic models Keywords: control; disease; equilibrium; hsi; model
Numerical Assessment of the Hepatitis B Virus Transmission Model Using a Non-standard Finite Difference Scheme and a Feedforward Neural Network by Khan, Tahir; Jung, II Hyo ; Zaman, Gul ; Khan, Ilyas (2025) - − s2∥+M2∥a1 − a2∥+M3∥c1 − c2∥+ π∥v1 − v2∥. Let M = max{M1,M2,M3, π}, the last inequality can be re-written as ∥f1(y1)− f1(y2)∥ ≤ M ( ∥s1− s2∥+ ∥a1− a2∥+ ∥c1− c2∥+ ∥v1− v2∥ ) λ2∥c1 − c2∥+ µ0∥r1 − r2∥ ≤ Q∥y1 Keywords: appl; dynamics; eur; hepatitis; khan; model; network; pure
Impact of Awareness Programs on Whitefly Dynamics in Coconut Farming: A Unified DDE and SDE Modeling Approach by Dhivyadharshini, B. ; Senthamarai, R. (2025) - In case of the delayed model Eq.(13), the endemic steady-state Ē is locally asymptotically stable for all τ > 0, if the following conditions are satisfied: λ1 > 0, λ4 > 0, λ1λ2 − λ3 > 0, (λ1λ2 − λ3)λ3 − λ21λ4 > 0. Math, 18 (4) (2025), 6691 19 of 28 dE = ( ϕHL 1 + γL − kE − bAE ) dt+ √ ϕX1X3dW1− √ kX2dW2− √ bX4X2dW4, (36) dL = (αE − µL− vAL) dt+ √ αdW3− √ µX3dW8, (37) dA = (δ + βE − ξA) dt+ √ δdW6+ √ δdW7− √ ξX4dW9− √ µX3dW12. Keywords: appl; awareness; coconut; delay; dhivyadharshini; figure; math; model; pure; rate; senthamarai; time; trees; values; whitefly
Modeling the Spread and Control of Drug Addiction: A Mathematical and Sensitivity Analysis Approach by Yaseen, Lubaba; Zanib, Syeda Alishwa; Abbas, Nadeem; Shatanawi, Wasfi (2025) - α2 0 0 0 (1− γ)σ −α3 − Λ1 − ϱ1 − µ λ1 0 0 0 0 This paper presents a comprehensive mathematical model that captures the dynamics of drug addiction by dividing the population into distinct groups: individuals at high and low risk of addiction (Si, Sd), those prone to addiction (P ), active drug users (ID), and people receiving treatment either in hospital (TH) or through outpatient programs (Tp), as well as those who have recovered (R). Keywords: addiction; days; drug; model; risk; time; tio; treatment
Fractal Fractional Modelling of Social Media Addiction with Mittag generalized Decay Stability and Recovery Analysis by Chithra, S. M.; Thangathamizh, R.; Gupta, Shivani ; Govindan, Vediyappan; Donganont, Mana (2025) - Social media addiction impacts mental health, social interaction, and productivity levels significantly. Social media addiction (SMA) is presently defined as a serious phenomenon, simulating other types of addiction like alcohol or drug abuse. Keywords: abc(η; addiction; dynamics; fractional; media; model; tϑ−1
Analysis of Monkeypox Transmission Dynamics Incorporating Quarantine and Surface Contamination by Puebla, Julito (2025) - [20] O. Diekmann, J. A. P. Heesterbeek, and J. A. J. Metz. However, the 2022 outbreak DOI: https://doi.org/10.29020/nybg.ejpam.v18i4.6750 Email address: julito.puebla@csucc.edu.ph (J. A. Puebla Jr.) https://www.ejpam.com 1 Keywords: equilibrium; model; monkeypox; seiqr; transmission
Efficient Treatment of Some Important Fractal-Fractional Models: Theoretical and Numerical Study by Adel, Mohamed; Khader, M. M.; Pamucar, Dragan ; Ahmad, Hijaz (2025) - The Brusselator model We will show a numerical simulation on a test case of the system, to show the quality and correctness of the given numerical method (26) in the interval [0, 4], h = 0.01 where fractional order % ∈ (0, 1], and fractal dimension ξ ∈ (0, 1], with different values of δ, γ, with initial conditions θ1,0 = θ2,0 = 1. − y − tj tj − tj−1 t%−1 j−1 f1 (Υ1,Υ2,Υ3,Υ4, tj−1) ] dy = ˆ̄Υ1 + % Γ(ξ) n∑ j=0 ∫ tj+1 tj (tn+1 − y)ξ−1 Keywords: fractal; fractional; model; numerical; system; tj−1
Backward Bifurcation and Optimal Control in an Age-Structured SVI Epidemic Model by Leo Amalraj, J. Leo ; Shukla, Pankaj ; Maguluri, Lakshmana Phaneendra ; Donganont, Siriluk; Avinash, N.; Govindan, Vediyappan (2025) - Math, 18 (4) (2025), 6775 27 of 32 Figure 5: Optimal treatment control α(t, x) at infection ages x = 0, 10, 20 for the age-structured SVI model (system (1)), comparing Scenario 1 (equal costs, solid lines) and Scenario 2 (higher treatment cost, dashed lines). According to the arithmetic–geometric mean inequality, both terms 2 − S S0 − S0 S and 3 − V V 0 − S0 S − S S0 V 0 V are nonnegative and the equality holds if and only if S = S0 and V = V 0. Keywords: age; amalraj; appl; bifurcation; control; disease; eur; leo; math; model; pure; system; treatment
Fractional Discrete-Time Modeling and Analysis of Oncolytic Adenovirus Therapy with Tumor-Specific Immune Response by Alshammari, Amal; Maan, Normah; A. M. Abdelaziz, Mahmoud (2025) - +(Sζ1 − 4)(S3ζ3 − 2S2ζ2 + 3Sζ1 − 4)− (S3ζ3 − 2S2ζ2 + 3Sζ1 − 4)2 − S2ζ2 + 3Sζ1 − 5 > 0. (15) − k23 − k2 + 1 > 0. (12) (Using Theorem 2), E4 is asymptotically stable if there exist feedback gains (j1, j2, j3, j4) satisfying (12); otherwise, E4 is unstable. Keywords: ai3; ai4; bifurcation; cancer; cells; figure; immune; math; model; oncolytic; system; tumor; virotherapy; virus; γ(1
Simulating Compositional Meaning in Natural Language Using Cartesian Decomposition and Tensor Product Operations by Yaseen, Maha; Alrimawi, Fadi (2025) - 2020 Mathematics Subject Classifications: 47A80, 15A03 ,47S40, 03B65, 91F20, 18C50 Key Words and Phrases: Cartesian decomposition, tensor product, compositional semantics, vector space models, operator theory, linguistic modeling, sustainable digital linguistics 1. Word Vectors and Semantic Dimensions In vector space semantics, words are mapped onto high-dimensional spaces where each dimension encodes a latent semantic feature. Keywords: decomposition; framework; hermitian; language; matrix; meaning; model; semantics; skew; tensor; vector
Optimized Nonlinear Grey Bernoulli Model for Nowcasting the Philippine Gross Domestic Product by Carillo, Shan Kierstin; Serra, Ian Jay (2025) - (β1, β2) 70/30 Split 80/20 Split (−0.1,−0.1) PSO-NGBM(1,1) PSO-NGBM(1,1) (0,−0.1) PSO-NGBM(1,1) NGBM(1,1) (0.1,−0.1) PSO-NGBM(1,1) Exponential NGBM(1,1) (0.2,−0.1) PSO-NGBM(1,1) Exponential NGBM(1,1) (−0.1, 0) PSO-NGBM(1,1) PSO-NGBM(1,1) (0.1, 0) PSO-NGBM(1,1) PSO-NGBM(1,1) (0.2, 0) PSO-NGBM(1,1) PSO-NGBM(1,1) (−0.1, 0.1) PSO-NGBM(1,1) PSO-NGBM(1,1) (0, 0.1) PSO-NGBM(1,1) NGBM(1,1) (0.1, 0.1) PSO-NGBM(1,1) NGBM(1,1) (0.2, 0.1) Exponential NGBM(1,1) Exponential NGBM(1,1) (−0.1, 0.2) PSO-NGBM(1,1) Exponential NGBM(1,1) (0, 0.2) PSO-NGBM(1,1) NGBM(1,1) (0.1, 0.2) Exponential NGBM(1,1) PSO-NGBM(1,1) (0.2, 0.2) Exponential NGBM(1,1) Exponential NGBM(1,1) Figure 1: Convergence plot of PSO for NGBM(1,1) convergence to a near-optimal solution with no substantial improvements thereafter. Exponential NGBM(1,1) attained the lowest in-sample MAPE (4.31%), followed by NGBM(1,1) (4.34%), GM(1,1) (4.41%), and PSO-NGBM(1,1) (4.45%). Keywords: data; gdp; grey; mape; model; ngbm(1,1; pso; sample
Fuzzy Fractal-Fractional Derivative-Based Modelling and Analysis of Monkeypox Transmission by Govindan, Vediyappan; Pimpunchat, Busayamas ; Kamran; Javad Ebadi, Mohammad ; Popa, Ioan-Lucian (2025) - Fuzzy fractional mathematical model of covid-19 epidemic. Fractional order mathematical model of monkeypox transmis- sion dynamics. Keywords: d h; d(η,ϑ; ffm; fractional; model; monkeypox; q h; q−1 h; r d; r q; s d; t d; t q; transmission; ϑτϑ−1 d
Analysis of a Fractional Order Enzymatic Reaction Model with Artificial Neural Network Validation by ., Asma; Ahmad, Israr; Ali, Zeeshan; Chasreechai, Saowaluck ; Sitthiwirattham, Thanin (2025) - Nevertheless, future studies may incorporate advanced ANN architectures and more detailed performance evaluations to further strengthen the computational validation of fractional enzymatic models. Taken together, these directions would not only advance the theoretical understanding of fractional enzymatic models but also foster their application in interdisciplinary areas of science and engineering. Keywords: analysis; fractional; model; pure
Cybersecurity-Focused Modeling of Computer Virus Propagation Incorporating Removable Media by Shah, Ismail; Ali, Gauhar ; ElAffendi, Mohammed (2025) - Organizations may struggle with the initial cost of deploying such systems and the need for continuous mon- itoring. The model integrates realistic cybersecurity features, including latent infections, automated quarantine, system recovery, and the permanent deactivation of critically compromised machines. Keywords: ali; analysis; baseline; baseline data; control; data; dfe; equilibrium; infection; model; pure; system; time
Malaria and Malnutrition Dynamics in Children Using the Caputo–Fabrizio Fractional Derivative by Shaikh, Amjad ; Howal, Sunil ; Nisar, Kottakkaran Sooppy (2025) - = 2(1− η) (2− η)N(η) u(t) + 2η (2− η)N(η) ∫ t 0 u(ℵ)dℵ, (3.2) Like the traditional Caputo derivative, this new operator offers CFDη t u(t) + 2(1− η) (2η)N(η) (χE(t)− (ξ + ϱ+ ∂)I(t)) + 2(1− η) (2− η)N(η) ∫ t 0 (χE(ℵ)− (ξ + ϱ+ ∂)I(ℵ))dℵ V (t) = V (0) + 2(1− η) 2ηN(η) Keywords: 2(1−; malaria; model; η(1−; σ +
A Computational Guide to Stability Analysis of Nonlinear Systems: The Lotka-Volterra and SIR Models as Case Studies by Saidat, Suhaila; Al-Shorman, Yanal; Hashim, Ishak ; Said Solaiman, Obadah; Al-Hammouri, Ahmad; Almousa, Mohammad; Alsoboh, Abdullah (2025) - 2020 Mathematics Subject Classifications: 34D20, 92D25 Key Words and Phrases: Nonlinear dynamics, stability analysis, linearization, phase portrait, Lotka-Volterra model, SIR model ∗Corresponding author. Math, 18 (4) (2025), 7020 3 of 16 the broad applicability of nonlinear stability analysis in applied mathematics. Keywords: analysis; equilibrium; lotka; model; stability; system; volterra
Statistical Inference of Accelerated Ishita Model Based on Type-I Generalized Hybrid Censoring Data with Applications by Badr, Souha (2025) - Analysis of accelerated life test data under two failure modes. 2020 Mathematics Subject Classifications: 62F10, 62F15, 62F40 Key Words and Phrases: Bayesian estimation, bootstrap confidence interval, classical estima- tion, generalized hybrid censoring scheme, Ishita distribution, MCMC 1. Keywords: data; distribution; interval; model; type
Mathematical Modeling for the Analysis and Optimization of Nutrient Dynamics in Edible Mushrooms by S.E, Fadugba; N, Jeeva; A.E, Fadugba; O, Faweya; Ahmad Aloqaily; Fady Hasan; Nabil Mlaiki (2025) - Substrate effects on mushroom nutrient content. Variations in α can represent changes in environmental conditions, such as temperature, moisture, or nutri- ent availability, which directly affect mushroom growth dynamics. Keywords: biomass; distribution; dynamics; figure; growth; model; mushroom; nutrient; production; waste
A Modern Approach to Teaching Econometrics by Hendry, David F.; Nielsen, Bent (2010) - Thus, building on the simple estimation of means leads to regression, and hence to logit regression, and then on to bivariate regression models. Next, the students are required to calculate the differences of Ur,t , namely ∆Ur,t = Ur,t − Ur,t−1 and plot the resulting series as in fig. Keywords: data; econometrics; hendry; model; nielsen; pure; regression
Stylized Facts of Financial Time Series and Three Popular Models of Volatility by Malmsten, Hans; TerÃ¤svirta, Timo (2010) - Many researchers have observed quite early on that for GARCH models, assuming normal errors is too strong a restriction, and they have suggested leptokurtic error distributions in their stead. This fact may be interpreted as support to the notion that a leptokurtic error distri- bution is a necessity when using GARCH models. Keywords: autocorrelation; errors; figure; function; garch; garch model; kurtosis; model; observations; order; panel; series; � �
A New Skew-normal Model for the Application-oriented Skew-t Model by Chen, John T. (2010) - In this paper, we initiate a new skew normal family that enhances the skew-t model in [10] and [7]. 2000 Mathematics Subject Classifications: 62E15, 62P20 Key Words and Phrases: Skew normal model, Student-t principle, excess kurtosis, asymmetry 1. Compared with existing skew models such as the generalized Gaussian model [11] or the model of skew normal sample mean [2], the new skew normal family enjoys more freedoms due to the explicit form taking two different skew factors in two halves of the real line. Keywords: model; skew
Diffusion Index Models and Index Proxies: Recent Results and New Directions by Armah, Nii Ayi; Swanson, Norman R. (2010) - Model 7 (Ordinary M( j) - bk Proxies Model): This forecast model is the same as Model 6, but bk factor proxies selected by the M( j) test are used: byT+h|T = ba0 + bα′SM T + bβ yT . • Model 9 (Smoothed A( j) - bk Proxies Model): This forecast model is the same as Model 5, except that the smoothed version of the A( j) test is used (see Section 3.3 for further discussion). Keywords: diffusion; factor; forecast; index; j t; model; prediction; proxies; proxy; test; variables
Editorâ€™s Forward for the Granger Special Volume by Bozdogan, Hamparsum (2010) - The unified theoretical framework is that of likelihood, using likelihood-ratio tests for inference and evaluation, and focusing on developing well- specified empirical models of interesting economic issues. K-th Moving, Weighted and Exponential Moving Average for Time Series Fore- casting Models by Chris P. Tsokos, Department of Mathematics and Statistics, University of South Florida, Tampa, FL, U.S.A. This paper investigates the effectiveness of developing a forecasting model of a given nonstationary economic realization using a k-th moving average, a k-th weighted moving average and a k-th exponential weighted moving average process. Keywords: department; economics; ejpam; granger; model; paper; professor; series; university
Approximating Expectation Functionals for Financial Optimization by Edirisinghe, N.C.P. (2010) - Instead, one may attempt to solve the semi-infinite dual problem of the GMP, given by φ∗(x) := sup π∈ℜN+1 { π0 + N∑ i=1 µiπi : π0 + N∑ i=1 fi(ξ)πi ≤ ϕ(x, ξ), ξ ∈ Ξ } . Define M as the convex hull of the moment conditions fi(ξ), i = 1, . . . , N for ξ ∈ Ξ, i.e., M := co {(f1(ξ), . . . Keywords: edirisinghe; expectation; function; model; moment; optimization; portfolio; return; risk; sample; ϕ(x
Multivariate Regression Models with Power Exponential Random Errors and Subset Selection Using Genetic Algorithms With Information Complexity by Liu, Minhui; Bozdogan, Hamparsum (2007) - Type II model captures such misspecification as a general and flexible model which †The GA is setup to search β in [0.001 10]. (4.2) We denote the multivariate regression model under this assumption as Type II MVPER model. Keywords: bozdogan; distribution; i=1; log; matrix; model; multivariate; mvper; selection; type; ′−1

Method

Applications of Fractional Differential Transform Method to Fractional Differential-Algebraic Equations by Ibis, Birol; Bayram, Mustafa; Agargun, A. Goksel (2011) - In this paper, we implement fractional differential transform method (FDTM), which is a semi analytical numerical technique, to fractional differential-algebraic equations (FDAEs). Comparisons are made between fractional differential transform method (FDTM), Homotopy Analysis Method (HAM) and the exact solutions. Keywords: differential; equations; method
Approximate Analytical Study of Fingero-Imbibition phenomena of time-fractional type in double phase flow through porous media by Iyiola, Olaniyi Samuel; Folarin, Samson Babatunde (2014) - The quest of getting accurate methods for solving resulted non-linear model involving fractional order is of almost concern of many re- searchers in this field today. In the recent years, Caputo [6] and He [10], fractional order have been incorporated into existing differen- tial equations which have deep meaning and applications inexhaustible giving hope for future research work in the field of sciences and other related fields. Keywords: fractional; method; � �
Radial Basis Functions for the Solution of an Inverse Problem of Mixed Parabolic-Hyperbolic Type by Parzlivand, Farzaneh; Shahrezaee, Alimardan (2015) - We collocate (32) in (N − 2)×M points Ω1 = {(xk, ts)|k = 2,3, . . . Radial basis functions methods for solving Fokker Planck equation. Keywords: equations; method; problem
Application of Meshless Methods for Solving an Inverse Heat Conduction Problem by Shahrezaee, Alimardan; Rostamian, Malihe (2016) - = n+m+l∑ j=1 λ jϕ(x − x j , t − t j), (34) where ϕ(x , t) The approximated solution U∗µ for problems (7)-(11) and (12)-(16) my be given as: U∗µ(x , t) = n+m+l∑ j=1 λ µ∗ j ϕ(x − x j , t − t j), (41) Finally the heat temperature at surface x = 0 and initial condition in x ∈ [0, x∗] are given, respectively, by: g(t) Keywords: method; problem; t j
Modification of Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton Raphson Formula by Rani, Dimple; Mishra, Vinod (2018) - Laplace decomposition method was ∗Corresponding author. Magdy and Mohamed [20] practiced Laplace decomposition method and Pade approximation to get the numerical solution of nonlinear system of partial differential equations. Keywords: equations; laplace; method; nonlinear; solution
On the Error Analysis of a Continuous Implicit Hybrid One Step Method by Anake, T. A.; Edeki, S. O. (2017) - A number of researchers have studied this situation for different numerical methods; for instance, Highhman(1993), Dor- mund et al.(1994), Calvo et al.(1996) and Stuart(1997) all studied the connection between local truncation error and global error for Runge-Kutta methods while Lambert(1979), ∗Corresponding author. It is a known fact that in the application of a continuous linear multistep method, the global error at a particular point is influenced by the accumulation of local truncation errors at each step from the initial point and thereby reduces the accuracy of the approximated result. Keywords: error; method
Modifications of the Multistep Optimal Homotopy Asymptotic Method to Some Nonlinear KdV-Equations by Fiza, Mehreen; Ullah, Hakeem; Islam, Saeed; Shah, Qayum; Chohan, Farkhanda Inayat; Mamat, Mustafa Bin (2018) - Solution Closed Form Solution (HAM) Solution 0 0.473333 0.47422 0.473333 20 0.510507 0.51122 0.51030 40 0.51328 0.513294 0.51324 60 0.513332 0.513333 0.513310 80 0.513333 0.513333 0.513333 100 0.513333 0.513333 0.513333 Table 2: Comparison of (MOHAM), HAM and Closed form solutions for v(ζ, t) at t = 1 ζ (MOHAM) Solution Closed Form Solution (HAM) Solution 0 0.334667 0.343533 0.334661 20 0.706406 0.713534 0.706402 40 0.73413 0.734269 0.73411 60 0.734657 0.734659 0.734654 80 0.734666 0.734667 0.734665 100 0.734667 0.734667 0.734667 Table 3: Comparison of (MOHAM), HAM and Closed form solutions for w(ζ, t) at t = 1 ζ (MOHAM) Solution Closed Form Solution (HAM) Solution 0 1.5 1.50222 1.5 20 1.59393 1.59472 1.59293 40 1.59987 1.5999 1.59985 60 1.6 1.6 1.6 80 1.6 1.6 1.6 100 1.6 1.6 1.6 H. Ullah et al. / Eur. Fundamental Mathematical Theory of (MOHAM) for a system of coupled PDEs Consider a system of n partial differential equations of the form A1 ( f1(ζ, t), f2(ζ, t), ..., fn(ζ, t) ) + s1(ζ, t) Keywords: method; moham; solution
On a Computational Method for Non-integer Order Partial Differential Equations in Two Dimensions by Chohan, Muhammad Ikhlaq; Shah, Kamal (2019) - It has been proved that many interesting process of electromagnetic, acoustics, viscoelasticity, electrochemistry and ma- terial sciences are well described by using fractional order partial differential equations, see [6, 14, 17, 35]. The area which has greatly attracted the attention of researches is devoted to the existence theory and numerical solution of fractional order partial differential equations. Keywords: differential; equations; fractional; method; order
Convergence of an Exponential Rungeâ€“Kutta Method for Non-smooth Initial Data by Gondal, Muhammad Asif; Rehman, Inayatur; Razzaque, Asima (2019) - − τ − tn h g(tn + h) ) dτ. (19) By using Taylor series we can write g(τ) = g(tn) + (τ − tn)g′(tn) = ∫ tn+1 tn e(tn+1−τ)ABu(τ)dτ − h(ϕ1(hA)− ϕ2(hA))Bun − hϕ2(hA)Bun2, (26) since we can write∫ tn+1 tn e(tn+1−τ)ABu(τ)dτ = ∫ tn+1 tn e(tn+1−τ)AB ( u(tn)− τ − tn h u(tn) + τ − tn h u(tn + h) + u(τ)− u(tn) + τ − tn h u(tn)− τ − tn h u(tn + h) ) dτ = hϕ1(hA)Bu(tn)− hϕ2(hA)Bu(tn) + hϕ2(hA)Bu(tn+1) + ∫ tn+1 tn e(tn+1−τ)AB ( u(τ)− u(tn) + τ − tn h u(tn) − τ − tn h u(tn + h) ) dτ. (27) Using (27) in (26) and simplifying, we have εn+1(u) Keywords: exponential; method; tn+1
Hybrid Third Derivative Block Method for the Solution of General Second Order Initial Value Problems with Generalized One Step Point by Abdelrahim, Ra'ft; Omar, Z.; Alaâ€™yed, O.; Batiha, B. (2019) - Order of the Methhod Extending to[7], the linear difference operator L associated with main block of (9) is defined as L[y(x);h] = K(0)YM − B̄R1 − h2 [ C̄nR2 + C̄n+1R3 ] − h3 10080s2 y ′′′ n + ((96s2−87s+23)) (1260(s−1)2) ∑∞ j=0 (1)jhj+3 j! yj+3 n + ((105s−41)) (2520s2(s−1)2(s−2)2) ∑∞ j=0 (s)jhj+3 j! yj+3 n − (s6(5s3−36s2+90s−84)) (10080(s−2)2) ∑∞ j=0 (2)jhj+3 j! yj+3 n ∑∞ j=0 (s)jhj j! yjn − yn − shy ′ n − h2s2(15s5−143s4+486s3−498s2−1008s+3528) 10080 y ′′ n − (s6(19s3−171s2+528s−504)) (2520(s−1)3) ∑∞ j=0 hj+2 j! Keywords: method; order
Voting Method Based on an Average Gap Assessment by Savadogo, Zoinabo; Compaore, Abdoulaye; Ouedraogo, Pegdwinde Ousseni Fabrice (2019) - Candidates 3 and 6 also have the same number of points, but candidate 6 seems more than candidate 3. In this system, each voter is free to vote for (approve) the number of candidates he wishes. Keywords: candidate; majority; method; voters; voting
The Higher-Order CESE Method for Two-dimensional Shallow Water Magnetohydrodynamics Equations by Ahmed, Sidrah; Zia, Saqib (2019) - The zoomed plot reveals better performance of 4th order CESE scheme near discontinuities as compared to the second order CESE scheme. Section 2 comprises of detailed formulation of fourth order CESE scheme for one dimensional SWMHD equations. Keywords: cese; method; n−1/2; order; scheme; solution; time
Choosing the Best Cowpea Varieties Appropriate for the Central-Eastern Region of Burkina Faso using PROMETHEE Methods by Metchebon Takougang, StÃ©phane AimÃ©; Nana, Naguiesmongho Christian; Batieno, Teyoure BenoÃ®t Joseph; SomÃ©, Blaise (2019) - EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 12, No. 4, 2019, 1717-1730 ISSN 1307-5543 – www.ejpam.com Published by New York Business Global Choosing the best cowpea varieties appropriate for the Central-Eastern region of Burkina Faso using PROMETHEE methods Stéphane Aimé Metchebon Takougang1,∗, Naguiesmongho Christian Nana2, Teyoure Benôıt Joseph Batieno3, Blaise Somé2 1 Faculty of Sciences and Technologies, New Dawn University, 06 B.P. 9283 Ouagadougou 06, Ouagadougou, Burkina Faso 2 Laboratory of Numerical Analysis of Computer Science and Biomathematics, Ouaga I Pr Joseph Ki-Zerbo University, 03 B.P. 7021 Ouagadougou 03, Ouagadougou, Burkina Faso 3 National Institute of Environmental and Agricultural Research, Kamboinsé 03 BP 7047. Afterward, PROMETHEE method (I and II) is used to aggregate the preference informa- tion stemming from the structuring process and make it possible to choose the best agricultural varieties suitable for a given region. Keywords: alternatives; cowpea; criteria; criterion; method; preference; promethee; region; varieties
The Ranking of Districts in Ouagadougou by the Risk of Flood and Runoff Using the PROMETHEE by YougbarÃ©, Jacob Wendpanga (2019) - PROMETHEE methods are used for analyzing the risk of flood runoff in urban areas of Ouagadougou in Burkina Faso. Our aim is, on one hand showing to the potential decision-maker the importance of such a multi-criteria analysis and on the other hand, of verifying the coherence of the hypotheses with the obtained weights 2010 Mathematics Subject Classifications: 90B50 Key Words and Phrases: Multi-criteria Decision Aiding, PROMETHEE method, preference indices, preference function, urban management 1. Keywords: criteria; method; preference; promethee; ranking; runoff
Identification of Parameters of Richards Equation Using Modified Hybrid Grey Wolf Optimizer-Genetic Algorithm (HmGWOGA) by Sawadogo, Wenddabo Olivier; Ouedraogo, Pengdwende Ousseni Fabrice; So, Ousseni; Barro, Genevieve; Some, Blaise (2019) - We also see that the curve obtained by HmGWOGA method is closer to the observed data than that obtained by GA. W. O. Sawadogo et al. / Eur. Keywords: algorithm; equation; function; hmgwoga; method; problem; richards; sawadogo
Performances Assessment of MOMA-Plus Method on Multiobjective Optimization Problems by Som, Alexandre; Some, Kounhinir; Compaore, Abdoulaye; Some, Blaise (2020) - Introduction Multi-objective optimization has been, for several decades, a discipline of Mathe- matics that allows to solve optimization problems where several criteria are involved simultaneously[1, 9, 13, 14]. But later, some authors adapted it to solve other types of optimization problems. Keywords: method; moma; nsga; plus; problem; somé
Using Area Method in Secondary School Geometry by Aliyev, Samed Jahangir; Aghazade, Shahin M.; Abdullayeva, Goncha Z. (2021) - 2020 Mathematics Subject Classifications: 97G10, 97G30, 97G40 Key Words and Phrases: Area method, additive property of area, excircles of a triangle, addition formula. Lets give some examples which illustrate the use of area method. Keywords: area; method; triangle
Group Splitting with SOR/AOR Methods for Solving Boundary Value Problems: A Computational Comparison by Saeed, Abdulkafi Mohammed; AL-harbi, Najah Mohammad (2021) - (5) If we use the standard five-point approximation scheme, SOR iterative method can be written as equations (5) This paper is concerned with the application of a suitable Explicit Group (EG) iterative method for solving EPDEs. Keywords: iterative; matrix; method; point
A Descent Four-Term of Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems by Alhawarat, Ahmad; Alolaiyan, Hanan; Masmali, Ibtisam A; Salleh, Zabidin; Ismail, Shahrina (2021) - k = gTk yk−1 dTk−1yk−1 , βPRP k = gTk yk−1 ∥gk−1∥2 , βLS k = − gTk yk−1 dTk−1gk−1 , βFR Algorithm 1 describes the steps of CG method to obtain the stationary point using SWP line search and equation (12) with stopping criteria∥gk∥ ≤ 10−6. Keywords: descent; dk−1; equation; gradient; gtk; line; method; search
New Spectral Idea for Conjugate Gradient Methods and its Global Convergence Theorems by Qasim, Aseel ; Salih, Zinah (2022) - However, when it is compared to other conjugate gradient methods, such as FR methods, the proposed method confirmed the globally convergent, indicating that it can be used in scientific data computation. Also, to avoid the negative case of βk we use Wolfe conditions to guarantee the convergence of non-linear conjugate methods for the research [24]. Keywords: gradient; method; new; ||gk+1||2
Toeplitz Matrix and Nyström Method for Solving Linear Fractional Integro-differential Equation by Raad, Sameeha; AlQurashi, Khawlah (2022) - = λ Γ(α) ∫ t 0 ∫ b a F (t, s)k(x, y)[un−1(y, s)− un−2(y, s)]dyds, (8) S. Raad, K. AlQurashi / Eur. (10) Inequality (10) for n = 1, yields ||ξ1(x, t)|| ≤ σ||ξ0(x, t)|| ; ( σ = |λ|BQ(b− a) Γ(α) ) , (11) from (4) and (7), we have |ξ0(x, t)| ≤ |u0(x)|+ 1 Γ(α) ∫ t 0 |F (t, s)||f(x, s)|ds, after applying Cauchy-Schwarz inequality, we get ||ξ0(x, t)|| ≤ max a≤x≤b |u0(x)|+ 1 Γ(α) (∫ T 0 ∫ T 0 |F (t, s)|2dsdt ) 1 2 max a≤x≤b ∣∣∣ ∫ Keywords: equation; error; method; nyström; solution; toeplitz
A Sufficient Descent Property to Improving a ThreeTerm Conjugate Gradient Algorithm by al-Naemi, Ghada M. ; Saeed, Firas Mahmood (2022) - CG methods are iterative methods in the form of: xk+1 = xk The performance of this class of CG methods is heavily dependent on how the scalar parameter is chosen. Keywords: gtk; method; optimization; term
The Convergent Properties of a New Parameter for Unconstrained Optimization by al-Naemi, Ghada M. (2022) - Nonlinear conjugate gradient methods for unconstrained optimization. A robust modification of hestenes–stiefel conjugate gradient method with strong wolfe line search. Keywords: conjugate; gtk; method; new; noi; optimization
Efficient New Conjugate Gradient Methods for Removing Impulse Noise Images by Hassan, Basim A.; Sadiq, Hameed (2022) - In this research, we derivation a new formula of conjugate gradient methods based on the quadratic model. To provide a broader context for developing conjugate gradient methods, Perry ex- tended the classical conjugate condition to: dTk+1yk = −(Hk+1gk+1) Keywords: gradient; image; method; new; noise
A New Type Coefficient Conjugate on the Gradient Methods for Impulse Noise Removal in Images by Hassan, Basim A.; Alashoor, Haneen (2022) - In the convergence analysis and implementations of conjugate gradient methods, the Wolfe condition is often used to find the step length αk satisfying: f(uk + akdk) Deriving new coefficient conjugate for conjugate gradient methods We will assume that f is quadratic and exact line search are being used. Keywords: conjugate; gradient; hassan; method
The Possible Solutions for the two KdV-type Equations Using a Semi-analytical Kamal-iteration Method by Mohammed, Amal Jasim; Al-Ramadhani, Sohaib Talal ; Darghoth, Rabeea Mohammed Hani (2022) - [3, 9, 11, 28] of the form (∂t − 6 w(x, t) ∂x + ∂xx)w(x, t) (1) is w = w(x, t) which is travelling wave solution tends to zero as |x| → ∞. This kind of equation is classified with the group of integrable equations such as; the nonlinear Schrödinger, Sine-Gordon, Kadomtsev-Petviashvili and Bogoyavlensky- Konopelchenko equations [12, 13, 19, 27]. Keywords: iteration; method; solution; w(x
Grey Wolves Attack Process for the Pareto Optimal Front Construction in the Multiobjective Optimization by Bamogo , Wendinda; Some, Kounhinir; Poda, Joseph (2023) - That is why, in this current work, we combined have it with the ϵ-constraint approach for the resolution of multiobjective optimization problems. Many recent studies have focused on solving multiobjective optimization problems us- ing metaheuristics. Keywords: algorithm; hmgwoga; method; objective; optimization; problems; solutions
The Homotopy Analysis Method to Solve the Nonlinear System of Volterra Integral Equations and Applying the Genetic Algorithm to Enhance the Solutions by Ahmed, Rasha F.; Al-Hayani, Waleed Mohammed; Al-Bayati, Abbas Y. (2023) - = n∑ m=1 (ui,m (x) − χmui,m−1 (x)) , = ui,1 (x) + (ui,2 (x) − ui,1 (x)) + (ui,3 (x) − ui,2 (x)) + · · · + (ui,n (x) − ui,n−1 (x)) [2]: U (x) = F (x) + ∫ g(x) f(x) K (x, t)R Keywords: equations; ham; method; solution
Selection of Quality Gemstones Based on Fuzzy Analytical Hierarchy Process by Dhaher, Ghanim Mahmood ; Abdullah, Tariq Hamad ; Algwauish, Ghanim M. (2023) - Many researchers use the similarity between triangles for fuzzy numbers As part of fuzzy set theory, fuzzy numbers are introduced which take the form of a set of real numbers with a correlated organic function. Keywords: ahp; ali; criteria; decision; matrix; method; numbers; process
Solving Geometry Problems by Alternative Methods in Mathematics Education by Aliyev, Samed Jahangir; Heydarova, Maftun N.; Aghazade, Shahin M. (2023) - Concluding Remarks This work deals with the solution of integer angled triangle problems in geometry. The point M is given inside the triangle ABC so that ∠ABM = 40◦, ∠CBM = 10◦, ∠ACM = 20◦, ∠BCM = 10◦ (Fig.1). Keywords: method; problem; triangle
Solving the First Order Differential Equations using Newton's Interpolation and Lagrange Polynomial by Neamvonk, Apichat; Sriponpaew, Boonyong (2023) - Therefore numerical method is an important tool to solve this kind of problems such as Euler’s method, Runge-Kutta method ([11],[14]) and Runge- Kutta-Fehlberg method ([8],[18]). Comparison of numerical methods for system of first order ordinary differential equations. Keywords: method; solutions
Computational Experience with Modified Coefficients Conjugate Gradient for Image Restoration by Hassan, Basim A.; Aziz, Maysoon (2023) - On image restoration problems using new conjugate gradient methods. 2020 Mathematics Subject Classifications: 65K10, 49M37, 90C06 Key Words and Phrases: Conjugate gradient method, Coefficient conjugate gradient, Image restoration 1. Keywords: conjugate; gradient; images; method; noise
An Iterative Approach to Solve Volterra Nonlinear Integral Equations by Saadeh, Rania (2023) - [29, 30] and solve nonlinear fractional integral equations of several types [23–25, 33]. Solving nonlinear differential equations using Ado- mian decomposition method through Sagemath. Keywords: method; solution; transform
Multigrid Methods for the Solution of Nonlinear Variational Inequalities by El Houda, Nesba Nour; Mohammed, Beggas; Essaid, Belouafi; Ahmad, Imtiaz; Ahmad, Hijaz; Askar, Sameh (2023) - 2020 Mathematics Subject Classifications: 65M55, 65N30, 49N05, 65K15, 35J86 Key Words and Phrases: Multigrid method, nonlinear variational inequality, finite element, iterative method, HJB equation 1. In contrast, multigrid methods offer a distinct advantage. Keywords: ahmad; convergence; iterations; method; multigrid; numerical; solution
Solving nth-order Integro-differential Equations by Novel Generalized Hybrid Transform by Khan, Sana Ullah; Khan, Asif; Ullah, Aman; Ahmad, Shabir; Awwad, Fuad A.; Ismail, Emad A. A.; Maitama, Shehu; Umar, Huzaifa; Ahmad, Hijaz (2023) - Recently, Shehu has introduced an integral transform called Shehu transform, which generalizes the two well-known integrals transforms, i.e. Laplace and Sumudu transform. In this article, for the first time, we use Shehu transform for the computation of solution of nth-order IDEs. Keywords: ahmad; equations; method; shehu; solution; transform
A Comparative Study of Numerical Solution of Second-order Singular Differential Equations Using Bernoulli Wavelet Techniques by Yadav, Kailash; Alsaadi, Ateq (2023) - Math, 16 (4) (2023), 2096-2105 2097 of singular boundary value problems has always been a complex and challenging utilize due to the unique behavior that happens at [9]. Numerical solution of singular boundary value problems by hermite wavelet based galerkin method. Keywords: equations; method; numerical; singular; value; wavelet
Cubic Trigonometric B-spline Method for Solving a Linear System of Second Order Boundary Value Problems by Heilat, Ahmed Salem (2023) - [8] Sinc method [9] CTBSM u(x) v(x) u(x) v(x) u(x) v(x) 0.08 3.3E − 03 7.7E − 03 3.2E − 03 1.5E − 03 1.1E − 04 3.2E − 04 0.24 7.7E − 03 2.2E − 02 9.4E − 04 7.0E − 03 1.5E − 04 7.8E − 04 0.40 9.7E − 03 2.7E − 02 2.0E − 03 7.4E − 03 1.3E − 04 1.1E − 03 0.56 9.5E − 03 2.7E − 02 2.2E − 04 1.0E − 02 1.2E − 04 1.1E − 03 0.72 7.3E − 03 2.0E − 02 4.1E − 03 4.4E − 03 8.2E − 05 0.8E = x2 − x and v(x) Keywords: method; order; solution; system
New Variants of Newton's Method for Solving Nonlinear Equations by Sapkota, Buddhi Prasad; Jnawali, Jivandhar (2023) - □ Next, we modify method (5) by using methods (6)-7) as below: If x0 is the initial approximation, then x∗0 = x0, x1 = x∗0 − f(x∗0) f ′[12(x ∗ 0 + z1)] , with z1 = x0 − f(x0) f ′ ( x0+x∗ 0 2 ) . Some mathematicians are modifying Newton methods to arrive at a novel technique. Keywords: convergence; method; newton; order
Numerical Simulation of Initial Value Problem of Integro-differential Equation Models by Alharbi, Faizah; Althubiti, Sharifah (2024) - System of Fredholm integral equations SFIEs The quadratic method has wide application in mathematical and physics problems, where the eigenvalues and eigenfunctions of integral equations are often studied and dis- cussed. A course on integral equations. Keywords: equation; method; solution
Exact Solutions for the Modified Burgers Equation with Additional Time-dependent Variable Coefficient by Babajanov, Bazar; Abdikarimov, Fakhriddin; Bazarbaeva, Sarbinaz (2024) - This method presents a wider applicability for handling nonlinear wave equations. Solitary wave solutions of nonlinear wave equations. Keywords: burgers; equation; method; nonlinear; solutions; variable; wave
Computational Treatment for the Coupled System of Viscous Burger’s Equations through Non-central Formula in the Method of Lines by Alharbi, Rawan; Alshareef, A. ; Bakodah, Huda; Alshaery, A. A. (2024) - − ηuux − γ(vu)x, vt = vxx − ηvvx − ξ(vu)x, c < x < [ −25V 2 0 + 48V 2 1 − 36V 2 2 + 16V 2 3 − 3V 2 4 ] − ξ 4!(∆x) (U1 [−25V0 + 48V1 − 36V2 + 16V3 − 3V4]− V1 Keywords: equations; formula; method; numerical; point; solution
An Efficient Convergent Approach for Difference Delayed Reaction-Diffusion Equations by Heydari, Marzieh; Ghovatmand, Mehdi; Noori Skandari, Mohammad Hadi; Baleanu, Dumitru (2024) - It is also easy to see that η̄(ζ, ι) for ι = ιl (l = 1, 2, .., Q − 1) and ζ ∈ [0,M ] satisfies conditions (2) and (3), by using the assumptions of theorem and the last three equations of system (22). Reaction diffusion equations and their application on bacterial communication. Keywords: diffusion; equations; method; η(ζ
On the Picture Fuzzy-TOPSIS Method by Sulaiman, Raden; Astuti, Yuliani Puji ; Yunianti, Dwi Nur; Awang, N. Azzah (2024) - In this article, we propose steps of TOPSIS picture fuzzy sets method. Picture fuzzy topsis method based on cpfrs model: An application to risk management problems. Keywords: decision; fuzzy; method; picture; topsis
An Efficient Numerical Approach Based on the Adomian Chebyshev Decomposition Method for Two-Point Boundary Value Problems by AL-Refaidi, A.; ALZaid, N.; Bakodah, Huda; AL-Mazmumy, M. (2024) - Moreover, in many BVPs of exact solutions, the obtained series provides the solution in a closed-form. Exact solution ACDM solution Absolute error 0.0 0 0 0 0.1 1.10517092× 10−1 1.10517094× 10−1 2.53649074× 10−9 0.2 2.44280552× 10−1 2.44280557× 10−1 5.09836706× 10−9 0.3 4.04957642× 10−1 4.04957650× 10−1 7.71122380× 10−9 0.4 5.96729879× 10−1 5.96729889× 10−1 1.04002264× 10−8 0.5 8.24360635× 10−1 8.24360649× 10−1 1.31822171× 10−8 0.6 1.09327128 1.09327130 1.60211319× 10−8 0.7 1.40962690 1.4096269 1.86512214× 10−8 0.8 1.78043274 1.78043276 2.00216909× 10−8 0.9 2.21364280 2.21364282 1.68194966× 10−8 1.0 2.71828183 2.71828183 1.× 10−29 Figure 1: Comparison between the exact and ACDM solutions in Example 1. Keywords: 10−1; bakodah; chebyshev; method; solution
Modeling Rugose Spiraling Whitefly Infestation on Coconut Trees Using Delay Differential Equations: Analysis via HPM by Dhivyadharshini, B. ; Senthamarai, R. (2024) - − τ)C(t − τ)−µY, d (X +Y ) dt +ηX = ( l − l(lebt − mbe−µt µ − vane−µt s ) v + l(l − mb µ − van s ) v ) ebt + ( 1 µsv2(µ +b− s)(−s+µ) ( l ( tavnµ 3b+tavnµ 2b2+tavnµbs2 + tmµ 2b2s+ tmb2s3 + avnµs(−s+µ)e(−b+s)τ−t(µ+b) −µ −b +(−µ −b + s) ( − m(e−µt µb2s+ vb2s2(−e−µt − e−µt)+ e−µtav2nµ2b+ e−µtvmµb2s − e−µts2b2 − e−µtvmb2(s2 − vµb2s(−e−µt − e−µt)− e−µtav2nµbs µ ) −b2s(−s+µ) ( µt2 2 − vm2e−2µt 2µ ) + vµa(−nbµ + s(vmw+nb))e−st s − av2mnµb(−s+µ)e−t(µ+s) −µ − s ) Keywords: appl; delay; homotopy; method; numerical; perturbation; senthamarai; time
Enhanced Conjugate Gradient Method for Unconstrained Optimization and its Application in Neural Networks by Omar, Dlovan Haji ; Ibrahim, Alaa Luqman; Hassan, Masoud Muhammed; Fathi, Bayda Ghanim; Sulaiman, Diman Abdulqader (2024) - Modified conjugate gradient method for training neural networks based on logistic mapping. Convergence properties of nonlinear conjugate gradient methods. Keywords: conjugate; gradient; math; method; new; optimization; problems
Comparative Analysis of Modified Admoian Decomposition Method and Homotopy Perturbation Mohand Transform Method for Solving Burger’s Equations by Adel, Mohamed; Khader, M.; Assiri, T. A. (2024) - DOI: https://doi.org/10.29020/nybg.ejpam.v17i4.5363 Email addresses: m.adel@iu.edu.sa and adel@sci.cu.edu.eg (M. Adel), mmkhader@imamu.edu.sa (M. M. Khader), taassiri@uqu.edu.sa (T. A. Assiri) https://www.ejpam.com 2812 (CC BY-NC 4.0) M. Adel, M. M. Khader, T. A. Assiri / Eur. Keywords: equations; method; solution
A Novel Analytical Approximate Solution for Strongly Nonlinear Third-Order Jerk Equations Using a Modified Iteration Method by Ismail, Gamal; Yamani, Mohammed I. (2024) - Math, 17 (4) (2024), 3622-3641 3632 Figure 1: Comparison between higher order analytical solution (black line), MGEMM Math, 17 (4) (2024), 3622-3641 3633 Figure 2: Comparison between higher order analytical solution (black line), MDTM Keywords: equations; iteration; method; nonlinear; solution
Employing the Sadik Residual Power Series Method to Analyze a System of Nonlinear Caputo Time-Fractional Partial Differential Equations by Pue-on, Prapart (2024) - , t ⩾ t0 is called fractional power series about t0. Resi,k(x, t) ∣∣∣ t=0 = 0. (9) Convergence criteria for Sadik residual power series method Theorem 5. Keywords: fractional; method; power; series; solution
Efficient Numerical Technique for Reaction-Diffusion Singularly Perturbed Boundary-Value Problems by Alzaid, Nawal; Alzahrani, Kholoud ; Bakodah, Huda (2024) - Math, 17 (4) (2024), 4211-4224 4218 Table 2: Comparison between different methods with different values of ϵ. Maximum Error Numerical Methods ϵ = 2−3 ϵ = 2−6 ϵ = 2−9 RSM 6.0× 10−39 1.9× 10−36 1.1× 10−5 SRKM4 5.3× 10−8 1.7× 10−6 Math, 17 (4) (2024), 4211-4224 4221 Table 4: Comparison between different methods with different values of ϵ. Maximum Error Numerical Methods ϵ = 2−3 ϵ = 2−6 ϵ = 2−9 RSM 1.4× 10−37 3.7× 10−36 4.9× 10−33 SRKM4 1.0× 10−9 2.1× 10−7 4.1× 10−5 IVT Keywords: method; order; problems; rsm; solution; value
New Newton Group Iterative Methods for Solving Large-Scale Multi-Objective Constrained Optimization Problems by Cheng, Peng; Sulaiman, Jumat; Ghazali, Khadizah ; Ali, Majid Khan Majahar ; Xu, Ming Ming (2025) - The methods for solving multi-objective optimization problems primarily consist of classical optimization techniques and intelligent optimization algorithms. In order to solve these difficulties, we combine four methods such as the Weighted method, Lagrange multiplier method, Newton method and Explicit Group Gauss-Seidel iterative method to propose new Newton Group iterative methods such as 2 and 4-point Explicit Group Gauss-Seidel iterative methods namely as Newton-2EGGS and Newton-4EGGS for solving large- scale multi-objective constrained optimization problems. Keywords: example; function; group; iterative; k+1; method; newton; optimization; problem; solution
Handling Degeneracy in Multi-objective Transportation Problem: An Efficient Branch-and-Bound Algorithm by Mezali, Zineb; Chergui, Mohamed El-Amine (2025) - D is a compact feasible region with a finite number of basic feasible solutions. Case 1: let Z(Xij) and Z(Xst) be the criterion vector of obtained basic feasible solution if (i, j) and (s, t) enters the basis, respectively. Keywords: algorithm; method; motp; node; problem; set; snd; solution; table; transportation
A Modified Conjugate Gradient Method with Taylor Approximation: Applications in Electric Circuits and Image Restoration by Alhawarat , Ahmad; Masmali, Sultanah; Masmali, Ibtisam; Al-Baali, Mehiddin; Ismail, Shahrina (2025) - The descent condition (DC), called the downhill condition, is written as ∇fT k dk < 0, ∀k ≥ 1. (7) is crucial in examining CG methods, which is also a crucial part in proving the global convergence analysis. Proposed CG method related to βFR k To maintain or improve the former useful behavior and rectify any formula related to βFR k , we construct a new 3-term CG method relying on [18] and based on Taylor’s expansion as given below: Let f(xk−1) Keywords: alhawarat; method; pure; sk−1; ∇ft; ∇ft k
Computational Study of a Meshless Approach for Multi-Term Time-Fractional Models in Drug Dispersion and Absorption in Biological Tissues by Ahmad, Imtiaz; Jan, Rashid; Abdul Razak, Normy Norfiza ; Khan, Aziz; Abdeljawad, Thabet (2025) - Modeling anomalous transport in fractal porous media: A study of fractional diffusion PDEs using numerical method. Fractional calculus models of complex dynamics in biological tis- sues. Keywords: ahmad; error; fractional; lucas; math; method; numerical; polynomials; pure; term; time; transport
Nonstandard Finite Difference Predictor Corrector Method for Quadratic Riccati Differential Equation by Rehman, Basit; Bin Iqbal, Muhammad Abdaal; Khan, Aziz; Almutairi, D. K. ; Abdeljawad, Thabet (2025) - Numerical integration of population models satisfying conservation laws: Nsfd methods. Riccati differential equation is 1st-order quadratic ode with several systems and control theory applications. Keywords: differential; equation; method; nsfd; riccati; solution; step
Development of the Nystr\"{o}m Method for Weakly Singular Functional Integral Equations by Darania, Parviz; Alrikabi, Bahaa Hussain; Pishbin, Saeed (2025) - = ∫ t 0 P1,h(ti, w)lN,j(w)dw, ω2,j(P2,h, θ(t)) = ∫ t 0 P1,h(t, w)y(w)dw − N∑ j=0 ω1,j(P1,h, t)y(tj), T2,N (P2,h, y; θ(t)) Keywords: equations; j=0; method; polynomials; θ(t
Solving Geometric Problems by Introducing an Equilateral triangle by Aliyev, Samed Jahangir; Heydarova, Maftun N. ; Seyidova, Aynura M. (2025) - 2020 Mathematics Subject Classifications: 97G10, 97G30, 97G40 Key Words and Phrases: Planimetric problem, equilateral triangle, isosceles triangle, auxiliary element 1. The concept of using equilateral triangles as auxiliary elements is grounded in classical geometry but finds renewed relevance in the context of mathematical competitions and advanced geometry education. Keywords: method; problem; sin; triangle
Analyzing Global Economic Shifts Due to the Afghan-America War Using Complex Cubic Fuzzy TODIM method by Fahmi, Aliya; Khan, A.; Abdeljawad, T.; Hassan, M.A.; Mukheimer, Aiman ; Thinakaran, Rajermani (2025) - Fuzzy decision making: Methodologies and applications preface. Key Words and Phrases: Intuitionistic fuzzy sets, Complex cubic fuzzy sets, MADM ∗Corresponding author. Keywords: ccf; decision; fahmi; fuzzy; making; method; pure; sets; step; table; todim; y i1; y i2; y i3
An Iterative Fractional Operational Matrix Method for Solving Fractional Undamped Duffing Equation with High Nonlinearity by Syam, Muhammed; Mwaffag, Sharadga ; Hashim, Ishak ; Alias, Mohd Almie; Abuomar, Mohammed; Momani, Shaher (2025) - [21] M. I. Syam, M. A. Raja, M. M. Syam, and et al. [22] A.-H. I. Mourad, A. M. Ghazal, M. M. Syam, O. D. Al Qadi, and H. Al Jassmi. Keywords: appl; equation; math; method; syam
A Comparative Study of finite Difference and Galerkin Finite Element Methods for Solving Boundary Value Problems by Almutairi , Shahad Saleh Ayad ; Saeed , Abdulkafi Mohammed (2025) - [3–5]. discretization to approximate differential equation solutions. Numerical techniques offer a potent substitute tool for resolving differential equations under the specified ini- tial condition or conditions in either scenario. Keywords: fdm; finite; gfem; method; solution
A Globally Convergent Conjugate Gradient Method Incorporating Perry’s Parameter for Unconstrained Optimization by Jameel, Hasan ; Ibrahim, Alaa Luqman; Zaya, Neven Eoarsh (2025) - Convergence properties of nonlinear conjugate gradient methods. Modified conjugate gradient method for training neural networks based on logistic mapping. Keywords: gradient; method; new; optimization
Novel Exact Solutions for a Biological Population Model Using the Power Index Method by Zeshan Haider; Khalil Ahmad (2025) - In recent years, substantial progress has been made in developing exact solution methods for nonlin- ear partial differential equations (NLPDEs), with numerous powerful techniques emerging including, Lie symmetry analysis [22], first integral method [23], modified exp-function method Using the Power Index Method, we derive exact solutions for this model. Keywords: equations; method; nonlinear; population; solutions
A Novel Explicit Two-Derivative Runge–Kutta–Nyström Method with Energy Conservation for the Integration of Second-Order Periodic ODEs by Sun, Zhuoyu; Lee, Khai Chien; Aziz, N.H. Abdul ; Hashim, Ishak; Alias, Mohd Almie; Senu, Norazak (2025) - method outperforms TFTDRKN3s5 method. The TTRKNM consists of a pair of methods derived from its continuous version, which are used to produce simultaneous approximations of the solution and its first derivative at each point in the interval of interest. Keywords: appl; eur; experiment; i=1; math; method; order; pure; stability; tfetdrkn(5
Petroleum Well Site Selection Using MCRAT Integrated with Rough Set Theory by M. Shaaban, Shaaban; M. El-Sherif , Anas ; A. Hammam, Ahmed ; M. Attaalfadeel, Husham ; I. Mesalam, Yehya (2025) - (CC BY-NC 4.0) S. M. Shaaban et al. / Eur. S. M. Shaaban et al. / Eur. Keywords: alternative; appl; criteria; decision; eur; max; method; oil; pure; shale; table; umax; umin
Modifying Spectral Conjugate Gradient Method for Solving Unconstrained Optimization Problems by Murad, Kamal; Shareef, Salah (2025) - Two new classes of conjugate gradient method based on logistic mapping. Global convergence of a modified fletcher–reeves conjugate gradient method with armijo-type line search. Keywords: algorithm; gradient; method; new; optimization; scg
A Computational Analysis of Convection-Diffusion Model with Memory using Caputo-Fabrizio Derivative and Cubic Trigonometric B-Spline Functions by Ahmad, Imtiaz; Saleem, Mehwish ; Ali, Arshed; Khan, Aziz; Abdeljawad, Thabet (2025) - Al-Refai [23] derived a closed form reduction order formula for Caputo-Fabrizio derivative to get second linearly independent solution of linear fractional differential equations. A nonlinear system of hybrid fractional differential equations with application to fixed time sliding mode control for Leukemia therapy. Keywords: 10−4; caputo; derivative; differential; equation; fabrizio; fractional; h =; method; numerical; order; solution; time
A Lattice Boltzmann Method for Image Inpainting Inspired by Fluid Dynamics by Douich, Yassine; Silkan, Hassan; Hanyf, Youssef (2025) - Inpainting mask Binary matrix: 1 inside the missing region, 0 elsewhere I Inpainted image Output image updated through iterative reconstruction fi Vorticity distribution LBM distribution function for vorticity gi In this paper, we propose a new LBM framework for image inpainting based on the vorticity–stream formulation of the Navier–Stokes equations, treating the image as a fluid medium. Keywords: appl; d2q5; d2q9; douich; eur; image; inpainting; lattice; lbm; math; method; pure
Mathematical Modeling and Analysis of Immobilized Glucose Dehydrogenase Reactions in Spherical Micro-reactors by S, Daniel; M, Mallikarjuna; R, Senthamarai (2025) - Math, 18 (3) (2025), 6203 10 of 26 B(χ) = 1 + n(χ− 1) + (χ− 1)2 2! ( −2n+ ϕ2 3 α+ 2β + γ + 2σ ) + (χ− 1)3 3!(α+ 2β + γ + 2σ)2 ( 6α2 + (ϕ2 3 + 24β + 12γ + 24σ)α+24(β + γ 2 + σ)2)n+ 2ϕ2 3(−α+ (l − 2)β − γ − 2σ) ) + (χ− 1)4 4!(α+ 2β + γ + 2σ)3  − 4αϕ2 3(β + γ 2 + σ)n2 + (8(−α 2 + (l − 1)β − γ 2 − σ)αϕ2 3− 192( γ 2 + σ + α 2 + β)3)n− 4ϕ2 3 ( −αϕ2 3 4 − 2α2 +((l2 + 2l − 8)β − 4γ − 8σ)α+ (4l − 8)β2 + ((l2 + 2l − 8)γ +(2l2 + 4l − 16)σ − ϕ2 1)β − 2(γ + 2σ)2 )  + (χ− 1)5 5!(α+ 2β + γ + 2σ)4  14 (( n 14 − 2 7 ) α+ ( l − 6n 7 − 4 7 ) Math, 18 (3) (2025), 6203 9 of 26 C(χ) = 1 +m(χ− 1)− (χ− 1)2 2! ( 2m+ 2ϕ2 2 α+ 2β + γ + 2σ ) + (χ− 1)3 3!(α+ 2β + γ + 2σ)2 ( 24 (γ 2 + σ + α 2 + β )2 m− 4 (n 2 − 1 ) α+ (l − 2)β − γ − 2σ)ϕ2 2 ) + (χ− 1)4 4!(α+ 2β + γ + 2σ)3  ( (8n− 16)α2 + ((8l2 + (−16n+ 16)l + 8n2 + 16n− 64)β +(4n2 + 8n− 32)γ + (8n2 + 16n− 64)σ Keywords: mallikarjuna; method; senthamarai
Analytic and Numerical Approaches for Solving Nonlinear Painleve' Equations I and II by Salman, Sangar Mohammed Hasan ; Mohammed, Sizar Abid ; Mohammed, Ramadhan A. (2025) - Nonlinear Painlevé equations play a pivotal role in various branches of mathematical physics, integrable systems, and applied mathematics. In this paper, we develop and present both analytical and numerical solutions for specific classes of nonlinear Painlevé equations. Keywords: abid; appl; decomposition; differential; equations; math; mern; method; painlevé; y(x
New Bright Soliton and Kink Wave Solutions for a Nonlinear Evolution Equation by Mohammed, Najla A.; Shahid, Naveed ; Shaikh, Tahira Sumbal; Ahmed, Nauman; Ghafoor, Farwa ; Baber, Muhammad Zafarullah ; Khan, Ilyas; Koh, Wei Sin (2025) - Numerous techniques have been developed to examine different facets of solutions and physical phenomena associated with nonlinear wave equations due to their significant mathematical features and broad range of applications. A sine-cosine method for handling nonlinear wave equations. Keywords: equations; method; nonlinear; solutions; wave; λ2 −; − 4µν
A Novel Maclaurin Series Approach to the Sakiadis Flow Problem and Its Fractal Formulation in Fluid Mechanics by Alameer, A (2025) - 2020 Mathematics Subject Classifications: 76D10, 34M10, 76M22 Key Words and Phrases: Maclaurin series method (MSM), Sakiadis equation, Padé approxi- mants, Hausdorff derivative 1. A simple perturbation approach to blasius equation. Keywords: blasius; equation; fluid; method; solution
Mean-Driven Accuracy: A Contraharmonic Extension of Heun’s Method by Syamsudhuha, Syamsudhuha; Imran, M.; Putri, Ayunda; Marjulisa, Rike (2025) - The following figure shows the stability region of CCH method, which was determined by evaluating the method over a grid in the complex plane. In this plot, the white (unshaded) region represents the stability region (G(z)) of CCH method. Keywords: cam; cch; hhm; method; numerical; step
Self-Similar Solutions to the Lin-Reissner-Tsien Equation via the Power Index Method by Zeshan Haider; Khalil Ahmad; Arif, Muhammad Shoaib ; Rehman, Ateeq Ur ; Qureshi, Muhammad Noman (2025) - [7] Vitanov, N.K. Simple Equations Method (SEsM): An effective algorithm for obtaining exact solutions of nonlinear differential equations. In aerodynamics, LambertW function appears in exact solutions of nonlinear equations involving compressible flow and similarity reductions. Keywords: appl; differential; equation; math; method; ode; self; solutions
Derivative-Free Method for Nonlinear Systems with Some Real-Life Applications by Al-Shorman, Yanal; Alsoboh, Abdullah; Said Solaiman, Obadah; Hashim, Ishak (2025) - − z − 11 y3 − 25z + 22 (3, 3, 2)  15 6 −4 6 10 −1 0 −18 −25  14 13 12 1.722963 2.4581 2.94914 1.03640452 1.08570343 0.93119446 Example 3. Math, 18 (3) (2025), 6262 5 of 20 Hence, the new iterative formula with no derivative terms expressed as follows xn+1 = xn − f (xn) (xn+1 − xn) f (xn+1)− f (xn) (10) Keywords: convergence; dfh; equations; method; nonlinear; order; systems
Exact Solutions of the Damped Telegrapher’s Equation with Harmonic Potential via the Generalized First Integral Method by Qureshi, Muhammad Noman; Soori, Atif Hassan ; Haider, Zeshan ; Khan, Waqar Azeem ; Arshad, Zohaib (2025) - Recent studies highlight the growing interdisciplinary interest and pro- vide a strong foundation for further exploration of nonlinear wave equations with damping and complex potentials. Unlike perturbative or numerical techniques, Generalized First Integral Method allows for the direct construction of exact traveling wave solutions. Keywords: damping; equation; method; solution; wave
Application of Search Algorithms to Root-Finding Problems in Algebraic and Transcendental Contexts by Köse, Bayram; Demirturk, Bahar; Konca, Şükran (2025) - The advantage of the golden ratio search is that, since the original points x1 and x2 are selected using the golden ratio, function values don’t need to be recalculated in each iteration, and a wider range is explored compared to bisection. Such functions reveal the algorithms’ sensitivity, stability, and sensitivity to the initial interval. Keywords: algorithm; error; function; interval; iterations; method; number; root; value
Theoretical and Computational Analysis of Delay Volterra Integro-Differential Equations via LaplaceTransform and Numerical Inversion by Kamran; Jan, Nadeem; Khan, Muhammad Ishfaq; Aloqaily, Ahmad ; Mlaiki, Nabil; Hasan, Fady (2025) - − et − et−1 + 1 + e−1. When t − σ ≥ 0, |u1(t − σ) − u2(t− σ)| ≤ ∥u1 Keywords: equations; method; numerical; problem; solution
An Enhanced Conjugate Gradient Method for Nonlinear Minimization Problems by Mustafa, Ahmed Anwer; Khatab, Hussein (2025) - Also, many parameters are proposed: Hussein Ageel Khatab and Salah Gazi Sha- reef suggested a new conjugate gradient method for solving nonlinear unconstrained op- timization problems by using three terms conjugate gradient method [4]. The properties of conjugate gradient methods have been explored greatly through their global convergence properties. Keywords: dtk; gradient; method; new; optimization
Exact Solutions of Nonlinear Delay Voltera Integro-Differential Equations Using Modified Homotopy Perturbation Method by Anakira, Nidal ; Amourah, Ala ; Almalki, Adel ; Alsoboh, Abdullah ; Sasa, Tala (2025) - − F (r) is named deformation, Furthermore, L(u) − L (v0) and N. Anakira et al. / Eur. = −x2 8 − 5x3 64 + 5x4 768 + 19x5 12288 − 7x6 184320 − 383x7 41287680 + 5x8 33030144 + 307x9 9512681472 − 97x10 237817036800 − 6143x11 83711596953600 + x12 502269581721600 , (31) u′3(x) = − x3 192 − 47x4 12288 + 329x5 122880 − 941x6 4718592 − 22217x7 165150720 + 471809x8 84557168640 + 1963291x9 761014517760 − 22998401x10 487049291366400 − 47100961x11 1785847401676800 + 37961641x12 164583696538533888 + 9442463747x13 53489701375023513600 − 25965661x14 34038900875014963200 − 1419107x15 1687625794584576000 + 24349x16 18001341808902144000 + 639917x17 229517108063502336000 − 17x18 11572291162865664000 − 2085431x19 337725745297071538176000 + 51622011x21 51843864409638174720000 + x22 209034461299661120471040000 − 1 2281130034024079687680000 + x23 161175523684005374412718080000 , (32) Up to the n′th order problem, and by solving these problems and substituting them in (??) , we have the HPM approximate solutions of order five ũ(x) = 1− x2 2 + x4 24 − x6 720 + x7 5284823040 + 133153x8 Keywords: anakira; differential; equations; error; homotopy; hpm; method; nonlinear; order; solution
A High-Order, Optimization-Free, Tangent Continuous Approximation of Conic Sections Using Cubic Bezier Curves by Hussain, Maria ; Wajid, Hafiz; Aqeel, Saira (2025) - This paper presents a high-order, optimization-free method for approximating conic sections using cubic Bézier curves. 2020 Mathematics Subject Classifications: 65D05, 65D07, 65D15, 65D17, 65D18 Key Words and Phrases: Conic section approximation, cubic Bézier curve, tangent continuity, absolute approximation error, approximation order, optimization-free method, CAD curve fitting 1. Keywords: approximation; arc; bézier; cubic; curve; method
Finite Elements Method for Solving Elliptic and Hyperbolic Partial Differential Equations by Saeed, Abdulkafi Mohammed; Almutairi , Shahad Saleh Ayad (2025) - Figure 8: Comparison of the analytical solution and the GFEM approximation solution for wave equation The GFEM exhibits lower error rates than the FDM, which suggests that the GFEM is more reliable for solving these kinds of equations, according to tables 2 and 3. Figure 9: Graph of the numerical solution of wave equation Using FDM. Keywords: equation; fdm; finite; method; solution
A Novel Simplified Yielded Aggregation Index (SYAI) Method for Enhancing Multi-Criteria Decision-Making by Wan Abdul Rahman, Wan Syaidatul Izzati ; Md Rodzi, Zahari; Zainuddin, Zaifilla Farrina ; Alias, Suriana; Al-Sharqi, Faisal (2025) - A brief overview on applications of multi-criteria decision making methods in web application security. Mcdm-efs: a novel ensemble feature selection method for software defect prediction using multi-criteria decision making. Keywords: alternatives; analysis; closeness; criteria; decision; ideal; making; matrix; mcdm; method; pure; scores; syai; table
A New Group Decision-making Method Based on Fuzzy Set Operations by Cagman, Naim; Wang, Xiaoting (2011) - [24] to deal with problems in which impreciseness was present, fuzzy decision making was suggested by Bellman and Zadeh The literature on fuzzy decision making have grown tremendously in recent years. Keywords: alternative; decision; making; method; set
Generalized Riccati Equation Mapping Method: 27 Solutions for Josephson Junctions and Nonlinear Optics Models by Phoosree, Sirasrete ; Phookwantong, Jiraphat ; Senmoh, Marisa ; Sanjun, Jiraporn; Thadee, Weerachai (2025) - Several analytical methods have been applied to fractional nonlinear equations, yet they typically generate only a narrow class of hyperbolic or trigonometric solutions. [2], first integral method [3], the Riccati-Bernoulli sub-ode method [4, 5], generalized Riccati equation mapping method Keywords: equation; method; solutions; − 4rk; −λ(s2 −; √ −φ
A New Numerical Solution for Prabhakar Fractional Differential Equations Using the Explicit Fractional Adams Method by Abdel Aal, Mohammad; S. Ghatasheh, Mohammad ; Albadawi, Hussien ; Momani, Shaher (2025) - This paper introduces a new way to solve Prabhakar fractional differential equations using an Explicit Fractional Adams Method. Section 3 looks at the concept of the Explicit Fractional Adams Method for solving Prabhakar fractional differential equations. Keywords: fractional; method; xk+1; − w)β−1mγ; − xk−2
Numerical Solutions of the SIR Mathematical Model of Computer Viruses Involving Non-linear Fractional Order Differential Equation by Kamble, Rajratana; Kulkarni, Pramod (2025) - The use of non-linear fractional order models is not limited to computer viruses; similar models can be applied to biological systems such as the spread of infectious diseases in populations. Numerical so- lution of fractional order smoking model via laplace adomian decomposition method. Keywords: fdtm; fractional; i(t; kamble; kulkarni; ladm; method; pure; r(t; s(t
A Method Employing Legendre Wavelets and a Finite Iterative Approach for Efficiently Solving Systems of Linear Fredholm Integral Equations by Ramadan , Mohamed A.; Adel, Mohamed; Arafa, Heba M. (2025) - ,M − 1 and the normalized time is denoted by t. The Legendre Polynomials Lm which are obtained in the above definition is proposed as follows: L0(t) C21 ∈ Cn×1 3- Set R1 = diag (F − f (C11 , C21) , (G− g (C11 , C21)) , S1 = AT 1 ( F− f (C11 , C21)) Keywords: equations; fredholm; method; ramadan; system
Comparative Analysis of the Differential Transform Method and Generalized Fibonacci Collocation Method for Solving Differential Equations by Maha Abdalla Abdou; Mohamed, Amany Saad (2025) - Math, 18 (4) (2025), 6734 17 of 20 Figure 8: Approximate and exact solutions at i=3, λ1 = 2, λ2 = 1 for Example 4 methods may solve higher-order, coupled, and fractional differential equations. Spectral tau algorithm for certain cou- pled system of fractional differential equations via generalized fibonacci polynomial M. A. Abdou, A. S. Mohamed / Eur. Keywords: differential; equations; fractional; method
Employing Cubic B-Spline Functions to Solve Linear Systems of Volterra Integro-Fractional Differential Equations with Variable Coefficients by Khalid, Diar; Shawki, Shazad; Hama-Faraj, Karwan (2025) - − x?r)(sξ − a)1−βij 2(Nh)3Γ(4− βij) ·  ϑj0 [ −3(Nh)2(2− βij)(3− βij) + 6(Nh)(3− βij)− 6(sξ − a)2 ] + 3ϑj1 [ (Nh)2(2− βij)(3− βij)− 4(Nh)(3− βij)(sξ − xr Bk−1 r (x) + xr+k+1 − x xr+k+1 − xr+1 Bk−1 r+1 (x) (7) Remark 1 ([29]). Keywords: ahmed; b{c,3; fractional; method; r+1; spline; x?r+1
Tau Approach for the Time-Fractional Diffusion Equation Using Certain Chebyshev Polynomials by Abd-Elhameed, W. M.; Alshehri, H. M. ; M.H. Alharbi; Adel, Mohamed; Atta, A. G. (2025) - Computational analysis of fractional diffusion equations occurring in oil pollution. High performance adaptive step size fractional numerical scheme for solving fractional differential equations. Keywords: abd; appl; elhameed; equation; fractional; math; method; polynomials; λ(x
Supplier Selection Using the TAOV Method under T-Spherical Fuzzy Soft Environment with Aczel-Alsina Operators by Sarfraz , Mehwish ; Alharbi, Talal (2025) - 1 λ  Definition 9: Consider that Ξij = (∆Ξij ,ΘΞij , φΞij ) is a set of T-SFSVs, and define T -SFSAAWG : L∗A → L∗ as: T -SFSAAWG(Ξ11,Ξ22, . . . Then T- SFSAAWA operator is a mapping T − SFSAAWA : L∗A → L∗ and is defined as: T − SFSAAWA(E11, E22, . . . Keywords: e −; fuzzy; i=1 ϱi(−; ij=1; j=1 ζj; ln(θt; ln(φt ξij; method; operators; ξij; ξnm; ϱi(− ln(1−∆t; ϱi(− ln(φt; ∑m j=1; ∑n i=1
A Comparative Study of Bernoulli Collocation and Hermite-Galerkin Methods for Solving Two-Dimensional Nonlinear Volterra Integral Equations of the Second Kind by Ahmed, M.; Aljabri, A. M. (2025) - = ( 1 2p , 1 2p ) Bernoulli collo- cation method N = 6 Hermite- Galerkin method N = 6 Method of [8] with N = 30 Method of [28] with N = M = 64 p = 1 1.61× 10−7 3.70× 10−5 6.0× 10−5 3.45× 10−7 p = 2 7.54× 10−8 5.56× 10−5 1.29× 10−4 1.28× 10−10 p = 3 1.33× 10−8 8.06× 10−5 7.0× 10−5 2.22× 10−11 p = 4 1.77× 10−8 1.0× 10−4 5.33× 10−5 1.67× 10−13 p = 5 4.69× 10−9 3.54× 10−5 5.959× 10−5 3.23× 10−13 p = 6 2.93× 10−10 4.33× 10−5 7.4588× 10−4 9.42× 10−15 Table 1: Numerical results for Example 1. N BC method HG method 2 1.5726× 10−2 1.0118× 10−2 4 7.7782× 10−5 5.3089× 10−5 6 1.6191× 10−7 3.7095× 10−5 7 6.0440× 10−11 6.9195× 10−5 Table 2: Effect of N on the absolute error for (χ, t) Description of the methods In this section, we solve Eq.(1) using Bernoulli collocation method and Hermite Galerkin method. Keywords: bernoulli; equations; integral; method; nonlinear
Numerical Scheme for Fractional Volterra Integro-Differential Equations: Handling Modified Atangana-Baleanu Operators by Kamran; Shah, Syed Musanif; Hasan, Fady; Mlaiki, Nabil (2025) - Hence, developing efficient numerical methods is necessary for solving such problems. In such cases, we employ numerical inversion methods. Keywords: error; eur; fractional; itm; method; numerical; problem; pure
Qualitative Study on Semi-Analytical Methods for Solving Nonlinear Time-Fractional Partial Differential Equations by Alhammad, Alaa Mohammed ; Saeed, Abdukkafi Mohammed (2025) - Fractional natural decomposition method for solving a certain class of nonlinear time-fractional wave-like equations with variable coefficients. The Riemann-Liouville derivative exhibits certain drawbacks for modeling real-world occurrences using fractional differential equations, as noted in [8, 12]. Keywords: decomposition; fractional; method; u(x
A Numerical Comparison Between the Standard and Modified Versions of the Optimal Homotopy Asymptotic Method (OHAM) for Solving Volterra Integro-Delay Differential Equations by Anakira, Nidal ; Bawaneh, Sameer ; Areen Al-khateeb; Amourah, Ala; Sasa, Tala (2025) - [1] applied the modified reproducing kernel method to linear Volterra integral equations, while Anakira et al. [5] for Lane–Emden type equations, Anakira et al. Keywords: anakira; c1x; equations; method; oham
Using the Multi-Domain Spectral Relaxation Method through a Numerical Simulation for the Brusselator System by Adel, Mohamed; Khader, M. M.; Ahmad, Hijaz; Oqilat, Osama ; Mohammed Abdelfattah, Waleed (2025) - https://doi.org/10.29020/nybg.ejpam.v18i4.7064 Email addresses: adel@sci.cu.edu.eg (M. Adel), mmkhader@imamu.edu.sa (M. M. Khader), hijaz.ahmad@neu.edu.tr (H. Ahmad), o.oqilat@ammanu.edu.jo (O. Oqilat), w.abdelfattah@ubt.edu.sa (W. M. Abdelfattah) https://www.ejpam.com 1 [15] N. H. Sweilem, M. M. Khader, and M. Adel. Keywords: domain; method; numerical; solutions; system
A Laplace-Chebyshev Spectral Method for Multi-Dimensional Anomalous Transport by Kamran; Zahra, Bibi; Ali, Zeeshan; Aloqaily, Ahmad ; Mlaiki, Nabil (2025) - Math, 18 (4) (2025), 7095 8 of 30 Next, we split the difference of integrals into three parts as follows:∣∣∣∣ ∫ τ1 0 (τ1 − ϑ)α−1 ( λ1∇2u(x̄1, ϑ)− λ2u(x̄1, ϑ) + f(x̄1, ϑ) ) dϑ − ∫ τ2 0 (τ2 − ϑ)α−1 ( λ1∇2u(x̄2, ϑ)− λ2u(x̄2, ϑ) + f(x̄2, ϑ) ) dϑ ∣∣∣∣ = [ ∫ τ1 0 [ (τ1 − ϑ)α−1 − (τ2 − ϑ)α−1 ] ( λ1∇2u(x̄1, ϑ)− λ2u(x̄1, ϑ) + f(x̄1, ϑ) ) dϑ︸︷︷︸ (iii) ] for the integral (i), using the mean value theorem, we have |(τ1 − ϑ)α−1 − (τ2 − ϑ)α−1| ≤ (α− 1)(τ2 − τ1)(τ1 − ϑ)α−2 Therefore: (i) ≤ (λ1∥∇2u∥∞ + λ2∥u∥∞ + ∥f∥∞)(α− 1)δ2 ∫ τ1 0 (τ1 − ϑ)α−2dϑ = (λ1∥∇2u∥∞ + λ2∥u∥∞ + ∥f∥∞)δ2τ α−1 1 . Keywords: example; fractional; method; numerical; solution; u(x̄; ϑ)α−1
Modified Optimal Homotopy Asymptotic Method for Singular Two-Point Boundary Value Problems by Anakira, Nidal ; Bawaneh, Sameer ; Al-khateeb, Areen; Amourah, Ala ; Sasa, Tala (2025) - − 0.0555556c6x9 − 0.296296c7x9 + 0.0238095c3x8 −0.0714286c5x8 1.33333C0x3 − 4.C2x3 −21.3333C3x3 − 4.C1x2 − 21.3333C2x2 − 4.C0x − 21.3333C1x − 21.3333C0 + 2 (24) Keywords: anakira; method; oham; value
New Trigonometric and Hyperbolic Stochastic Fractional Solutions for the Conformable Derivative Coupled Schrödinger-KdV Equations Using Sardar Subequation Method by Mohammed, Wael; Iqbal, Naveed; Alshammary, Hijyah M. ; Gassem, F.; Algolam, M. S. (2025) - Case I-2: If ℏ1 < 0, and ℏ2 = 0, then Y1,3 = ±2 √ −pqℏ1 (ℏ1 − k − 3k2 + 3δ) secpq(− √ ℏ1ζ)eiΘ+ρW− 1 2 ρ2t, (33) Z1,3 = {k2 − δ − ℏ1 + 2pqℏ1 sec2pq( √ ℏ1ζ)}eρW− 1 2 ρ2t, (34) and Y1,4 = ±2 √ −pqℏ1 (ℏ1 − k − 3k2 + 3δ) cscpq(− √ ℏ1ζ)eiΘ+ρW− 1 2 ρ2t, (35) Z1,4 = {k2 − δ − ℏ1 + 2pqℏ1 csc2pq( √ ℏ1ζ)}eρW− 1 2 ρ2t, (36) for ( ℏ1 − k − 3k2 + 3δ ) > 0. Math, 18 (4) (2025), 7172 8 of 22 Y1,7 = ± √ −2ℏ1 (ℏ1 − k − 3k2 + 3δ)[cothpq( √ −2ℏ1ζ)± √ pqcschpq( √ −2ℏ1ζ)]eiΘ+ρW− 1 2 ρ2t, (41) Z1,7 = {k2 − δ − ℏ1 + ℏ1[cothpq( √ −2ℏ1ζ)± √ pqcschpq( √ −2ℏ1ζ)]2}eρW− 1 2 ρ2t, (42) and Y1,8 = ±1 2 √ −ℏ1 (ℏ1 − k − 3k2 + 3δ)[tanhpq( √ −ℏ1 8 ζ) + cothpq( √ −ℏ1 8 ζ)]eiΘ+ρW− 1 2 ρ2t, (43) Keywords: method; solutions

Fractional

Convolution And Rayleighâ€™s Theorem For Generalized Fractional Hartley Transform by Sontakke, Pritibala Krushnarao (2009) - Hence fractional Hartley transform is also useful tool in many fields, due to it’s close relation with fractional Fourier transforms. He had shown that for all non negative integer m, )(2 2 tHe m t− is the eigen function of the Hartley transform and had given the formula for fractional Hartley transform as, { } ∫ ∞ ∞− = ,),()()()( dtstKtfstfH α α where [ ]).csc()1().(csc)1( 2 1. 2 cot1),( cot 2 cot 2 22 stcasiestcasieeeistK ii tisi φφ π φ φφφφ α −++− − = . Keywords: cot; fractional; hartley; transform
On Hybrid Caputo Fractional Differential Equations with Variable Moments of Impulse by Vasundhara Devi, J; Giribabu, N (2014) - = x0, 0< q < 1 if and only if it satisfies corresponding Volterra fractional integral equation x(t) = x0 + 1 Γ(q) t ∫ t0 (t − s)q−1 f (s, x(s))ds, t0 ≤ t ≤ t0 + a. = g(t,u(t)), t ≥ t0, Keywords: differential; fractional; solution; x(t
On solving Partial Differential Equations of Fractional Order by Using the Variational Iteration Method and Multivariate PadÃ© Approximations by Turut, Veyis; Guzel, Nuran (2013) - x i y j ∑ i+ j=m+n−1 ci j x i y j · · · ∑ i+ j=m ci j x i y j � � � � � � � � � � (11) and q(x , y) x i y j ∑ i+ j=m+n−1 ci j x i y j · · · ∑ i+ j=m ci j x i y j � � � � � � � � � (12) Keywords: fractional; iteration; multivariate; padé; � �
Fractional Helmholtz and Fractional Wave Equations with Riesz-Feller and Generalized Riemann-Liouville Fractional Derivatives by Saxena, Ram K; Tomovski, Zivorad; Sandev, Trifce (2014) - y a f (y ′) (y − y ′)1−µ dy ′, y > a, ℜ(µ)> 0. (6) For µ= 0, this is the identity operator, � y I0 a+ f � (y) = f (y). Similarly, R-L fractional derivative is defined by [11, 18, 36] � y Dµa+ f � (y) = � d dy �n � y In−µ a+ f � (y), ℜ(µ)> 0, n= � ℜ(µ) � + 1, (7) R. Saxena, Ž. Tomovski, T. Sandev / Eur. Keywords: derivative; equation; f �; fractional; n(x; riesz; yµ/2 �; � y; � |x; � �
Fractional Orders of the Generalized Bessel Matrix Polynomials by Abdalla, M.; Haidan, M. M. (2017) - Math, 10 (5) (2017), 995-1004 997 2. Generalized Bessel matrix functions of fractional order The classical (GBMPs) Yn(z,A,B) are defined by Rodrigues’ type formula (see [1, 22]) (8) By taking the the Liouville-Caputo fractional derivative Dα in (7), we introduce functions which are naturally refereed to as generalized Bessel matrix functions (GBMFs). Keywords: 1)i; fractional; math; matrix
Can Fractional Calculus be Generalized: Problems and Efforts by Sen, Syamal K.; Vasundhara Devi, J.; Ravi Kumar, R.V.G. (2018) - = df1 dx f2 + f1 df2 dx (26) But the LPR is not valid for fractional order derivatives: dα dx (f1(x)f2(x)) 6= These questions, though appear to be out of context for generalization, are still important to support the scope of fractional order systems in calculus and to make it an integral part of the current calculus that we are taught globally. Keywords: appl; calculus; derivative; devi; differential; eur; fractional; function; integer; j. pure; j. v.; k.sen; kumar; math; matrix; order; r.v.g; system
Existence and Uniqueness of Solutions for the Nonlinear Fractional Differential Equations with Two-point and Integral Boundary Conditions by Sharifov, Yagub; Zamanova, S.A.; Sardarova, R.A. (2021) - Fractional boundary value problems with integral boundary conditions. Engineers and scientists have developed some new models that involve fractional differential equations for which the Riemann Liouville derivative is not considered appropriate. Keywords: fractional
Periodic Solution of Caputo-Fabrizio Fractional Integroâ€“differential Equation with Periodic and Integral Boundary Conditions by Rafeeq, Ava Shafeeq (2022) - g ( s, u ( s, uk0 )) ds ) − 2(1−α) (2−α)N(α) 1 T ∫ T 0 h ( s, u ( s, uk0 ) , ∫ a(s) 0 g ( τ, u ( τ,uk0 )) dτ ) ds+ 2α (2−α)N(α) ∫ t 0 (h(s, u ( s, uk0 ) , ∫ a(s) 0 g ( τ, u ( τ,uk0 )) dτ)− 1 T ∫ T 0 h(s, u ( s, uk0 ) , ∫ a(s) 0 g ( τ, u ( τ,uk0 )) dτ)ds)ds (4.24) where k = 1, 2, from (4.24), we get∣∣u (t, u10)− u ( t, u20 )∣∣ ≤| u10 − u20 ] + 4(1−α) (2−α)N(a) (k1 + aTL1k2) ∣∣u (t,u10)− u ( t, u20 )∣∣+ αT (2− α)N(α) (k1 + aTL1k2) ∣∣u (t, u10)− u ( t, u20 )∣∣ (4.25) Existence and uniqueness of periodic Solution of (1.1) with integral boundary condition In this section, we investigate the periodic solution of the problem (1.1) with integral boundary conditions: u(0)− u(T ) = ∫ T 0 H(u(s))ds (4.28) Where the function H(u(s)) defined and continuous on are compact subset of R and periodic on t of periodic T. A. S. Rafeeq / Eur. Keywords: fractional
Existence and Uniqueness of Solutions for Nonlinear Fractional Integro-Differential Equations with Nonlocal Boundary Conditions by Mardanov, M.J. ; Sharifov, Y.A. ; Aliyev, Humbet (2022) - For more details about fractional differential equations and their applications, we provide the following references As to the initial value problems for fractional differential equations with fractional derivatives in the Riemann-Liouville sense, they should be given as (bounded) initial values of the fractional integral Jn−α and of its integer derivatives of order k = 1, 2, ..., n− 1. Keywords: differential; equations; fractional
Fractional Order Techniques for Stiff Differential Equations Arising from Chemistry Kinetics by Wannan, Rania; Aslam, Muhammad ; Farman, Muhammad ; Akgül, Ali ; Kouser, Farhina ; Asad, Jihad (2022) - By using norm properties, then the iteration is H-Stable ∥H[y1(n)(t)]−H[y1(m)(t)]∥ ≤ ∥y1(n)(t)− y1(m)(t)∥+ ST−1[ 1− α B(α)αΓ(α+ 1)Eα(− 1 (1−α)w α) ×ST (−M1∥y1(n) − y1(m)∥+M3∥y2(n)y3(n) − y2(m)y3(m)∥)], ∥H[y2(n)(t)]−H[y2(m)(t)]∥ ≤ ∥y2(n)(t)− y2(m)(t)∥+ ST−1[ 1− α B(α)αΓ(α+ 1)Eα(− 1 (1−α)w α) ×ST (M1∥y1(n) − y1(m))∥+ ∥M3y2(n)(y3(n) Keywords: fractional; st−1
Solving Conformable Fractional Differential Equations with ``EJS Software and Visualization of Sub-diffusion Process by Noshad, Mahlagha; Pishkoo, Amir; Darus, Maslina (2022) - Solving conformable fractional differential equations by using EJS202 Easy Java simulation software can be used to visualize mathematical physics problems. 2020 Mathematics Subject Classifications: 26A33, 34A0812 Key Words and Phrases: Conformable fractional derivative, easy java simulations (EJS), frac-13 tional differential equation, sub-diffusion.14 15 1. Introduction16 Computer modeling and simulation are tightly intertwined. Keywords: derivative; differential; diffusion; easy; equations; fractional; java; simulations
An Iterative Approach for Numerical Solution to the Time-fractional Richards Equation with Implicit Neumann Boundary Conditions by Zeki, Mustafa; Tatar, Salih (2023) - In this paper, we develop an iterative method of lines scheme for the numerical solution to the time fractional Richards equation with implicit Neumann boundary conditions, which is an effective tool for describing a process of flow through unsaturated media. Theory and applications of fractional differential equations, volume 204. Keywords: equation; fractional; solution; time
A New Scheme for Solving a Fractional Differential Equation and a Chaotic System by Qazza, Ahmad; Abdoon, Mohamed; Saadeh, Rania; Berir, Mohammed (2023) - A new definition of fractional derivative without singular kernel. New numerical approximation of fractional derivative with non-local and non-singular kernel: application to chaotic models. Keywords: abc; fractional; numerical
Analytical and Approximate Solutions for Fractional Systems of Nonlinear Differential Equations by Abdl-Rahim, H. R.; Ahmad, Hijaz; Nofal, Taher A.; Ismail, G. M. (2023) - Solution of fractional ordinary differential equations by natural transform. Fractional differential equations, mathematics in science and engi- neering, 1999. Keywords: fractional; n=0; transform
Numerical Solutions of Some Classes of Partial Differential Equations of Fractional Order by ALdarawi, Iman; Maayah, Banan; Aldabbas, Eman; Abuteen, Eman (2023) - Fractional fourier series with sepa- ration of variables technique and its application on fractional differential equations. WSEAS Transactions on Mathematics, 20:461–469, 2021. Conformable fractional derivatives and it is applications for solving fractional differential equations. Keywords: equation; fractional; solution
Solving Fractional Riccati Differential Equation with Caputo-Fabrizio Fractional Derivative by Abuteen, Eman (2024) - Fractional differential equations: an introduction to fractional deriva- tives, fractional differential equations, to methods of their solution and some of their applications. [2] Kilbas Anatolĭı Aleksandrovich, Srivastava Hari M, and Trujillo Juan J. Theory and applications of fractional differential equations, volume 204. Keywords: caputo; differential; equation; fabrizio; fractional; riccati; solution
A Novel Numerical Scheme for Fractional Bernoulli Equations and the Rössler Model: A Comparative Analysis using Atangana-Baleanu Caputo Fractional Derivative by Boulehmi, Kaouther (2024) - [2], which highlighted the ef- ficacy of fractional methods in solving multi-dimensional equations, influenza modeling, and integrating master theorems, respectively. They have facilitated significant strides in Controlling robotic manipulators with fractional-order modeling [9], offering innovative schemes in order to solve fractional differential equations and chaotic systems [39]. Keywords: abc; equation; fractional; numerical; order; scheme; solutions; systems
A Spectral Collocation Method for Solving Caputo-Liouville Fractional Order Fredholm Integro-differential Equations by Saad, Khaled ; Khirallah, Mustafa (2024) - Fractional differential equations : an introduction to fractional deriva- tives, fractional differential equations, to methods of their solution and some of their applications. In Eq. (6), the approximate solution of the main problem is given in terms of shifted Chebyshev polynomials polynomials. Keywords: fractional; j=0; k=1; m∑ j=0; simpson
Utilization of the Modified Adomian Decomposition Method on the Bagley-Torvik Equation Amidst Dirichlet Boundary Conditions by Al-Mazmumy, Mariam ; Alsulami, Mona (2024) - Fractional differential equations: an introduction to fractional deriva- tives, fractional differential equations, to methods of their solution and some of their applications. Notably, various real-life models are discovered to be perfectly captured through the application of fractional differential equations (FDEs). Keywords: anx; fractional; l−1
A Novel Fractional Edge Detector Based on Generalized Fractional Operator by Elgezouli, Diaa Diaa Eldin ; Abdoon, Mohamed; Belhaouari, Samir Brahim; Khalid Almutairi, Dalal (2024) - This work pioneers a novel approach in image edge detection through the utilization of the generalized fractional operator. Conclusion This work pioneers a novel approach in image edge detection through the utilization of the Generalized Fractional. Keywords: detection; edge; edge detection; fractional; image; operator; order; prewitt; sobel; values
On a Novel Fractional Calculus and its Applications to Well-known Problems by Ait Brahim, A.; El Hajaji, A. ; Hilal, K. ; Ghordaf, J. El (2024) - 2020 Mathematics Subject Classifications: 26A33, 34A08, 65M70, 35R11, 92D25 Key Words and Phrases: New conformable fractional derivative, population grow model, body coolig model, fractional heat equation. Then form of fractional heat equation represented by : ∂α ∂tα ∂αz(x, t) ∂tα = ∂2z(x, t) ∂x2 , (27) z(0, t) = 0, t > 0, (28) z(1, t) Keywords: conformable; equation; fractional; new
A Comparative Analysis of Conformable, Non-conformable, Riemann-Liouville, and Caputo Fractional Derivatives by Aitbrahim, Aabdessamad; Ghordaf, J. El ; El Hajaji, A. ; Hilal, K. ; Valdes, J. E.Napoles (2024) - Fractional ordinary differential equation with Riemann Liouville, Ca- puto, and conformable fractional Derivatives This section discusses solutions to fractional Ordinary Differential Equations using Rie- mann Liouville, Caputo, and conformable fractional Derivatives and then their numerical simulations. Conclusion Numerical simulations conducted on the solutions to initial value problems of fractional ordinary differential equations reveal that the graphs of solutions using Riemann-Liouville and conformable fractional derivatives exhibit significant proximity for 0 < α < 1. Fur- thermore, the solutions’ graphs employing all three fractional derivatives show substantial similarity for 1/2 < α < 1. Keywords: calculus; conformable; derivative; fractional; k−1
On a Hybrid Class of $p$-Laplacian Initial Value Problems with Modified Mittag-Leffler Kernel by Sowmiya Ramasamy ; Kavitha Velusamy; Dumitru Baleanu; Mani, Mallika Arjunan (2024) - For ∆ < 1, by (21)-(23), consider the following norm ∥w − w∗∥ = ∥w − Φw +Φw − w∗∥ M. M. Arjunan / Eur. Theory of fractional hybrid differential equations. Keywords: fractional; w(7; γ(β
Conformable Sumudu Transform Based Adomian Decomposition Method for Linear and Nonlinear Fractional-Order Schrödinger Equations by Liaqat, Muhammad Imran; Aljarrah, Hussam (2024) - For problem 4.3, the 2D diagrams of App-Ss for various levels of µ and Ex-Ss in the range φ ∈ [0, 1.0] at ϱ = 0.1 are shown for: (a) δ1(ϱ, φ); (b) δ2(ϱ, φ). Figure 8: For problem 4.2, the 3D diagrams of Ex-S in the range φ ∈ Keywords: app; derivatives; equations; fractional; liaqat; s−1; s−1 µ; ρ=0; ωsµ
The Impact of White Noise on Chaotic Behavior in a Financial Fractional System with Constant and VariableOrder: A Comparative Study by Berir, Mohammed (2024) - We analyze the chaotic behavior of these fractional-order hyperchaotic systems through simulations, study the effects of white noise on chaotic dynamics, and provide a comparison between fractional hyperchaotic systems of constant and variable orders. A symmetry chaotic model with fractional derivative order via two different methods. Keywords: financial; fractional; hyperchaotic; noise; order; system; variable
Bernstein Polynomials for Solving Fractional Differential Equations with Two Parameters by A.K.Alomari; Al-Shatnawi, Abdul Rhman ; Adel Almalki ; Anakira, Nidal (2024) - The method used to analyze and solve fractional differential equations is im- plemented. Using orthonormal Bernstein polynomials has led to the development of fractional poly- nomials, which offer an approximate solution for ordinary fractional differential equations. Keywords: bernstein; differential; equations; fractional; polynomials; solution
Generalized Conformable Hamiltonian Dynamics with Higher-Order Derivatives by M. Alawaideh, Yazen; Ramazanova, Aysel; Issaadi, Hayat; Al-khamiseh, Bashar. M.; Bilal, Muhammad ; Baleanu, Dumitru Baleanu (2025) - Fractional hamiltonian analysis of higher order derivatives systems. This work builds upon fractional mechanics and conformable derivatives to derive a generalized form of Euler-Lagrange equations for higher order conformable derivatives, establishing energy and momentum conservation in the presence of time independence and translational invariance of the Lagrangian [26]. Keywords: derivatives; fractional; hamiltonian; order; s|tqi; t qi
Solution of Well-known Physical Problems with Fractional Conformable Derivative by Abuteen, Eman; Ait Brahim, Abdessamad ; El Hajaji, Abdelmajid ; Hilal, Khalid ; Charhabil, Ayoub (2024) - Definition of new fractional derivative In this section, we begin by introducing the Mittag-Leffler function, which plays a significant role in various physical processes and often emerges in the solutions to fractional differential equations. This paper presents a new definition of fractional derivatives and integrals through the conformable derivative approach. Keywords: derivative; equation; fractional; function
New Integral Transforms of the Extended k- Generalized Mittag-Leffler Function with Graphical Representations by D'Costa, Liya ; Menaria, Naresh (2024) - Beta function and its applications. Integral transforms of the s-functions. Keywords: bk(ρ; ekg; equation; fractional; function; integral; n=0; transform
Stability Analysis of Fractional Chaotic and Fractional-Order Hyperchain Systems Using Lyapunov Functions by Abdulrhman, Thwiba (2025) - Stability control of fractional chaotic systems based on a simple lyapunov function. Stability control of fractional chaotic systems based on a simple lyapunov function. Keywords: analysis; derivative; fractional; function; khalid; lorenz; order; pure; stability; system
Gronwall-Type Inequalities and Qualitative Studies onHigher-Variable Orders of Atangana-Baleanu Fractional Operators via Increasing Functions by Hammad, Hasanen A.; De la Sen, Manuel (2024) - κ ψ′(r)Lθu ( −θu 1− θu (ψ(z)− ψ(r))θu ) ℘ (k+1) ψ (r) dr = Λ(ϖu − k) (k + 1−ϖu) × z∫ κ ψ′(r)Lϖu−k ( − (ϖu − k) k + 1−ϖu (ψ(z)− ψ(r))ϖu−k ) ℘ (k+1) ψ (r) dr, where ℘ (k) ψ (z) = ( 1 ψ′(z) = k + 1−ϖu Λ(ϖu − k) RL ℜk,ψκ ℘ (z) + ϖu − k Λ(ϖu − k) RL ℜϖu,ψκ ℘ (z) , where ℜk,ψκ takes the form ℜk,ψκ ℘ (z) = 1 Γ (k) z∫ κ ψ′(r) Keywords: fractional
Langevin Fractional System Driven by Two $\psi$-Caputo Derivatives with Random Effects by Ziane, Mohamed ; Al-Taani, Hussein ; Abudayah, Mohammad Ali; Zentar, Oualid ; Abu Hammad, Ma’mon (2025) - f2(ξ, z1(ξ, ω), z2(ξ, ω), ω), ξ ∈ (0, b], lim ξ→0+ ξ1−ϑ1z1(ξ, ω) = Z3(ω), ω ∈ Ω, lim ξ→0+ ξ1−ϑ2z2(ξ, ω) = Z4(ω), ω ∈ Ω, where Z3,Z4 : Ω → G are random variables, Dϑi 0+ represents the standard Riemann- Liouville FD of order ϑi ∈ (0, 1] for each i = 1, 2 and fi : [0, b] The map u 7−→ f(ξ, u, ω) is continuous for all ξ ∈ I and ω ∈ Ω. (ii) Keywords: fractional; let; γ(ϑi
Employing the Limit Residual Function Method to Solve Systems of Fractional Differential Equations by El-Ajou , Ahmad; Burqan, Aliaa (2025) - To demonstrate the procedures of the LRF method, we will be studying the following class of fractional differential equation systems: Dαui (x) = Hi (x, u1 (x) , u2 (x) , . . . This study aims to solve systems of fractional differential equations analytically using a simple new technique, the limit residual function method. Keywords: fractional; solution
Existence of Solutions to a System of Fractional Differential Equations With Applications to Beam Deflections by Hammad, Hasanen A.; Abdalla, Manal Elzain Mohamed (2025) - In this manuscript, we introduce a novel system of fractional differential equations in- corporating both Caputo and conformable derivatives. Beam deflection coupled sys- tems of fractional differential equations: Existence of solutions, ulam-hyers stability and travelling waves. Keywords: fractional; math; γjγ
Comparative Analysis of Analytical Solutions for Seepage Flow Derivatives in 4D Porous Media by M.Mirgani, Safa (2025) - By analyzing the convergence properties, computational efficiency, and solution accuracy of these methods, the study offers insights into their applicability to fractional seepage flow problems in porous media. Comparison of ADM, FDTM, and HAM for Seepage Flow Problem The HAM serves as a robust alternative for solving fractional differential equations, particularly where traditional methods like the ADM or FDTM encounter convergence or nonlinearity challenges. Keywords: differential; fractional; solution
New Generalized Results for Modified Atangana-Baleanu Fractional Derivatives and Integral Operators by Rahman, Gauhar; Samraiz, Muhammad; Yildiz, Cetin; Abdeljawad, Thabet; Alqudah, Manar A. ; Mukheimer, Aiman (2025) - By expanding their kernels, the authors [8, 15, 27] has recently defined the gen- eralization of fractional operators. They used the (k, s) form of fractional operators to solve the Cauchy problems after proving them. Keywords: fractional; g(ξ; r(δ; ℏ(a; ℏ(ξ)−
Analytic Solutions of the Time-Fractional Date-Jimbo-Kashiwara-Miwa Equation via New Function Transformations by Yasmeen, Bushra; Ahmad, Khalil; Fatima, Nahid (2025) - The solitons and nonlinear wave solutions are depicted in each plot. We address previously unsolved problems in nonlinear PDEs, are deriving exact solutions for nonlinear wave equations with fractional time derivatives. Keywords: equation; fractional; nonlinear; ode; solutions; time; wave
Quantization of Singular Systems using Fractional Calculus by Hasan, Eyad (2025) - = 1 Γ(n− α) ( d dt )n ∫ t a (t− τ)n−α−1f(τ)dτ (1) and the Right Riemann–Liouville derivative is given by: tD α b f(t) = 1 Γ(n− α) ( − d dt )n ∫ b t (τ − t)n−α−1f(τ)dτ (2) and these derivatives have properties as follows: aD α t f(t) = ( d dt )α f(t) (3) tD α b f(t) Keywords: fractional; systems
Effective Analytical-Approximate Technique for Caputo Nonlinear Time-Fractional Systems Emerging in Shallow Water Waves and Hydrodynamic Turbulence by Alaroud, Mohammad; Aldosari, Faten (2025) - On the other hand, the proposed method may face convergence issues for fractional equations with singularities or highly nonlinear terms. Math, 18 (1) (2025), 5784 4 of 25 LT-RFPS method to create series solutions of a hyperbolic system of time-PDEs with variable coefficients in the light of Caputo FD sense. Keywords: fractional; i=0; j−1∑; solutions
$\mathcal{C}_\alpha$-Rectifying Curves in a New Conformable Differential Geometry by Has, Aykut; Yilmaz, Beyhan; Abdeljawad, Thabet (2025) - Obtaining fractional electromagnetic curves in optical fiber using fractional alternative moving frame. Conformable special curves in euclidean 3-space. Keywords: calculus; curve; derivative; fractional; frame; x(s
Computational Methods, Existence and Uniqueness for Solving 2-D Fractional Nonlinear Fredholm Integro-Differential Equation by Albugami, Abeer; Alharbi, Nuha A.; Mahdy, Amr M. S. (2025) - Solving nonlinear fractional differential equations by using shehu transform and adomian polynomials. [7] developed a new algorithm for the decomposi- tion solution of nonlinear differential equations, further advancing the method. Keywords: equations; fractional; solution
Existence of Solutions for Fractional Order Differential Equations: Extended Results by Aljurbua, Saleh; Alrashidi, Munirah; Alrashidi, Asrar ; Alharbi, Reham ; Almutairi, Rawan ; Saad, Majd ; Alharbi, Najla ; Alrawji, Wejdan ; Alharbi, Najd ; Alharbi, Dhay ; Alashwan, Rawan ; Alluhayb, Asamh ; Alfuraih, Nuha (2025) - κ 0 (κ−ϖ)q−1δ(ϖ) ] a1 = α− β ω − κ + 1 Γ(q)(ω − κ) [ ∫ ω 0 (ω −ϖ)q−1δ(ϖ)dϖ − ∫ κ 0 (κ−ϖ)q−1δ(ϖ)dϖ ] by using the values of a0, a1 we get ξ(ρ) = αω − βκ ω − κ + β − α ω − κ ρ+ 1 Γ(q) ∫ ρ 0 (ρ−ϖ)q−1δ(ϖ) dϖ − ρ− κ Γ(q)(ω − κ) Keywords: fractional; − κ
Investigation of Existence and Ulam's type Stability for Coupled Fractal Fractional Differential Equations by Ali, Amjad; Bibi, Farha; Ali, Zeeshan; Shah, Kamal; Abdalla, Bahaaeldin; Abdeljawad, Thabet (2025) - For the better understanding of consider coupled system FFDEs, we carry out investigations and analysis for model via the tools of mathematical analysis. Coupled systems have numerous applications in different fields, such as modeling of brain activities and spreads of disease in biology and medicine, modeling of mechanical systems, electrical circuits in engineering, and modeling of population dy- namics, predator-prey models in ecology and financial mathematical in economics. Keywords: ffdes; fractional; r(t; r(δ; solution; stability; system; γ(η; δ)η−1δξ−1f(δ
Unique Solution Analysis for Generalized Caputo-Type Fractional BVP via Banach Contraction by Bekri, Zouaoui ; Aljohani, Sarah ; Samei, Mohammad Esmael ; Akg¨ul, Ali ; Belhenniche, Abdelkader ; Aloqaily, Ahmad; Mlaiki, Nabil (2025) - [ (ϑϱ − θϱ)σ−1(τϱ − θϱ)− (τϱ − θϱ)σ ] . (7) Proof. [ (ϑϱ − θϱ)σ−1(τϱ − θϱ)− (τϱ − θϱ)σ ] . Implies that∫ ϑ θ ∂|ℏ(τ,r)| ∂τ dr = 1 ϱσ−1σΓ(σ) Keywords: fractional; σ σ; σ−1
Helical Estimation of Atangana-Baleanu-Caputo Fractionalized Magnetohydrodynamic Second Grade Fluid for Generalized Boundary Conditions under Porous Environment by Zafarullah, Muhammad ; Khan, Ilyas; Abid, Kanwal; Jamil, Muhammad ; Albidah, A. B.; Alharthi, Thoraya N.; Aljohani, A. F. ; Koh, Wei Sin (2025) - [V2g4(t)−V1g3(t)](µ+αao)− H(t)αa0 ρ ln(Π2/Π1) ∫ t 0 i ∫ t 0 [U2J1(Π1ρn)g2(t− δ)− U1J1(Π2ρm)g1(t− δ)]M1,i 0 (−(νGp +Gm), δ)dδ. (50) M. Zafarullah et al. / Eur. Keywords: appl; eur; fluid; fractional; grade; math; pure
A New Trend of Fractional Inequalities for Differentiable Monotone Convexities Through Generalized Operators with Applications by Rana, Rana Safdar Ali; Talib, Naila ; Etemad, Sina ; Tariboon, Jessada ; Hafeez, M. I. (2025) - In the last few decades, many researchers have worked to develop fractional operators having generalized special functions as its kernel, which have many applications in the field of operator theory, fractional inequalities. Hermite– hadamard’s inequalities for fractional integrals and related fractional inequalities. Keywords: fractional; κ ν; υ̌(α; υ̌(ρ)−; υ̌−1
Advanced Mathematical Approaches for Solving Fractional-Order Korteweg-de Vries Equations by Iqbal, Naveed; Hussain, Shah; E. Hamza, Amjad; Jawarneh, Yousef; Ghani, Fazal (2025) - These methods are enhanced, according to the visual information, by being able to get good approximations for fractional differential equations, covering a large number of scientific and engineering situations. Applications on double ara-sumudu transform in solving fractional partial differential equations. Keywords: equations; fractional; nintm; ψ(υ
Analytical Investigation for Some Problems Under Different Fractional Differential and Integral Operators by Sohail, Muhammad; ., Eiman; Khan, Hassan; Sarwar, Muhammad; Shah, Kamal; Abdeljawad, Thabet (2025) - Moreover, fractional order solutions are converging to integer order solutions. Math, 18 (4) (2025), 6378 2 of 20 the numerous uses of fractional differential equations (FDEs) in the fields of science and engineering, mathematicians are increasingly focusing on this area of study. Keywords: differential; fractional; fνk(κ; θ χ(θ; νk+1(κ
Analytical and Numerical Investigation of a Fractional Order 4D Chaotic System via Caputo Fractional Derivative by Kadri, Ilhem; Saadeh, Rania Saadeh; M. AlMutairi, Dalal ; E. Dafaalla, Mohammed; Berir, Mohammed; A. Abdoon, Mohamed (2025) - The findings show that a decrease in h is directly proportional to increased ac- curacy, which supports the consistency of CFD in solving fractional order systems. Exploring chaos in fractional order systems: A study of constant and variable-order dynamics. Keywords: caputo; dynamics; fractional; numerical; order; pure; res; system; γ(2ν; γ(ν
Qualitative Analysis and Simulation of Fractional Hybrid Boundary Value Problems in Orthogonal Cone Metric Spaces by Baleanu, Dumitru; Khuddush, Mahammad; Boddu, Muralee Bala Krushna; Tikare, Sanket (2025) - = 1 Γ(y) { ωy−1(1− ξ)y−1 − (ω − ξ)y−1, ξ ≤ ω, ωy−1(1− ξ)y−1, ω ≤ ξ. (4) D. Baleanu et al. / Eur. + m∑ i=1 kiω y−i, where ki ∈ R, i = 1, m, m ≤ y ≤ Keywords: 0(ω; f(ω; fractional; math; metric; r(ω
A study of a Coupled System of Fractional Differential Equations with Two Points Integral Boundary Conditions by Al-Omari, Shrideh; Momani, Shaher ; Hamzeh Zureigat; Mohammad, Mona ; ., Khandaqji; Al-Smadi, Mohammed (2025) - ∫ H 0 ∫ = τ Λ ( ζη ∫ µ 0 (µ− s)β−2 Γ(β − 1) y(s) ds− η ∫ H 0 ∫ Keywords: fractional; system; γ(β
Stability Results for Stochastic Delay Differential Equations in the Framework of Conformable Fractional Derivatives by Liaqat, Muhammad Imran ; Baleanu, Dumitru; Yousif, Majeed Ahmad; Mohammed, Pshtiwan Othman (2025) - This conformity facilitates the development and analysis of fractional stochastic differential equations (FSDEs), as it allows researchers to leverage their existing knowledge and techniques from classical calculus. Qualitative analysis of fractional stochastic differential equations with variable order fractional derivative. Keywords: differential; equations; fractional; sim; solutions; stochastic
Fractional Discrete Modeling and Numerical Analysis of Hepatitis B and C Dynamics with Neural Network Approximation by Shah, Sajid Ali; Rehman, Nasir; Ahmad, Sadique ; A.Elaffendi, Mohammed ; Ateya, Abdelhamied Ashraf (2025) - For t ∈ [ξ − 1, b+ ξ]Nξ−1 , one has |g(t)− ḡ(t)| = ∣∣∣g(t)− ( g(0) + 1 Γ(ξ) t−ξ∑ s=0 (t− s− 1)ξ−1F (s + ξ − 1, g(s + ξ − 1)) )∣∣∣, ≤ Dψϵ+ 1 Γ(ξ) t−ξ∑ s=0 (t− s− 1)ξ−1 × |F (s + ξ − 1, g(s + ξ − 1))− F (s + ξ − 1, ḡ(s + ξ − 1))|, ≤ Dψϵ+ 1 Γ(ξ) t−ξ∑ s=0 (t− s− 1)ξ−1K∥g − ḡ∥ (18) which further means ∥g − ḡ∥ ≤ [ Dψ 1−KDψ ] ϵ = Dgϵ. (19) Also set Dg = Dψ 1−KDψ > 0, we conclude that solution of (2) is UH stable. = ηH(t+ ξ − 1)V (t+ ξ − 1)− γI(t+ ξ − 1), C∆ξR(t) Keywords: data; fractional; nns; outputs; targets; γ(ξ
Novel Fractional Hermite–Hadamard and Product-Type Inequalities via Raina Function and Preinvex Mappings with Entropy Applications by Muhammad Tariq; Waqar, Afzal ; Nadeem, Muhammad ; Munoz-Zavala, Angel E. ; Mac´ıas-D´ıaz, Jorge E. (2025) - − la) ) ≤ xΛ(lb) + (1− x)Λ(la), (2.6) for all la, lb ∈ X, where la < lb and x ∈ − la) Keywords: + ∆ϱ; fractional; inequalities; la iγ; γ +; ϵ,σ(lb −; ∆ϱ ϵ,σ(lb; − la
A Comparative Analysis of the Non-linear Time Fractional Whitham-Broer-Kaup Equations under Aboodh Decomposition Transform by Kadri, Ilhem; Gundogdu, Hami; Modawy, Yousif M.; Imam, Ayman; Helal, Khadeeja A. A.; Elshamy, Ibrahim; Tahir, Ranya A. (2025) - By studying fractional WBK equations, we expect to achieve a greater intensive understand- ing of the effect of fractional derivatives on the dynamics of nonlinear wave phenomena. Approximate solutions to the time fractional WBK equations This section is dedicated to the numerical findings of solutions obtained for the time- fractional WBK equations. Keywords: equations; fractional; γ(β; ∂x2β
Modeling Dengue Dynamics Using Classical, Caputo Fractional, and Fractal Derivatives by Saadeh, Rania; Al-Kuleab, Naseam; Al-Soudi, Maha; A. . A.Helal, Khadeeja ; Imam, Aymen ; Elshamy, Ibrahim ; Jamiel M. Abdalla, Suliman Jamiel M. Abdalla (2025) - Fractional models, however, cannot account for time variations [21–23]. Specifically, we explore how the role of memory effects in fractional models and spatial heterogeneity in fractal models influence disease transmission dynamics and outbreak generation. Keywords: dengue; disease; dynamics; fractal; fractional; models; order; pure; saadeh; transmission
Nonlinear Dynamics of Dengue Fever with Vaccination and Saturated Incidence by Alsulami, Mansoor ; Jan, Rashid; Antonescu, Elisabeta (2025) - These computational investigations enable the systematic exploration of disease transmission dynamics over time, offering insights into how infection trajectories evolve in response to varying initial states and parameter regimes. Based on these assumptions, the dynamics of dengue are represented by: dSh dt = Λh − bβ1 1+αhIv ShIv − µhSh − pSh + υRh, dVh dt = pSh − bβ2 1+αhIv VhIv − µhVh, dIh dt = bβ1 1+αhIv ShIv + bβ2 1+αhIv VhIv − (µh + γh + τ)Ih, dRh dt = γhIh + τIh Keywords: dengue; fractional; j h; j−1 h; j−1 v; s j; v j
Stochastic Stability and Controllability Analysis of Impulsive Multi-Term Fractional Differential System by Lavanya, M. ; Sundara Vadivoo, B.; Alraddadi, Ibrahim; Pamucar, Dragan ; Oqilat, Osama ; Ahmad, Hijaz (2025) - r 0 (r − s)n−x−1a(n)(s)ds, n− 1 < x ≤ n, n ∈ N For each r ∈ (rt, rt+1], t = 1, 2, 3..., s, we obtain (Λa)(r) = ∫ r 0 pm(r − q)δdq + x∑ g=1 ug r m−1pm,1+m−Ng(r)δ + s∑ θ=1 Jθ(a(r − θ )) (11) + ∫ r 0 (r − q)m−1pm,m(r − q)[V (q, a(q)) + Ey(q)]dq + ∫ r 0 (r − q)m−1pm,m(r − q)H(q, a(q))dξ(q) The control of (9), for each r ∈ (0, r1], for a0 ∈ R y(r) = (r − q)m−1d∗pm,m(r − q)E{a0 − ∫ r 0 pm(r − q)δdq (12) − x∑ g=1 ug r m−1pm,1+m−Ng(r)δ − ∫ r 0 (r − q)m−1pm,m(r − q)[V (q, a(q))]dq − ∫ r 0 (r − q)m−1pm,m(r − q)H(q, a(q))dξ(q)/Gs} Keywords: fractional; g=1; m(r −; pm(r −; r m−1pm,1+m−ng(r)δ; r −; stochastic; − q)m−1pm; − q)δdq
Two Numerical Approaches to Solving Fractional Differential Equations with a Generalized Mittag–Leffler Kernel Using Bernstein Polynomials by Tamimi, Shreen; Alomari, A.K.; Alaroud, Mohammad (2025) - This paper presents a solution to fractional differential equations containing three parameters, utilizing Bernstein polynomials through two efficient computational approaches. Successive midpoint method for fractional differential equations with nonlocal kernels: Keywords: abc; approach; equations; fractional; solution
Time-Fractional Free Convection of Maxwell, Williamson, and Micropolar Nanofluids over a Vertical Plate in Saturated Porous Media by Nabwey, Hossam A. ; Nour, M; Zaki, Assma ; Khan, Waqar ; Rashad, A; EL-Hakiem, Amal ; Aldurayhim, Abdallah ; Awad, Mohamed ‎ (2025) - A double diffusive convection in non-newtonian fluid flow with quadratic radiation and variable viscos- ity: Heat generation effects in lower stagnation point of solid sphere. This study develops a unified time-fractional framework to investigate free convection of Maxwell, Williamson, and micropolar nanofluids in porous media under the combined effects of magnetic field, thermal radiation, and internal heat generation. Keywords: boundary; buoyancy; convection; effects; et al; field; flow; fractional; generation; heat; heat generation; heat transfer; mass; maxwell; micropolar; micropolar nanofluid; nanofluid; number; transfer; viscosity; wall; williamson
Criteria for Finite-Time Convergence in Discrete Variable-Order Fractional FitzHugh–Nagumo Reaction–Diffusion Systems by Anakira, Nidal ; H. Jebri, Iqbal ; M. Batiha, Iqbal ; S. Hijazi, Mohammad ; Sasa, Tala (2025) - Time t (seconds) ∥u(t)∥+ ∥v(t)∥ 0.0 0.2186 0.5 0.2080 1.0 0.2059 1.5 0.2064 2.0 0.2076 2.5 0.2088 3.0 0.2100 These findings underscore the practical utility of our stability criterion for predicting the transient behavior of discrete fractional systems with variable-order dynamics. Finite time stability analysis of fractional order time delay systems. Keywords: discrete; fractional; stability; system; time; ℏδn
Numerical Solution of Two-Dimensional Fractional Optimal Control Problems Using Fractional Vieta-Fibonacci Wavelets by Bahaa, G. M.; Qamlo, Ahlam (2025) - x D0.9 y p(x, y) = 0 (6.6) D0.9 y p(x, y) = 2z(x, y) + p(x, y) (6.7) Keywords: bahaa; control; fractional; fvfw; p(x; system; z(x
Theory of Fractional Differential Equations in a Banach Space by Lakshmikantham, V.; Devi, J. Vasundhara (2007) - =t0 = x0, (2.1) where f ∈ C[R0, E] with R0 = [(t, x) : t0 ≤ t ≤ t0 + a and B(x0, b)], Dqx is the fractional derivative of x of order 0 < + 1 Γ(q) ∫ t t0 (t− s)q−1f(s, x(s))ds, t0 ≤ t ≤ t0 + a; (2.2) that is, every solution of (2.2) is a solution of (2.1) and vice versa. Keywords: fractional; g(t

Pure

Sequentially Complete S-acts and Baer Type Criteria Over Semigroups by Barzegar, Hasan (2013) - Ebrahimi and Mahmoudi [4] has introduced the concept of s-pure monomorphism in the category of Projection Algebras by a system of equations such as xs = as(s ∈ S, as ∈ A). We say that A is s-pure in an extension B of A if every sequential system of equations with constants from A such as ΣA = {xs = as : s ∈ S, as ∈ A} has a solution in A whenever it has a solution in B. Keywords: act; injective; pure
Application of Combinatorial Techniques to the Ghanaian Board Game Zaminamina Draft by Donkoh, Elvis Kobina; Davis, Rebecca; Owusu-Ansah, Emmanuel D.J; Antwi, Emmanuel A.; Mensah, Michael (2019) - Variations in the Zaminamina Draft Game Many board games share the element of trying to be the first to get in-a-row, including Three Men’s Morris, Nine Men’s Morris, Pente, Gomoku, Qubic, Connect Four, Quarto, Gobblet, Order and Chaos, Toss Across, and Mojo. Games happen to be a part of our contemporary culture and way of life. Keywords: board; game; player; pure; strategy; toe; win; zaminamina
Pride and Passion: Remarks on Thomas L. Saaty's Final Papers by Cetin, Eyup; Kiremitci, Baris (2018) - We just would like to remember and honor Saaty’s memory by publishing his final papers at EJPAM and this humble remarks dedicated to the memory of Thomas L. Saaty on the occasion of the first anniversary of his passing, August 14, 2018. 2010 Mathematics Subject Classifications: 90B50, 90C29,91B06,92B20, 91C05, 82C32 Key Words and Phrases: Thomas L. Saaty, Measurement theory, Neural networks, Analytic Hierarchy Process, AHP, Analytic Network Process, ANP 1. Origin of Neural Firing and Synthesis in Making Comparisons Thomas L. Saaty submitted his final paper (co-authored by Prof. Luis G. Vargas, his colleague at University of Pittsburgh) on neural firing and synthesis in making comparison in Saaty and Vargas Keywords: mathematics; pure; saaty; thomas
Mathematical Modeling of Wastes Pile-Up in Kwadaso Municipality in Ashanti, Ghana by Barnes, Benedict; Boateng, Francis Ohene; Sebil, Charles; Owusu, Enock (2020) - Ghana as a developing country has its share of the problem of wastes management. In other words solid waste can be defined as the useless and unwanted products in solid state derived from the activities of human beings. Keywords: pure; rate; table; wastes
Foreword by Srivastava, Hari M. (2020) - The main emphasis of this Special Dedication Issue was to include some selected peer- reviewed papers which stemmed from the International Conference on Advances in Mathe- matics and Computing (ICAMC 2020) Finally, on my own behalf as well as on behalf of the Members of the Organizing Committee of ICAMC 2020 (including the Convener, Dr. Susanta Kumar Paikray), I am exceedingly delighted to thank all of the participating authors and the referees for their invaluable contributions toward the remarkable success of this Special Dedication Issue. Keywords: mathematics; pure
A Novel Inspection of a Time-Delayed Rolling of a Rigid Rod by Alluhydan, Khalid; Moatimid, Galal; Amer, Tarek; Galal, Abdallah (2024) - Even in nonlinear systems, if the nonlinearities are symmetric, the phase plane curves can remain symmetric. A novel methodology for a time- delayed controller to prevent nonlinear system oscillations. Keywords: fig; frequency; galal; journal; moatimid; nonlinear; pure; rod; solution; stability; system; time
Site Selection for Thermal Power Plant Based on Sombor Index in Neutrosophic Graph by Alqahtani, Mohammed ; Kaviyarasu, M.; Rajeshwari, Murugesan (2024) - = √ (dα)2 + (dβ)2. = ∑ α,β∈E(G) √ (ϖ(α)dG(α))2 + (ϖ(β)dG(β))2. Keywords: alqahtani; appl; eur; fuzzy; graph; index; indices; kaviyarasu; neutrosophic; nsoi(g; pure; rajeshwari; β∈e(g
Non-Perturbative Approach in Scrutinizing Nonlinear Time-Delay of Van der Pol-Duffing Oscillator by Alanazy, Asma ; Moatimid, Galal; Amer, Tarek; Galal, Abdallah (2025) - The objective of the NPA is to comprehend the intricacies of nonlinear systems independently, without depending on minor perturbations from a known solution. A significant technique for deriving analytical approximations in the study of nonlinear oscillators was utilized. Keywords: appl; eur; frequency; nonlinear; oscillator; pure; stability; systems; time
Spectral Properties of Structured Matrices in Transportation Problems by Rehman, Mutti-Ur; Aminov, Behkzod ; Alshehri, Mohammed N.; Mohammed, Mustafa M.; Mustafa, Arafa O. ; Abdalrahman, Nhla A. ; Magzoub, Mona ; Mahgoub, Hala S.; Hamed, Sakeena E. M.; Bashir, Runda A. A.; Bakery, Awad A. (2025) - Furthermore, we also provide numerical experimentation on the computation of singular values and pseudo-inverse of transportation matrices. Next, we give numerical examples on the computation of singular values and pseudo inverse of transportation matrices. Keywords: appl; eur; math; matrices; matrix; problem; pseudo; pure; singular; spectrum; transportation; values
Insights in Inspecting Two-Degree-of-Freedom of Mathieu-Cubic-Quintic Duffing Oscillator by Alanazy, Asma; Moatimid, Galal; A. A. Mohamed, Mona (2025) - The Duffing oscillator (DO) is a conspicuous example of nonlinear ordinary differential equations (ODEs), particularly in simulating nonlinear systems [5], including micro and nanomechanical resonators. [32] Moatimid G.M., Amer T.S., and Ellabban Y.Y., A novel methodology for a time- delayed controller to prevent nonlinear system oscillations, Journal of Low Frequency Noise, Vibration and Active Control, 43(1), 525-542 (2024). Keywords: a. a.; a. mohamed; frequency; m. a.; moatimid; nonlinear; oscillator; parametric; pure; solutions; system
Parametric Estimation for a new Pareto-type model Based on Constant-Stress Partially Accelerated Censoring data by Taha, Osama; Soliman, Ahmed ; Abd-Elmougod, Gamal ; Farghal, Alwageh (2025) - To address this, experimenters uses accelerated life testing (ALT) or partially accelerated life testing (PALT) to quickly gather sufficient failure data and A. A. Soliman et al. / Eur. Even though the major goal of partial ALT is to reduce the testing period of the experiment, the experimenter spends a significant amount A. A. Soliman et al. / Eur. Keywords: a. a.; avg; data; distribution; estimates; estimation; function; i=1; likelihood; log; parameters; pure; soliman; step; type
Corporate Governance Mechanisms and Board Characteristics as Determinants of Financial Failure: A Cox Proportional Hazards Model by Jamal Rabaia, Duha; Ibrahim Nour, Abdulnaser; Abu Alia, Muiz; Kanj, Hassan ; AlAkkoumi, Mouhammad ; Jebreen , Kamel (2025) - Corporate board size, composition and corporate failures in retailing industry. Additionally, the analysis revealed that board size, board independence, board age, board education firm size, and liquidity were significantly and negatively associated with CF. Keywords: appl; audit; board; board size; business; diversity; eur; failure; firm; governance; impact; journal; management; math; ownership; palestine; performance; pure; rabaia; research; size; structure; study; survival; theory
Controllability of a System with Nonlinear Damping Devices and Nonlinear Source Terms in Elasticity Problems: Existence, Time Blow-up, and Numerical Results by Al-Mahdi, Adel M. ; Al-Gharabli, Mohammad; M. D. Kassim; Abdelaziz Soufyane; Mostafa Zahri; Mukiawa, Soh Edwin (2025) - As k goes to +∞, we easily check that ∀j < k, ∫ Ω ztwj(x)dx− ∫ Ω z1wj(x)dx+ a1 ∫ t 0 ∫ Ω zxwjx(x)dxds+ a2 ∫ t 0 ∫ Ω uxwjx(x)dxds + γ ∫ t 0 ∫ Ω |zt|p(.)−2ztwj(x)dxds = ∫ t 0 ∫ Ω wjf(x, t)dxds,∫ Ω utwj(x)dx− ∫ Ω u1wj(x)dx+ a3 ∫ t 0 ∫ Ω uxwjx(x)dxds+ a2 ∫ t 0 ∫ Ω zxwjx(x)dx + β ∫ t 0 ∫ Ω |ut|q(.)−2utwj(x)dxds = ∫ t 0 ∫ Ω wjg(x, t)dxds. Messaoudi [27]considered the following nonlinear viscoelastic wave equation utt −∆u+ ∫ t 0 g(t− s)∆u(s)ds+ a|ut|m−2ut = b|u|p−2u, x ∈ Ω, t > 0, (8) where Ω is a bounded domain of Rn. Keywords: appl; blow; eur; mahdi; pure; ∫ ω
Domination in Bipolar Fuzzy Rough Digraphs with Applications to Decision-Making by Arif, Anessa; Fahmi, Aliya; Khan, Aziz; Aiman Mukheimer; Abdeljawad, Thabet; Thinakaran, Rajermani (2025) - Rough fuzzy sets and fuzzy rough sets. Bipolar fuzzy rough set model on two different universes and its application. Keywords: bfrd; domination; fuzzy; graphs; pure; set; sets; −0.1
A Novel SPN based Multiple RGB Images Security over the Residue Classes of Quaternion Integers H[K]_δ by Sajjad, Muhammad; A. Alqwaifly, Nawaf (2025) - NIST Test779 Randomness of quaternion integer multiple RGB image encryption: The NIST sta-780 tistical test suite is a standard method for testing random and security strength of the781 encryption scheme, especially for the multiple RGB image encryption over integers. Quaternion based encryption does this by separately753 transforming the scalar and vector part of each pixel by modular arithmetic, affine trans-754 formation, and quaternion rotation. Keywords: alqwaifly; appl; attacks; boxes; differential; diffusion; encryption; eur; image; image encryption; integers; j. pure; linear; math; original; pixel; pure; pure appl; quaternion; quaternion integers; rgb; sajjad; scalar; security; substitution; table; transformations; values; vector
Applying LPA to Analyze the 3D Motion of a Symmetric Rigid Body with a Large Displacement of a Center of Mass by Amer, T. S.; Ismail, A.; Amer, W. S.; El-Kafly, H. El-Kafly (2025) - = ρ2 2ρ1 Γ15 + 1 2Γ24, G110 = 1 2Γ61A3[ 1 ρ1 (ρ1 − ρ2)A 2 1 − 2(A2 1 +A2 2)], G111 = −(3− ρ2 ρ1 )A1A2A3Γ16, G112 = − 1 2ρ1 (ρ1 + ρ2)Γ26, G113 = − 1 2ρ1 (ρ1 − ρ2)Γ26, G114 = − 1 2ρ1 (ρ1 + ρ2)A 2 3Γ25, G115 = − 1 2ρ1 (ρ1 + 2ρ2)A 2 3Γ28, G116 = − 1 ρ1 (ρ1 − ρ2)Γ36 − (1 + ρ2 2ρ1 )Γ18 ε−3/2n−1{ χ 2ρ2 [2(Γ81 + Γ83)− Γ65A (0)2 3 ] + 1 2ρ1 [2Γ41 − Γ27 − Γ18 + (2Γ43 − Γ25)A (0)2 3 ] + { χt 2nA (0) 3 [Γ88 − Γ75 + λ́2r10 ρ2 ×(δΓ65 − (1 + δχ)Γ55)]− χ 2ρ2 Keywords: + a2; 0)2; amer; appl; body; cos; eur; math; motion; pure; sin; solutions; λ́2r10; ρ1 t; ρ2 ρ1; ρ2)t
An Exploration of the Topological Structure and Bifurcation of Liouville Tori in Models of Galactic Motion by Amer, T. S.; El-Saba, F. M. ; Fakharany, M. ; Gad, H. M. (2025) - After some adjustments, the following differential equations may be obtained ξ̈ + Lξ +Mη = 0, η̈ +Nη +Mξ = 0, (36) where VXX(Xp, Yp) = L, VY Y (Xp, Yp) = N, VXY (Xp, Yp) = M . The Hamiltonian function associated with the potential V is H = 1 2 ( P 2 X + P 2 Y +X2 + Y 2 ) +XY 2 − 1 3 X3. Keywords: amer; motion; points; publisher; pure
Nano Quantum Explanation of the Changes in the Spectra of Some Oils Used for the Determination of the4 Degree of its Purity by Ahmed, Najwa Idris ; Ahmed, Umsalama; Bashari , Abeer ; M.A. Widaa, Einas ; A. E. Mohammed, Elharam ; Ahmed Mohammed Yousef, Mashair ; Noureldaim, Emadeldeen ; Mohamed Modawy, Yousif ; Salman, Montasir (2025) - Oil impurities, often in the form of nanoscale particles, necessitate advanced analytical techniques, confirmed by a theoretical model, for detection. Many studies have used Fourier transform infrared spectroscopy (FTIR), UV-vis spec- troscopy, and laser absorption spectroscopy (LAS) to detect oil adulteration. Keywords: absorption; adulteration; energy; ftir; impurities; oil; oils; olive; pure; sesame; spectra; spectroscopy; wave
On the Edge-Gracefulness of Water Wheel-Type Graphs and Their Splitting Graphs by Angel, Aaron; Antalan, John Rafael; Gamurot, John Loureynz; Tagle, Richard (2025) - We recall the definition of water wheel graphs (WWn) and introduces two new related graphs, the right water wheel graphs (RWWn) and left water wheel graphs (LWWn). In this paper, we used essential graph theory concepts to study the basic properties of water wheel, right water wheel, and left water wheel graphs, and their splitting graphs. Keywords: -0.33; angel; appl; edge; equation; eur; graceful; graceful labeling; graph; labeling; math; n1 +; pure; splitting; theorem; water wheel; wheel graph
Multiple RGB Images Security based on Substitution–Permutation Network over the Residue Classes of Eisenstein Integer Z[Ω]π by Alammari, Maha; Sajjad, Muhammad; Abdalrahem, Mushtaq K. ; Julian Serna, Robinson (2025) - Un- like text encryption, image encryption must handle large data volumes, spatial redundancy, and high inter-pixel correlation. Math, 18 (3) (2025), 6470 3 of 30 of chaotic maps, conservative hyperchaotic systems, Knuth–Durstenfeld algorithms, and Hopfield neural networks in image encryption has also been widely studied [11–16]. Keywords: alammari; appl; boxes; eisenstein; encryption; eur; image; integers; linear; math; original; pixel; pure; rgb; security; table
A Multi-Level Optimization Framework for Blockchain Security: Integrating Metaheuristics, Reinforcement Learning, and Game Theory by Danach, Kassem; Tarhini, Abbas; Aly, Wael Hosny Fouad ; Hejase, Hussin Jose (2025) - Section 2 provides a comprehensive review of54 existing work in cryptographic optimization and blockchain security. This sec-65 tion reviews existing approaches in cryptographic optimization for blockchain security,66 smart contract efficiency, and consensus mechanisms.67 2.1. Keywords: appl; blockchain; consensus; contract; danach; efficiency; eur; execution; fees; framework; game; gas; learning; math; optimization; performance; pos; pure; reinforcement; security; stake; transaction; validator
A New Method for Multi-Criteria Decision-Making: Adaptive Ranking with Ideal Evaluation (ARIE) by Mohamad Fauzi, Nur Fathiah Fatin ; Md Rodzi, Zahari; Zainuddin, Zaifilla Farrina; Mustapha, Norzieha ; Al-Sharqi, Faisal (2025) - There are many66 MCDM methods that differ in their basic concepts, strengths and weaknesses. [48, 49].99 A range of comparative analysis study between MCDM methods has been conducted100 to discuss the benefits and weaknesses of every MCDM method. Keywords: alternative; analysis; appl; aras; arie; criteria; decision; et al; eur; f. f.; fauzi; figure; ideal; mabac; making; math; mcdm; methods; moora; multi; performance; pure; ranking; saw; supplier; topsis; values; vikor
A Hybrid Metaheuristic Framework with Reinforcement Learning–Based Heuristic Selection for Large-Scale Combinatorial Optimization by Danach, Kassem; Harb, Hassan; Jose Hejase, Hussin; Saker, Louai (2025) - Objective, Research Questions, and Hypothesis The complexity of combinatorial optimization problems (COPs) has significantly in- creased due to the rapid growth of real-world applications such as logistics, manufacturing, and telecommunications. Hybrid approaches for combinatorial optimization problems. Keywords: algorithms; appl; combinatorial; convergence; danach; framework; hmf; hybrid; learning; math; metaheuristic; optimization; parameter; problem; pure; reinforcement; solution; time; tuning
Harnessing Quantum Superposition in Soft Set Theory: Introducing Quantum Hypersoft and SuperHyperSoft Sets by Fujita, Takaaki; Smarandache, Florentin (2025) - 2020 Mathematics Subject Classifications: 06D72 Key Words and Phrases: Superhypersoft set, Soft Set, Hypersoft set, Quantum Hypersoft Set, Quantum Soft Set, Quantum Superhypersoft Set 1. Table 2: Overview of Quantum Soft Set, Quantum HyperSoft Set, and Quantum SuperHyperSoft Set T. Fujita, F.Smarandache / Eur. Keywords: appl; fujita; fuzzy; h(u; hypersoft; hypersoft set; pure; quantum; set; sets; superhypersoft
Neutrosophic Soft n-Super-HyperGraphs with Real-World Applications by Fujita, Takaaki; Smarandache, Florentin (2025) - Neutrosophic soft graphs with application. We present a concise overview of neutrosophic soft graph models in Table 3. Keywords: a(c; appl; eur; fujita; hypergraph; neutrosophic; pure; set; sets; super
Enhancing Deep Image Prior with Multiscale Attention, SVD Pooling, and Preconditioned Optimizers for Image Processing by Israr, Muhammad ; Afzal, Waqar ; Ahmad , Shahbaz ; Breaz, Daniel ; Cotîrlă , Luminiţa-Ioana (2025) - Image PSNR (dB) SSIM Butter 32.07 0.97 Jet 35.88 0.96 Library 30.55 0.94 Vase 34.47 0.99 Table 2: Inpainting results using DIP-SVD over 3000 epochs, evaluated via PSNR and SSIM for four benchmark images. Conven- tionally used optimizers such as Adam tend to be suboptimal on ill-conditioned inverse problems as seen in image restoration. Keywords: attention; denoising; dip; image; inpainting; learning; network; noise; optimizers; pooling; psnr; pure; restoration; row; ssim; svd; training
Soft Directed n-SuperHyperGraphs with Some Real-World Applications by Fujita, Takaaki; Smarandache, Florentin (2025) - [12], and soft directed graphs Soft directed graphs, their vertex degrees, associated matrices and some product operations. Keywords: a(c; b(c; fujita; graphs; math; pure; set; sets; soft; superhypergraph
The Mgamma Distribution: Statistical Properties and Application to Real-life Data by Khan, M. I. ; Ruidas, Molay Kumar (2025) - = θ3x ( 1 + x 2 ) e−θx 1 + θ ; x > 0, θ > 0 (1) 0 2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Plot of pdf of Mgamma distribution x f(x) θ = 0.5 θ = 0.8 θ = 1 θ = 3 θ = 5 Figure 1: p.d.f. plot of Mgamma distribution for different θ denoted by x ∼ M(θ) Math, 18 (4) (2025), 6653 4 of 22 0 2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Plot of cdf of Mgamma distribution x F(x ) θ = 0.5 θ = 0.8 θ = 1 θ = 3 θ = 5 Figure 2: c.d.f. plot of Mgamma distribution for different θ So, the mode(x) of the new distribution is given by mode(x) Keywords: appl; distribution; eur; khan; mgamma; pure; ruidas
Stagnation Point Flow of a Casson Hybrid Nanofluid over a Vertical Plate with MHD and Heat Source/Sink Effects by Saqib, Muhammad ; Abbas, Imran; Hasnain, Shahid; Farman, Muhammad ; Hafez, Mohamed (2025) - In Hybrid nanofluids for convection heat transfer, pages 215–254. Convection heat transfer. Keywords: al2o3; appl; boundary; casson; convection; effects; engineering; eur; flow; heat; heat transfer; hybrid; impact; journal; math; nanofluid; parameter; pure; temperature; values; velocity
Toward Transparent Optimization: A Systematic Review of Explainable AI in Decision-Making Systems by Danach, Kassem; Aly, Wael Hosny Fouad; Tarhini, Abbas; Laouadi, Saad (2025) - In explainable optimization systems, domain expertise and regulatory constraints can be directly incorporated into the mathematical model structure through constraint-based knowledge injection. Addressing these sector-specific challenges requires integrating domain expertise with technical innovation, ensuring that explainable optimization methods are both legally compliant and practically useful. Keywords: appl; approaches; constraints; danach; decision; eur; explainability; explanation; interpretability; learning; making; math; methods; models; optimization; pure; research; solution; systems; techniques; xai
Mathematical Modelling of Radicalization and Terrorism Dynamics by Zorom, Malicki; Leye, Babacar ; Diop, Mamadou ; Coly, Serigne M'backé ; Lawane Gana, Abdou ; Bologo/Traore , Maïmouna ; Niang, Dial (2025) - After extensive algebraic manipulation using all equilibrium relationships and the strategic choice of constants, we obtain: dV2 dt = −T ∗S∗ S [ (S − S∗)2 S∗ + k(T − T ∗)2 T ∗ ] ≤ 0 (46) The equality dV2 dt = 0 holds if and only if S = S∗ and T = T ∗, which by the system dynamics implies Q = Q∗. M. Zorom et al. / Eur. For terrorism models, this translates to the expected number of new terrorists created by a single terrorist during their entire period of terrorist activity when introduced into a completely susceptible population. Keywords: analysis; appl; bifurcation; dynamics; equilibrium; eur; figure; global; mathematical; parameter; population; pure; rate; sensitivity; stability; system; terrorism; zorom
Prediction of Thermal Behavior in Ferromagnetic Carreau Fluids Using Neural Networks Algorithm by Khan , Saraj ; Asjad, M. Imran; Aslam, Muhammad Naeem ; Alqarni , M.S ; Guran, Liliana (2025) - On heat transfer in carreau fluid flow with thermal slip: an artificial intelligence (ai) based decisions integrated with lie symmetry. 2020 Mathematics Subject Classifications: 76W05, 80A20, 68T07, 76A05 Key Words and Phrases: Levenberg–Marquardt algorithm, ferromagnetic Carreau fluid, ther- mal boundary layer, thermal behavior prediction, magnetohydrodynamics ∗Corresponding author. Keywords: appl; carreau; concentration; et al; ferromagnetic; figure; flow; fluid; heat; khan; lmt; math; network; neural; number; pure; temperature; thermal; transfer
Data-Driven Modeling of Boussinesq-Burgers Equations: Comparing Physics-Informed Neural Networks (PINNs) with Exact Solutions by Ahmad Shafee; Yousuf Alkhezi; Kavikumar Jacob (2025) - Math, 18 (4) (2025), 6803 11 of 18 Figure 7: Exact solution and PINN solution ϕ(α, β) at specific time values. Figure 8: Exact solution and PINN solution ρ(α, β) at specific time values. Keywords: appl; equations; error; eur; exact; math; networks; nonlinear; physics; pinn; pure; solution
Hierarchical Uncertainty Modeling via (m, n)-Superhyperuncertainand (h, k)-ary (m, n)-Superhyperuncertain Sets: Unified Extensions of Fuzzy, Neutrosophic, Soft, Rough, and Plithogenic Set Theories by Fujita, Takaaki; Smarandache, Florentin (2025) - For m = n = h = k = 1, an (1, 1)-ary (1, 1)-SuperhyperSoft Set is a map F : P̃1(S) → P̃1(U), e.g. F ({a}) Every classical soft set Fcl : S → P(U) is naturally represented by an (h, k)-ary (m,n)-SuperhyperSoft Set with m = n = h = k Keywords: appl; define; eur; f.smarandache; fujita; f−1; level; math; nonempty; pcf; proof; pure; set; sets; theorem; ˜pdf
Random n-SuperHyperGraphs: A Probabilistic Model and Generation Algorithm for Hierarchical Networks by Fujita, Takaaki; Smarandache, Florentin (2025) - But random graph models assume independent edge formation, ignore higher-order correlations, lack hierarchical structure, and cannot capture multi-scale interactions or nested dependencies present in real-world networks. While random graph and hypergraph models form edges independently with prob- ability p, they do not account for higher-order, multi-scale, or nested dependencies often observed in real-world networks. Keywords: appl; eur; fujita; fuzzy; graph; hypergraph; math; neutrosophic; probability; pure; set; smarandache; superhypergraph
Multi-Parametric Study of Convective Heat Transfer in a Magnetized Wavy Cavity Using Hybrid Nanofluids for Thermal Management Applications by Al Kalbani, Khamis ; Anakira, Nidal ; Uddin, M. J. ; Al Jassar, Ali ; Amourah, Ala; Sasa, Tala (2025) - The results show that increasing the Rayleigh number significantly enhances convective heat transfer, while variations in base fluid composition lead to only marginal differences in the average Nusselt number. Convective heat transfer, a key process in these systems, is often limited by the thermophysical properties of conventional fluids, such as water, ethylene glycol (EG), or their mixtures. Keywords: flow; fluid; heat; hybrid; nanofluid; number; pure; rayleigh; transfer; wall; water; wavy
A Robust Decision-Making Framework for Recruitment Optimization via Hybrid Dombi–Archimedean Operators in Complex q-Rung Orthopair Fuzzy Sets by Ullah, Ikhtesham ; Kamran; Sajjad Ali Khan, Muhammad ; Hussain, Fawad ; Hussain, Fawad ; Khan, Madad; Popa, Ioan-Lucian (2025) - Problem Solution A method for addressing MCDM problems utilising Cq − ROFNs data will be created using the Cq − ROFDAWA, Cq − ROFDAOWA, Cq − ROFDAWG, and Cq − ROFDAOWG operators. Since the Cq−ROFDAWA, Cq−ROFDAWG, Cq−ROFDAOWA, and Cq − ROFDAOWG operators consistently provide distinct rankings, with Ă5 rank- ing highest and Ă4 ranking second, there is evident agreement among the recommended procedures. Keywords: aggregation; ă1; ă3; ă4; ă5; fuzzy; j=1; math; operators; pure; q j; r∑ j=1; ullah; −1 q; −1(ℜk(θ q
The Discrete Laplace Transform (DLT) Order: A Sensitive Approach to Comparing Discrete Residual Life Distributions with Applications to Queueing Systems by A shokeralla, Alshaikh (2025) - s DLT (Technical Support) DLT (Contract-Related) DLT Order 0.1 3.54497 3.51858 > 0.5 0.01685 0.01679 > Im- portant future directions include the construction of multivariate DLT order statistics for A. A. Shokeralla / Eur. Keywords: a. a.; distributions; dlt; hazard; order; pure; reliability; service; shokeralla; stochastic; systems; time
Salp Swarm Optimization: A Comprehensive Review of Recent Advances, Variants, Applications, and Future Research Directions by El-Shorbagy, M.A.; Nasar, Islam (2025) - Future Research Directions While various Salp Swarm Algorithm (SSA) variants, including Chaotic SSA (CSSA), Quantum-inspired SSA (QSSA), and Adaptive SSA (ASSA), have demonstrated significant improvements, multiple opportunities remain for further research and development: • Hybridisation with Other Metaheuristics: Integrating SSA variants with com- plementary Optimization methods, such as Differential Evolution, Particle Swarm Optimization, or Genetic Algorithms, has the potential to enhance convergence speed and solution quality, particularly in high-dimensional and multimodal contexts. • Rigorous Benchmarking and Comparative Analysis: Future studies should prioritise systematic benchmarking of SSA variants against classical metaheuristics M. A. El-Shorbagy, I. Nassar / Eur. Keywords: algorithm; appl; convergence; eur; m. a.; math; nassar; objective; optimization; power; problems; pure; results; salp; salp swarm; search; selection; ssa; swarm; swarm algorithm
Game-Theoretic Electromagnetic Isolation Framework for Wireless Connectivity in Mineral and Phosphate Mining Environments by Ayari, Mohamed; Gharbi, Atef; Klai, Zeineb; Hasnaoui, Abdelhalim ; Elsayed, Mahmoud Salaheldin ; Abdelrahim, Elsaid (2025) - The proposed framework formulates electromagnetic isolation design as a non-cooperative122 game where each isolation technique—such as Buried Diffused Layers (BDL), metallized123 grids, guard rings, and EBG structures—is modeled as a strategic player. By modeling isolation techniques as strategic players in a non-cooperative game, the framework derives equilibrium solutions that balance isolation, insertion loss, fabrication complexity, and deployment cost. Keywords: appl; ayari; complexity; design; electromagnetic; equilibrium; eur; fabrication; framework; frequency; game; ghz; guard; insertion; isolation; loss; math; mining; optimization; pure; substrate; techniques; theoretic
Optimizing Communication Network Routing with A* Algorithm: A Comparative Study Against Bellman-Ford and Dijkstra for Enhanced Quality of Service by Ayari, Mohamed; Gharbi, Atef; Klai, Zeineb; Hasnaoui, Abdelhalim; Elsayed, Mahmoud Salaheldin; Abdelrahim, Elsaid (2025) - The weighted variant uses fω(v) = g(v) + ω h(v), ω ≥ 1, (14) to trade additional pruning for a controlled increase in path cost with respect to the scalarized objective. Weighted A* exposed a practical speed–quality knob: moderate values of ω provided substantial reductions in expansions with small stretch in path cost. Keywords: appl; ayari; bellman; cost; dijkstra; energy; ford; heuristic; jitter; latency; loss; math; networks; path; pure; qos; routing; time
Fractional-Order Neutrosophic MR-Metric Spaces: Theory, Fixed Point Theorems, and Applications by Malkawi, Abed Al-Rahman; Rabaiah, Ayat (2025) - 2020 Mathematics Subject Classifications: 47H10, 54E35, 26A33, 03E72 Key Words and Phrases: Fractional-order metric spaces, Neutrosophic logic, MR-metric spaces, Fixed point theory, Fractional calculus, Anomalous diffusion, Uncertainty modeling 1. The recent introduction of MR-metric spaces by Malkawi et al. Keywords: malkawi; metric; point; pure; spaces
Neutrosophic Statistical Manifolds: A Unified Framework for Information Geometry with Uncertainty Quantification by Malkawi, Abed Al-Rahman; Rabaiah, Ayat (2025) - 2020 Mathematics Subject Classifications: 53B12, 62B11, 46S50, 03E72, 68T37 Key Words and Phrases: Neutrosophic logic, information geometry, MR-metric spaces, Jensen–Shannon divergence, statistical manifolds, uncertainty quantification, fixed point theory 1. Math, 18 (4) (2025), 7120 2 of 16 In parallel, the notion of MR-metric spaces was introduced by Malkawi et al. Keywords: malkawi; metric; neutrosophic; pure; spaces
Mathematical Analysis for Magnetohydrodynamic Peristaltic Flow of Cerebrospinal Fluid in the Glymphatic System by El-Shorbagy, mohammed; Elsawy, Ahmed; Henedy, Abdallah; Nabwey, Hossam; Alreshidi, Bandr; Abdelwahab, Essam (2025) - This article examines the ef- fect of a transverse magnetostatic field and pertinent physiological conditions on CSF flow. The effective Navier–Stokes governing equations describe the peristalsis of CSF flow subjected to a magnetostatic field. Keywords: appl; csf; deformation; eur; field; figure; flow; fluid; pressure; pure; pvs; tissue; velocity
Foundations of Neutrosophic MR-Metric Spaces with Applications to Homotopy, Fixed Points, and Complex Networks by Hussein, Eman; Malkawi, Abed Al-Rahman; Amourah, Ala; Alsoboh, Abdullah; Al Kasbi, Ahmed; Sasa, Tala; Rabaiah, Ayat M. (2025) - 2020 Mathematics Subject Classifications: 47H10, 54H25, 05C82, 68R10, 03E72 Key Words and Phrases: Neutrosophic MR-metric spaces, fixed point theorems, graph theory, net- work robustness, neutrosophic homotopy, centrality mapping, contraction mappings 1. Quantitative Results and Performance Analysis Network Type n R L(G) η(G) Social (Facebook) 2.8B 1.08 4.7 0.15 Neural (C. elegans) 302 1.23 2.3 0.22 Internet AS 74K 1.15 3.2 0.08 Power Grid 4.9K 1.32 18.7 0.08 Protein Interaction 6.5K 1.19 4.1 0.12 Table 1: Neutrosophic MR-Metric parameters for real networks Application Success Rate Computation Time Robustness Gain Influencer Identification 92% 45min 1.8× Network Hardening 88% 2.3hr 2.1× Path Planning 95% 8.7s 1.5× Folding Analysis 83% 34min 1.9× Table 2: Performance metrics for neutrosophic MR-metric applications Remark 1 (Practical Implementation Considerations). Keywords: applications; contraction; metric; neutrosophic; point; pure; spaces
Complex Neutrosophic Soft Topology with Multivariate Analysis: A Unified Framework for Signal-Template Relationships by Mohammed Saeed, Maha; Hatamleh, Raed; Ali Abujabal, Hamza ; Hussain, Aqeedat; Khattak, Arif Mehmood; Elashiry, M. I; Hasnaoui, Abdelhalim; M. Abd El-latif, Alaa (2025) - Let (F̃1, E) and (F̃2, E) be two complex single-valued neutrosophic soft sets over the universe set X. Then, the AND operation on them is denoted by (F̃1, E) ∧ (F̃2, E) = (F̃3, E × E) and is defined by: (F̃,E×E) = {( (e1, e2), ⟨x, TF̃3(e1,e2) (x), IF̃3(e1,e2) (x), FF̃3(e1,e2) (x)⟩ : x ∈ X ) : (e1, e2) ∈ E×E } . 2020 Mathematics Subject Classifications: 03E72, 06F25, 62H25, 54A10 Key Words and Phrases: Complex neutrosophic soft sets, complex neutrosophic soft topology, cotan- gent similarity measures, data visualization techniques 1. Keywords: 0.2eιπ(0.1; appl; cluster; complex; fuzzy; f̃1; f̃2; math; neutrosophic; pure; sets; similarity; vol
A Comprehensive Review on Structure of Heat and Fluid Flow in Liquid Metals at Low Grashof Number by Nabwey, Hossam A. ; Nadeem, Hajra ; Ashraf, Muhammad ; Rashad, A; Chamkha, Ali (2025) - Gr < 107 Onset of measurable convec- tion Convection begins to domi- nate heat transfer Gr ≈ 107 and above Turbulent convection Strong buoyancy flow Table 3: Assessment of liquid metal heat transfer from various studies Reference Fluid Geometry Parameter Range Method Key Findings Lyon & Poppen- dick Assessment of liquid metal heat transfer from various studies Reference Fluid Geometry Parameter Range Method Key Findings Singh & Chen [80] Fluids Concentric spheres Moderate Gr Numerical Numerical results for free convec- tion between concentric spheres, including flow structure and Nu– Gr data for comparison to exper- iments. Keywords: convection; et al; flow; fluid; grashof; heat; heat transfer; high; international; journal; liquid; metals; nabwey; number; numerical; pure; review; transfer; transport
QoS-Aware Cloud Service Composition via an Enhanced Multi-Agent Bird Swarm Algorithm by Dahan, Fadl (2025) - Following on the work of developing a multi-Agent swarm based algorithm, this paper presents an improved and adaptive solution to web service Composition: Multi-Agent Bird Swarm Algorithm (MA-BSA). 2020 Mathematics Subject Classifications: 68M14, 68T05, 90C59 Key Words and Phrases: Web service composition, service-oriented computing, bird swarm al- gorithm, multi-agent, bird swarm algorithm, United Nations sustainable development goals (SDGs) 1. Keywords: agent; algorithm; appl; bsa; cloud; colony; composition; dahan; math; optimization; pure; qos; search; service; service composition; swarm; web
Artificial Intelligence Enhanced Framework for Complex Double Valued Neutrosophic Soft Sets and Emotional Affinity Evaluation via Cotangent Similarity by Noorwali, Maha ; Hatamleh, Raed ; Heilat, Ahmed Salem ; Qawaqneh, Haitham ; Khattak, Arif Mehmood; Hussain, Aqeedat ; J. Hamja, Jamil ; L. Armada, Cris (2025) - Then, the AND operation on them is represented by (F̃1, E)∧ (F̃2, E) = (F̃3, E × E) and is described as follows: (F̃,E × E) = {( (e1, e2), ⟨x, TF̃3(e1,e2) (x),RT F̃3(e1,e2) (x), RF F̃3(e1,e2) (x),FF̃3(e1,e2) (x)⟩ : x ∈ X ) : (e1, e2) ∈ E × E } . Consider (F̃1, E) and (F̃2, E) be CDVNS sets over the universe X. Then, the OR operation on them is represented by (F̃1, E) ∨ (F̃2, E) = (F̃3, E × E) and is given as: (F̃, E × E) = {( (e1, e2), ⟨x, TF̃3(e1,e2) (x),RT F̃3(e1,e2) (x), RF F̃3(e1,e2) (x),FF̃3(e1,e2) (x)⟩ : x ∈ X ) : (e1, e2) ∈ E × E } . Keywords: 0.2eιπ(0.1; appl; cdvns; e)c; eur; fuzzy; f̃1; f̃2; math; neutrosophic; noorwali; pure; set; sets; signal; similarity; template
Institutional and Personal Tributes to Professor Sir Clive W.J. Granger by ., EJPAM (2010) - Math, 3 (2010), 337-346 340 The University of Melbourne Sir Clive Granger, who won the Nobel prize in economics in 2003 and was knighted in 2005, passed away on May 27th 2009 at the age of 74. Math, 3 (2010), 337-346 343 European Journal of Pure and Applied Mathematics On 27 May 2009, at the age of 74, Sir Clive Granger, one of our distinguished Advisory Editors, passed away. Keywords: clive; granger; professor; pure; series; time; university
Autobiography by Granger, Clive W.J. (2010) - Over the years we worked on a variety of questions including seasonal adjustment, aggregation, and several new types of time series models. Take three active workers who interact, mix in a group of good students, and later add Jim Hamilton, Graham Elliott, and Allan Timmer- mann, and in under thirty years you produce a couple of Nobel Prizes, at least. Keywords: book; break; granger; mathematics; pure; series; time; university; year
Letter from the Editors by Chief, Editors in (2008) - ISSN 1307-5543 – www.ejpam.com 1 Letter From the Editors “Biologically we are all mathematicians even if we are unable to articulate successfully what goes on inside our brains” Thomas Saaty As a group of young researchers, we are pleased to announce that the genesis of the new electronic journal European Journal of Pure and Applied Mathematics (EJPAM) is in January 2008. We all wish European Journal of Pure and Applied Mathematics has every success in the contemporary scientific world. Keywords: journal; mathematics; pure
Sequentially pure monomorphisms of acts over semigroups by Ebrahimi, Mohammad Mehdi; Barzegar, H (2009) - For a subset H of A× A let H e be the equivalence relation generated by H and H c = {(as, bs) : (a, b) ∈ H, s ∈ S} The cofree functor H : Set → Act-S is defined by HX = X S1 , the set of all functions from S1 to the set X , with the action of S on X S1 given by ( f s)(t) = f (st) for f ∈ X S1 , s ∈ S, and t ∈ S1. Keywords: act; let; monomorphisms; pure

Math

Stringy and Orbiforld Cohomology of Wreath Product Orbifolds by Matsumura, Tomoo (2012) - g,h ∪ vh|X g,h ∪ cg ,h � , cg ,h := ctop � R(g,h) � (3) where q : X g ,h ,→ X gh is the obvious inclusion. = ∫ X g vg ∪ ι ∗wg−1 , and η(vg , wh) = 0 if gh 6= 1 (5) where ι : X g −→ X g−1 is the identity map. Keywords: algebra; frobenius; math; orbifold; product; theorem
Euler and Divergent Series by Kowalenko, Victor (2011) - Via the key concept of regularisation, which results in the removal of the infinity in the remainder of a divergent series, regularised values can be evaluated for elementary series outside their circles of absolute convergence such as the geometric series and for more complicated asymptotic series called terminants. Because the finite value is the same to the right and to the left of the barrier or line at ℜ z=1 and in keeping with the fact that regularisation is effectively the removal of the first term in the last member or rhs of Eq. (10), we take 1/(1− z) to be the finite or regularised value when ℜ z=1. Keywords: arg; arg z; equivalence; euler; integral; kowalenko; math; ref; result; series; stokes; terms; type; value; ℜ z
From right PP monoids to restriction semigroups: a survey by Hollings, Christopher (2009) - We record some of the basic results in the theory of left restriction semigroups, before moving on to Section 5, where we consider the special case of left ample semigroups. Just as we did for left restriction semigroups, we now provide an abstract characterisation of left ample semigroups. Keywords: e(s; inverse; left; math; monoid; restriction; right; semigroups; theorem; type
Reduction of modern problems of mathematics to the classical Riemann-Poincare-Hilbert problem by Durmagambetov, Asset (2018) - = − k 4π ∫ S2 A(k, θ ′ , θ)Ψ−(k, θ ′ , x)dθ ′ , k ∈ R. (4) This equation is the key to solving the inverse scattering problem and was first used by Newton Using the equation Ψ+(k, θ, x)−Ψ−(k, θ, x) = − k 4π ∫ S2 A(k, θ ′ , θ)Ψ−(k, θ ′ , x)dθ ′ , k ∈ R, we can write T+g+ − T−g− = D(T−g− + Ψ0). Keywords: + ∞; equation; function; lemma; math; problem; proof; riemann; sup; ∣∣∣∣; ∫ s2
Literature Survey on Non-Associative Rings and Developments by Shah, Syed Tariq; Razzaque, Asima; Rehman, Inayatur; Gondal, Muhammad Asif; Faraz, Muhammad Iftikhar; Shum, Kar Ping (2019) - [71] endeavored to establish conditions which guarantee the semi-simplicity of alternative loop rings with respect to any nil radical and with respect to the Jacobson radical. [28] in 1990 continued their investigation of loops which gave rise to alternative loop rings. Keywords: algebra; alternative; alternative rings; amer; associative; class; elements; finite; groups; ideals; jordan rings; lie rings; loop rings; loops; math; nilpotent; prime; right; rings; theory
On the Nonchaotic Nature of Monotone Dynamical Systems by Hirsch, Morris W. (2019) - EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 12, No. 3, 2019, 680-688 ISSN 1307-5543 – www.ejpam.com Published by New York Business Global On the nonchaotic nature of monotone dynamical systems Morris W. Hirsch1,2 1 Department of Mathematics, University of Wisconsin at Madison, WI 53706, USA 2 Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720-384, USA Abstract. Monotone dynamical systems with dense peri- odic points, J. Differential Equations 265 (1918), no. 11, 5709–5715, [4] C. Good & S. Macı́as, What is topological about topological dynamics?, Discrete Contin. Keywords: differential; equations; hirsch; math; systems
A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems by Paikray, Susanta Kumar; Parida, Priyadarsini; Mohiuddine, S. A. (2020) - If we put an = 0, bn = n, sn = tn = 1 and α = β = γ = 0 in our Theorem 1, then we get the statistical versions of the fuzzy Korovkin-type approximation theorem, which was demonstrated earlier by Anastassiou and Duman (see [3]). Statistical fuzzy approximation by fuzzy positive linear operators. Keywords: convergence; math; γ h
Solution of Delay Differential Equation via N^v_1 Iteration Algorithm by Sharma, Nisha; Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Pandey, Shikha (2020) - − xδ‖ − ‖f(T, tn)− xδ‖ ≤ ξ3(ξ − (1− ξ)σ0n)‖tn − xδ‖+ εn This implies that limn→∞ tn = 0. − xδ‖ = ξ(1− (1− ξ)σ0n)‖ζn − xδ‖ also, ‖ηn − xδ‖ ≤ ‖Tθn − xδ‖ = ‖Tθn − Txδ‖ ≤ ξ‖θn − xδ‖ using the value of ‖θn − xδ‖, we have ‖ηn − xδ‖ ≤ ξ2(1− (1− ξ)σ0n)‖ζn − xδ‖ similarly, we have ‖ζn+1 Keywords: iteration; math; xδ‖
Global Existence of Weak Solutions to 3D Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosity by Ouya, Jules; Ouedraogo , Arouna (2023) - Math, 16 (4) (2023), 2247-2285 2264 − ∫ T 0 ∫ Ω ξuv∂yΦdXdt+ ∫ T 0 ∫ Ω ∇xξ 2 · ΦdXdt+ r ∫ T 0 ∫ Ω ξ|u|uΦdXdt + r1 ∫ T 0 ∫ Ω uΦdXdt+ α ∫ T 0 ∫ Ω ∆xu ·∆xΦdXdt = − ∫ T 0 ∫ Ω 2ξDx(u) : ∇xΦdXdt+ ϵ ∫ T 0 ∫ Ω (∇xξ · ∇xu) ΦdX − r2 ∫ T 0 ∫ × Ω. Due to the lower semi-continuity of convex functions, we can obtain the following energy inequality (116) and B-D entropy (117) by passing to the limits in (100) and (101) as r2, δ −→ 0,∫ Ω ( 1 2 ξu2 + ξ2 + k1|∇x √ ξ|2 ) dxdy + r1 ∫ T 0 ∫ Ω u2dxdydt + r ∫ T 0 ∫ Ω ξ|u|3dxdydt+ ∫ T 0 ∫ Ω 2ξ|Dx(u)|2dxdydt+ g ∫ T 0 ∫ Ω vξ ln ξdxdydt + ∫ T 0 ∫ Ω ξ|∂yu|2dxdydt ≤ ∫ Ω ( 1 2 ξ0u 2 0 + ξ20 + k1|∇x √ ξ0|2 ) ddxdy (116) and∫ Ω (1 2 ξ|u+ 2∇x ln ξ|2 − 2r1 ln ξ ) dxdy + 2 ∫ T 0 ∫ Ω ξ|∂yv|2dxdydt+ r ∫ T 0 ∫ Ω ξ|u|3dxdydt + r1 ∫ T 0 ∫ Ω u2dxdydt+ ∫ T 0 ∫ Ω ξ|∂yu|2dxdy + k1 ∫ T 0 ∫ Ω ξ|∇2 x ln ξ|2dxdydt J. Ouya, A. Ouédraogo / Eur. Keywords: appl; dxdy; l2(ω; math; ξk1,r1; ∈ l2; − ∫; ∫ t; ∫ ω
On a Parameter-controlled Method for Multiple Zeros by Geum, Young Hee (2024) - Table 1: Color palette for a n-periodic orbit with n ∈ N ∪ {0} n Cn n = 1 C1 =  magenta, for fixed point ∞ cyan, for fixed point 0 yellow, for fixed point 1 red, for other strange fixed point , 2 ≤ n ≤ 68 C2 = orange, C3 = light green, C4 = dark red, C5 = dark blue, C6 = dark green, C7 = dark yellow, C8 = floral white, C9 = light pink, C10 = khaki, C11 = dark orange, C12 = turquoise, C13 = lavender, C14 = thistle, C15 = plum, C16 = orchid, C17 = medium orchid, C18 = blue violet, C19 = dark orchid, C20 = purple, C21 = power blue, C22 = sky blue, C23 = deep sky blue, C24 = dodger blue, C25 = royal blue, C26 = medium spring green, C27 = spring green, C28 = medium sea green, C29 = sea green, C30 = forest green, C31 = olive drab, C32 = bisque, C33 = moccasin, C34 = light salmon, C35 = salmon, C36 = light coral, C37 = Indian red, C38 = brown, C39 = fire brick, C40 = peach puff, C41 = wheat, C42 = sandy brown, C43 = tomato, C44 = orange red, C45 = chocolate, C46 = pink, C47 = pale violet red, C48 = deep pink, C49 = violet red, C50 = gainsboro, C51 = light gray, C52 = dark gray, C53 = gray, C54 = charteruse, C55 = electric indigo, C56 = electric lime, C57 The points z = ∞ and z = 0 are critical points associated with (z − A)(z − B). Keywords: math; |ℑ(t)|
On a Sixth-order Solver for Multiple Roots of Nonlinear Equations by Geum, Young Hee (2024) - Table 1: Color palette for a n-periodic orbit with n ∈ N ∪ {0} n Cn n = 1 C1 =  magenta, for fixed point ∞ cyan, for fixed point 0 yellow, for fixed point 1 red, for other strange fixed point , 2 ≤ n ≤ 68 C2 = orange, C3 = light green, C4 = dark red, C5 = dark blue, C6 = dark green, C7 = dark yellow, C8 = floral white, C9 = light pink, C10 = khaki, C11 = dark orange, C12 = turquoise, C13 = lavender, C14 = thistle, C15 = plum, C16 = orchid, C17 = medium orchid, C18 = blue violet, C19 = dark orchid, C20 = purple, C21 = power blue, C22 = sky blue, C23 = deep sky blue, C24 = dodger blue, C25 = royal blue, C26 = medium spring green, C27 = spring green, C28 = medium sea green, C29 = sea green, C30 = forest green, C31 = olive drab, C32 = bisque, C33 = moccasin, C34 = light salmon, C35 = salmon, C36 = light coral, C37 = Indian red, C38 = brown, C39 = fire brick, C40 = peach puff, C41 = wheat, C42 = sandy brown, C43 = tomato, C44 = orange red, C45 = chocolate, C46 = pink, C47 = pale violet red, C48 = deep pink, C49 = violet red, C50 = gainsboro, C51 = light gray, C52 = dark gray, C53 = gray, C54 = charteruse, C55 = electric indigo, C56 = electric lime, C57 A zero α of h(x) = 0 is called a multiple root Keywords: math; parameter
Analyzing Cancer Survival Times Using the Exponentiated Fréchet-Gompertz Distribution by Alsaggaf, Ibtesam (2024) - − n β ln γ + β n∑ i=1 xi − ( λ γ )β n∑ i=1 (eθxi − 1)−β − (β + 1) n∑ i=1 ln (eθxi − 1) + (α − 1) n∑ i=1 ln Math, 17 (4) (2024), 3856-3898 3860 Figure 1a shows a variety of shapes of EFG distribution, symmetric and asymmetric with different degrees of skewness. Keywords: cancer; data; distribution; e −; efg; estimation; math; α −; − exp; − ;  λ; 1 −; 
A Bipolar Fermatean Fuzzy Hamacher Approach to Group Decision-Making for Electric Waste by Fahmi, Aliya; Shehzad Hassan, Muhammad Arshad ; Khan, Aziz; Abdeljawad, Thabet; Almutairi , D. K. (2025) - These kinds of issues are resolved by using the indication of fuzzy sets, which was projected by Zadeh in 1965. Fuzzy sets are widely applied in modeling uncer- tainty across fields such as decision-making and artificial intelligence, while intuitionistic fuzzy sets and others extend this framework by incorporating hesitation degrees, enhanc- ing applications in complex decision-making scenarios [31–33]. Keywords: decision; fahmi; fermatean; fuzzy; j=1; making; math; n∏ j=1; operators; sets; waste; ; 
A Four-Step Semi-Implicit Midpoint Approximation Scheme for Fixed Point with Applications by Mohammad Akram (2025) - − ϱ ∥∥∥] ≤ εk 2 (∥ϱk − ϱ∥+ ∥θk − ϱ∥), where εk = (1− γk + τγk), which turns after simplification into ∥θk − ϱ∥ ≤ εk (2− εk) ∥ϱk − ϱ∥. (15) − ϱ ∥∥∥+ βkτ ∥∥∥(ϑk + θk 2 ) − ϱ ∥∥∥ ≤ τ 2 ∥ϑk − ϱ∥+ τ 2 [(1− βk)∥ϱk − ϱ∥+ βk∥θk − ϱ∥], which yields into ∥ϑk − ϱ∥ ≤ τ (2− τ) Keywords: appl; mapping; math; point
Properties of Bazilevic Functions Involving $q$-analogue of the Generalized $M$-series by Kadhavoor R, Karthikeyan; Dharmaraj , Mohankumar; Breaz, Daniel (2025) - Making use of the defined operator, we define a new family of analytic functions expressed as a combination two differential characterizations. 2020 Mathematics Subject Classifications: 30C45; 30C50, 30C55 Key Words and Phrases: Generalized M -series, Mittag-Leffler function, generalized hyper- geometric function, quantum calculus, analytic function, univalent function, Schwarz function, Bazilevič functions, subordination, coefficient inequalities, Fekete-Szegő inequality. Keywords: functions; math
The Relationship of Borel Distribution and Horadam Polynomials Leads to Analytical Bi-Univalent Functions by Alnajar, Omar; Khabour, Omar; Amourah, Ala; Darus, Maslina (2025) - (2) A function is said to have the property of being bi-univalent in B if both f(φ) and f−1(φ) have the property of being univalent in B. Let us refer to the group of bi-univalent functions in B as Σ, which is defined by the Eq. To the best of our knowledge, we have not been able to locate any previous work in the literature that deals with bi-univalent functions for subordinate Horadam polynomi- als that use the Borel distribution. Keywords: functions; math; polynomials
The Neutrosophic Poisson Distribution Applied to Horadam Polynomial-Subordinate Bi-Univalent Functions by Alnajar, Omar; Alshammari, Khalid ; Amourah, Ala (2025) - The characteristics of inclusion pertaining to univalent functions associated with bell distribution functions. 2020 Mathematics Subject Classifications: 30C45 Key Words and Phrases: Horadam polynomials, bi-univalent functions, analytic functions, Fekete-Szegö problem 1. Keywords: amourah; distribution; functions; math; polynomials
Comparative Results on Stability Analysis for Three Dimensional Functional Equations by Jakhar, Jagjeet ; Baleanu, Dumitru; Sharma, Shalu ; Yousif, Majeed A. ; Jakhar, Jyotsana ; Chorfi, Nejmeddine; Mohammed, Pshtiwan Othman (2025) - Collectively, these contributions offer a broader and deeper understanding of functional equation stability, bridging deterministic and stochastic approaches in a unified framework. Hence, in complete space V , the sequence < 2−3mf(2mu) > is a Cauchy sequence. Keywords: cubic; math; spaces; stability; δn−1||β
Boundary Blowing Up Solutions for an Elliptic Neumann Problem with Nearly Critical Exponent by Almushahhin, Rakan; Ben Ayed, Mohamed (2025) - , n+ 2 } , (See Proposition 1 of [32] and equation (19) by taking Ω = B (0, 1), K = γ̄ and N = 1). , N}, λk = O ( |z′|+ (if n ⩾ 5) ε+ (if n = 4) ε |ln ε| ) D2f1 (bk) ((z ′, 0) , ·) = O ( ε+ |z′|2 ) , k ∈ {1, . . . , N}. (52) Since D2f1 (bk) is assumed to be non-degenerate, the last equation in (52) implies that |z′| ⩽ c ( ε+ |z′|2 ) , and therefore, the system (52) can be rewritten as ρk = O ( ρ2k + |z′|2 + ε |ln ε| ) , k ∈ {1, . . . Keywords: ai,µi; math; n−2; proof; solutions; ω ω
A Novel Generalization of the Inverted Nadarajah–Haghighi Distribution with Estimation Methods and Medical Applications by Aloufi, Sara F. ; Alsaggaf, Ibtesam (2025) - Least-squares estima- tion of distribution functions in johnson’s translation system. For the NLTE-X family, the CDF and PDF are expressed as follows: F (x; ϑ, ζ) = 1 − {1 − G(x; Ω) eϑG(x;Ω) } ; ϑ > 0, x > 0, (1) f(x; ϑ, ζ) = g(x){1 + ϑG(x; Ω)} eϑG(x;Ω) ; ϑ > 0, x > 0, (2) where ϑ represents the vector of distribution parameters, and the parameter ϑ is unique to the NLTE-X family. Keywords: alsaggaf; data; distribution; e-01; estimation; i=1; math; neinh
Numerical Investigation based on the Chebyshev-Homotopy Perturbation Method for the Breast Cancer as a Mathematical Model by Adel, Mohamed; Khader, M. M.; Messaoudi, M. (2025) - DOI: https://doi.org/10.29020/nybg.ejpam.v18i2.6166 Email addresses: adel@sci.cu.edu.eg (M. Adel), mmkhader@imamu.edu.sa (M. M. Khader), mmessaoudi@imamu.edu.sa (M. Messaoudi) https://www.ejpam.com 1 (CC BY-NC 4.0) M. Adel, M. M. Khader, M. Messaoudi / Eur. Keywords: appl; k=0; l−1; m. m.; math; numerical; solution
Enhancing Shape Analysis with Persistent Homology for Edge Detection and Topological Feature Extraction by Sanjay, Shivam Kumar Jha ; Natarajan, Mohana (2025) - Following Theorem 1, we see that Hκ 0 (X) = Z for every κ-connected graph like digital image, This completes the proof. These applications demonstrate how persistent homology offers a mathematically grounded framework for analyzing structural features in digital images. Keywords: digital; faces; homology; image; math; points; simplex
The Stability of the Generalized Function Equation by Lyu, Gang ; Jiang, Yingxiu; Liu, Qi; Park, Choonkil (2025) - The stability of the generalized function inequations This section primarily investigates the stability of functional equations, improves ex- isting results through a novel direct method, and explores the dependency relationships among different parameters in generalized functional equations along with their related properties. The paper proposes a new direct method, which is not only used to solve specific functional equations but also to construct and study a series of functional equations. Keywords: appl; math; stability
Heptapartitioned Neutrosophic Soft Topologies and Machine Learning Techniques for Exploring Romantic Feelings by Saeed, Maha Mohammed ; Hatamleh , Raed ; Abujabal, Hamza Ali ; Khan, Yahya ; Al-Husban, Abdallah ; Laja, Amy A. ; M. Pangilan, Sulfaisa M. ; Armada, Cris L. ; Hamja, Jamil J.; Khattak, Arif Mehmood (2025) - Let (F̃ , E) and (G̃, E) be two hepta-partitioned neutrosophic soft sets over the key set X then “AND” operation on them is denoted by (F̃ , E) ∧ (G̃, E) = (H̃, E × E) and is defined as: (H̃, E×E) = { ( (e1, e2), ⟨x,AbTH̃(e1, e2)(x),ReTH̃(e1, e2)(x),UH̃(e1, e2)(x) CH̃(e1, e2)(x),GH̃(e1, e2)(x),ReFH̃(e1, e2)(x),AbFH̃(e1, e2)(x) : x ∈ X⟩) : (e1, e2) ∈ E × E. } Where, AbTH̃(e)(x) Let (F̃ , E) and (G̃, E) be two hepta-partitioned neutrosophic soft sets over the key set X then “OR” operation on them is denoted by (F̃ , E) ∨ (G̃, E) = (H̃, E × E) and is defined as: (H̃, E×E) = { ( (e1, e2), ⟨x,AbTH̃(e1, e2)(x),ReTH̃(e1, e2)(x),UH̃(e1, e2)(x), CH̃(e1, e2)(x),GH̃(e1, e2)(x),ReFH̃(e1, e2)(x),AbFH̃(e1, e2)(x) : x ∈ X⟩) : (e1, e2) ∈ E × E. } Where, AbTH̃(e)(x) Keywords: analysis; appl; complex; data; e)(x; feelings; fuzzy; hpns; math; neutrosophic; set; sets
Mapping Love: A Heptapartitioned Neutrosophic Machine Learning Study of University Students’ Romantic Sensations by Hatamleh, Raed ; Odat, Nasir ; Al-Husban, Abdallah ; Khattak, Arif Mehmood; M. Abd El-latif, Alaa ; M. Attaalfadeel, Husham ; Abdelfattah, Walid ; M. Abdel-Mageed, Ahmad. (2025) - [6] Wang, H.; Smarandache, F.; Zhang, Y.; Sunderraman, R. Single valued neutrosophic sets. [4] filled in this gap by introducing extremely a new theory which is known as neutrosophic set theory (NST).One effective mathematical paradigm for handling partial, ambiguous, uncertain, or confusing data is (NST). Keywords: appl; clustering; data; feelings; fuzzy; math; neutrosophic; set; sets; svhns; values
Image Edge Detection Enhancement Using Coefficient Estimates for Classes of Quasi-Subordination: Fekete-Szego Problems by Kamali, R. ; Prema , S.; Ajay Shrikaanth, A. S. ; Govindan, Vediyappan; Donganont, Mana (2025) - Image edge detection enhancement using coefficients of sakaguchi type functions mapped onto petal shaped domain. A new proposed model for image enhancement using the coefficients obtained by a subclass of the sakaguchi-type function. Keywords: coefficient; contrast; detection; edge; enhancement; fekete; functions; image; kamali; math; quasi; szegö; univalent
On the Boundedness of the Intrinsic Square Function on Continual Herz Spaces with Variable Exponents by Ali Basendwah, Ghada ; Sultan, Mehvish; Sultan, Babar; Popa, Ioan-Lucian (2025) - [13] S. Samko, Variable exponent Herz spaces, Mediterr. Our aim in this paper is to prove the boundedness of the intrinsic square function on Herz spaces with variable exponents. Keywords: boundedness; function; herz; math; spaces; sultan; variable
A Cheeger-type Inequality for the Sub-Laplacian on Pseudo-Hermitian CR Manifolds by Ben Ahmed , Ali (2025) - For a compact quotient M = Γ\Hn (with Haar measure), the horizontal structure is homogeneous and torsion-free; classical isoperimetric and Sobolev inequalities are sharp in this case In this paper, we introduce a CR Cheeger constant and establish Cheeger-type and Buser-type inequalities for the first nonzero eigenvalue of the sub-Laplacian on compact strictly pseudoconvex pseudo-Hermitian CR manifolds. Keywords: cheeger; horizontal; inequality; math
Operations on Complex Neutrosophic Soft Sets and Their Topological Spaces: A New Approach with Applications to Decision-Making by A zzam, A.; M. Abd El-latif, Alaa ; Alreshidi, B. ; Aldawood, M. ; M. Awad, Mohamed; Ali Abujabal, Hamza ; L. Armada, Cris ; Khattak, Arif Mehmood (2025) - Math, 18 (4) (2025), 7171 13 of 37 of complex fuzzy soft sets in τ1, {[IF̃i(e) (X)]e∈É}i∈I is the collection of complex fuzzy soft sets in τ2, {[FF̃i(e) (X)]e∈É}i∈I is a family of complex fuzzy soft sets in τ3. Then {[TF̃i(e) (X)]e∈É}i=1,n is a family of complex fuzzy soft sets in τ1, {[IF̃i(e) (X)]e∈É}i=1,n is a family of complex fuzzy soft sets in τ2, {[FF̃i(e) (X)]e∈É}i=1,n is a family of complex fuzzy soft sets in τ3. Keywords: 0.2eιπ(0.1; cns; fuzzy; f̃1; f̃2; math; neutrosophic; sets; similarity; vol

Graph

A Comparison on Metric Dimension of Graphs, Line Graphs, and Line Graphs of the Subdivision Graphs by Klein, Douglas J; Yi, Eunjeong (2012) - In this paper, we study metric dimension of para-line graphs; we also compare metric dimension of graphs, line graphs, and para-line graphs. In this paper, we study metric dimension of para-line graphs; we also compare metric dimension of graphs, line graphs, and para-line graphs. Keywords: graph; metric; vertex
Modeling of Prey Predator Problem by a Graph Dierential Equation by Vasundhara Devi, J; Ravi Kumar, R V.G (2014) - Further, we model the well known pre- predator problem by graph differential equations and show that the nonlinearity is naturally preserved. On graph differential equations and its asso- ciated matrix differential equations. Keywords: differential; graph; matrix; prey
On Degree Sum Energy of a Graph by Hosamani, Sunilkumar M; S. Ramane, Harishchandra (2016) - [12] introduced the concept of degree sum energy, which is defined as follow: Definition 1. Bounds for the degree sum eigenvalues and degree sum energy of a graph. Keywords: graph; i=1
Certain Classes of Fuzzy Graphs by Al-Hawary, Talal Ali (2017) - In this paper, several classes of balanced fuzzy graphs are characterized; namely the classes of complete fuzzy graphs, fuzzy graphs induced by the complete graph, fuzzy graphs with balanced components, fuzzy graphs induced by trees and fuzzy graphs induced by cycles. EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 10, No. 3, 2017, 552-560 ISSN 1307-5543 – www.ejpam.com Published by New York Business Global Certain Classes of fuzzy graphs Talal Al-Hawary Department of Mathematics, Faculty of Sciences, Yarmouk University, Jordan Abstract. Keywords: graph
A Systematic Approach to Group Properties Using its Geometric Structure by Bello, Muhammed; Ali, Nor Muhainiah Mohd; Zulkifli, Nurfarah (2020) - Math, 13 (1) (2020), 84-95 87 Figure 1: Order product prime graph of D3 The general presentation for the order product prime graph on dihedral group and cyclic group are given in Theorem 1 to Theorem 3. 2020 Mathematics Subject Classifications: 05C25, 20F65 Key Words and Phrases: Order product prime graph, Vertex adjacency, Graph invariant, Nilpotency of a group 1. Keywords: graph; group; i=1; γopp(g
On Tosha-degree of an Edge in a Graph by Rajendra, R.; Kota Reddy, P. Siva (2020) - For simple graph G, TL(G) = L(G) and so by Proposition 7 the result follows. Also, we introduce the concepts - zero edges in a graph, T -line graph of a multigraph, Tosha-adjacency matrix, Tosha-energy, edge- adjacency matrix and edge energy of a graph G and obtain some results. Keywords: degree; edges; graph; tosha
On Plick Graphs with Point-outercoarseness Number One by Lokesha, V.; Hosamani, Sunilkumar M; Patil, Shobha V. (2020) - /compile/output.dvi EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 13, No. 5, 2020, 1300-1305 ISSN 1307-5543 – www.ejpam.com Published by New York Business Global Special Issue Dedicated to Professor Hari M. Srivastava On the Occasion of his 80th Birthday On plick graphs with point-outercoarseness number one V. Lokesha1, Sunilkumar M. Hosamani2,∗, Shobha V. Patil3 1 Department of Studies in Mathematics VSK University, Bellary, Karnataka, India 2 Department of Mathematics, Rani Channamma University, Belagavi, Karnataka, India 3 Department of Mathematics, KLE’s Dr. M. S. Sheshgiri College of Engineering and Technology Belagavi, Karnataka, India Abstract. On plick graphs with coarseness number one. Keywords: graph; theorem
Transmission and Reciprocal Transmission Based Topological Co-Indices of Graphs by Ramane, Harishchandra S.; Talwar, Saroja Y.; Cangul, Ismail Naci (2020) - The transmission augmented Zagreb index of a graph G, [15], denoted by TAZ(G), is defined by TAZ(G) (4) The reciprocal transmission augmented Zagreb index of a graph G, [14], is denoted by RTAZ(G) and it is defined by RTAZ(G) Keywords: graph; transmission
Harmonic Index and Zagreb Indices of Vertex-Semitotal Graphs by Yurttas Gunes, Aysun; Togan, Muge; Demirci, Musa; Cangul, Ismail Naci (2020) - Then augmented Zagreb index of T1(G) is AZI(T1(G)) Re-defined versions of Zagreb indices of T1(G) are i) ReZG1(T1(G)) Keywords: graph; index; zagreb
Efficient Zero Ring Labeling of Graphs by Chua, Dhenmar Enriquez; CampeÃ±a, Francis Joseph Hernandez; Franco, Floresto (2020) - A3 A0 A1 A2 A4 Figure 2: Zero ring labeling of C5 using M0 2 (Z5) Given a graph G with zero ring labeling f , we consider the set K = {f(u) + f(v) : uv ∈ E(G)}. Zero ring labeling of graphs. Keywords: graph; labeling; path; ring; ring labeling; vertex; vertices
A Breadth-first Search Tree Construction for Multiplicative Circulant Graphs by Antalan, John Rafael Macalisang; Campena, Francis Joseph (2021) - Since the reproduction starts at vertex mh−1 which is of distance 1 to the 0−vertex, we need to add another |L[bfs0(Γmh−1)]|. [12] in 1997 when he studied a particular class of circulant graph called recursive circulant graph or RC graph that was introduced by Park and Chwa Keywords: distance; graph; vertex; vertices
On Efficient Zero Ring Labeling and Restricted Zero Ring Graphs by Campena, Francis Joseph Hernandez; Chua, Dhenmar; Franco, Jr., Floresto; Casica, Jon-jon (2021) - Introduction One of the fields in graph theory that has been a study of interest of many mathematical researchers is graph labeling. Most of the methods or schemes in graph labeling can be traced to or have links to a paper by Rosa [9]. Keywords: bn2; graph; labeling; ring
On the Spectral-Equipartite Graphs and Eccentricity-Equipartite Graphs by Yurfo, Arnel M.; Adanza, Joel G.; Baldado, Michael Jr. Patula (2021) - The latest study on equipartite graphs is by Shirdareh Haghighi et al. [9], which characterizes equipartite graphs in terms of their Laplacian spectra. 2. Keywords: graph
On the Wiener and Harary Index of Splitting Graphs by Campena ̃, Francis Joseph H. ; G. Egan, Ma. Christine; Antalan, John Rafael M. (2022) - If S = V, then the graph Γ(G,V ) is the splitting graph of a graph G as defined by Sampathkumar et al. If S = V and v ∈ S, then degΓ(v) = 2degG(v). (iii) If v ∈ S′, then degΓ(v ′) = degG(v). (iv) If G is a connected graph, then Γ(G,S) is also connected. F.J.H. Campeña, M.C.G. Egan, J.R.M. Antalan / Eur. Keywords: graph; index; matrix; vertices
On Weakly Connected Closed Geodetic Domination in Graphs Under Some Binary Operations by Hamja, Jamil; Aniversario, Imelda S. ; Rara, Helen M. (2022) - Also, some relationships between weakly connected closed geodetic dominating set, weakly connected closed geodetic set, geodetic dominating set, and geodetic connected dominating set are established. To show that S is a weakly connected dominating set of G. Since G is connected, for every u, v ∈ S, dG(u, v) = 2 and for all y ∈ V (Kp), y is in u-v geodesic. Keywords: dominating; graph; set
Some Parameters of the Central Graphs of the Identity Graphs of Finite Cyclic Groups by Alib, Clarence; Magpantay, Daryl M. (2022) - 2020 Mathematics Subject Classifications: 05C07, 05C12, 05C25 Key Words and Phrases: Cyclic group, Identity graph of a group, Handshaking lemma, Central graph of a graph, Distance, Eccentricities, Radius, Diameter, Center of a graph, Periphery of a graph, Girth 1. They represented every finite group in the form of graph and choose to call these graphs as identity graphs since the main role of obtaining the graph is played by ∗Corresponding author. Keywords: c(γcn; graph; group
On the Cospectrality of Hermitian Adjacency Matrices of Mixed Graphs by Alomari, Omar; Abudayah, Mohammad; Ghanem, Manal (2022) - 2020 Mathematics Subject Classifications: 05C20, 05C50, 15A30 Key Words and Phrases: Adjacency Matrix, Mixed graphs, Hermitian Matrix, Spectrum, Cospectrality 1. Recently, many researchers have proposed other Hermitian adjacency matrices of mixed graphs. Keywords: graph
Hermitian Adjacency Matrices of Mixed Graphs by Abudayah, Mohammad Ali; Alomari, Omar; Sander, Torsten (2022) - Altogether, these arcs and digons form the edge set E(D) of D. The graph G is called the underlying graph Γ(D) of the mixed graphD. Much of the traditional terminology (e.g. being regular, being connected, vertex degree deg(·), maximum degree ∆) that is used for undirected graphs simply carries over to mixed graphs, in the sense that, D is said to have a property whenever Γ(D) has this property. To overcome this obstacle, several authors have recently defined and studied various Hermitian adjacency matrices of digraphs or mixed graphs. Keywords: graph; theorem
On Some Properties of Non-traceable Cubic Bridge Graph by Nieva, Alex Ralph; Nocum, Karen P. (2022) - For the converse, suppose G is non-traceable graph. Fillar et al. in 2010 presented in their paper the ratio of cubic bridge graphs over cubic non-Hamiltonian graph and observed that the ratio is closer to 1 [4]. Keywords: graph; vertices
Supercliques in a Graph by Dela Cerna, Ramil; Canoy, Sergio (2022) - Let x, y ∈ C with x ̸= y. Suppose first that C ⊆ V (Hv) and let x, y ∈ C where x ̸= y. Since C is a superclique in G ◦ H, there exists z ∈ V (G◦H)\C such that z ∈ NG◦H(x)\NG◦H(y) or z ∈ NG◦H(y)\NG◦H(x). Keywords: graph; superclique
Path-Induced Closed Geodetic Domination of Some Common Graphs and Edge Corona of Graphs by Anoche, Jesica; Aniversario, Imelda; Merca, Catherine I. (2023) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Geodetic set, geodetic dominating set, path-induced closed geodetic set, path-induced closed geodetic dominating set, path-induced closed geodetic domination number 1. But these sets are not closed geodetic sets of G. Hence, G does not admit path-induced closed geodetic dominating set. Keywords: dominating; graph; path; set
On the study of Rainbow Antimagic Connection Number of Corona Product of Graphs by Septory, Brian Juned; Susilowaty, Liliek ; Dafik; Lokesha, V.; Nagamani, G (2023) - Some results on rainbow vertex connection number can see in [19], [23]. The graph K1+Sm is a connected graph with vertex set V (K1+Sm) = {a1}∪ {b1} ∪ {xj , 1 ≤ j ≤ m}, and the edge set E(K1 + Sm) = {a1b1} ∪ {a1xj , b1xj , 1 ≤ j ≤ m}. Keywords: graph; j ≤; rainbow; ⌈n2
Graph Automata and Graph Colorability by Kalampakas, Antonios (2023) - Engelfriet and Vereijken, in [7], presented an algorithm that inductively constructs every graph G ∈ GR(Σ) from the set Σ ∪ {Π, I01, I21, I10, I12, } by using graph product and graph sum. Math, 16 (1) (2023), 112-120 118 where graph product and graph sum are denoted, for simplicity, by horizontal and vertical concatenation. Keywords: graph; set
Convex Hop Domination in Graphs by Hassan, Javier; Canoy, Jr., Sergio; Saromines, Chrisley Jade (2023) - Any clique pointwise non-dominating set in G with cardinality cpnd(G) is called a cpnd-set in G. The shadow graph S(G) of graph G is constructed by taking two copies of G, say G1 and G2, and then joining each vertex u ∈ V (G1) to the neighbors of its corresponding vertex u′ ∈ V (G2). = { nm if G /∈ C γclh(G)cpnd(H) if G ∈ C. The next result is taken from [10]. Keywords: convex; dominating; dominating set; graph; hop; hop dominating; set
Relations Between Vertex$–$Edge Degree Based Topological Indices and $M_{ve}$-Polynomial of $r-$Regular Simple Graph by Rasool, Kavi B.; Rashed, Payman A.; Ali, Ahmed M. (2023) - τv = 6| = 20, |V4| = |v ∈ V (ℵn) : τv = 8| = 21, |V5| = |v ∈ V (ℵn) : τv = 9| = 2n−1 − 4. K. Rasool, P. Rashed, A. Ali / Eur. Thus, for any graph, we provide some relationships between vertex–edge degree topological indices. Keywords: degree; graph; vertex
The Basis Number of Mycielski ’s Graph for Some Cog- Graphs by Sulaiman, Barah M.; Hasan, Rasha S.; Mustafa, Raghad (2023) - Math, 16 (2) (2023), 953-964 958 M5 = u1u2mv1u3u1, M6 = u2m−2u2m−1u2mv2m−1u2m−2, M7 = v1u2m−1u2mv1, M8 = v2mu2m−1u2m−3v2m−1wv2m. In order B to be the base for the cycles space of graph µ(Cc m) must be |B| = dimC(µ(Cc m)), and B must be a linearly independent set of cycles. Hosoya polynomial and wiener indices of distances in graphs. Keywords: c m; cycles; edges; graph; number
On Weighted Vertex and Edge Mostar Index for Trees and Cacti with Fixed Parameter by Asmat, Farwa; Asmat, Humaira; Askar, Sameh; Ahmad, Hijaz; Khan, Muhammad Ijaz (2023) - Similarly, if K transform to path graph with end vertex u, then weighted vertex index Mowv (Ω) decreases. By using the definition of weighted vertex Mostar index, we have Mowv (Ω) = ∑ e=uv∈E(Ω) (dΩ(u) + dΩ(v))|nu(e|Ω)(v)− nv(e|Ω)(v)|, Mowv (Ω1)−Mowv (Ω2) = (dΩ(u) + dΩ(v))|nu(e|Ω1)(u)− nv(e|Ω1)(u)| + 2∑ m=1 ∑ xy∈E(T1) (dΩ(x) + dΩ(y))|nx(e|Ω1)(x)− ny(e|Ω1)(y)| − (dΩ(u) + Keywords: edge; graph; index; mostar; vertex; vertices
Connected Outer-Hop Independent Dominating Sets in Graphs Under Some Binary Operations by Manditong, Jahiri; Hassan, Javier; Laja, Ladznar S.; Laja, Amy A.; Mohammad, Nurijam Hanna M.; Kamdon, Sisteta U. (2023) - [7] introduced the concept of hop independent sets in a graph. A set D ⊆ V (G ◦H) is a connected outer-hop independent dominating set in G ◦H if and only if D = V (G) ∪ ( ⋃ v∈V (G)Dv), where Dv ⊆ V (Hv) and V (Hv) \ Dv is clique in Hv for each v ∈ V (G). Keywords: dominating; graph; hop; set
Spectral Analysis of Splitting Signed Graph by Kumar, Sandeep ; Sinha, Deepa (2024) - = a(i, j) 3: Check 4: if N mod 2 = 1 then 5: Print: matrix is of odd order, splitting root signed graph dose not exist 6: Terminate 7: else 8: for i = 1 : N do 9: for j = 1 : N do 10: check 11: if a(i,j)==1 then 12: countp = countp + 1 13: else 14: if a(i,j)== -1 then 15: countq = countq + 1 16: end if 17: end if 18: end for 19: end for 20: end if 21: check 22: if countp mod 3 == 0 && countq mod 3 == 0 then 23: Print: Splitting root signed graph is possible 24: else 25: Print: Splitting root signed graph is not possible and Terminate 26: end if 27: Assign: positive[i] = countp 28: negative[i] = countq 29: boole[i] = F 30: for i = 1 : N do 31: for j = i+ 1 : N do 32: Assign: k A signed graph Σ is called a splitting signed graph if it is isomorphic to the splitting signed graph Γ(U) of some signed graph U , where U is referred to as the splitting root signed graph of Σ. 1 2 3 4 5 1 2 1 ' 2' 3' 4' 5' 35 4 Figure 1: Signed graph Σ and its splitting signed graph Γ(Σ) Keywords: graph; matrix; root; splitting
Prime Graph Generation through Single Edge Addition: Characterizing a Class of Graphs by Alorini, Ayesha; Ben Amira, Aymen; Alzohairi, Mohammad; Bouaziz, Moncef (2023) - Indecomposable graphs with at least four vertices are prime graphs. The introduction and the study of the construction of prime graphs obtained from a given decom- posable graph by adding one edge constitue the central points of this paper. Keywords: graph; module; prime
The Generator Graph of a Group by Tacbobo, Teresa L. (2023) - Relationship between generating graph and generator graph of group The concept of the generating graph of a group was introduced by Luchini et al in [7]. Therefore, the generator graph ggG can be described as the join of complete graph of order |SG| and null graph of order n− |SG|. Keywords: generator; graph; group; vertices
Vertex-weighted $(k_{1},k_{2})$ $E$-torsion Graph of Quasi Self-dual Codes by Pilongo, Jupiter; Paleta, Leonard Mijares; Benjamin, Philip Lester P. (2024) - 2020 Mathematics Subject Classifications: 05C25, 05C60, 05C62, 05C90, 11H71, 14G50 Key Words and Phrases: quasi-self dual codes, rings, torsion codes, E-codes, E-torsion graphs, graph representation, quasi-self dual codes 1. In this paper, we have introduced a graph GEC generated by type-(k1, k2) E-codes which is (k1, k2) E-torsion graph. Keywords: codes; graph; torsion
On the j-Edge Intersection Graph of Cycle Graph by Bonifacio, Jhon Cris; Andaya, Clarence Joy; Magpantay , Daryl (2023) - In the paper [4], they investi- gated The class of edge intersection graphs of a collection of paths in a tree (EPT graphs) where two paths edge intersect if they share an edge. [1] that presents some other results about edge intersection graphs of paths on a grid and shows several results of the other clsses of graphs. Keywords: ec(n; edge; graph
Characterizations of $J$-Total Dominating Sets in Some Special Graphs and Graphs under Some Operations by Hassan, Javier; Manditong, Jahiri; Bakkang, Alcyn; Kamdon, Sisteta U.; Salim, Jeffrey Imer (2023) - = V (G) ∪ V (H) and edge set E(G+H) = E(G) ∪ E(H) ∪ {uv : u ∈ V (G), v ∈ V (H)}. Weakly convex hop dominating sets in graphs. Keywords: dominating; dominating set; graph; set
Universal Distance Spectra of Join of Graphs by Kaliyaperumal, Sakthidevi; Desikan, Kalyani (2024) - − r2 − 2)β + γn2 + δ (2β + γ)n3 (β + γ)n1 (2β + γ)n2 α (2N + n1 − r2 − 2)+ (2n3 − r3 − 2)β + γn3 + δ  , n1, [ α (2N + n1 − r2 − 2)− 2β+ δ ] − βλ2 m; m = 2, 3, . . . Keywords: distance; graph; matrix; universal
Certified Hop Independence: Properties and Connections with other Variants of Independence by Kaida, Sharmia H. ; Maharajul, Kaimar Jay S. ; Hassan, Javier; Laja, Ladznar S. ; Lintasan, Abdurajan B. ; Pablo, Aljon A. (2024) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Hop independence, certified independent set, certified hop indepen- dence number 1. We characterize certified hop independent sets in some graphs and we use these results to obtain the exact values or bounds of the parameter. Keywords: graph; hop; set
Eigenvalue Interlacing of Bipartite Graphs and Construction of Expander Code using Vertex-split of a Bipartite Graph by Manickam, Machasri; Desikan, Kalyani (2024) - In coding theory, Expander codes are Error Correcting codes made up of bipartite expander graphs. The error-correcting codes known as expander codes are constructed from bipartite expander graphs. Keywords: bipartite; graph; matrix; vertex
Legal Hop Independent Sequences in Graphs by Hassan, Javier; Langamin, Mercedita A. ; Laja, Amy A. ; Amiruddin-Rajik, Bayah J. ; Ahmad, Eman C. ; Manditong, Jahiri U. (2024) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: legal sequence, hop independent set, legal hop independent sequence, legal hop independence number 1. In this paper, new variant of hop independence called legal hop independent sequences in a graph is introduced and investigated. Keywords: graph; hop; sequence; set
Exploring Lung Cancer Protein Network: Understanding Structure and Function through Metric Space Modeling by Fadhal, Emad (2024) - Zone Number of proteins Growth Total 1 1 1(0.95%) 2 105 3(2.43%) 3 123 3(2.70%) 7 4 111 0(0%) 5 28 0(0%) Table 5 shows the distribution of cell cycle proteins in the BCPIN zone. Table 5: Distribution of cell cycle proteins in zones of BCPIN. Keywords: analysis; cancer; cell; cycle; distribution; drug; graph; lcpin; lung; network; nodes; pathways; potential; progression; proteins; regulation; table; targets; zones
J-Open Independent Sets in Graphs by Hassan, Javier; Bakar, Nuruddina M. ; Dagsaan, Norwajir S. ; Langamin, Mercedita A. ; Mohammad, Nurijam Hanna M. ; Kamdon, Sisteta U. (2024) - Then O1 and O2 are maximum J-open inde- pendent and maximum hop independent sets of K2 + P5, respectively. The structure and maximum number of maximum independent sets in trees. Keywords: graph; set
The Block Topological Space and Block Topological Graph Induced by Undirected Graphs by Macaso, Justine Bryle; Balingit, Cherry Mae (2024) - Suppose that vertex v is not a cut- vertex adjacent to w. Let O be a τB(G)-open containing v. Suppose on the contrary that w /∈ O. Observe that vertex v is not a cut-vertex of G that is adjacent to w. By Theorem 5, any τB(G)-open containing v also contains w. Hence, the block topological space of G is not a Hausdorff space. Keywords: block; cut; graph; vertex
Restrained Global Defensive Alliances in Graphs by Consistente, Leocint; Cabahug, Isagani (2024) - Now, since S = V is the only rgda in K3, it is also the minimum rgda in K3. In particular, a global defensive alliance S is a restrained global defensive alliance if the induced subgraph of V ∖ S has no isolated vertex. Keywords: graph; vertex
The Wiener Index of Prime Graph $PG(\mathbb{Z}_n)$ by Hidayat, Noor; Krisnawati, Vira Hari; Husnul Khuluq, Muhammad; Fatimah, Farah Maulidya; Musyarrofah, Ayunda Faizatul (2024) - All Wiener index formulas that have been constructed for ring graphs (zero divisor graph, unit graph, total graph, and prime graph) can be seen in the survey results arranged by Asir et al For every prime number p, q, the ring Zpq has u = (p − 1)(q − 1) units and p+ q − 2 nontrivial zero divisors. Keywords: graph; index; prime; vertex
On the k-restricted Intersection Graph by Pelagio, Mariane Eliz; Mendoza, Kathlen; Mame, Neil (2024) - Furthermore, if k = 0 or ⌊ n 2 ⌋ < k ≤ n, GS(n,k) is a [( n k ) If 1 ≤ k ≤ ⌊ n 2 ⌋ , then ⌊ n 2 ⌋ ≤ n− k. This implies that k ≤ n− k so |S(n−k,k)| = ( n−k k ) . Keywords: graph; gs(n
Polynomial Representation and Degree Sequence of Graphs Resulting from Some Graph Operations by Cruz, Jayhan; Malacas, Gina; Canoy, Sergio Jr. (2024) - A simple proof of the erdös-gallai theorem on graph sequences. Let G and H be non-trivial connected graphs. Keywords: graph
Investigating Metric Dimension and Edge Metric Dimension of Hexagonal Boron Nitride and Carbon Nanotubes by Abbas, waseem ; Chudhary, Faryal ; Farooq, Umar; Azeem, Muhammad ; Shang, Yilun (2024) - Hexagonal boron nitride graph 3× 3 • Case 1. Hexagonal boron nitride graph 3× 3 U. Farooq et al. / Eur. Keywords: emd; graph; metric; vertices
Bounds on Spectral Radius and Signless Laplacian Spectral Radius for Generalized Core-satellite Graphs by V, Malathy; Desikan, Kalyani (2025) - Core–satellite graphs: Clustering, assortativity and spectral properties. In this graph G, consider the vertex v taken from satellite graph Sk, since dαk = max(dαi), for i = 1, 2, ..., k. Keywords: core; graph; i=1
Relationship Between the Second Largest Adjacency and Signless Laplacian Eigenvalues of Graphs and Properties of Planar Graphs by Manickam, Machasri; Desikan, Kalyani (2024) - Graph skewness, graph thickness, and graph crossing number are a few metrics that describe how much a graph deviates from planarity. Particularly in computational biol- ogy, graph thickness can aid in the analysis of biological networks, such as protein-protein interaction networks. Keywords: graph; number; theorem
On Spectrum and Energy of Identity Graph for Groupof Integers Modulo n, Zn by Romdhini, Mamika Ujianita; Nawawi, Athirah ; Al-Sharqi, Faisal ; ., Salwa (2024) - This paper focuses on group structures that can be expressed in graphs known as identity graphs. 2020 Mathematics Subject Classifications: 05C25, 15A18 Key Words and Phrases: Energy of a graph, Identity graph of a group, Zn 1. Keywords: graph; γzn
Local Total Antimagic Chromatic Number for the Disjoint Union of Star Graphs by Sandhiya, Venkatesan ; Nalliah, Moviri Chettiar (2024) - 2020 Mathematics Subject Classifications: 05C78, 05C15 Key Words and Phrases: Local antimagic graphs, chromatic number, total coloring 1. Graph coloring and graph labeling are the significant research areas in graph theory. Keywords: antimagic; graph; j ≤; labeling; nalliah
On b-Coloring Analysis of Graphs: An Application to Spatial-Temporal Graph Neural Networks for Multi-Step Time Series Forecasting of Soil Moisture and pH in Companion Farming by Kristiana, Arika Indah; Rachmasari, Elisa ; ., Dafik; Agustin, Ika Hesti ; Mursyidah, Indah Lutfiyatul; Alfarisi, Ridho (2024) - We have determined the exact value of the b-chromatic number of Pn ▷v1 Pm graph for n,m ≥ 8 and Ln ▷v1 Pm graph for n,m ≥ 5. Figure 7: Pn ▷v1 Pm graph with 64 vertices and companion farming adjacency matrix Figure 8: The distribution of soil moisture, temperature and pH with 64 companion farming vertex on 30 days to training and testing dataset Based on the previously described algorithm, an vertex embedding with 64 planting vertices is required. Keywords: b−coloring; graph; j ≡; mod; vertex; ≡ 0mod; ≡ 1mod; ▷v1
Middle Graph of the Identity Graph of Finite Cyclic and Dihedral Groups by Magpantay, Daryl M.; Jagmis, Jiel Mark (2025) - Power domination of middle graph of central graph460 of path, cycle, and star. They represented the16 finite groups in terms of graphs which they called identity graphs or identity graphs since17 the identity element of the group is the main role in order to create a graph.18 19 A.D. Godase Keywords: graph; m(γcn; middle; vertex; vertices
Advancing Graph Theory with Genetic Algorithms: AFocus on Non-Inclusive Vertex Irregular Labeling by Santoso, Kiswara Agung; Cristyanto, Febyan Gilang ; Halikin, Ikhsanul; Alfarisi, Ridho (2024) - Non-inclusive irregular vertex labeling is a labeling on a graph where the vertex labels are real numbers that have weights. Discussion This research using the genetic algorithm to solve non-inclusive vertex irregular labeling of graph. Keywords: algorithm; figure; graph; labeling; matrix; process; vertex
Achieving Edge Consensus in Hybrid Multi-AgentSystems: Scaled Dynamics and Protocol Design by Park, Choonkil ; Donganont, Siriluk; Donganont, Mana (2025) - In the framework of edge consensus, the objective is for the states of all edges in the network to asymptotically converge to a common value or consensus state through interactions and information exchange among neighboring edges. (3) Theoretical framework for edge consensus: The paper develops a theoretical framework that outlines the conditions necessary for achieving edge consensus in both di- rected and undirected topologies, contributing to the understanding of how edge dynamics operate within multi-agent systems. Keywords: consensus; donganont; edge; graph; matrix
Edge Geodetic Dominating Sets of Some Graphs by Quije, Clint Joy; Mariano, Rochelleo; Ahmad, Eman (2025) - The edge geodetic number ge(G) of G is the minimum cardinality of edge geodetic set. Edge geodetic domination number of a graph. Keywords: dominating; edge; geodetic; graph; set
Graph-Based Approach to the Radio Assignment Problem in Wireless Communication Networks with Applications in Cryptography by Nour Eldeen, Nawal M.; Badr, Elsayed; Hagag, Ismail M.; Shabana, Hanan (2025) - In literature, there are some algorithms for finding an upper bound for radio number of a given graph. The Upper bound of the radio number of a given graph G Input: The adjacency matrix of the graph G and the diameter D of G. Output: The upper bound of radio number of G. Begin 1: For all u ∈ V (G) compute, ds(u) Keywords: algorithm; bound; cpu; graph; labeling; number; radio; time; ub2; vertex
Another Look at Hop Independence in Graphs by Anoche, Jesica; Canoy, Jr., Sergio (2025) - = n if and only if G = Kn; and (ii) for n ≥ 3, αh(G) = n− 1 if and only if G ̸= Kn and there exists v ∈ V (G) such that G \ v = Kn−1. Observation 1: Let G be a graph of order n. (i) ∅ and cliques in G are hop independent sets. (iii) S = SG1 ∪ SG2 ∪ I1 ∪ I2 and satisfies the following conditions: (a) I1 ⊆ I(G1) and I2 ⊆ I(G2). (b) SG1 and SG2 are hop independent sets in G1 and G2, respectively, not containing isolated vertices. Keywords: graph; hop; set
Total Edge Irregularity Strength of Star Snake Graphs by Attiya, Hala; Ahmed, Nasr ; Salama, Fatema (2025) - In different fields in our life, like physics, coding theory and computer science, graph labeling plays a vital role and appears in many applications. A dynamic survey of graph labeling. Keywords: graph; ζ−1
Distance-2 Chromatic Number of the Central and Shadow Graphs of a Cycle and its Application to Computer Science by Libao, Merliza; Abarca, Kyla B. (2025) - In addition to chromatic and distance-2 chromatic numbers, graph theorists have also explored the properties of more complex graph structures, such as Shadow graphs and Central graphs. Central graphs, first studied by Sampathkumar and Walikar in 1974 Keywords: color; coloring; graph; vertices
On the Recognition Capacity of Abelian Graph Automata by Papadopoulos, Kyriakos (2025) - Regarding the recognition ability of unitary graph automata, i.e., graph automata employing unitary graphoids, we know that they recognize for every positive integer k, the set of all directed k-colorable graphs with- out inputs and outputs [20]. Math, 18 (1) (2025), 5850 7 of 13 Figure 1: The class hierarchy of graph automata graph languages recognized by abelian graph automata and by Urec(Σ) the set of graph languages recognized by unitary graph automata. Keywords: abelian; automata; automaton; graph; graphoids; len; set
Total Safe Domination on Some Known Families of Graphs by Jumalon, Wendel Glenn ; Cabahug, Isagani (2025) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Total domination, safe domination, safe set, total safe domination 1. = |V (Cn)| = n. Conclusions The concept of total safe domination has been introduced and explored in this study. Keywords: dominating; dominating set; graph; set; vertex
Internally-Locating Dominating Sets in Graphs by Tropico, Irish S.; Cabahug, Jr, Isagani S. (2025) - Let G be a graph with n ≥ 4 and G = Pn ◦ H, for any graph variation of H. By Corollary 1, γ(G) = n. By definition of path graph Pn and since G = Pn ◦ H, V (Pn) = {v1, v2, . . . if G = Pn ◦H, for any graph variation of H. Proof. Keywords: dominating; graph; set; |i|
Proximity Prestige of a Vertex in Some Graph Families by Toladro, Lysandra A. ; Cabahug, Isagani (2025) - The proximity prestige (PP ) of a vertex vi is the sum of the shortest path distance between vertex vi and vj all over the number of vertices in the graph. = ∑ dG(vi, vj) |V (G)| where, • PPG(vi) : proximity prestige of vertex vi; • dG(vi, vj): length of the shortest path from vi to any vj; and • |V (G)|: number of vertices in the graph. Keywords: deg(vi; graph; vertex
Spatio-Temporal Graph Neural Network for Time Series Forecasting: Local Antimagic Coloring Based Companion Farming by Kristiana, Arika Indah; Izza, Rifda; Agustin, Ika Hesti; Monalisa, L. A. ; Mursyidah, Indah Lutfiyatul; Baihaki, Rifki Ilham; Agustina, K. H. ; Dafik (2025) - The study of graph colorings has been an essential area of research in combinatorics, particularly due to its wide-ranging applications in network optimization, scheduling, and cryptographic systems As a subfield of graph coloring, local edge-antimagic (a, d)-coloring (lea(a, d) color- ing) has been the subject of numerous studies. Keywords: antimagic; coloring; edge; graph; stgnn
Bounds on the Energy of Zero-divisor Graph of Quotient Ring and Its Topological Indices by Krisnawati, Vira Hari ; Hidayat, Noor; Musyarrofah, Ayunda Faizatul (2025) - The eigenvalues of G are 0, with multiplicity ℘4 − ℘2 − 2, and −1, with multiplicity ℘2 − 3. (ii) = 1 2 (2℘8 − 4℘5 − ℘4 + ℘2 + 2). Keywords: energy; graph; i=1; index; indices
Hop $k$-Rainbow Domination in Graphs by Hamja, Jamil; Sheikholeslami, Seyed Mahmoud ; Imelda, Aniversario; Cabardo, Lyster Rey (2025) - Applying the bounds presented in Theorem 4, for any positive integer k ≥ 1 and every graph G of order n, we have that 2min{n, k + 1} ≤ γhrk(G) + γhrk(G) ≤ 2n. = { k, if n ≥ k, n, if n < k. Proposition 3. Keywords: graph; γhrk(g
On Density of Some Graphs and Their Mycielski Graph by Racma, Sango; Cabahug, Isagani, Jr. (2025) - 2020 Mathematics Subject Classifications: : 05C07, 05C12 Key Words and Phrases: graph density, Mycielski graph, special graph families 1. The concept of graph density serves as a fundamental metric in network analysis. Keywords: edges; graph; number; vertices
Independent Double Roman Domination Stability in Graph by Hamja, Jamil; Sheikholeslami, Seyed Mahmoud ; Esmaeeli, Mina; Cris L. Armada; Aniversario, Imelda S. (2025) - Then the function g defined on T − x1 by g(x3) − {x3}, is an IDRD- function of T − x1 of weight at most ω(f) Keywords: function; graph
Stability and Maximum Independent Bond Set Polynomials of Painkiller Molecules Using Maximum Matching by Ali, Jiwan Jalal; Ali, Didar Abdulkhaleq (2025) - Math, 18 (2) (2025), 5992 5 of 22 The following Table 1 enlisted some standard topological indices based on degrees of maximum independent bond set and their derivation from the maximum independent bond set polynomials, where Dx = x∂f(x,y) ∂x , Dy = y ∂f(x,y) ∂y , Sx = ∫ DOI: https://doi.org/10.29020/nybg.ejpam.v18i2.5992 Email addresses: jiwan.ali@uoz.edu.krd (J. J. Ali), didar.ali@uoz.edu.krd (D. A. Ali) https://www.ejpam.com 1 Keywords: ali; drug; graph; matching; maximum; r=1; structure; v4v5; ∀uv∈xr
Independent Edge Domination Topology of Some Graph Families by Ontulan, Jhon Neceir; Balingit, Cherry Mae (2025) - 2020 Mathematics Subject Classifications: 05C70, 54A05, 54A25, 05C75 Key Words and Phrases: Independent edge domination topology, Independent edge dominating sets, Complete graph, Friendship graph, Complete bipartite graph 1. The same association of edge sets is the study of Alsinaia et al. Keywords: edge; graph; set; topology
Lower and Upper Acyclicities on Unitary Cayley Graphs of Finite Commutative Rings by Pongpipat, Denpong ; Nupo, Nuttawoot (2025) - In this paper, we determine the lower and upper acyclic numbers for unitary Cayley graphs of Zn and their complements. Some prominent results of unitary Cayley graphs were studied by several researchers. Keywords: cayley; graph; set; vertices
On Certified Perfect Domination in Graphs by Hamja, Jamil; Laja, Amy; Copel, Hounam; Amiruddin-Rajik, Baya; Mohammad, Nurijam Hanna (2025) - The certified perfect domination number of G γcerp(G) represents the smallest size of a certified perfect dominating set in G. A certified perfect dominating set of G that attains this minimum size, i.e., |J | = γcerp(G) is referred to as a γcerp-set. We also examine the behavior of certified perfect dominating sets under graph operations such as the lexicographic and Cartesian products. Keywords: dominating; graph; perfect; set; γcerp(g
Total Exact Domination in Graphs by Aguinod, Ritchie; Armada, Cris; Kiunisala, Edward (2025) - Graphs that do not have total exact dominating sets were identified as non-γte-graphs, examples of which include complete graphs, fan graphs, and wheel graphs with more than two vertices. The lexicographic product or composition of two graphs G and H is the graph G[H] with vertex set V (G[H]) Keywords: graph; set; vertices; γte
Fuzzy Geodetic and Detour Spectra: Geodetic-Laplacian Energy in Fuzzy Graphs by R, Rajeshkumar; A. M, Anto; Rose, V. Mary Mettilda (2025) - This study addresses these gaps by extending the concept of fuzzy graph energy to include fuzzy geodetic energy, fuzzy detour energy, and, most notably, fuzzy geodetic- Laplacian energy and fuzzy detour-Laplacian energy. The concept of fuzzy graph energy, in particular, introduces additional complexity, as the fuzziness of both vertices and edges must be integrated into spectral computations. Keywords: detour; distance; energy; fuzzy; graph; laplacian; matrix
Spectral Properties of Coprime Graphs for Dihedral Groups by Romdhini, Mamika Ujianita; Abdurahim; Maharani, Andika Ellena Saufika Hakim (2025) - 2020 Mathematics Subject Classifications: 05C25, 15A18 Key Words and Phrases: Coprime graph, Dihedral group, Spectral radius, Energy of a graph 1. The degree, radius, and diameter of coprime graph of dihedral group. Keywords: 2n−; graph; γd2n
A Degree-Based Exponential Fuzzy Graph for Pollution Impact Analysis by Al-Omeri, Wadei Faris; Kaviyarasu, M.; Venitha, R. (2025) - Some fundamental aspects such as vertex degree, order and size are explored in relation to the idea of exponential fuzzy graphs (EFGs). In this study, we introduce the innovative idea of exponential fuzzy graphs. Keywords: fuzzy; graph; membership; vertex
Resolving Parameters in Generalized Sierpi ́nski3 Networks Over Cycle of Length Five by K., Bharani Dharan; S., Radha (2025) - [62], certain classes of planar graphs [63], and the identification of graph network with higher dimension Additionally, researchers have investigated graph operations such as join of graph networks, lexicographic product and corona product Keywords: dimension; edge; fault; graph; h c5; networks; set; sierpiński; vertices
The Energy of Cameron-Walker Graphs by Ulker, Alper ; Oner, Tahsin ; Iampan, Aiyared; Ordin, Burak (2025) - 2020 Mathematics Subject Classifications: 05C50, 05C70, 05C35 Key Words and Phrases: Cameron-Walker graph, matching number, graph energy, lower bound 1. Moreover, we provide lower bounds on graph energy with respect to the induced matching number. Keywords: energy; graph; matching; number
Paley, Cubic Paley, Quadruple Paley, and Generalized Paley Graphs with an Edge-Graceful Labeling by Elsawy, Ahmed Noubi Sayed; Almohammadi, Reyoud Nasser (2025) - 2020 Mathematics Subject Classifications: 05C25, 05C78 Key Words and Phrases: Paley graphs, cubic Paley graphs, quadruple Paley graphs, generalized Paley graphs, edge-graceful labeling, edge-even graceful labeling, edge-odd graceful labeling 1. In this paper, we prove that Paley graphs and generalized Paley graphs of prime order are edge graceful, edge-even graceful, and edge-odd graceful graphs. Keywords: edge; graceful; graph; labeling; paley; step
Folding on Topological Graphs and Their Fundamental Group by Abu Saleem, Mohammed (2025) - . , n, which induces a folding �̂�n : n∗ k=1 π1(Gk) −→ n∗ k=1 π1(Gk) such that �̂�n( n∗ k=1 π1(Gk)) is a free group of rank m− n. Consequently, rank (�̂�h( n∗ k=1 π1(Gk) )) Jn → Jn which induces �̂� : π1(Jn) → π1(Jn) such that rank (�̂�(π1(Jn))) Keywords: folding; graph; k=1; rank
Exploring Certified Domination Subdivision Numbers in Graph Theory by G. , Navamani; N., Sumathi; Dharmaraj, Mohankumar; Cotîrlă, Luminiţa-Ioana ; Breaz, Daniel (2025) - Domination in subdivision graphs. An edge uv ∈ E(G) is subdivided if the edge uv is deleted, but a new vertex called subdivision vertex w is added along with two new edges uw and vw. Keywords: graph; set; subdivision; vertex; γcer(g
On (H1,H2)-magic generalized total composition by Maryati, Tita Khalis; Hadiputra, Fawwaz Fakhrurrozi; Bača, Martin; Semaničová-Feňovčíková, Andrea (2025) - For every Γ ∈ {F1, F2, F1 ∩ F2, H1 − F ∗}, where F ∗ = Amal(F1, F2;A), let Γ(i) be a subgraph isomorphic to Γ which is originated from vi ∈ V (Pn). For more insights about graph labeling, please see [12]. Keywords: 2tf; graph
Mathematical Modeling of Signed Graphs for Balancing Dynamic Systems by Alotaibi, Abdulaziz ; Al-Tahat, Khalid ; Aljamal, Khaled Mustafa (2025) - Sign-symmetry and frustration index in signed graphs. Main Results In this section, we will discuss how to determine the stability of a system at equilibrium points using signed graph theory. Keywords: damping; equilibrium; graph; stability; system
Vertex-Generator Subgraphs of Complete Bipartite and Tadpole Graphs by Sepillo, Gino Derek; Valdez, Ma. Joyce; Eyao, Meguilito; Mame, Neil (2025) - Building on the concept of vertex spaces and induced subgraphs, Torino and Mame [3] introduced the vertex-generator subgraph, a concept parallel to the edge- generator subgraph (or generator subgraph) first explored by Gervacio A key difference is that vertex-generator subgraphs can contain isolated vertices, while generator subgraphs do not allow isolated vertices. Keywords: graph; subgraph; vertex

Fuzzy

Subalgebras and Ideals in BCK/BCI-algebras Based on Uni-hesitant Fuzzy Set Theory by Muhiuddin, G.; Aldhafeeri, Shuaa (2018) - Characterizations of uni-hesitant fuzzy algebras and uni-hesitant fuzzy (closed) ideals are considered, and a new uni-hesitant fuzzy algebra (resp. In this paper, we introduce the notions of uni-hesitant fuzzy algebras and uni-hesitant fuzzy (closed) ideals in BCK/BCI-algebras, and investigate several related properties. Keywords: fuzzy; hesitant
On Some Properties of Doubt Bipolar Fuzzy H-ideals in BCK/BCI-algebras by Al-Masarwah, Anas Mohammad; Ahmad, Abd Ghafur (2018) - Math, 11 (3) (2018), 652-670 654 (I) ((x ∗ y) ∗ (x ∗ z)) ∗ (z ∗ y) = 0, (II) (x ∗ (x ∗ y)) ∗ y = 0, (III) x ∗ x = 0, (IV) x Math, 11 (3) (2018), 652-670 657 Since x ∗ (y ∗ z) ∈M and y ∈M, we have x ∗ z ∈M. So C̃PM (x ∗ z) = 0 and C̃NM (x ∗ z) = 0. Keywords: doubt; fuzzy; x ∗; y ∗; µna; ∗ z
Characterizations of Non-associative Rings by Their Intuitionistic Fuzzy Bi-ideals by Kausar, Nasreen; Waqar, Muhammad Azam (2019) - [7], initiated the notion of intuitionistic fuzzy subrings and intuitionistic fuzzy ideals of a ring. Subsequently many authors studied the intu- itionistic fuzzy subrings and intuitionistic fuzzy ideals of a ring by describing the different properties (see [8]). Keywords: fuzzy; ideal; left; ring
Fuzzy Soft Sets over Fully UP-Semigroups by Satirad, Akarachai; Iampan, Aiyared (2019) - In this paper, we introduce ten types of fuzzy soft sets over fully UP-semigroups, and investigate the algebraic properties of fuzzy soft sets under the operations of (extended) intersection and (restricted) union. Further, we discuss the relation between some conditions of fuzzy soft sets and fuzzy soft UPs-subalgebras (resp., fuzzy soft UPi-subalgebras, fuzzy soft near UPs-filters, fuzzy soft near UPi-filters, fuzzy soft UPs-filters, fuzzy soft UPi-filters, fuzzy soft UPs-ideals, fuzzy soft UPi-ideals, fuzzy soft strongly UPs-ideals, fuzzy soft strongly UPi-ideals) of fully UP-semigroups. Keywords: filter; fuzzy; upi; ups
Direct Product of Finite Intuitionistic Anti Fuzzy Normal Subrings over Non-associative Rings by Kausar, Nasreen (2019) - [17], introduced the concept of intuitionistic fuzzy normal subrings over a non-associative ring (LA-ring). [17], have introduced the concept of intuitionistic fuzzy normal subrings over a non-associative ring. Keywords: fuzzy; ring; subring
Intuitionistic Fuzzy Ideals with Thresholds (Î±, Î²] in LA-rings by Kausar, Nasreen; Islam, Badar ul; Ahmad, Syed Amjad; Waqar, Muhammad Azam (2019) - ∧ β ∧ β ∧ β} ∨ α = {((µA ∧ µB)(x) ∧ β) ∧ ((µA ∧ µB)(y) ∧ β ∧ β ∧ β} ∨ α = {((µA ∧ µB)(x) ∧ β) ∧ ((µA ∧ µB)(y) Keywords: fuzzy; ideal; r ◦; thresholds; βα r; ∧ β; ◦ βα
Inf-hesitant Fuzzy Subalgebras and Ideals in BCK/BCI-algebras by Muhiuddin, G.; Alanazi, Abdulaziz M.; Elnair, Mohamed E. A.; Shum, K. P. (2020) - Introduction The motivation for introducing hesitant fuzzy sets is that it is sometimes difficult to determine the membership of an element into a set and in some circumstances this dif- ficulty is caused by a doubt between a few different values. Torra [25] proposed the concept of hesitant fuzzy sets as a new generalization of fuzzy sets [33], which allows the membership of an element of a set to be represented by several possible values. Keywords: fuzzy; inf
Anti Fuzzy Interior Ideals on Ordered AG-groupoids by Kausar, Nasreen; Alesemi, Meshari; ., Salahuddin (2020) - They studied fuzzy ideals and fuzzy bi-ideals of fuzzy semigroups. [4] K. A. Dib and N. Galham, Fuzzy ideals and fuzzy bi-ideals in fuzzy semigroups, Fuzzy sets and system, 92(1997) 203-215. Keywords: anti; fuzzy; ideal
On Intuitionistic Fuzzy Hyper GR-ideals in Hyper GR-algebras by Macodi-Ringia, Amila Pagadilan; Petalcorin, Gaudencio Cempron (2020) - Moreover, let x, y ∈ H and let t̃, s̃ ∈ Some of these studies are intuitionistic fuzzy hyper BCK-ideals of hyper BCK-algebras [3] and intuitionistic fuzzy ideals in hyper BCI-algebras [15]. Keywords: fuzzy
Further Results on Fuzzy Soft BCK/BCI-algebras by Al-Kadi, Deena S.; Muhiuddin, G. (2020) - [10] defined and studied fuzzy soft sets. [19] considered the notion of fuzzy soft set and used it to present a theoretic approach to decision making problems and Jun et al. Keywords: bci; bck; fuzzy
Some New Results of Fixed Point in Fuzzy Soft G-metric Spaces by Sayed, Abdelhamied Farrag; Alahmari, Abdullah (2021) - [25] defined the notions of some mappings and proved several fixed point theorems in fuzzy soft metric spaces. On fuzzy soft metric spaces. Keywords: fe2; fe3; fuzzy; gen+1; g̃(fe; g̃(gen+1; t fe; t gen+1
Fuzzy Sets in Hyper UP-algebra by Amairanto, Rohaima M.; Isla, Rowena T. (2021) - Let {µα : α ∈ A} be a nonempty family of fuzzy hyper UP-subalgebras of H. Let x, y ∈ H. Let x, y ∈ H with x ∈ µt and x ⊛ y ⊆ µt. Keywords: fuzzy; hyper; subalgebra
Pythagorean Fuzzy Small Submodules by Almuhaimeed, Areej (2022) - We prove various characterisations for pythagorean fuzzy small submodules. In addition, some important properties regarding pythagorean fuzzy small submodules are investigated. Keywords: fuzzy; pythagorean; submodule
Data Envelopment Analysis on the Context of Spherical Fuzzy Inputs and Outputs by Mohanta, Kshitish Kumar; Sharanappa, Deena Sunil; Dabke, Devika; Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan (2022) - The difference between Intuitionistic fuzzy set, Pythagorean fuzzy set, Neutrosophic fuzzy set, and spherical fuzzy set are shown in Figure (1) where TA, FA and IA represents the truth, falsity and indeterminate membership grade for the fuzzy set A. Figure 1: Representation of the fuzzy set and it’s extension in geometrically 7 3d drawing ⟨0, 0, 0⟩ ⟨1, 0, 0⟩ ⟨0, 1, 0⟩ ⟨0, 0, 1⟩ TA FA IA Spherical Fuzzy Set Neutrosophic Fuzzy Set Intuitionistic Fuzzy Set Pythogorean Fuzzy Set 4 V. N. Mishra et al. / Eur. In this study, Data Envelopment Analysis (DEA) models are improved by employing spherical fuzzy sets (SFSs), which is an extension of generalized fuzzy sets. Keywords: data; dea; fuzzy; i=1; k=1
Lukasiewicz Fuzzy BE-algebras and BE-filters by Jun, Young Bae; Ahn, Sun Shin (2022) - If ξ is a fuzzy BE-algebra of X, then its Lukasiewicz fuzzy set Lε ξ satisfies: (∀x, y ∈ X) ( Lε ξ(y) Assume that Lε ξ satisfies the condition (15) and let x, y ∈ X be such that x, y ∈ ( Lε ξ, t)∈ for t ∈ (0.5, 1]. Keywords: fuzzy
Ideals in BE-algebras Based on Lukasiewicz Fuzzy Set by Ahn, Sun Shin; Roh, Eun Hwan ; Jun, Young Bae (2022) - Hence Lεψ(x∗y) ≥ t, and so x∗y ∈ ( Lεψ, t)∈. Let x, y ∈ X and t ∈ (0.5, 1] be such that x ∈ ( Lεψ, t)∈ and y ∈ ( Lεψ, t)∈. Then Lεψ(x) ≥ t and Lεψ(y) ≥ t, which imply from (19) that 0.5 < t ≤ min{ Lεψ(x), Lεψ(y)} ≤ max{ Lεψ((x ∗ (y ∗ z)) ∗ z), 0.5} for all z ∈ X. Hence ⟨1/max{ta, tb}⟩ ∈ Lεψ by (22), and thus 1 ∈ ( Lεψ,max{ta, tb})∈. Let x, y, z ∈ X be such that x ∗ (y ∗ z) ∈ ( Lεψ,max{ta, tb})∈ and y ∈ ( Lεψ,max{ta, tb})∈. Then Lεψ(x ∗ (y ∗ z)) ≥ max{ta, tb} > 1 − max{ta, tb} and Lεψ(y) ≥ max{ta, tb} > 1 − max{ta, tb}, that is, ⟨(x ∗ (y ∗ z))/max{ta, tb}⟩ q Lεψ and ⟨y/max{ta, tb}⟩ q Lεψ. Keywords: fuzzy; lεψ; y ∗; ∗ z
On g-regularity and g-normality in Fuzzy Soft Topological Spaces by Saleh, Salem Ali Mohammed; Al-Mufarrij, Jawaher (2023) - 2020 Mathematics Subject Classifications: 54A40, 54C08, 54D15 Key Words and Phrases: Fuzzy soft set, fuzzy soft g-closed set, quasi coincident, fuzzy soft g-continuous maps, fuzzy soft g-regular, fuzzy soft g-normal space 1. [30] defined and studied the notion of topological structure for fuzzy soft sets and studied many related concepts. Keywords: fuzzy; set
Double Fuzzy $\delta$-Continuous Functions in Double Fuzzy Topological Spaces by Al-Omeri, Wadei Faris (2025) - For any double fuzzy set ρ in an double fuzzy topology (T , T ∗) on X, IT ,T ∗(CT ,T ∗(ρ, r, s)) is a (r, s)-FRO set. (ii) double fuzzy set ρ in an double fuzzy topology (T , T ∗) on X, such that xiqρ, IT ,T ∗(CT ,T ∗(ρ, r, s)) is a (r, s)-FRO Q-neighborhood of xi. Proof. Keywords: fuzzy; t ∗(ρ
Note on Generalized Neighborhoods Structures in Fuzzy Bitopological Spaces by Ahmed Alharbi, Ahlam; Kilicman, Adem (2023) - Conversely, assume E is fuzzy set of X, Assume x0.7 is fuzzy point of X = {a, b, c} and E is fuzzy set of X defined as E(a) = 0.4, E(b) = 0.5, E(c) Keywords: fuzzy; gφ−; j)−
Some Properties of Operations in the Collection of Intuitionistic Fuzzy Sets : A Novel Approach by Yunianti, Dwi Nur; Hidayat, Noor; Sulaiman, Raden; Alghofari, Abdul Rouf (2023) - 2020 Mathematics Subject Classifications: 03E72, 03G25 Key Words and Phrases: Intuitionistic fuzzy sets, Collection of intuitionistic fuzzy sets, Inter- section, Union 1. Adopting definition of intuitionistic fuzzy set, collection of intuitionistic fuzzy sets also give membership and non-membership degree for every members of the universe set. Keywords: fuzzy; sets
Generalized Different Types of Mappings in Fuzzy Bitopological Spaces by Ahmed Alharbi, Ahlam; Kilicman, Adem (2023) - = h. One may notice that M c is fuzzy σ2 − closed of Y and t−1(M c) is fuzzy (1, 2) Suppose t : (X, δ1, δ2) → (Y, σ1, σ2) is fuzzy δj − ψ − conts. Keywords: fuzzy; j)−; mapping; − cld; − conts
On Generalized Compactness in Fuzzy Bitopological Spaces by Ahmed Alharbi, Ahlam; Kilicman, Adem (2024) - Some scholars have presented many important papers on the development types of fuzzy sets; for example, Singal and Prakash presented a study of a fuzzy pre-open set [20]. It is clear from Definition 10 and the relations between types of fuzzy sets where Remark 2. Keywords: fuzzy; j)−; sets
More Results on Intuitionistic Fuzzy Ideals of BE-algebras by Elnair, Mohamed (2024) - We investigate the fundamental concepts and prop- erties of intuitionistic fuzzy ideals and provide characterizations of an intuitionistic fuzzy ideal in BE-algebras. Our study focuses on examining the fundamental concepts and properties of these ideals and provides characterizations of intuitionistic fuzzy ideals in BE-algebras. Keywords: algebras; fuzzy; ∗m1; ∗m2
Fuzzy SSPO-separation Axioms and Fuzzy α-SSPO Compactness by Makolli, Shkumbin; Krsteska, Biljana (2024) - Similarly, we will define the concept of α-SSPO shading and α∗-SSPO shading that are collections of fuzzy sets that constitute only from fuzzy strong semi pre-open sets. Preliminaries The concept of fuzzy set was initially formulated by Zadeh in [33]. Keywords: compact; fuzzy; pre; set; sets; space; sspo
A Linear Interactive Solution Concept for Fuzzy Multiobjective Games by Cevikel, Adem C.; Ahlatcioglu, Mehmet (2009) - In this paper, we deal with multiobjective two-person zero-sum games with fuzzy payoffs and fuzzy goals. The aim of the paper is to explain new concepts of solutions for multiobjective two-person zero-sum games with fuzzy payoffs and fuzzy goals. Keywords: attainment; degree; fuzzy; goal; player
Bipolar Fuzzy Commutative Ideals in BCK-algebras by Almuhaimeed, Areej; Alshehri, Halimah (2024) - ≥ ϱ+(a ∗ g) ϱ−(a ∗ (g ∗ (g ∗ a))) ≤ ϱ−(a ∗ g) (3) Proof. Applying (1), ϱ+(a ∗ (g ∗ (g ∗ a))) ≥ min {ϱ+((a ∗ g) ∗ w), ϱ+(w)}, ϱ−(a ∗ (g ∗ (g ∗ a))) Keywords: fuzzy; ∗ g; ∗ w
Some Results On Mathai-Haubold Fuzzy Entropy by Joshi, Vaishali Manish; Dar, Javid (2024) - In recent years, many researchers [3],[4],[7],[11],[1],[8] etc. have studied and introduced several generalizations of fuzzy entropy measures. Hence all the four properties of fuzzy entropy measure are satisfied by Mα(B). Keywords: 2−α; entropy; fuzzy; set; ηb(xi
On Fuzzy Soft α-open Sets, α-continuity, andα-compactness: Some Novel Results by Alqurashi, Wafa ; Taha, Islam (2024) - The concept of fuzzy soft sets was defined by Maji et al. A new approach to studying separation and regularity axioms via fuzzy soft sets was introduced by the author of [29, 31] based on the paper by Aygünoǧlu et al. Keywords: fuzzy
On Intuitionistic Fuzzy Implicative Hyper GR-ideals by Macodi, Amila; Dorig, Archie G. (2024) - are fuzzy implicative ideals of H. Consequently by Theorem 1, I = (µ A(I) )t1 is an implicative hyper GR-ideal of H. References [1] K Atanassov. A = (x⊛ z)⊛ (y ⊛ x) y = 0 y = 1 y = 2 y = 0 y = 1 y = 2 0 0 {0,1} {0,1} {1} {0,2} {0,1} {0,1} {0,1} 0 1 {0,1} {0,1} {1} {0,2} {0,1} {0,1} {0,1} 0 2 {0,1} {0,1} {1} {0,2} {0,1} {0,1} {0,1} 1 0 {1} {0,1} {0,1} {0,2} {0,1} {0,1} {0,1} 1 1 {0,1} {0,1} {0,1} {0,2} {0,1} {0,1} {0,1} 1 2 {0,1} {0,1} {0,1} {0,2} {0,1} {0,1} {0,1} 2 0 {0,2} {0,1} {0,1} H H H H 2 1 {0,2} {0,1} {0,1} H H H H 2 2 H {0,1} {0,1} H H H H Table 2: IFGR2 A. Macodi, A. Dorig / Eur. Keywords: 0,1; fuzzy; � �
On Lie Homomorphisms of Complex IntuitionisticFuzzy Lie Algebras by Shaqaqha, Shadi; Al-Deiakeh, Mounther Y. (2024) - This result, combined with the insights from Theorem 2, allows us to expand this understanding into the realm of complex intuitionistic fuzzy Lie algebras. 2020 Mathematics Subject Classifications: 17B99, 08A72, 03E72 Key Words and Phrases: Lie ideal, Lie algebra homomorphism, fuzzy set, fuzzy Lie subalgebra, intuitionistic fuzzy set, intuitionistic fuzzy Lie subalgebra, homogeneous complex intuitionistic fuzzy Lie subalgebra, complex intuitionistic fuzzy Lie ideal 1. Keywords: algebras; fuzzy; lie
Quadri-Polar Fuzzy Fantastic Ideals in BCI-Algebras: A TOPSIS Framework and Application by Balamurugan, M. ; Hakami, Khalil H.; Ansari, Moin A.; Al-Masarwah, Anas ; Loganathan, K. (2024) - = { ρ̃ ∈ (0, 1]q, if ς̇ ∈ ℵ̃ 0̃, if ς̇ /∈ ℵ̃ Let ς̇ , ϱ̇ ∈ ℵ̃. To verify that ð̃ is a qP-FFI of ℵ̃. Case 1: If (ς̇ ≬ ϱ̇) ≬ κ̇ ∈ ð̃ and κ̇ ∈ ð̃, then (ς̇ ≬ (ϱ̇ ≬ (ϱ̇ ≬ ς̇))) = ρ̃ ∧ ρ̃ = ρ̃. Case 2: If (ς̇ ≬ ϱ̇) ≬ κ̇ ̸∈ ð̃ and κ̇ ̸∈ ð̃, then (ς̇ ≬ (ϱ̇ ≬ (ϱ̇ ≬ ς̇))) Keywords: 2τ̃; fuzzy; ð̃(ς̇ ≬; ϱ̇ ≬; ∨qτ̃; ≬ κ̇; ≬ κ̇)ρ̃; ≬ ς̇
Pythagorean Fuzzy Soft Somewhat Continuous Functions by Azzam, A.A.; Aldawood, Mohamed; Abu-Gdairi, Radwan (2024) - In this work, we presented the idea of PyFSsw open sets as a new extension of PyFS open sets. Math, 17 (4) (2024), 4147-4163 4155 Figure 1: The relationships between some generalizations of PyFS open sets. Keywords: fuzzy; gη̃; open; pyfs; pyfssw; set; sets
$\varepsilon$-Lukasiewicz fuzzy UP (BCC)-ideals: A new frontier in UP (BCC)-algebras by Iampan, Aiyared; Subasini, Ramasamy ; Rajesh, Neelamegarajan (2024) - [9] A nonempty subset S of X is called (1) a BCC-subalgebra of X if it satisfies the following property: (∀x, y ∈ S)(x ◦ y ∈ S) (2.19) (2) a BCC-ideal of X if it satisfies the following properties: 0 ∈ S (2.20) (∀x, y, z ∈ X)(x ◦ Lukasiewicz fuzzy sets using the Lukasiewicz t-norm derived from a given fuzzy set. Keywords: fuzzy; y ◦; ◦ z
A Novel Bipolar Valued Fuzzy Group based on Dib's approach by Al-Zu’bi, Fadi; Ahmad, Abdul Ghaffur; Alkouri, Abd Ulazeez; Darus, Maslina (2024) - 2020 Mathematics Subject Classifications: 08A72, 06D72 Key Words and Phrases: Fuzzy space, bipolar valued fuzzy space, fuzzy binary operation, bipolar valued fuzzy binary operation, fuzzy function, bipolar valued fuzzy function, fuzzy group, and bipolar valued fuzzy group subgroup ∗Corresponding author. In 2000, Lee [23, 24] created the concept of bipolar valued fuzzy sets. Keywords: bipolar; bvf; fuzzy; group; groupoid; set; space
Translation of a Bipolar Fuzzy Set in Hilbert Algebras by Iampan, Aiyared; Rajesh, N. ; Princivishvamalar, J. ; Arivazhagi, C. (2024) - Bipolar fuzzy Hilbert algebras. These findings contribute significantly to the REFERENCES 4069 theoretical framework supporting bipolar fuzzy systems, which hold promise for handling nuanced and uncertain information across diverse applications. Keywords: fuzzy; hilbert
Some Algebraic structures of Complex Fermatean Fuzzy Subgroups by AbuHijleh, Eman ; Alkouri, Abd Ulazeez (2025) - Complex fuzzy groups based on rosenfeld’s approach. al. defined complex fuzzy set (CFS) on a crisp set in 2002 Keywords: cffsg; fermatean; fuzzy; group; set; sets; subgroup; ∗ y
Some New Types of Fuzzy Closed Sets, SeparationAxioms, and Compactness via Double Fuzzy Topologies by Alsharari, Fahad ; Taha, Osama ; Taha, Islam (2024) - I◦, and s ∈ I1, then we have (i) ν is called an (r, s)-fsc ⟨resp., (r, s)-fpc and (r, s)-frc⟩ set if ν ≥ Iη,η∗(Cη,η∗ (ν, r, s), r, s) ⟨resp., ν ≥ Math, 17 (4) (2024), 4093-4111 4097 Definition 6. Let (V, η, η∗) be a dfts, ν, ρ ∈ IV , r ∈ I◦, and s ∈ I1, then we have: (i) ρ is called an (r, s)-strongly generalized fuzzy semi-closed ⟨briefly, (r, s)− g⊖fsc⟩ if SCη,η∗(ρ, r, s) ≤ ν whenever ρ ≤ ν and ν is (r, s)− gfo set, (ii) ρ is called an (r, s)-strongly∗ generalized fuzzy semi-closed ⟨briefly, (r, s)− g⊛fsc⟩ if SCη,η∗(ρ, r, s) ≤ ν whenever ρ ≤ ν and ν is (r, s)− gfso set. Keywords: fuzzy; set
Fuzzy $(m, n)$-Ideals and $n$-Interior Ideals in Ordered Semigroups by Khramrot, Pannawit; Iampan, Aiyared; Gaketem, Thiti (2025) - In 2020 Kehayopulu and Tsingelis [5] extended the concept of fuzzy semigroups to the fuzzy ordered semigroups and studied some properties of fuzzy left (right) ideals and fuzzy filters in ordered semigroups. Fuzzy semigroup. Keywords: fuzzy
Graphical Representation of Zadeh's Max-Min Composition Operator for Two 3-Dimensional Quadratic Fuzzy Numbers by Yun, Yongsik ; Lee, Bongju (2025) - = { fα 1 (t)− gα1 (t+ π), if 0 ≤ t ≤ π fα 1 (t)− gα1 (t− π), if π ≤ t ≤ 2π and yα(t) = { fα 2 (t)− gα2 (t+ π), if 0 ≤ t ≤ π fα 2 (t)− gα2 (t− π), if π ≤ t ≤ 2π (3) parametric multiplication A(·)pB: (A(·)pB)α = {(fα 1 (t) · gα1 (t), fα 2 (t) · gα2 (t)) Keywords: fuzzy
Intuitionistic Fuzzy Structures on Sheffer Stroke UP-algebras by Rajesh, Neelamegarajan ; Oner, Tahsin ; Iampan, Aiyared; Senturk, Ibrahim (2025) - Their approach offers valuable insights into how dual prop- erties (such as anti-fuzziness) can coexist with standard fuzzy frameworks, laying a concep- tual groundwork for integrating intuitionistic fuzzy sets into Sheffer stroke UP-algebras. Intuitionistic fuzzy sets (IFSs), introduced by Atanassov Keywords: fuzzy; sup
Determining Electrical Vehicle Charging Stations using Dominance in Neutrosophic Fuzzy Directed Graphs by Alqahtani, Mohammed Aeyed M (2025) - The concept of dominations in fuzzy graphs, fuzzy directed graphs, intuitionistic fuzzy graphs, neutrosophic fuzzy graphs, and picture fuzzy graphs is well- documented in the literature. Our study fills two important gaps in the literature: it extends the concept of domination from fuzzy directed graphs to neutrosophic fuzzy directed graphs, and it provides a detailed characterization of dominations within this advanced framework. Keywords: appl; arc; domination; fuzzy; graphs; neutrosophic
On r-fuzzy Soft δ-open Sets with Applications in Fuzzy Soft Topological Spaces by Alshammari, Ibtesam ; Taha, Osama; El-Bably, Mostafa; Taha, Islam (2025) - [23] defined the notion of fuzzy soft sets which combines soft sets [25] and fuzzy sets The notion of fuzzy soft topology was defined and some of its properties such as fuzzy soft continuity, interior fuzzy soft set, closure fuzzy soft set, and fuzzy soft subspace topology were obtained in [15, 20] based on fuzzy topologies in Šostaks sense [41]. Keywords: fuzzy
Pythagorean Fuzzy HX-subgroups and Their Applications by Almuhaimeed, Areej (2025) - This study aims to establish the groundwork for a novel theory of pythagorean fuzzy HX-subgroup as it is the extension of fuzzy HX groups and intuitionistic fuzzy HX- subgroup. This study aims to establish the groundwork for a novel theory of pythagorean fuzzy HX-subgroups as it is the extension of fuzzy HX groups and intuitionis- tic fuzzy HX-subgroup. Keywords: fuzzy
An Investigation of q-Rung Orthopair Fuzzy Subgroups and Fundamental Isomorphism Theorems by Razzaque, Asima (2025) - If ( µQ(ϵλϵ −1) )q ≥ (µQ(λ)) q and ( νQ(ϵλϵ −1) )q ≤ (νQ(λ)) q for all λ, ϵ ∈ V , then Q is a q-ROFNS of V . Then q-rung orthopair fuzzy left coset (q-ROFLC) of Q associated to λ is denoted by λQ such that λQ = {(ϵ, µλQ(ϵ), νλQ(ϵ)) : ϵ ∈ V }, where (µλQ(ϵ)) q = (µQ(λ −1ϵ))q and (νλQ(ϵ)) q = (νQ(λ −1ϵ))q. Keywords: fuzzy; rofsg
Almost (m, n)-quasi-ideals and Fuzzy almost (m, n)-quasi-ideals in Ordered Semigroups by Khramrot, Pannawit; Chaisuwan, Paramaphon ; Keawton, Panara; Wangsamphao, Chadarat; Gaketem, Thiti (2025) - Conversely, suppose that χB is a minimal fuzzy almost (m,n)-quasi-ideal of T. Then χB is a fuzzy almost (m,n)-quasi-ideal of T. Thus by Theorem 6, B is an almost (m,n)-quasi-ideal of T. Let R be an almost (m,n)-quasi-ideal of T such that R ⊆ B. Then χR is a fuzzy almost (m,n)-quasi-ideal of T such that χR ≤ χB. Hence, R = supp(χR) = supp(χB) It is clearly, every fuzzy strongly prime almost (m,n)-quasi-ideal of a ternary semigroup is a fuzzy prime almost (m,n)-quasi-ideal, and every fuzzy prime almost (m,n)-quasi-ideal of a ternary semigroup is a fuzzy semiprime almost (m,n)-quasi-ideal. Keywords: fuzzy; ideal; n)-quasi
On Weakly Regular Semigroups Characterized in Terms of Cubic Bipolar Fuzzy Ideals by Khramrot, Pannawit; Deetae, Natthinee ; Gaketem, Thiti (2025) - The main thing this study adds is a way to describe weakly regular semigroups using the features of cubic bipolar fuzzy ideals. 2020 Mathematics Subject Classifications: 03E72, 18B40 Key Words and Phrases: Cubic bipolar fuzzy ideal, weakly regular semigroup 1. Keywords: cbf; fuzzy; ideal
Novel Categories of Spaces in the Frame of Generalized Fuzzy Topologies via Fuzzy $g\mu$-closed sets by Saleh, Salem Ali Mohammed ; Birkea, Fathea M.; AL-shami, Tareq; Arar, Murad; Omran, M. (2025) - uα ∈ H if α ≤ H(u). (iii) Fµ-T2 iff for any uα, vβ ∈ FP (U) with uαq̃vβ, there are G,H ∈ µ such that uα ∈ G, vβ ∈ H and Gq̃H. (iv) Fµ-regular (or Fµ-R2) iff for any uα ∈ FP (U) and any H ∈ FµC(U) with uαq̃H, there are F,G ∈ µ such that uα ∈ F,H ⊆ G and F q̃G. (v) Fµ-normal (or Fµ-R3) iff for any Fµ-closed sets F1, F2 with F1q̃F2, there are H,G ∈ µ such that F1 ⊆ H,F2 ⊆ G and Hq̃G. (vi) Fµ-T3 (resp. Keywords: fuzzy; set; sets; spaces
Einstein Aggregation Operators with Cubic Fermatean Fuzzy Sets by Fahmi, Aliya; Khan, A.; Abdeljawad, T.; S. hassan, M. A. ; Almutairid, D.K. (2025) - Intuitionistic fuzzy aggregation operators. Several Fermatean fuzzy aggregation operators were proposed by Aydemir et al. Keywords: 3)l; 3)l n∏; aggregation; charging; criteria; decision; et al; fahmi; fermatean; fuzzy; j=1 lj; k+1∏ j=1; making; n∏ j=1; operators; 
Structural Analysis of Intuitionistic Fuzzy Implicative WSBG-Ideals by Oner, Tahsin ; Iampan, Aiyared; Rajesh, Neelamegarajan ; Senturk, Ibrahim (2025) - An intuitionistic fuzzy set L = (L,α, β) of a WSBG-algebra L = ⟨L; |, 0⟩ is referred to as an intuitionistic fuzzy implicative WSBG-ideal of L if the following conditions hold: (∀ζ, η, θ ∈ L) An intuitionistic fuzzy set L = (L,α, β) of a WSBG-algebra L = ⟨L; |, 0⟩ is called an intuitionistic fuzzy sub-implicative WSBG-ideal of L if it satisfies the following conditions: for all ζ, η, θ ∈ L, α(0) ≥ α(ζ) and β(0) ≤ β(ζ), (1) α((η|(η|(ζ|ζ)))|(η|(η|(ζ|ζ)))) Keywords: fuzzy; ideal; wsbg
Fuzzy Hom-Groups: A New Perspective on Algebraic Generalization by Shaqaqha, Shadi (2025) - By estab- lishing the connection between fuzzy Hom-subgroups of G and classical Hom-subgroups of G, we can better understand how fuzzy membership functions relate to subgroup proper- ties within the framework of Hom-groups, supporting further analysis on fuzzy structures in Hom-algebraic systems. Math, 18 (2) (2025), 5915 15 of 16 • Extending fuzzy Hom-groups to other algebraic structures, such as fuzzy Hom-Lie algebras and fuzzy Hom-rings. Keywords: fuzzy; hom; subgroups; u(µ
An Innovative Analytical Result of Two-Dimensional Heat Equation Using Joint Mechanism of Natural Transform and Adomian Decomposition Method by Muhammad Usman; Khan, Hidayat Ullah; Muhammad Sarwar; Nahid Fatima ; Kamaleldin Abodayeh (2025) - Due to the fact that there are so many real-world issues in computer science, artificial intelligence, physics, and industrial engineering, fuzzy fractional integral equations have a lot more applications. Series type solution of fuzzy fractional order swift–hohenberg equa- tion by fuzzy hybrid sumudu transform. Keywords: fuzzy; φ̆(x
On Common Fixed Point Theorems for Generalized Contractions Involving Rational Expressions and Auxiliary Functions by Thakur, Sahil ; Mani, Naveen ; Shukla, Rahul (2025) - [2] was the first to introduced the notion of fuzzy metric space. [3] with the aim of incorporating Hausdorff topology into fuzzy metric spaces. Keywords: fuzzy; metric; t λ
Domination in Rough $m$-Polar Fuzzy Digraphs Based on Trade Networking by Fahmi, Aliya; Khan, Aziz; Gull, Kinza; Mukheimer, Aiman; Abdeliawad, Aliya Thabet; Hashmi, Arshia ; Thinakaran, Rajermani (2025) - By fusing the advantages of directed graphs, m-polar fuzzy sets, and rough sets, rough m-polar fuzzy digraphs become a more sophisticated model that makes it possible to depict uncertain and multifaceted systems more flexibly and realistically. By examining domination in rough m-polar fuzzy digraphs—a hybrid model that combines directed graphs, m-polar fuzzy logic, and rough set theory—this work presents a fresh expansion of this idea. Keywords: digraphs; domination; fuzzy; min; pi(rv1; pig; polar; set; sets
Interval Valued Spherical Fuzzy Matrix in Decision Making by Padder, Riyaz Ahmad; Alqurashi, Taghreed; Rather, Yasir; Malge, Shilpa (2025) - 2020 Mathematics Subject Classifications: 03E72, 15B15, 90B50 Key Words and Phrases: Interval valued spherical fuzzy sets, Interval valued spherical fuzzy matrix, Least eigenvalue, Greatest eigenvalue Abbreviations IVSFS Interval valued spherical fuzzy set IVSFSs Interval valued spherical fuzzy sets IVSFM Interval valued spherical fuzzy matrix IVSFMs Interval valued spherical fuzzy matrices ∗Corresponding author. We obtain interval valued spherical fuzzy sets from these matrices on a given uni- verse. Keywords: aijυu; fuzzy; interval; sets; xij; zij
A Study on Essential Fuzzy Ideals of Semirings by Chinram, Ronnason; Hangsawat, Saranya (2025) - In this paper, we define essential fuzzy ideals of semirings and investigate some prop- erties of them. We give some properties of essential ideals and essential fuzzy ideals. Keywords: fuzzy; ideal
Triangular Intuitionistic Fuzzy Frank Aggregation for Efficient Renewable Energy Project Selection by Fahmi, Aliya; Hashmi, Arshia ; Khan, Aziz; Mukheimer, A.; Abdeljawad , Thabet ; Thinakaran, Rajermani (2025) - Intuitionistic fuzzy aggregation operators. Optimizing renewable energy project selection presents a complex challenge that demands intelligent decision-making under conditions of uncertainty. Keywords: + n∏; aggregation; decision; energy; fahmi; fuzzy; j=1; log 1; making; n∏ j=1; operators; β 1−gj; β−1)λ−1; − log; −1)λj; 1 +; 
Almost n-ary Subsemigroups and Fuzzy Almost n-ary Subsemigroups of n-ary Semigroups by Chinram, Ronnason; Singavananda, Pattarawan (2025) - Let S be a semiprime almost n-ary subsemigroup of A. By Theorem 3, χS is a fuzzy almost n-ary subsemigroup of A. Let a ∈ A. Fuzzy semigroups. Keywords: ary; ary subsemigroup; fuzzy; subsemigroup
Spherical Picture Fuzzy Sets with Application to Multicriteria Decision-Making by Ahmad, Sadique; Roome, Badshah-e-; Begum, Anisa; Ahmad, Naveed (2025) - A new distance measure of spherical picture fuzzy sets is illustrated, and it is shown that it satisfies conditions of the distance measure. 2020 Mathematics Subject Classifications: 94D05,03B52, 03E72, 28E10 Key Words and Phrases: Spherical picture fuzzy set, Hesitancy degree, Multi-criteria decision making ∗Corresponding author. Keywords: aav; criteria; decision; degree; distance; fuzzy; picture; set; sets; ∆s1s2
Planarity of Intuitionistic Pythagorean Fuzzy Graphs and its Application in Decision Making by Obbu , Ramesh; Nainaru, Tarakaramu; G. YuvaRoopa Lakshmi; S, Sharief Basha; Sarvar Iskandarov; Akbar Toyirov; Sardor. Sabirov; Yuldoshev Jushkinbek Erkaboy ugli; K. K. Prashanth (2025) - 2020 Mathematics Subject Classifications: 05C10, 03E72, 68T37 Key Words and Phrases: Intuitionistic Pythagorean fuzzy graph, Crossing point, Strong Pla- narity and Weak Planarity ∗Corresponding author. The precise structuring of a street or communication network is made possible through the concepts of intuitionistic Pythagorean fuzzy graphs (IPFGs), Pythagorean fuzzy planar graphs (PFPGs), and Pythagorean fuzzy dual graphs (PFDGs), which are discussed in this study. Keywords: crossing; fuzzy; graphs; membership; planarity; pythagorean
A Generalization of Similarity Measure in Collection of Intuitionistic Fuzzy Sets by Yunianti, Dwi Nur; Noor Hidayat; Raden Sulaiman; Abdul Rouf Alghofari (2025) - A collection of intuitionistic fuzzy sets is a new approach to intuitionistic fuzzy set theory. In collections of intuitionistic fuzzy sets, a similarity measure can determine the degree of similarity based on the information carried by the collections. Keywords: aj)−; fuzzy; measure; sets
Completeness and Compactness on Hesitant Fuzzy Normed Linear Spaces by Kavitha Krishnamoorthy; Muralikrishna, Prakasam (2025) - Conclusion We extended the foundational work on fuzzy normed linear space, initially proposed by Samanta et al., to the domain of hesitant fuzzy normed linear space and also examine the properties of completeness and compactness on hesitant fuzzy normed linear space, also address the same properties on intuitionistic hesitant fuzzy normed linear space in finite dimension using definitions, lemmas, and theorems. Consider (V,H, ∗) to become hesitant fuzzy normed space, along with W exists as a subset of V. A sequence {wn} within W converges towards y,if and only if y ∈ w. Definition 10. Keywords: fuzzy; linear; normed
A Pythagorean Fuzzy Digital Fine Space Approach for Selecting Menstrual Hygiene Products in Rural Areas by N. Preethi; G.K. Revathi (2025) - 2020 Mathematics Subject Classifications: 54A40, 03E72 Key Words and Phrases: Pythagorean fuzzy digital fine topological space, Pythagorean fuzzy digital b≈f -Baire space, Pythagorean fuzzy digital b≈f D-Baire space Pythagorean fuzzy digital b≈f - Hausdorff space, Pythagorean fuzzy digital b≈f -door spaces 1. Proposed study to identify the best menstrual hygiene product for Rural Women using Pythagorean fuzzy digital fine topological space In order to make this process, consider three different menstrual hygiene products as cloth pads, menstrual cups and sanitary pads say H = {H1,H2,H3} and the six factors C = {C1,C2,C3,C4,C5,C6}. Keywords: definition; digital; fuzzy; pfdb≈f; pythagorean; set; space; topology
Decision-Making under Uncertainty with Bipolar Complex n,m-Rung Orthopair Fuzzy Sets: A Water Crisis Application by Ibrahim, Hariwan Z.; Dawood, Suzan N. (2025) - = (Y ⊗ Y1)⊗ Y2. (v) Y ⊕ (Y1 ∪ Y2) = (Y ⊕ Y1) ∪ (Y ⊕ Y2). = (Y ⊕ Y1) ∩ (Y ⊕ Y2). (vii) Keywords: + y2; bcn; b− y2; c+ y1; fuzzy; ib+ y; id+ y; n m; y |m; y1 |m; y2 |m; y2 |n; |c− y; |d− y1; |d− y2; − y; − y1; − yi; − |d−; − ≤; ≤ −
Bipolar-Valued Fuzzy Subgroups, Normal Subgroups, and Homomorphisms on Dib’s Fuzzy Space by Al-Zu’bi, Fadi; Ahmad, Abd Ghafur ; Alkouri, Abd Ulazeez ; Darus , Maslina ; Damrah, Sadeq (2025) - Also, the bipolar valued fuzzy subgroups are induced by bipolar valued fuzzy subsets and then a relationship between bipolar valued fuzzy subgroups and classical fuzzy subgroups in terms of induction is demonstrated. Theorem 4. (Sl(B), F ), (Su(B), F ) and (S◦(B), F ) are bipolar valued fuzzy subgroups of ((G, [−1, 0], [0, 1]), F ) iff : (1) xFy ∈ B◦, ∀x, y ∈ B◦, (6) (2) f−xy(B −(x), B−(y)) Keywords: bipolar; bvf; fuzzy; group; subgroup

Open

On Ï‰b-open sets and b-Lindelof spaces by Noiri, Takashi; Al-omari, Ahmad Abdullah; Noorani, Mohd. Salmi Md. (2008) - (1) Assume A is ω-open then, for each x ∈ A, there is an open set containing x such that Ux − A is countable set. [4] introduced a new class of generalized open sets in a topological space, the so-called b-open sets. Keywords: open; set
Beta-Closed Spaces and (Beta-Theta) Subclosed graphs by Basu, Chanchal Kumar; Ghosh, Manob Kumar (2008) - if for each V ∈ βO(X , x), there is an F ∈ F such that F ⊂ β cl(V ). Since F → x then F ⊂ W for some F ∈ F . Keywords: open
On Semi-open Sets with Respect to an Ideal by Michael, Friday Ifeanyi (2013) - We introduce a notion of semi-open sets in terms of ideals, which generalizes the usual notion of semi-open sets. 2010 Mathematics Subject Classifications: 54C10 Key Words and Phrases: Semi-open sets, Semi-closed sets, Generalized closed sets, Ideals 1. Keywords: -semi; open
Weak Forms of Ï‰-open Sets and Decompositions of Continuity by Noiri, Takashi; Al-omari, Ahmad Abdullah; Noorani, salmi (2009) - [10] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. The complement of an ω-closed set is said to be ω-open. Keywords: open; set
New Type of Strongly Continuous Functions in Topological Spaces via Î´-Î²-Open Sets by Farhan, Alaa Mahmood; Yang, Xiao Song (2015) - If g is strongly θ − δ − β -continuous, then f is strongly θ − δ − β -continuous. First, we show that f is strongly θ − δ − β -continuous. Keywords: open; set
Some Forms of C-continuity for Multifunctions by Noiri, Takashi; Popa, Valeriu (2007) - [25] J. H. Park, B. Y. Lee and M. J. Son, On δ-semi-open sets in topological spaces, J. Indian Acad. A ⊂ F, X − F ∈ mX}, (2) mX -Int(A) = ∪{U : U ⊂ A,U ∈ mX}. Keywords: open; set
New Generalized Classes of tau-omega by Rajasekaran, I; Ravi, O .; Kanna, S Satheesh; Paranjothi, M (2016) - Semi-open sets and semi-continuity in topological spaces, American Mathemat- ical Monthly, 70, 36 - 41. 1963. Then, we have U ⊂ H ⊂ cl(U). Keywords: open
Contra deltagb-Continuous Functions in Topological Spaces by Benchalli, S.S.; Patil, P G; Toranagatti, J.B.; Vighneshi, S.R. (2017) - Introduction and Preliminaries In 1996, Dontchev[6] introduced contra continuous functions. If f:X→Y is contra δgb-continuous and Y is Urysohn then G(f) is contra δgb-closed in the product space X×Y. Proof: Let (x,y)∈(X×Y)-G(f), then y 6=f(x) and there exist open sets A and B such that f(x)∈A, y∈B and cl(A)∩cl(B)=φ. Keywords: closed; contra; open; δgb
On omega-Connectedness and omega-Continuity in the Product Space by Labendia, Mhelmar Avila; C. Sasam, Jan Alejandro (2018) - (i)⇔ (iii): (i) implies (iii) holds since (subbasic) basic open sets are open sets. After this noteworthy work of Levine several mathematicians became attracted in presenting other topological concepts which can substitute the concepts of open sets. Keywords: open
Other Kinds of Soft Î² maps via Soft Topological Ordered Spaces by AL-shami, Tareq; El-Shafei, Mohammed; Asaad, Baravan (2019) - [44] initiated the concept of soft topological spaces and gave its fundamental notions such as soft open and soft closed sets, soft neighborhoods, soft interior and soft closure points. They examined which results related to β-open sets and βTi-spaces from the topological spaces remain valid in the context of soft topological spaces. Keywords: mapping; open; resp; soft
Beta1-paracompactness with respect to an Ideal by Cahis, Abdo Mohammed (2019) - = {Vλ \ Iλ : λ ∈ Λ, Vλ ∈ τ, Iλ ∈ I} of U such that X \∪{Vλ \ Then f(X\∪{Vλ : λ ∈ Λ}) ∈ f(I). Keywords: open; paracompact; ∈ λ
Some Characterizations of Î²-paracompactness in Ideal Topological Space by Dalan Yildirim, Esra; Bedre Ozbakir, Oya; Caksu Guler, Aysegul (2019) - The concept of β-open sets is equal to that of semi-preopen sets in [7]. A space (X, τ) is said to be β-compact [2] if every cover of X by β-open sets has a finite subcover. Keywords: open
On B-Open Sets by Alabdulsada, Layth Muhsin Habeeb (2019) - The first notion due to Levine [12] in 1963 was semi-open sets, while in 1965 Nj̊astad Semi-open sets and semi-continuity in topological spaces. Keywords: contra; open
On Î²-Open Sets and Ideals in Topological Spaces by Catalan, Glaisa T.; Padua, Roberto N.; Baldado, Michael Jr. Patula (2019) - Tahiliani [23] introduced an operation on a family of β-open sets; and using the operation, the concept β-γ-open sets was defined and investigated. 2. β-Open Sets with Respect to an Ideal In this section, we investigated the concept β-open in a direction parallel to the inves- tigation of semi-open sets in [32]. Keywords: open; set; space
Operation on Fine Topology by Powar, P. L.; Asaad, Baravan; Rajak, K.; Kushwaha, R. (2019) - Later, Ogata [12] defined and studied the concept of γ-open sets, and applied it to inves- tigate operation-functions and operation-separation axioms. Suppose that the empty set φ is also fγ-open set for any operation γ : τf → P (X). Keywords: open; set
On Generalized Î²-Open Sets in Ideal Bitopological Space by Bukhatwa, Ibtissam; Demiralp, Sibel (2020) - Let W ∈ ξi-open set in Z. Since g is pairwise (δ, ξ)i-continuous, then g−1(W ) ∈ δi-open set in Y . [17] in 1963, introduced the notion of semi-open sets in bitopological spaces. Keywords: open; set; γij
Limit Points and Separation Axioms with Respect to Supra Semi-open Sets by AL-shami, Tareq M.; Abo-Tabl, E. A.; Assad, Baravan; Arahet, Mohamed (2020) - EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 13, No. 3, 2020, 427-443 ISSN 1307-5543 – www.ejpam.com Published by New York Business Global Limit points and separation axioms with respect to supra semi-open sets T. M. Al-shami1,∗, E. A. Abo-Tabl2,3, B. A. Asaad4,5, M. A. Arahet6 1 Department of Mathematics, Sana’a University, Sana’a, Yemen 2 Department of Mathematics, College of Arts and Sciences,Methnab, Qassim University, P. O. Box 931, Buridah 51931, Methnab, Saudia Arabia 3 Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt 4 Department of Computer Science, College of Science, Cihan University-Duhok, Kurdistan Region, Iraq 5 Department of Mathematics, Faculty of Science, University of Zakho, Kurdistan Region, Iraq 6 Department of Mathematics, Amran University, Amran, Yemen Abstract. 2020 Mathematics Subject Classifications: 54A05, 54C10, 54D10, 54D15 Key Words and Phrases: Supra semi-open set, supra semi limit point, SsTi-space (i = 0, 1, 2, 3, 4) 1. Keywords: open; semi; set; supra; x,µ
On Ïˆgs-closed Sets in Bitopological Spaces by Tutanes, Lezel Mernilo (2021) - In 2000, the concepts between closed sets and g-closed sets in topological spaces were studied in [10] and a few years later, the same author [11] studied ψ- closed sets in topological spaces. Every τi closed set is (i, j)-ψgs-closed set. Keywords: open; set; sets
Weakly Covering Spaces in Coc-open Sets by AbuShaheen, Fuad A; Alrimawi, Fadi (2022) - coc ⊆ Uα(x), and clearly the family { Wα(x)|α(x) ∈ ∆ } is coc-regular cover of X, so there exists a finite elements x1, x2, ..., xn ∈ X such that X = n⋃ i=1 Wα(xi) coc ⊆ n⋃ i=1 Uα(xi), therefore X is coc-nearly-compact space. Let U = { Uα|α ∈ ∆ } be coc-regular open cover of X, so for each x ∈ X, there exists α(x) ∈ ∆ such that x ∈ Uα(x), but X is coc-almost regular space, so there exist coc-regular open sets Vα(x) and Wα(x) such that x ∈ Vα(x) ⊆ Vα(x) Keywords: coc; open; regular
Nearly Soft Î² - Open Sets via Soft Ditopological Spaces by Abu-Gdairi, Radwan Ahmad; Azzam, Abdelfattah; Noaman, Ibrahim (2022) - 2020 Mathematics Subject Classifications: 54A05, 54A20, 54E55 Key Words and Phrases: Soft set, soft topological space, ditopological space, soft β - open and soft β - closed sets, soft β - continuous, soft β - compact 1. Introduction and Preliminaries In the late twentieth century, Molodtsov[11] introduced the theory of soft set as a generalization of the set theory, which widely used to deal with incomplete, insufficient information for its study and analysis, which similar to the rough set theory. Keywords: open; soft; ũe
Infra Pre-open Sets and Their Applications to Generate New Types of Operators and Maps by Al-shami, Tareq M.; Othman, Hakeem A. (2022) - Herein, we introduce the concepts of infra soft pre-open infra soft pre-closed sets which are respectively generalizations of infra soft open and infra soft closed sets. Then, we apply infra soft pre-open infra soft pre-closed sets to define the operators of infra pre-interior, infra pre-closure, infra pre-limit and infra pre-boundary. Keywords: infra; open; pre; set
A Note on Strongly δθ-I-continuous Functions by Sanabria, José ; Lozada-Yavina, Rafael ; Tormet, José (2022) - y and as (Y, σ) is T2, there exist open sets V and W in Y containing f(x) and y, respectively, such that V ∩W A strongly δθ-I-continuous retraction is a strongly δθ-I-continuous func- tion f : (X, τ, I) → (Y, σ), where Y ⊂ X and f |Y = 1Y the identity function on Y . Keywords: open
Generalized ωe∗-closed Sets by Şaşmaz, Pınar; Özkoç, Murad (2022) - = ωe∗-cl(X \A) \ (X \A) A ∈ gωe∗O(X)⇒ X \A ∈ gωe∗C(X) } ⇒ Theorem 3⇒ X \ X \A ⊆ U ∈ O(X)⇒ (X \ U ∈ C(X))(X \ U ⊆ A) Keywords: open; space
Some Forms of Open Multifunctions in Ideal Topological Spaces by Noiri, Takashi; Popa, Valeriu (2023) - As generalizations of open sets and I-open sets, semi-I-open sets, pre-I-open sets, α-I-open sets, β-I-open sets and b-I-open sets are introduced and used to obtain decompositions of continuity. As generalizations of open sets and I-open sets, the following subsets are introduced and investigated. Keywords: open
Codimension One Foliation and the Prime Spectrum of a Ring by Alharbi, Badr (2024) - [5] if it is (1) sober (i.e., every nonempty irreducible closed subset of Y is the closure of a unique point), (2) quasi-compact, (3) the quasi-compact open subsets of X form a basis and (4) the family of quasi-compact open subsets of X is closed under finite intersections. There is a basis of quasi-compact open subsets of Spec(A). Keywords: compact; open; quasi; space
On the Construction of a Groupoid from an Ample Hausdorff Groupoid with Twisted Steinberg Algebra not Isomorphic to its Non-twisted Steinberg Algebra by Bongcawel, Rizalyn; Cabardo, Lyster Rey; Petalcorin Jr, Gaudencio; Vilela, Jocelyn (2024) - × T = {(χ, z, γ) : χ ∈ Âr(γ), z ∈ T, and γ ∈ G}. (3) The image of i is central in Σ, in the sense that i(r(ϵ), z)ϵ = ϵi(s(ϵ), z) for all ϵ ∈ Σ and z ∈ T . Keywords: â⋊r; groupoid; open
Upper and Lower almost $(\tau_1,\tau_2)$-continuous Multifunctions by Klanarong, Chalongchai ; Sompong, Supannee ; Boonpok, Chawalit (2024) - Semi-open sets, preopen sets, α-open sets, β-open sets and δ-open sets play an important role in the researches of generaliza- tions of continuity in topological spaces. In particular, F−(y) = {x ∈ X | y ∈ F (x)} for each point y ∈ Y . Keywords: open; set; τ1τ2
Upper and Lower Weak $(\tau_1,\tau_2)$-continuity by Thongmoon, Montri ; Sompong, Supannee ; Boonpok, Chawalit (2024) - Weakly continuous multifunctions. Introduction The concept of weakly continuous functions was introduced by Levine Keywords: cl(v; open; σ1σ2; τ1τ2
$c$-$(\tau_1,\tau_2)$-continuity for Multifunctions by Khampakdee, Jeeranunt ; Sompong, Supannee ; Boonpok, Chawalit (2024) - In particular, F−(y) = {x ∈ X | y ∈ F (x)} for each point y ∈ Y . For a multifunction F : (X, τ1, τ2) → (Y, σ1, σ2), the following properties are equivalent: (1) F is upper c-(τ1, τ2)-continuous at x ∈ X; (2) x ∈ τ1τ2-Int(F +(V )) for each σ1σ2-open set V of Y containing F (x) and having σ1σ2-compact complement; (3) x ∈ F−(σ1σ2-Cl(B)) for each subset B of Y having the σ1σ2-compact σ1σ2-closure such that x ∈ τ1τ2-Cl(F −(B)); (4) x ∈ τ1τ2-Int(F +(B)) for each subset B of Y such that Y − σ1σ2-Int(B) is σ1σ2- compact and x ∈ F+(σ1σ2-Int(B)). Keywords: open; σ1σ2; τ1τ2
$\delta(\tau_{1},\tau_{2})$-Continuous Functions by Prachanpol, Chatchadaporn ; Boonpok, Chawalit; Viriyapong, Chokchai (2024) - For a subset A of a bitopological space (X, τ1, τ2), the following properties hold: (1) δ(τ1, τ2)-Int(X −A) = X − δ(τ1, τ2)-Cl(A). (2) δ(τ1, τ2)-Cl(X −A) = X − δ(τ1, τ2)-Int(A). Keywords: open; set; δ(τ1; σ1σ2
Employing a Generalization of Open Sets Defined by Ideals to Initiate Novel Rough Approximation Spaces with a Chemical Application by Hosny, M.; Al-shami, Tareq (2024) - 1 Ask the the expert(s) to give a relation L over X; 2 Choose a λ type; 3 for every y ∈ X do 4 compute Gλ(y) 5 end 6 Construct a topology ϑλ = {V ⊆ X : ∀y ∈ V,Gλ(y) ⊆ V } on X; 7 Initiate C1 = {clλ(V ) : V ∈ ϑλ}; 8 Construct a θ-topology ϑθλ = {V ∈ ϑλ : intθλ(V ) Math, 17 (4) (2024), 3436-3463 3452 (i) V is αλ-exact ⇒ V is Sλ-exact ⇒ V is βλ-exact ⇒ δβλ-exact ⇒ V is L-θβλ-exact. (ii) V is Pλ-exact ⇒ V is βλ-exact ⇒ V is δβλ-exact ⇒ V is L-θβλ-exact. (iii) V is αλ-exact ⇒ V is Sλ-exact ⇒ V is βλ-exact ⇒ V is ∧ βλ -exact ⇒ V is L-θβλ- exact. (iv) V is Pλ-exact ⇒ V is βλ-exact ⇒ V is ∧ βλ -exact ⇒ V is L-θβλ-exact. (v) V is λ-exact ⇒ V is L-θβλ-exact. (vi) V is L-θβλ-rough ⇒ V is δβλ-rough ⇒ V is βλ-rough ⇒ V is Sλ-rough ⇒ V is αλ-rough. (vii) V is L-θβλ-rough ⇒ V is δβλ-rough ⇒ V is βλ-rough ⇒ V is Pλ-rough. (viii) V is L-θβλ-rough ⇒ V is ∧ βλ -rough ⇒ V is βλ-rough ⇒ V is Sλ-rough ⇒ V is αλ-rough. (ix) V is L-θβλ-rough ⇒ V is ∧ βλ -rough ⇒ V is βλ-rough ⇒ V is Pλ-rough. (x) V is L-θβλ-rough ⇒ V is λ-rough. Keywords: open; rough; sets; θβλ; λ(v
$c$-quasi $(\tau_1,\tau_2)$-continuous multifunctions by Pue-on, Prapart ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2024) - For a multifunction F : (X, τ1, τ2) → (Y, σ1, σ2), the following properties are equivalent: (1) F is upper c-quasi (τ1, τ2)-continuous; (2) F+(V ) is (τ1, τ2)s-open in X for every σ1σ2-open set V of Y having σ1σ2-compact complement; (3) F−(K) is (τ1, τ2)s-closed in X for every σ1σ2-compact σ1σ2-closed set K of Y ; (4) τ1τ2-Int(τ1τ2-Cl(F −(B))) A multifunction F : (X, τ1, τ2) → (Y, σ1, σ2) is upper c-quasi (τ1, τ2)- continuous if F−(K) is (τ1, τ2)s-closed in X for every σ1σ2-compact set K of Y . Proof. Keywords: open; σ1σ2; τ1τ2
Characterizations of Faintly $(\tau_1,\tau_2)$-continuous functions by Srisarakham, Napassanan ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2024) - The relationships between faint (τ1, τ2)-continuity and other forms of (τ1, τ2)-continuity are considered. 2020 Mathematics Subject Classifications: 54C08, 54E55 Key Words and Phrases: (τ1, τ2)θ-open set, (τ1, τ2)θ-closed set, faintly (τ1, τ2)-continuous function 1. Keywords: open; τ1τ2
Analysis of Some Structures in Ternary Soft Topological Spaces by Nawaz, Mubashir ; Liu, Yuxin ; Ramaswamy, Seethalakshmi ; Saeed, Maha Mohammed ; Khattak, Arif Mehmood (2025) - The objective of this research is to explore ternary soft sets over three initial universal sets, incorporating a parameter set, also known as the set of decision variables. The behavior and properties of ternary soft sets are analyzed, with examples provided for clarification. Keywords: open; set; sets; space; ternary
Characterizations of Generalized Paracompactness in Ideal Topological Spaces by Boonpok, Chawalit ; Sama-ae, Areeyuth; Raktaow, Palin (2025) - For every closed subset F of X and every x ̸∈ F , there exist disjoint δ-βI-open sets U and V such that x ∈ U and F − V ∈ I. (ii) As F − ∪{Wy : y ∈ F} = F − (∪{Wy : y ∈ F} ∪ {G}) ⊂ X − (∪{Wy : y ∈ F} ∪ {G}), we get that F −∪{Wy : y ∈ F} ∈ I. It follows that V = ∪{Wy : y ∈ F} is a δ-βI-open set in X and F − V ∈ I. Keywords: open
Some Types of Tri-Lindelöfness Spaces by Oudetallah, Jamal ; Alharbi, Rehab; Batiha, Iqbal; Rawashdeh, Salsabiela ; Amourah, Ala (2025) - In the next section, we introduce the fundamental concepts of topological spaces and tri-topological spaces, along with key notions in tri-topological spaces, such as open and closed sets, derived sets, closure sets, interior and exterior sets, and separation axioms. We then discuss the Lindelöf property in tri-topological spaces, analyze its characteristics, and examine its applicability to other spaces. Keywords: open; space; tri
More on Ideal Topological Groups by Alammar , Saud M.; Alshumrani, Mohammed; Özel, Cenap (2025) - Ideal topological groups In this section, we define ideal topological groups and give their basic properties. In this article, we define and study the concept of ideal topological groups. Keywords: group; ideal; open; set; topological
$s$-$(\tau_1,\tau_2)$-continuity for multifunctions by Chiangpradit, Monchaya ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - Moreover, several characterizations and some proper- ties concerning upper s-(τ1, τ2)-continuous multifunctions and lower s-(τ1, τ2)-continuous multi- functions are investigated. 2020 Mathematics Subject Classifications: 54C08, 54C60 Key Words and Phrases: Upper s-(τ1, τ2)-continuous multifunction, lower s-(τ1, τ2)-continuous multifunction 1. This paper deals with the concepts of upper s-(τ1, τ2)-continuous multifunctions and lower s-(τ1, τ2)-continuous multifunctions. Keywords: open; σ1σ2; τ1τ2
Almost Near $(\tau_1,\tau_2)$-continuity for Multifunctions by Chutiman, Nipaporn ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - almost weakly (τ1, τ2)-continuous multifunc- tions, weakly quasi (Λ, sp)-continuous multifunctions, ⋆-continuous multifunctions, β(⋆)- continuous multifunctions, α-⋆-continuous multifunctions, almost α-⋆-continuous multi- functions, almost quasi ⋆-continuous multifunctions, weakly α-⋆-continuous multifunc- tions, sβ(⋆)-continuous multifunctions, weakly sβ(⋆)-continuous multifunctions, θ(⋆)-quasi continuous multifunctions, almost ı⋆-continuous multifunctions, weakly (Λ, sp)-continuous multifunctions, α(Λ, sp)-continuous multifunctions, almost α(Λ, sp)-continuous multifunc- tions, weakly α(Λ, sp)-continuous multifunctions, almost β(Λ, sp)-continuous multifunc- tions, slightly (Λ, sp)-continuous multifunctions, (τ1, τ2)-continuous multifunctions, al- most (τ1, τ2)-continuous multifunctions, weakly (τ1, τ2)-continuous multifunctions, weakly quasi (τ1, τ2)-continuous multifunctions, almost quasi (τ1, τ2)-continuous multifunctions, c- (τ1, τ2)-continuous multifunctions, c-quasi (τ1, τ2)-continuous multifunctions and s-(τ1, τ2)p- continuous multifunctions were established in [5], [28], [66], [3], [7], [17], [24], [6], [21], [20], Preliminaries Throughout the present paper, spaces (X, τ1, τ2) and (Y, σ1, σ2) (or simply X and Y ) always mean bitopological spaces on which no separation axioms are assumed unless explicitly stated. Keywords: open; set; τ1τ2
Almost Nearly Quasi $(\tau_1,\tau_2)$-continuous Multifunctions by Khampakdee, Jeeranunt ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - The complement of an α(τ1, τ2)- open set is said to be α(τ1, τ2)-closed. EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS 2025, Vol. 18, Issue 1, Article Number 5720 ISSN 1307-5543 – ejpam.com Published by New York Business Global Almost Nearly Quasi (τ1, τ2)-continuous Multifunctions Jeeranunt Khampakdee1, Areeyuth Sama-Ae2, Chawalit Boonpok1,∗ 1 Mathematics and Applied Mathematics Research Unit, Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham, 44150, Thailand 2 Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani Campus, Pattani, 94000, Thailand Abstract. Keywords: multifunctions; open
Almost Weakly $(\tau_1,\tau_2)$-continuous Functions by Boonpok, Chawalit; Sompong, Supunnee ; Khampakdee, Jeeranunt (2025) - Furthermore, several characterizations of almost (Λ, p)-continuous functions, strongly θ(Λ, p)-continuous func- tions, almost strongly θ(Λ, p)-continuous functions, θ(Λ, p)-continuous functions, weakly (Λ, b)-continuous functions, θ(⋆)-precontinuous functions, (Λ, p(⋆))-continuous functions, ⋆-continuous functions, θ-I -continuous functions, almost (g,m)-continuous functions, pairwise almost M -continuous functions, (τ1, τ2)-continuous functions, almost (τ1, τ2)- continuous functions and weakly (τ1, τ2)-continuous functions were presented in [33], [34], ∗Corresponding author. Preliminaries Throughout the present paper, spaces (X, τ1, τ2) and (Y, σ1, σ2) (or simply X and Y ) always mean bitopological spaces on which no separation axioms are assumed unless explicitly stated. Keywords: open; σ1σ2; τ1τ2
Quasi $\theta(\tau_1,\tau_2)$-continuous Functions by Srisarakham, Napassanan ; Sompong, Supunnee ; Boonpok, Chawalit (2025) - A function f : (X, τ1, τ2) → (Y, σ1, σ2) is said to be quasi θ(τ1, τ2)- continuous if for each x ∈ X and each σ1σ2-open set V of Y containing f(x), there exists a (τ1, τ2)s-open set U of X containing x such that f((τ1, τ2)-sCl(U)) For a function f : (X, τ1, τ2) → (Y, σ1, σ2), the following properties are equivalent: (1) f is quasi θ(τ1, τ2)-continuous; (2) θ(τ1, τ2)-sCl(f −1(σ1σ2-Int((σ1, σ2)θ-Cl(B)))) ⊆ f−1((σ1, σ2)θ-Cl(B)) for every sub- set B of Y ; (3) θ(τ1, τ2)-sCl(f −1(σ1σ2-Int(σ1σ2-Cl(V )))) Keywords: cl(v; open; σ1σ2
Characterizations of $\delta_1\text{-}{\beta}_{\mathcal{I}}$-paracompactness concerning an ideal by Sama-ae, Areeyuth; Boonpok, Chawalit (2025) - I : U ∈ τ and I ∈ I}. Since (X, τ∗, I) is δ1-βI-paracompact, U has τ∗-locally finite refinement V = {Gλ : λ ∈ Λ2} of open sets in (X, τ∗, I) such that X − ∪{Gλ : λ ∈ Λ2} ∈ I, where Gλ = Vλ − Iλ, Vλ ∈ τ and Keywords: open; paracompact
Some Types of Tri-Locally Compactness Spaces by Amourah, Ala; Oudetallah, Jamal ; Batiha, Iqbal M.; Salah, Jamal ; Alsaadi, Sultan; Sasa, Tala (2025) - Let K1 and K2 be disjoint tri-compact sets. 2020 Mathematics Subject Classifications: 47B38 Key Words and Phrases: Tri-locally compact spaces, Tri-topological spaces, Locally compact- ness, Metacompactness 1. Keywords: open; set; space; tri
$\sigma$-compact Spaces in N$^{th}$-Topological Space by Amourah, Ala; Oudetallah, Jamal ; Batiha, Iqbal ; Salah, Jamal ; Shatnawi, Mutaz (2025) - proof: Let (K, η1, η2, ..., ηn) be nth topological space and K is nth σ-compact space and let K be a locally compact nth σ-compact space, and let K = ⋃∞ n=1M(ni), where each M(ni) is nth compact. Every second-countable compact space is nth σ-compact space. Keywords: compact; nth; open; set; space
A Breakthrough Approach to Quadri-Partitioned Neutrosophic Soft Topological Spaces by Saeed, Maha Mohammed ; Hatamleh, Raed ; AbdEl-latif, Alaa M. ; Al-Husban, Abdallah Al-Husban; Attaalfadeel, Husham M. ; Fujita, Takaaki ; Aldwoah, Khaled A. ; Khattak, Arif Mehmood (2025) - 2020 Mathematics Subject Classifications: 54A05 Key Words and Phrases: Neutrosophic soft set, QPNSS, QPNSTS, QPNS p- New family of neutrosophic soft sets. Keywords: é)c; neutrosophic; open; qpns; quadri; set; sets
Supra Soft Somewhat Open Sets: Characterizations and Continuity by Abd El-latif, Alaa M.; Abu-Gdairi, Radwan ; Azzam , Abd elfattah; Gharib , Fatouh ; Aldwoah , Khaled (2025) - [10] Z. A. Ameen, and M. H. Alqahtani, Some classes of soft functions defined by soft open sets modulo soft sets of the first category, Mathematics, 11 (2023), 4368. Also, for any soft set (G, η), if (G, η) ∈ σ, then (G, η) is called soft open set and its soft complements (Gc̃, η) is called soft closed set. Keywords: open; sets; soft
A Comprehensive Study of Bipolar Vague Soft Expert P-Open Sets in Bipolar Vague Soft Expert Topological Spaces with Applications to Cancer Diagnosis by Al-Husban, Abdallah ; Saeed, Maha Mohammed ; Nordo, Giorgio; Fujita, Takaaki ; Khattak, Arif Mehmood; Hatamleh, Raed; Abubaker, Ahmad A.; Hamja, Jamil J.; Armada, Cris L. (2025) - Building upon these advancements, Alkhazaleh and Salleh [10] integrated fuzzy soft sets with expert sets, resulting in the concept of soft expert sets. Soft expert sets were first proposed by Alkhazaleh and Salleh Keywords: 10−1⟩; bipolar; bvse; definition; expert; e⟩⟩; e⟩⟩ ϵ̃; open; ses; set; sets; τbv; ⟨⟨f̃1; ⟨⟨f̃2
On Contra-$(\tau_1,\tau_2)p$-continuity and Almost Contra-$(\tau_1,\tau_2)p$-continuity for Multifunctions by Viriyapong, Chokchai ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - Furthermore, several characterizations of almost (Λ, p)-continuous functions, strongly θ(Λ, p)-continuous functions, almost strongly θ(Λ, p)-continuous func- tions, θ(Λ, p)-continuous functions, weakly (Λ, b)-continuous functions, θ(⋆)-precontinuous functions, (Λ, p(⋆))-continuous functions, ⋆-continuous functions, θ-I -continuous func- tions, almost (g,m)-continuous functions, pairwise almostM -continuous functions, (τ1, τ2)- continuous functions, almost (τ1, τ2)-continuous functions, weakly (τ1, τ2)-continuous func- tions and slightly (τ1, τ2)s-continuous functions were presented in [5], [6], [7], [8], [9], [10], Math, 18 (2) (2025), 6009 3 of 18 multifunctions, α(Λ, sp)-continuous multifunctions, almost α(Λ, sp)-continuous multifunc- tions, weakly α(Λ, sp)-continuous multifunctions, almost β(Λ, sp)-continuous multifunc- tions, slightly (Λ, sp)-continuous multifunctions, weakly quasi (τ1, τ2)-continuous mul- tifunctions, almost quasi (τ1, τ2)-continuous multifunctions, c-(τ1, τ2)-continuous multi- functions, c-quasi (τ1, τ2)-continuous multifunctions, s-(τ1, τ2)p-continuous multifunctions, slightly α(τ1, τ2)-continuous multifunctions and slightly (τ1, τ2)p-continuous multifunctions were established in [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60], [61], [62], [63] and [64], respectively. Keywords: open; τ2)p
Upper and Lower Almost Contra-$(\tau_1,\tau_2)$-continuity by Khampakdee, Jeeranunt ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - Journal of Advanced Research in Pure Mathematics, 2(1):11–25, 2010. European Journal of Pure and Applied Mathematics, 16(1):29–43, 2023. Keywords: open; τ1τ2
On $R$-$(\tau_1,\tau_2)$-continuous Functions by Srisarakham, Napassanan ; Sompong, Supunnee; Boonpok, Chawalit (2025) - 2020 Mathematics Subject Classifications: 54C08, 54E55 Key Words and Phrases: τ1τ2-open set, R-(τ1, τ2)-continuous function 1. Furthermore, several characterizations and some properties concern- ing R-(τ1, τ2)-continuous functions are established. Keywords: open; τ1τ2
$\theta(\tau_1,\tau_2)$-continuity for Functions by Thongmoon, Montri ; Sompong, Supunnee ; Boonpok, Chawalit (2025) - Introduction Stronger and weaker forms of open sets in topological spaces such as semi-open sets, preopen sets, α-open sets, β-open sets, δ-open sets and θ-open sets play an important role in the research of generalizations of continuity. [36] A bitopological space (X, τ1, τ2) is said to be (τ1, τ2)-regular if for each τ1τ2-closed set F and each x ̸∈ F , there exist disjoint τ1τ2-open sets U and V such that x ∈ U and F ⊆ V . Keywords: cl(v; open; σ1σ2
On Strongly $\theta(\tau_1,\tau_2)$-continuous Functions by Pue-on, Prapart ; Sompong, Supunnee ; Boonpok, Chawalit (2025) - The set of all points x ∈ X at which a function f : (X, τ1, τ2) → (Y, σ1, σ2) is not strongly θ(τ1, τ2)-continuous is identical with the union of the (τ1, τ2)θ-frontier of the inverse images of σ1σ2-open sets containing f(x). 2020 Mathematics Subject Classifications: 54C08; 54E55 Key Words and Phrases: (τ1, τ2)θ-open set, strongly θ(τ1, τ2)-continuous function 1. Keywords: open; set; τ1τ2
Characterizations of Contra-$(\tau_1,\tau_2)$-continuous Functions by Chutiman, Nipaporn ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - 2020 Mathematics Subject Classifications: 54C08, 54E55 Key Words and Phrases: τ1τ2-open set, contra-(τ1, τ2)-continuous function 1. Furthermore, several characterizations and some properties concerning contra-(τ1, τ2)-continuous functions are investigated. Keywords: open; σ1σ2; τ1τ2
Almost Contra-$(\tau_1,\tau_2)p$-continuity for Functions by Pue-on, Prapart ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - In [4], the present authors introduced and investigated a new class of functions called contra-super-continuous functions which lies between classes of RC-continuous func- tions and contra-continuous functions. On the other hand, the present authors introduced and studied the notions of of (τ1, τ2)-continuous functions Keywords: open; τ2)p
On Contra-$(\tau_1,\tau_2)p$-continuous Functions by Chiangpradit, Monchaya ; Sompong, Supunnee ; Boonpok, Chawalit (2025) - On the other hand, the present authors introduced and studied the notions of (τ1, τ2)-continuous functions Preliminaries Throughout the present paper, spaces (X, τ1, τ2) and (Y, σ1, σ2) (or simply X and Y ) always mean bitopological spaces on which no separation axioms are assumed unless explicitly stated. Keywords: open; τ2)p
Strong $\beta$-$\mathcal{I}$-Submaximality and $\beta$-$\mathcal{I}$-Paracompactness in Ideal Topological Spaces by Boonpok, Chawalit ; Raktaow, Palin ; Sama-ae, Areeyuth (2025) - Math, 18 (3) (2025), 6297 5 of 23 (2) If A is closed, then A is strong β-I-closed; (3) sβ IntI(A) is strong β-I-open, and Int(A) ⊆ sβ IntI(A); (4) sβ clI(A) is strong β-I-closed, and sβ clI(A) ⊆ cl(A); (5) A is strong β-I-open if and only if A = sβ IntI(A); (6) A is strong β-I-closed if and only if A = sβ clI(A); and (7) x ∈ sβ clI(A) if and only if U ∩A ̸= ∅ for every strong β-I-open set U containing x. Proof. if and only if A = sβ clI(A). (7): Assume that x ∈ sβ clI(A). Keywords: ideal; open; set
An Exploration of Compactness and Separation Axioms in Generalized Primal Topological Spaces by Shahbaz, Muhammad ; Kamran, Tayyab ; Imtiaz, Mariam ; Ishtiaq, Umar; Akram, Mohammad ; Popa, Ioan-Lucian (2025) - ∈ Gpt-S∗ gO(V). Let Mα ⊆ V. E is Gpt-T1 space if for every explicit point r and s of V, s /∈ Keywords: gpt; open; sets; space; s∗ g
On Nearly α-Compact Topological Spaces by Oudetallah, Jamal ; Almalkawi, Ahmad ; Amourah, Ala; Alsoboh, Abdullah; Al Mashrafi, Khaled ; Sasa, Tala (2025) - The study of α-compact spaces naturally fol- lowed, with various researchers investigating different aspects and generalizations of this concept. [3] on α-compact spaces in digital topology (2021), and the investigations by Chen and Liu Keywords: finite; open; sets; space
Almost Continuity for Multifunctions Defined from an Ideal Topological Space into a Bitopological Space by Viriyapong, Chokchai ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - The union of all τ1τ2-δ-open sets of X contained in A is called the τ1τ2-δ-interior of A and is denoted by τ1τ2-δ-Int(A). Since Y − V is (σ1, σ2)r-closed and by (7), X − F+(V ) Keywords: open; set
On Weak Forms of Upper and Lower Continuous Multifunctions between an Ideal Topological Space and a Bitopological Space by Pue-on, Prapart ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - Furthermore, several characterizations of upper ⋆-continuous multifunctions, lower ⋆-continuous multifunctions, upper almost ⋆-continuous multifunc- tions, lower almost ⋆-continuous multifunctions, upper weakly ⋆-continuous multifunctions and lower weakly ⋆-continuous multifunctions were considered in [20]. This paper presents new concepts of continuous multifunctions defined from an ideal topological space into a bitopological space, called upper weakly τ⋆(σ1, σ2)-continuous multifunc- tions and lower weakly τ⋆(σ1, σ2)-continuous multifunctions. Keywords: open; set
On Almost $\tau^\star(\sigma_1,\sigma_2)$-continuity and Weak $\tau^\star(\sigma_1,\sigma_2)$-continuity by Viriyapong, Nongluk ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - Then, Y − σ1σ2-Cl(V ) is σ1σ2-open in Y . Then, Y − σ1σ2-Cl(V ) is σ1σ2-open and hence Y − σ1σ2-Cl(V ) is (σ1, σ2)p-open in Y . Keywords: cl(v; open; set; σ1σ2
Almost Weak Continuity for Multifunctions Defined between an Ideal Topological Space and a Bitopological Space by Viriyapong, Chokchai ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - Then, Y − σ1σ2-Cl(V ) is σ1σ2-open in Y . = σ1σ2-Cl(V ) for every σ1σ2- open set V of Y . Keywords: open; set; σ1σ2
Almost Quasi Continuity and Weak Quasi Continuity for Multifunctions Between an Ideal Topological Space and a Bitopological Space by Thongmoon, Montri ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - A multifunction F : (X, τ,I ) → (Y, σ1, σ2) is said to be upper weakly quasi τ⋆(σ1, σ2)-continuous if F is upper weakly quasi τ⋆(σ1, σ2)-continuous at each point x of X. Remark 1. For a multifunction F : (X, τ,I ) → (Y, σ1, σ2), the following properties are equivalent: (1) F is upper weakly quasi τ⋆(σ1, σ2)-continuous; (2) for each x ∈ X and every σ1σ2-open set V of Y such that F (x) ⊆ V , there exists a semi-I ⋆-open set U of X containing x such that F (U) ⊆ σ1σ2-Cl(V ); (3) Int⋆(Cl⋆(F−(σ1σ2-Int(K)))) Keywords: open; set
Almost Quasi $\tau^\star(\sigma_1,\sigma_2)$-continuous and Weakly Quasi $\tau^\star(\sigma_1,\sigma_2)$-continuous Functions by Kong-ied, Butsakorn ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - Semi-open sets and semi-continuity in topological spaces. [5] introduced and studied the notion of weakly quasi continuous functions. Keywords: cl(v; open; set; σ1σ2
On Weak Forms of Open and Closed Functions via $(\tau_1,\tau_2)\beta$-open Sets by Chiangpradit, Monchaya ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - Moreover, Caldas and Navalagi [4] introduced and investigated the concepts of weakly semi-open functions and weakly semi-closed functions as a new generalization of weakly open functions and weakly closed functions, respectively. The concept of weakly open functions was first introduced by Rose [1]. Keywords: open; σ2)β; τ1τ2
On Weak Forms of Open and Closed Functions Between Bitopological Spaces by Chutiman, Nipaporn ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - [1] intro- duced and studied the notions of weakly open functions and almost open functions. Preliminaries Throughout the present paper, spaces (X, τ1, τ2) and (Y, σ1, σ2) (or simply X and Y ) always mean bitopological spaces on which no separation axioms are assumed unless explicitly stated. Keywords: open; σ2)b; τ1τ2
Upper and Lower $\tau^\star\alpha(\sigma_1,\sigma_2)$-continuity by Khampakdee, Jeeranunt ; Sama-ae, Areeyuth ; Boonpok, Chawalit (2025) - [3] extended the concept of α-continuous functions to multifunctions and presented two classes of multifunctions defined from a topological space into a topological space, called upper α-continuous multifunctions and lower α- continuous multifunctions. In 1993, Popa and Noiri [4] obtained several characterizations and some basic properties of upper α-continuous multifunctions and lower α-continuous multifunctions. Keywords: multifunctions; open
On Upper and Lower Almost $\tau^\star\alpha(\sigma_1,\sigma_2)$-continuous Multifunctions by Viriyapong, Chokchai ; Sama-Ae, Areeyuth; Boonpok, Chawalit (2025) - Then, Y − V is σ1σ2-closed in Y and by (11), Cl⋆(Int⋆(Cl⋆(F−((σ1, σ2)sInt(Y −V ))))) The union of all τ1τ2-δ-open sets ofX contained in A is called the τ1τ2-δ-interior [8] of A and is denoted by τ1τ2-δ-Int(A). Keywords: open; set
Weakly $\tau^\star\alpha(\sigma_1,\sigma_2)$-continuous Multifunctions by Viriyapong, Nongluk ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - This paper presents new classes of continuous multifunctions defined between an ideal topological space and a bitopological space, called upper weakly τ⋆α(σ1, σ2)-continuous multifunc- tions and lower weakly τ⋆α(σ1, σ2)-continuous multifunctions. Furthermore, several characteri- zations and some properties concerning upper weakly τ⋆α(σ1, σ2)-continuous multifunctions and lower weakly τ⋆α(σ1, σ2)-continuous multifunctions are considered. Keywords: open; set
Upper and Lower $\tau^\star\beta(\sigma_1,\sigma_2)$-continuity by Pue-on, Prapart ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - [16] studied some characterizations of upper (τ1, τ2)-continuous multifunctions and lower (τ1, τ2)-continuous multifunctions by using τ1τ2-δ-open sets and τ1τ2-δ-closed sets. The union of all τ1τ2-δ-open sets of X contained in A is called the τ1τ2-δ-interior Keywords: multifunctions; open; set
Almost $\tau^\star\beta(\sigma_1,\sigma_2)$-continuity for Multifunctions by Srisarakham, Napassanan ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - Then, Y − V is σ1σ2-closed in Y and by (11), Int⋆(Cl⋆(Int⋆(F−((σ1, σ2)-sInt(Y − V ))))) Since Y − (σ1, σ2)-sCl(V ) is (σ1, σ2)r-closed, we have F−(Y − (σ1, σ2)-sCl(V )) is τ⋆-β- closed in X. Thus, F+((σ1, σ2)-sCl(V )) is a τ⋆-β-open set of X containing x and so Keywords: open; set
On upper and lower weakly $\tau^\star\beta(\sigma_1,\sigma_2)$-continuous multifunctions by Thongmoon, Montri ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - A multifunction F : (X, τ,I ) → (Y, σ1, σ2) is said to be upper weakly τ⋆β(σ1, σ2)-continuous if F is upper weakly τ⋆β(σ1, σ2)-continuous at each point of X. Theorem 1. For a multifunction F : (X, τ,I ) → (Y, σ1, σ2), the following properties are equivalent: (1) F is upper weakly τ⋆β(σ1, σ2)-continuous at a point x ∈ X; (2) x ∈ Cl⋆(Int(Cl⋆(F+(σ1σ2-Cl(V ))))) for every σ1σ2-open set V of Y containing F (x); (3) x ∈ βInt⋆(F+(σ1σ2-Cl(V ))) for every σ1σ2-open set V of Y containing F (x). Keywords: cl(v; open; set
Almost $\mu(\sigma_1,\sigma_2)$-continuous Multifunctions by Pue-on, Prapart ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - Since Y − V is (σ1, σ2)r-closed and by (7), X − F+(V ) The union of all τ1τ2-δ-open sets of X contained in A is called the τ1τ2-δ-interior [18] of A and is denoted by τ1τ2-δ-Int(A). Keywords: open; set
Almost Weak $\mu(\sigma_1,\sigma_2)$-continuity for Multifunctions by Kong-ied, Butsakorn ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - Since Y − σ1σ2-Cl(V ) is σ1σ2-open and by (2), we have X − F−(σ1σ2-Cl(V )) By (5), F (cµ(π)(F +(Y −B))) ⊆ σ1σ2-Cl(F (F+(Y −B))) ⊆ σ1σ2-Cl(Y −B) = Y − σ1σ2-Int(B). Keywords: open; set; σ1σ2
On (delta_alpha), (delta_p) and (delta_s)-irresolute Functions by Beceren, Yusuf; Noiri, Takashi (2011) - [2] if f −1(V ) is semi-open set in X for every α-open subset V of Y . [3] if f −1(V ) is semi-open set in X for every preopen subset V of Y . Keywords: irresolute; open; resp

Appl

Study on the Dynamical Analysis of a Family of Optimal Third Order Multiple-zero Finder by Geum, Young Hee (2023) - = (z − A)m(z − B)m, regardless of t-values. Math, 16 (4) (2023), 2775-2785 2780 Table 1: Color palette for a q-periodic orbit with q ∈ N ∪ {0} q Cq q = 1 C1 =  magenta, for fixed point ∞ cyan, for fixed point 0 yellow, for fixed point 1 red, for other strange fixed point , 2 ≤ q ≤ 68 C2 = orange, C3 = light green, C4 = dark red, C5 = dark blue, C6 = dark green, C7 = dark yellow, C8 = floral white, C9 = light pink, C10 = khaki, C11 = dark orange, C12 = turquoise, C13 = lavender, C14 = thistle, C15 = plum, C16 = orchid, C17 = medium orchid, C18 = blue violet, C19 = dark orchid, C20 = purple, C21 = power blue, C22 = sky blue, C23 = deep sky blue, C24 = dodger blue, C25 = royal blue, C26 = medium spring green, C27 = spring green, C28 = medium sea green, C29 = sea green, C30 = forest green, C31 = olive drab, C32 = bisque, C33 = moccasin, C34 = light salmon, C35 = salmon, C36 = light coral, C37 = Indian red, C38 = brown, C39 = fire brick, C40 = peach puff, C41 = wheat, C42 = sandy brown, C43 = tomato, C44 = orange red, C45 = chocolate, C46 = pink, C47 = pale violet red, C48 = deep pink, C49 = violet red, C50 = gainsboro, C51 = light gray, C52 = dark gray, C53 = gray, C54 = charteruse, C55 = electric indigo, C56 = electric lime, C57 = lime, C58 = silver, C59 = teal, C60 = pale turquoise, C61 = sandy brown, C62 = honeydew, C63 = misty rose, C64 = lemon chiffon, C65 = lavender blush, C66 = gold, C67 = crimson, C68 = tan. Keywords: appl; order
A New Septupling Point 7P Arithmetic Formula for LD Coordinate and Affine Over Binary Elliptic Curve Cryptosystem by Abdulraheem, Waleed (2025) - Fast multibase methods and other several optimizations for elliptic curve scalar multiplication. New quintupling point arithmetic 5p formulas for lǒpez-dahab coordinate over binary elliptic curve cryptography. Keywords: appl; cost; curve; formula; point
Fuzzy Logic-Driven Assessment Model for Mathematical Proof Grading in Education by Alkandari, Maryam; Alajmi, Amal Hussain (2025) - In summary, these works demonstrate the potential of fuzzy logic systems for accommodating uncertainty and subjectivity in student assessment whereas conventional methods do not [13,14]. The system was tested using student data while fuzzy grades were assessed together with the grades assigned by the professor. Keywords: appl; course; course grade; grade; grading; logic; performance; professor; q1[’excellent; students; system

Dominating

Forcing Subsets for Î³c-sets and Î³t-sets in the Lexicographic Product of Graphs by Armada, Cris Laquibla; Canoy, Sergio, Jr. R.; Go, Carmelito E. (2019) - This implies that y ∈ S and u ∈ NG(y). If u ∈ V (G) \ S, then because S is a dominating set of G, there exists y ∈ S such that u ∈ NG(y). Keywords: dominating; set
Hop Dominating Sets in Graphs Under Binary Operations by Canoy, Jr, Sergio; Mollejon, Reynaldo Villarobe; Canoy, John Gabriel E. (2019) - = {u ∈ V (G) : uv ∈ E(G)} and its closed neighbourhood is the set NG[v] = NG(v) ∪ {v}. = V (G) ∪ V (H) and edge set E(G+H) = E(G) ∪ E(H) ∪ {uv : u ∈ V (G) and v ∈ V (H)}. Keywords: dominating; hop; set
Total Partial Domination in Graphs Under Some Binary Operations by Macapodi, Roselainie Dimasindil; Isla, Rowena (2019) - Then C1 = S1 × V (H) and C2 = V (G)× S2 are total α-partial dominating sets in G�H if and only if S1 and S2 are α-partial dominating sets in G and H, respectively. × V (H) and C2 = V (G)× S2 are total α-partial dominating sets in G�H. Then by Remark 6, C1 and C2 are α-partial dominating sets in G�H. By Theorem 6, S1 and S2 are α-partial dominating sets in G�H. Suppose S1 and S2 are α-partial dominating sets in G and H, respectively. Keywords: dominating; set
On Independent Transversal Dominating Sets in Graphs by Sevilleno, Daven Sapitanan; Jamil, Ferdinand P. (2021) - For corona of graphs G ◦H, if H = K1, we write G ◦H = cor(G). On corona of graphs It is worth noting that G ◦H is composed of the joins Hv + v = Hv + 〈v〉, v ∈ V (G), joined together by the edges of G. Thus, V (G ◦H) Keywords: dominating; set; transversal
Global Hop Domination Numbers of Graphs by Salasalan, Gemma; Canoy, Jr, Sergio (2021) - The Cartesian product of graphs G and H, denoted by G�H, is the graph with vertex set V (G�H) A subset C = ∪x∈S [{x}×Tx] of V (G�H) is a global hop dominating set of G�H if and only if the following conditions hold: (i) Keywords: dominating; dominating set; hop; set
Minimal and Upper Cost Effective Domination in Graphs by Maglanque, Hearty Nuenay; Jamil, Ferdinand P. (2021) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: cost effective dominating set, minimal cost effective dominating set, minimal cost effective domination number, upper cost effective domination number 1. . , v2k−1, v2k+1} are minimal cost effective dominating sets in Pn for j = 0 and j = 1, respectively, we have γmce(Pn) Keywords: cost; dominating; set
Total Perfect Hop Domination in Graphs Under Some Binary Operations by Rakim, Raicah Cayongcat; Rara, Helen M (2021) - In the next section, we introduce total perfect hop dominating set and explore some of its properties. Let S = A∪ ( ⋃ v∈V (G) Sv) be a minimum total perfect hop dominating set of G ◦H. By Theorem 4.2, A is a γ∗pt1,2 -set of G and (ii) and (iii) hold. Keywords: dominating; dominating set; hop; set
Resolving Restrained Domination in Graphs by Monsanto, Gerald Bacon; Rara, Helen M. (2021) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Dominating set, resolving set, resolving dominating set, resolving restrained dominating set, join, corona, lexicographic product 1. The strictly resolving dominating number of G, denoted by γSR(G), is the smallest cardinality of a strictly resolving dominating set of G. A strictly resolving dominating set of G of cardinality γSR(G) is referred to as γSR-set of G. Let G = (V (G), E(G)) be a graph. Keywords: dominating; set
Stable Locating-Dominating Sets in Graphs by Ahmad, Eman Camad; Malacas, Gina Alquiza; Canoy, Sergio Jr. Rosales (2021) - A set S is a stable locating-dominating set of G+H if and only if S = SG ∪ SH and SG and SH are stable locating sets of G and H, respectively, and at least one of them is a stable strictly locating set or both of them are strictly locating sets. Therefore, SG is a strictly locating set of G. Similarly, SH is a strictly locating set of H. Conversely, suppose that S = SG∪SH and SG and SH are stable locating sets of G and H, respectively, such that at least one of them is a stable strictly locating set or both of them are strictly locating sets. Keywords: dominating; dominating set; locating; locating set; set
On Connected Co-Independent Hop Domination in Graphs by Nanding, Sandra Abo; Rara, Helen (2021) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Connected co-independent hop dominating set, connected co-independent hop domination number, strictly co-independent set, strictly co-independent number, join, corona, lexicographic product 1. Math, 14 (4) (2021), 1226-1236 1227 of connected co-independent hop domination in graphs. Keywords: dominating; hop; set
On Restrained Strong Resolving Domination in Graphs by Sumaoy, Helyn Cosinas; Rara, Helen M. (2021) - i or S = V (K1 +G) \ Ci where Ci is a superclique in Gi, for i = 1, 2, . . if and only if at least one of the following is satisfied: (i) S = V (G+H) \ CG where CG is a superclique of G. (ii) S = V (G+H) \ CH where CH is a superclique of G. (iii) If γ(G) = 1 and γ(H) Keywords: dominating; resolving; set
Revisiting Domination, Hop Domination, and Global Hop Domination in Graphs by Salasalan, Gemma Puebla; Canoy, Jr, Sergio R (2021) - If S2 is a dominating of G \ v, then γ(GG) = |S0| ≥ 1+ γ(G \ v). Clearly, D′ = D2 ∪D∗ 2 is a dominating set of G \ v and so γ(GG) Keywords: dominating; hop; set
On Connected Partial Domination in Graphs by Cabulao, Jessa Mae Carpentero; Isla, Rowena T. (2021) - We first introduce the following concept which will be used to characterize the con- nected α-partial dominating sets in the join of graphs. Then C1 = S1 × V (H) and C2 = V (G)× S2 are connected α-partial dominating sets in G□H if and only if S1 and S2 are connected α-partial dominating sets in G and H, respectively. Keywords: dominating; set
Restrained Disjunctive Domination in Graphs under Some Binary Operations by Malalay, Rolando Penafiel; Jamil, Ferdinand Paler (2022) - If u is the end vertex of graph G and degG(v) ≤ 2, then u ∈ S for all restrained disjunctive dominating sets S of G. Proposition 1. Under the same condition, the minimum of the sets between disjuntive total domination number of graph G and twice of distance-2 domination number of graph G, denoted by min{γdt (G), 2γ2(G)} proves to be a sharp bound for the restrained disjunctive domination number of the lexicographic product of graphs G and H. REFERENCES 222 Acknowledgements This research was undertaken at the Technische Universitat Kaiserslautern, Germany, under the Faculty and Student Exchange Program of the project ”Graph Theory and Optimization (GraThO) with Applications in Industry and Society” and funded by the Zamboanga Peninsula Polytechnic State University, Philippines. Keywords: dominating; set
A Variant of Hop Domination in Graphs by Canoy, Jr., Sergio ; Salasalan, Gemma Puebla (2022) - Let (x, p) ∈ V (G[H])\C. Since S = V (G), p /∈ In either case, γcs(G) = n− 1. (ii) Let Gm and Gr be non-trivial components and pick v ∈ V (Gm) and w ∈ V (Gr). Keywords: dominating; hop; set; super
Monophonic Eccentric Domination Numbers of Graphs by Gamorez, Anabel ; Canoy Jr., Sergio (2022) - Then S is a monophonic eccentric dominating set of G + H if and only if S = SG ∪ SH , where SG and SH are monophonic eccentric dominating sets of G and H, respectively. = dmH(a, b) = dmG[H]((z, a), (z, b)), where (z, b) ∈ C. Therefore, C is monophonic eccentric dominating set of G[H]. Keywords: dominating; set
On Movable Strong Resolving Domination in Graphs by Sumaoy, Helyn Cosinas; Rara, Helen (2022) - Thus , S ̸= V (G)\Ci showing that S = V (G) or S = V (K1+G)\Ci where Ci is a γ-set of Gi for some i ∈ {1, 2, . . . Math, 15 (3) (2022), 1201-1210 1205 and (S \ {x}) ∪ {y} = V (G) \ ((C \ {x}) ∪ {y}), by Lemma 1 C ∪ {x} is a dominated superclique or (C \ y) ∪ {x} is a dominated superclique in G. For the converse, suppose C = ∅. Then, S = V (G) is strong resolving dominating set of G. Thus, S \ {x} = V (G) \ {x} is strong resolving dominating since {x} is a dominated superclique for each x ∈ V (G). Keywords: dominating; resolving; set
Restrained 2-Resolving Dominating Sets in the Join, Corona and Lexicographic Product of Two Graphs by Cabaro, Jean Mansanadez; Rara, Helen (2022) - A set S ⊆ V (G ◦ H) is a restrained 2-resolving set in G ◦ H if and only if S = A ∪ ( ⋃ v∈V (G) Sv) satisfying the following conditions. Then S ⊆ V (G ◦ H) is a restrained 2-resolving dominating set in G ◦ H if and only if S = A ∪ ( ⋃ v∈A Sv)( ⋃ w∈V (G)\A Sw) satisfying the following conditions. Keywords: dominating; resolving; set
Outer-Connected Semitotal Domination in Graphs by Aradais, Alkajim; Jamil, Ferdinand (2022) - A semitotal dominating set S of G is an outer-connected semitotal dominating set if either S = V (G) or S ̸= V (G) satisfying the prop- erty that the subgraph induced by V (G) \ S is connected. Let S ⊆ V (Pn), be γ̃t2 - set of Pn with S ̸= V (Pn). Keywords: dominating; dominating set; set
Grundy Hop Domination in Graphs by Hassan, Javier; Canoy, Jr., Sergio (2022) - It is routine to show that any rearrangement of the terms of S is not legal closed hop neighborhood sequence of G. G : v1 v2 v3v4 v5 Figure 1: A graph G such that V (G) does not form a legal closed hop neighborhood sequence Remark 2. Grundy dominating sequences on x-join product. Keywords: dominating; grundy; hop; neighborhood; sequence
Hop Independent Hop Domination in Graphs by Hassan, Javier; Canoy, Jr., Sergio (2022) - The minimum cardinality of hop independent hop dominating set of G, denoted by γhih(G), is called the hop independent hop domination number of G. In this paper, we show that the hop independent hop domination number of a graph G lies between the hop domination number and the hop independence number of graph G. We characterize these types of sets in the shadow graph, join, corona, and lexicographic product of two graphs. Any total dominating hop independent hop dominating set D with cardinality γhiht (G) is referred to as a γhiht -set. Keywords: dominating; hop; hop dominating; independent; set
On 2-Resolving Hop Dominating Sets in the Join, Corona and Lexicographic Product of Graphs by Mahistrado, Angelica Mae; Rara, Helen (2022) - A set C ⊆ V (G ◦ H) is a hop dominating set of G ◦H if and only if C = A ∪  ⋃ v∈V (G)∩NG(A) A set S ⊆ V (G ◦H) is a 2-resolving hop dominating set of G ◦H if and only if S = A ∪  ⋃ v∈V (G)∩NG(A) Keywords: dominating; lnpnd; resolving; set
Weakly Connected Hop Domination in Graphs Resulting from Some Binary Operations by Hamja, Jamil; Aniversario, Imelda S. ; Merca, Catherina I. (2023) - Pick u ∈ S ∩ V (G) and v ∈ S ∩ V (H). The corona G ◦H of graphs G and H, is the graph obtained by taking one copy of G and |V (G)| copies of H, and then joining the ith vertex of G to every vertex of the ith copy of H. For every v ∈ V (G), denote by Hv the copy of H whose vertices are attached one by one to the vertex v. Subsequently, denote by v+Hv the subgraph of the corona G ◦H corresponding to the join ⟨{v}⟩+Hv, v ∈ V (G), Harary Keywords: dominating; set
Outer-connected Hop Dominating Sets in Graphs by Saromines, Chrisley Jade; Canoy, Jr., Sergio (2022) - Then a subset C of V (G ◦H) is an outer connected hop dominating set of G ◦H if and only if C = A ∪  ⋃ v∈V (G) Sv  where Sv ⊆ V (Hv) for each v ∈ V (G) and satisfies each of the following statements: (i) A = V (G) or ⟨V (G) \A⟩ is connected. Let C be an outer-connected hop dominating set of G ◦H, Sv = V (Hv)∩C for each v ∈ V (G) and set A = V (G)∩C. Suppose A ̸= V (G). Keywords: dominating; hop; set
Transversal Hop Domination in Graphs by Bonsocan, Maria Andrea; Jamil, Ferdinand (2023) - We also denote by Hv + v that subgraph ⟨{v} ∪ V (Hv)⟩ of G ◦H induced by {v} ∪ V (Hv). To show that S∗ is a hop dominating set of G ◦H, it is enough to consider only the vertices in V (G) ∩ (NG(z) ∪NG(w)). Keywords: dominating; hop; set; γ̂h(g
Resolving Domination in Graphs under Some Binary Operations by Monsanto, Gerald Bacon; Rara, Helan (2023) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Resolving dominating set, resolving domination number, join, corona, lexicographic product 1. A set S ⊆ V (G) is strictly resolving dominating set of G if it is a resolving dominating set of G and NG ∩ S ̸= S for Keywords: dominating; set
Stable Locating-Dominating Sets in the Edge Corona and Lexicographic Product of Graphs by Malacas, Gina A.; Canoy, Jr., Sergio; Chacon, Emmy (2023) - By (ii), Ty \ {a} is a locating set and Tx are stable locating sets of H for each x ∈ S \ {y}. Location with dominating sets. Keywords: dominating; locating; set
Geodetic Hop Dominating Sets in a Graph by Saromines , Chrisley Jade ; Canoy, Jr., Sergio (2023) - Some of the studies dealing with geodetic sets, geodetic number, and geodetic dominating sets can be found in [4], [5], [6], [7], [8], [9], [10], [14], and [24]. Characterizations of geodetic hop dominating sets in the corona and lexicographic product of two graphs are given. Keywords: dominating; geodetic; hop; set
On 1-movable Strong Resolving Hop Domination in Graphs by Abragan, Armalene; Rara, Helen M. (2023) - It follows that (S′ \ {x}) ∪ {y} is strong resolving set of G. Then S is strong resolving set in G. By Lemma 1, C = ∅ or C is a dominated superclique in G. Keywords: dominating; hop; resolving; set
Restrained 2-Resolving Hop Domination in Graphs by Mahistrado, Angelica Mae; Rara, Helen (2023) - Recently, 2-resolving hop dominating sets in graphs was studied in [11]. Restrained 2-Resolving Hop Dominating Sets in the Edge Corona of Graphs This section presents characterizations on the 2-resolving hop dominating sets and restrained 2-resolving hop dominating sets in the edge corona of graphs. Keywords: dominating; dominating set; hop; point; resolving; set
1-Movable Resolving Hop Domination in Graphs by Mohamad, Jerson; Rara, Helen (2023) - Then W ⊆ V (G ◦ H) is a resolving hop dominating set of G ◦ H if and only if W ∩ V (Hv) ̸= ∅ for every v ∈ V (G) and W = A ∪B ∪D where A ⊆ V (G), B = ∪ {Bv : v ∈ V (G) ∩NG(A) and Bv is a locating set of Hv} and D = ∪ {Du : u ∈ V (G) \NG(A) and Du is a strictly locating set of Hu} . Then W ⊆ V (G ◦ H) is a 1-movable resolving hop dominating set of G ◦ H if and only if W ∩ V (Hv) ̸= ∅ for every v ∈ V (G) and W = A ∪  ⋃ v∈NG(A) Keywords: dominating; hop; resolving; set
Hop Differentiating Hop Dominating Sets in Graphs by Canoy, Jr., Sergio; Saromines , Chrisley Jade (2023) - In particular, we characterize the hop differentiating hop dominating sets in graphs under some binary operations. Let S be a hop differentiating hop dominating set of G. Since S is a hop domi- nating set, N2 G[v]∩S Keywords: differentiating; dominating; hop; set
Some Properties and Realization Problems Involving Connected Outer-hop Independent Hop Domination in Graphs by Hassan, Javier; Lintasan, Abdurajan B.; Mohammad, Nurijam Hanna M. (2023) - The corona G and H, denoted by G ◦H, the graph obtained by taking one copy of G and |V (G)| copies of H, and then joining the ith vertex of G to every vertex of the ith copy of H. A set C ⊆ V (G ◦H) is a connected outer-hop independent hop dominating set of G ◦H if and only if C = V (G) ∪ ( ⋃ a∈V (G)Ca), where Ca ⊆ V (Ha) and V (Ha) \ Keywords: dominating; hop; set; γohich
Connected Grundy Hop Dominating Sequences in Graphs by Hassan, Javier; Canoy, Jr., Sergio R. (2023) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Connected hop domination, closed hop neighborhood sequence, con- nected Grundy hop dominating sequence, connected Grundy hop domination number 1. Grundy dominating sequences on x-join product. Keywords: dominating; grundy; hop; hop dominating; sequence; γchgr
Grundy Dominating and Grundy Hop Dominating Sequences in Graphs: Relationships and Some Structural Properties by Hassan, Javier; Canoy, Jr, Sergio R. (2023) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Grundy dominating sequence, Grundy hop dominating sequence, Grundy domination number, Grundy hop domination number 1. Grundy dominating sequence and zero forcing sets. Keywords: dominating; grundy; sequence; set; γgr(g
Global Stable Location-Domination in Graphs by Ortega, Marivir; Malacas, Gina; Canoy, Jr., Sergio R. (2023) - A set S is a stable locating-dominating set of G+H if and only if S = SG ∪ SH and SG and SH are stable locating sets of G and H, respectively, and at least one of them is a stable strictly locating set or both of them are strictly locating sets. Therefore since G ⋄H is connected and γ(G ◦ H) ̸= 1, G ◦ H admits a global stable locating-dominating set by Corollary 1. Keywords: dominating; dominating set; locating; set; stable
Perfect Isolate Domination in Graphs by Armada, Cris L.; Hamja, Jamil (2023) - The next four results follow directly from the definition of perfect isolate dominating set. Conclusion The paper has introduced the concept of perfect isolate dominating sets of some graphs resulting from some binary operations such as join, corona, and lexicographic product of two graphs. Keywords: dominating; dominating set; isolate; perfect; set
Weakly Convex Hop Dominating Sets in Graphs by Canoy, Jr., Sergio; Hassan, Javier (2023) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Weakly convex set, weakly convex hop dominating set, weakly convex hop domination number 1. Characterizations of weakly convex hop dominating sets in the shadow graph, and in the join, corona, and lexicographic product of two graphs were formulated. Keywords: convex; dominating; hop; set
$1$-movable $2$-Resolving Hop Domination in Graph by Mahistrado, Angelica Mae; Rara, Helen (2023) - A set S of vertices in G is a 1-movable 2-resolving hop dominating set of G if S is a 2-resolving hop dominating set in G and for every v ∈ S, either S\{v} is a 2-resolving hop dominating set of G or there exists a vertex u ∈ ( (V (G)\S) ∩NG(v) ) such that ( S\{v} ) ∪ {u} is a 2-resolving hop dominating set of G. The 1-movable 2-resolving hop domination number of G, denoted by γ1 m2Rh(G) is the smallest cardinality of a 1-movable 2- resolving hop dominating set of G. Recently, 2-resolving hop dominating sets in graphs was studied in [9]. Keywords: dominating; dominating set; resolving; set
Outer-Connected 2-Resolving Hop Domination in Graphs by Mahistrado, Angelica Mae; Rara, Helen (2023) - Recently, 2-resolving hop dominating sets in graphs was studied in [12]. Moreover, other variations of resolving sets and hop dominating sets in graphs were also studied in [4–6, 8, 13–15], respectively. Keywords: dominating; hop; resolving; set
Another Look at Geodetic Hop Domination in a Graph by Saromines , Chrisley Jade; Canoy Jr. , Sergio (2023) - Since S is a hop dominating set, by Theorem 3, SG and SH are pointwise non-dominating sets of G and H, respectively. The smallest cardinality of a pointwise non-dominating set of G, denoted by pnd(G), is called the pointwise non-domination number of G. A pointwise non-dominating set S ⊆ V (G) of a graph G is called a 2-path closure absorbing pointwise non-dominating set if it is a 2-path closure absorbing set. Keywords: dominating; set
Outer-Convex Hop Domination in Graphs Under Some Binary Operations by Isahac, Al-Amin Y.; Hassan, Javier; Laja, Ladznar S.; Copel, Hounam B. (2023) - Weakly convex hop dominating sets in graphs. Thus, CG ̸= ∅. Similarly, SH ̸= ∅. Now, since C is a hop dominating set of G + H, it follows that CG and CH are pointwise non-dominating sets of G and H, respectively by Theorem 4. Keywords: convex; dominating; hop; set
Grundy Total Hop Dominating Sequences in Graphs by Hassan, Javier; Canoy, Jr., Sergio R. (2023) - Two sequences S and S′ in G are loh-identical if they are legal open hop neighborhood sequences (or Grundy total hop dominating sequences) and Ŝ = Ŝ′ (i.e., one is a reaarrangement of the terms of the other). , t}, and so S is Grundy total hop dominating sequence. Keywords: dominating; grundy; hop; hop dominating; sequence; total
$J$-Domination in Graphs by Hassan, Javier; Salim, Jeffrey Imer (2023) - On the other hand, suppose that D = DG ∪ DH , where either DH = ∅ and DG = D is γJ - set in G or DG = ∅ and DH = D is γJ -set in H. Then by Theorem 10, D is a J-dominating set in G + H. The closed neighborhood of X in G is the set NG[X] = NG(X)∪X. A subset D of V (G) is called a dominating of G if for every x ∈ V (G) \ D, there exists y ∈ D such that xy ∈ E(G). Keywords: dominating; dominating set; set
Certified Perfect Domination in Graphs by Hamja, Jamil (2023) - A perfect dominating set S ⊆ V (G) is called certified perfect dominating set of G if every u ∈ S has either zero or at least two neighbors in Math, 16 (4) (2023), 2763-2774 2764 In 1990, Livingston M. et.al, investigated the concept of perfect dominating set of a graph. Keywords: dominating; dominating set; perfect; set
$J^2$-Hop Domination in Graphs: Properties and Connections with Other Parameters by Hassan, Javier; Bakkang, Alcyn R.; Sappari, Amil-Shab S. (2023) - Observe that ai−2 ∈ N2 Pk [ai] \ N2 Pk [aj ] and aj+2 ∈ N2 Pk [aj ] \ N2 Pk [ai] for all j > i, where i, j ∈ {3, 4, . . Let u ∈ NG(a) and v ∈ NG(b), then u ∈ N2 G+H Keywords: dominating; hop; set
Some Properties of Zero Forcing Hop Dominating Sets in a Graph by Manditong, Jahiri; Tapeing, Aziz; Hassan, Javier; Bakkang, Alcyn R. ; Mohommad, Nurijam Hanna M. ; Kamdon, Sisteta U. (2024) - The minimum cardinality among all zero forcing hop dominating sets in G, denoted by γzh(G), is called the zero forcing hop domination number of G. A zero forcing hop dominating set Z with |Z| = γzh(G), is called the minimum zero forcing hop dominating set of G or a γzh-set of G. Example 1. The minimum cardinality among all zero forcing hop dominating sets in G, denoted by γzh(G), is called the zero forcing hop domination number of G. Keywords: dominating; forcing; hop; let; set
Vertex Cover Hop Dominating Sets in Graphs by Bilar, Vergel; Bonsocan, Maria Andrea; Hassan, Javier; Dagondon, Susan (2024) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Vertex cover, vertex cover hop dominating set, vertex cover hop domination number 1. (i) Let C be a minimum vertex cover hop dominating set of G. Keywords: cover; dominating; set; vertex
Formulas and Properties of 2-Hop Domination in Some Graphs by Hassan, Javier; Gomorez, Anabel E. ; Laja, Ladznar S. ; Ahmad, Eman C. (2024) - Some properties of zero forcing hop dominating sets in a graph. Weakly convex hop dominating sets in graphs. Keywords: dominating; hop
Zero Forcing Domination in Some Graphs: Characterizations and Derived Formulas by Hassan, Javier; Bonsocan, Maria Andrea O. ; Langamin, Mercedita A. ; Bilar, Vergel T. ; Aming, Sharifa Dianne A. ; Amiruddin-Rajik, Bayah J. (2024) - We char- acterize zero forcing dominating sets in some special graphs and the join of two graphs, and we derive some formulas of the zero forcing domination using characterization results. 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Zero forcing set, zero forcing dominating set, zero forcing domination number 1. Keywords: dominating; forcing; set
Convex 2-Domination in Graphs by Canoy, Sergio; Jamil, Ferdinand; Fortosa, Rona Jane Gamayot; Macalisang, Jead (2024) - Then |NG(v)| ≥ 2. Let S = V (G)\{v}. Hence, A = V (G) and S = V (G)∪ (⋃ v∈V (G) Sv ) . Keywords: convex; dominating; let; set
Differentiating Odd Dominating Sets in Graphs by Carbero, Mary Ann; Malacas, Gina; Canoy, Sergio (2024) - Then S ⊆ V (G + H) is a differentiating odd dominating set in G + H if and only if S = SG ∪ SH , where SG and SH are differentiating sets in G and H, respectively, either SG or SH is strictly differentiating, and one of the following statements holds: (i) |SG| and |SH | are even, and SG and SH are both odd dominating sets in G and H, respectively. (ii) |SG| and |SH | are odd, and SG and SH are both even dominating sets in G and H, respectively. (iii) |SG| is odd, |SH | is even, SG is odd dominating in G, SH is even dominating set in H. (iv) |SG| is even, |SH | is odd, SG is even dominating in G, and SH is odd dominating sets in H. Proof. In this paper, we discuss differentiating odd dominating sets and give bounds or exact values of the differentiating odd domination numbers of some graphs. Keywords: differentiating; dominating; dominating set; set
Closed Geodetic Hop Domination in Graphs by Adolfo, Niña Jeane; Aniversario, Imelda; Jamil, Ferdinand (2024) - If G = K2, then we are done. 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Closed geodetic cover, hop dominating set, geodetic hop dominating set, closed geodetic hop dominating set, closed geodetic hop domination number, join, corona, edge corona ∗Corresponding author. Keywords: dominating; dominating set; hop; hop dominating; set
On Minimal Geodetic Hop Domination in Graphs by Catian, Dyjay Bill; Aniversario, Imelda ; Jamil, Ferdinand (2024) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: minimal geodetic hop dominating set, upper geodetic hop dominating number, 2-path closure absorbing pointwise non-dominating set 1. , xn−1, xn} to be minimal geodetic hop dominating set. Keywords: dominating; dominating set; geodetic; hop; set
Study on Even Sum Domination Number of Some Graphs by Karkar, Sejal; Pandya, D.D.; Sonchhatra, S.G.; Maheta, P.D.; Rathod, H.M.; Bhanderi, S.D. (2024) - Introduction We consider simple, finite, connected and undirected graph G with vertex set V (G) and edge set E(G). If v is not even sum dominated by any vertex of S −{u} but even sum dominated by any vertex of S, then vertex v has only one even sum neighbor u in S, that is Nes(v)∩S = {u}. Keywords: dominating; set; sum; vertex
Characterizing 2-Distance Certified Hop Dominating Sets Using Co-Certified Pointwise Non-domination Concept by N. Ulal, Noor-Sharief; Hassan, Javier; Langamin, Mercedita A. ; Ulal, Noor-Han N. (2025) - Then by Theorem 4, OG and OH are co-certified pnd sets of G and H, Suppose that M = {v2} is a minimum co-certifed pnd set of ¯(K2). Keywords: dominating; hop; pnd; set
2-Step Movability of Hop Dominating Sets in Graphs by Estrella, Roger; Malacas, Gina ; Canoy, Sergio (2025) - Since hop domination and domination have similar applications in networks, it is also worthwhile to consider movability of hop dominating sets in graphs. In this paper, we introduce 2-step movability of hop dominating sets. Keywords: dominating; hop; hop dominating; set; step
Secure Hop Dominating Sets in Graphs by Alfeche, Farene Loida; Malacas, Gina; Canoy Jr, Sergio (2025) - (iii) S = SG1 ∪ SG2 such that SG1 ∪ S′ G2 and S′ G1 ∪ SG2 are secure hop dominating sets in G1 and G2, respectively. The minimum cardinality among all secure hop dominating sets of G, denoted by γsh(G), is called the secure hop domination number of G. Keywords: dominating; hop; hop dominating; set
Connected Degree Equitable Domination in Graphs by Maglanque, Hearty Nuenay (2025) - The notion of connected equitable domination has been introduced where dominating sets are not only degree-balanced but also induce connected subgraphs. A subset S ⊆ V (G) is called minimal connected equitable dominating set in G if no proper subset of S is a connected equitable dominating set in G. The concept of connected equitable domination has many real life applications where both connectivity (connectedness) and fairness (equitability) in workload distribution or influence distribution are essential. Keywords: dominating; set
Friendly Domination in Graph by Cabahug, Isagani, Jr; Eballe, Rolito; Fernandez, Reynard (2025) - Math, 18 (4) (2025), 6326 4 of 15 v1 v2 v3 v4 vertex in F vertex in V \ F Clearly N [F ] = V (P4), since v1 dominates v2 and v4 dominates v3. Finally, we give complete structural characterizations of friendly dominating sets in the join and corona of two graphs. Keywords: dominating; set; vertex
On Pairs of Disjoint Hop Dominating Sets in Graphs by Besana, Viralou Abrille; Jamil , Ferdinand; Canoy, Sergio (2025) - Clearly, for G ∈ G of order n, 2 ≤ γh(G) ≤ γ̃h(G) ≤ n − γh(G) ≤ n − 2. For every pair of positive integers m and n with 2 ≤ m ≤ n, there exists G ∈ G for which γh(G) Keywords: dominating; dominating set; hop; set
Secure Pointwise Non-Domination and Secure Hop Domination in Graphs by Alfeche, Farene Loida; Canoy Jr., Sergio (2025) - Then S ⊆ V (G+H) is a secure hop dominating set if and only if S = SG ∪ SH and SG and SH are secure pointwise non-dominating sets in G and H, respectively. Suppose S is a secure hop dominating set in G+H. Since S is a hop dominating set, S = SG ∪ SH where SG and SH are pointwise non-dominating sets in G and H, respectively, by Theorem 5. Keywords: dominating; pointwise; secure; set
Vertex-Edge Dominating Sets of Some Graphs Under Binary Operations by Tayab, Jerry; Jamil, Ferdinand; Aniversario, Imelda (2025) - Let S ⊆ V (GG) be a γve-set of GG with v ∈ S. Let S∗ = {w ∈ V (G − v) : w ∈ S}, and put T = S∗ ∪ (S ∩ V (G − v)). A subset S ⊆ V (G) is a vertex-edge dominating set of G if for each xy ∈ E(G), there exists u ∈ S such that u vertex-edge dominates xy. Keywords: dominating; set
Connected Disjunctive Domination in Graphs by Aradais, Alkajim ; Jamil, Ferdinand; Canoy, Sergio Jr. (2025) - A set S of vertices of a graph G is a disjunctive dominating set if for every v ∈ V (G)\S, v is adjacent to a vertex in S or S contains two vertices each of distance two from v. A disjunctive dominating set For a graph G, the symbols V (G) and E(G) refer to the vertex-set and edge-set, respectively, of G. For S ⊆ V (G), |S| is the cardinality of S. Keywords: dominating; dominating set; set; γdc

Solution

Stability Results for Set Differential Equations Involving Causal Operators with Memory by Devi, J. Vasundhara; Naidu, Ch. Appala (2012) - Let E = C[[t0, T], Kc(R n)] and E0 = C[[t0 − h1, T], Kc(R n)], where U ∈ E0 implies U(t) = Φ0(t), t0 − h1 ≤ t ≤ t0 and U(t) is any arbitrarily continuous function on [t0, T]. Let 0 < ε < ρ and t0 ∈ R+ be given. Keywords: solution; u(t
Comparative Analysis of the Modified SOR and BGC Methods Applied to the Poleness Conservative Finite Difference Scheme by Erdem, Arzu (2013) - The solution u ∈ �H1(ΩRβ) of the integral identity (3) is defined as a weak solution of the boundary value problem (1)-(2). Due to the singularity at r = 0 in the considered polar domain Ωrϕ , a special technique of deriving the finite difference scheme in the neighbourhood of the pole point r = 0 is described. Keywords: difference; finite; problem; solution
An Unconventional Splitting for Korteweg de Vries-Burgers Equation by Aydin, Ayhan (2015) - In [10], a finite differences with variable mesh and the semi-analytic Adomian decomposition method are used to solve KdVB equation. For this we put a real parameter into a KdV-Burgers equation and split the vector field of the equations into two parts both of which are KdVB equation. Keywords: burgers; equation; kdvb; solution
A Compensatory Fuzzy Approach to Multi-Objective Linear Transportation Problem with Fuzzy Parameters by Gonce Kocken, Hale; Ahlatcioglu Ozkok, Beyza; Tiryaki, Fatma (2014) - Solving fuzzy transportation problems based on extension principle. [3] examined the solution of MOTP which has fuzzy cost, source and destination parameters. Keywords: compensatory; solution
Analytical Approximate Solution of Fractional Wave Equation by the Optimal Homotopy Analysis Method by Elsaid, Ahmed; Shamseldeen, Samir; Madkour, Seham (2017) - Series solutions of non-linear riccati differential equations with fractional order. Table 1: The estimated optimal convergence parameter ~ and the corresponding residual error Em for 0 ≤ x ≤ 2.0 and 0 ≤ t ≤ 2.0 at different fractional derivative α for Example (1). Keywords: equation; order; solution
Origin of Neural Firing and Synthesis in Making Comparisons by Saaty, Thomas L.; Vargas, Luis G. (2017) - If the periodic function of period 1, P (u) satisfies the semigroup condition, P (u+ v) = P (u)P (v) then w̃(uv) = w̃(u)w̃(v). The solution of the functional equation P (u + v) = P (u)P (v) is given by P (u) = eu. Keywords: equation; functions; octonions; saaty; solution
Monotone Iterative Technique and Ulam-Hyers Stability Analysis for Nonlinear Fractional Order Differential Equations with Integral Boundary Value Conditions by Ali, Sajjad; Shah, Kamal; Khan, Hassan; Arif, Muhammad; Mahmood, Shahid (2019) - In same way, we obtain the bounded monotone sequence {zn}, that is z0 ≤ z1 ≤ z2 ≤ ...zn−1 ≤ zn ≤ β on [0, 1], (15) where zn = Tzn−1. The stability of extremal solutions is also obvious from plots in the given Figure 1. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -0.05 0 0.05 0.1 0.15 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 z * 1 (s)=Maximal solution z 1 (s)=Minimal solution z * 2 (s)=Maximal solution z 2 (s)=Minimal solution Figure 1 Keywords: r(s; solution
Analysis of the Picard's Iteration Method and Stability for Ecological Initial Value Problems of Single Species Models with Harvesting Factor by Rahmani Doust, Mohammad Hossein; Lokesha, V.; Ghasemabadi, Atena (2020) - Anybody is able to find out the answer of question ”How great an effect does self-generated spatial structure have on logistic population growth?” which is studied by Law et al in [7]. Two simple models of population growth use deterministic equations to describe the rate of change in the size of a population over time. Keywords: growth; i.v.p; population; solution
A Finite Difference Fictitious Domain Wavelet Method for Solving Dirichlet Boundary Value Problem by Boateng, Francis Ohene; Ackora-Prah, Joseph; Barnes, Benedict; Amoah-Mensah, John (2021) - In this paper, we introduce a Finite Difference Fictitious Domain Wavelet Method (FDFDWM) for solving two dimensional (2D) linear elliptic partial differential equations (PDEs) with Dirichlet boundary conditions on regular geometric domain. In this section we present the results obtained from numerical experiments carried out using the FDFDWM on some linear elliptic PDEs with Dirichlet boundary conditions. Keywords: boundary; dirichlet; domain; fdfdwm; problem; solution
Existence of Weak Solution of Navier-Stokes-Fourier System with a New Successive Approximation Method by Bade, RabÃ©; Chaker, Hedia (2021) - Wg = ( Zg,D1Z g,D2Z g,D3Z g ) ∈ L∞(0, T ; Hs+1(Ω)20) (31) R. Bade, H. Chaker / Eur. For the second part of the proposition, let us choose a test function test V ∈ V with V = { V ∈ D(Ω)20/Vi+5 = D1Vi, Vi+10 = D2Vi, Vi+15 = D3Vi, for i = 1, 5 } . Keywords: c01(ρ̄; i=1; k+1; l)β; solution; system
Application of a Heuristic Method to Solve Nonlinear Oscillators with Irrational Forces by GonzÃ¡lez-Gaxiola, Oswaldo; Ruiz de ChÃ¡vez, Juan (2022) - This paper applies another amplitude-frequency relationship as of late established by Yazdi and Tehrani (Alexandria Engineering Journal 54 99-103, 2015) to analyze periodical solu- tions of nonlinear oscillators; such oscillators are considered emphatically nonlinear on the grounds that they contain an irrational force term. Finally, the methodology used can be very useful for the study of nonlinear oscillators in basic undergraduate physics and mechanics courses. Keywords: doi; nonlinear; solution
Isogeometric Analysis Approximation of Linear Elliptic Equations with L1 Data by Bassonon , Yibour Corentin; Ouedraogo , Arouna (2023) - For every r with 1 < r < +∞, we denote by Lr,∞(Ω) the Marcinkiewicz space whose norm is defined by ∥f∥Lr,∞(Ω) = sup ν>0 ( ν ∣∣∣{x ∈ Ω : |f(x)| ≥ ν} ∣∣∣1/r). = f in Ω, u = 0 on ∂Ω, (1) where Ω is an open, bounded and Lipschitz set of Rd, with d = 2 or d = 3, A is a coercive matrix with coefficients in L∞(Ω) and f belongs to L1(Ω). Keywords: solution
Inverse Boundary Value Problem Solution for Deflected Beams Joined Together by Elastic Medium by Alomari, Omar; Dubovski, Pavel B. (2023) - In this paper, we develop and implement a numerical scheme to represent the model in Figure 1 in non-denominational approach using the one-dimensional Euler-Bernoulli beam theory for bending boundary value problem [5, 8, 11, 12]. 2020 Mathematics Subject Classifications: 65L09, 31A25, 34A55, 35R30, 65M32 Key Words and Phrases: Adjoint equation, Euler-Bernoulli beam theory, Inverse problem, Keywords: figure; inverse; problem; shows; solution; value
Solving Fuzzy System of Boundary Value Problems by Homotopy Perturbation Method with Green’s Function by Al-Hayani, Waleed Mohammed; Mahasin Thabet Younis (2023) - [(4π − 2απ − 4α+ 6)x] cos (πx) , + 1.681E − 04 0.3 −0.0517160 −0.0519550 2.389E − 04 0.5 −0.0599281 −0.0598771 5.100E − 05 0.7 −0.0483163 −0.0477882 5.280E − 03 0.9 −0.0195831 −0.0189384 6.447E − 04 0.75 0.1 −0.0505406 −0.0509607 4.200E − 04 0.3 −0.1163610 −0.1171638 8.027E − 04 0.5 −0.1348384 −0.1353070 4.685E − 04 0.7 −0.1087117 −0.1084163 2.953E − 04 0.9 −0.0440621 −0.0433940 6.680E − 04 1.00 0.1 −0.0898500 −0.0906715 8.214E − 04 0.3 −0.2068641 −0.2085212 1.657E − 03 0.5 −0.2397127 −0.2409320 1.219E − 03 0.7 −0.1932653 −0.1932705 5.257E − 06 0.9 −0.0783326 −0.0775769 7.557E − 04 W. Al-Hayani, M T. Younis / Eur. Keywords: solution
On the Diophantine Equations $a^x+b^y+c^z=w^2$ by Laipaporn, Kittipong; Kaewchay, Saowapak; Karnbanjong, Adisak (2023) - Since 1+by+cz ≡ 3 (mod 4) and w2 ≡ 0, 1 (mod 4), equation ax+by+cz = w2 has no solution for the case x = 0. Therefore, in this article, we investigate the exponential Diophantine equation in the form ax + by + cz = w2, using only elementary tools related to modulo concepts. Keywords: mod; solution
A Force Function Formula for Solutions of Nonlinear Weakly Singular Volterra Integral Equations by Sarfo, Kwasi Frempong; Obeng-Denteh, William; Takyi, Ishmael; Darkwah, Kwaku Forkuoh (2024) - An effective method for solving nonlinear integral equations involv- ing the riemann-liouville fractional operator. Daftardar-Jafari discovered the iterative method[12], popularly known as DJM, for solving general functional equations, including nonlinear Volterra integral equations, algebraic equations and systems of ordinary differential equations, nonlinear algebraic equations, and fractional differential equations. Keywords: solution; tµ−1; γk1
The Non-Perturbative Approach in Examining the Motion of a Simple Pendulum Associated with a Rolling Wheel with a Time-Delay by Alluhydan, Khalid; Moatimid, Galal M. ; Amer, T. S. (2024) - The goal of the NPA is to understand the details of nonlinear systems on their own, without relying on small changes from a known solution. A novel methodology for a time- delayed controller to prevent nonlinear system oscillations. Keywords: alluhydan; amer; approach; delay; equation; frequency; moatimid; nonlinear; solution; stability; system; time
Investigation of a Fourth-Order Nonlinear Differential Equation with Moving Singular Points of Algebraic Type by Gasanov, Magomedyusuf (2025) - movable singular points make nonlinear differential equations in general unsolvable in quadratures. The second method for solving this type of nonlinear differential equations is analytical. Keywords: cauchy; equations; nonlinear; point; problem; singular; solution; theorem
A numerical Study of Cubic-quartic Optical Soliton Solutions in Birefringent Fibers by Almalki, Afrah; A. A. Alshaery; H. O. Bakodah; A.A. AlQarni (2025) - A variety of nonautonomous complex wave solutions for the (2+1)-dimensional nonlinear schrodinger equation with variable coefficients in nonlinear optical fibers. [33, 34] with cubic- quartic nonlinearity - not only in polarization-preserving fibers but also in birefringent fibers, which present a more complex scenario - various researchers have proposed differ- ent sets of optical solutions using analytical techniques to enhance the efficiency of optical signal processes. Keywords: birefringent; fibers; iadm; nonlinear; solution
Modeling of the Euler-Poisson Equations for Rigid Bodies in the Context of the Gyrostatic Influences: An Innovative Methodology by Amer, T. S.; Amer, W. S.; Fakharany, M.; Elneklawy, A. H. ; El-Kafly, H. F. (2025) - This approach allows for the derivation of a system of motion equations with multiple parameters. 2020 Mathematics Subject Classifications: 70E17, 70F07, 70H45, 65L05 Key Words and Phrases: Nonlinear dynamics, Rigid body, Euler-Poisson’s equations, Gyro- static moment, Exact solution ∗Corresponding author. Keywords: amer; body; curve; equations; euler; motion; rgb; solution; value
Bio-Inspired Optimization Through Photosynthesis: A Novel Approach for Balancing Exploration and Exploitation in Complex Systems by Danach, Kassem; Harb, Hassan; Fouad Aly, Wael Hosny; Kanj, Hassan; Kwekha Rashid, Ameer Sardar (2025) - In order to evaluate the robustness of the proposed PSIO algorithm, we conducted a series of sensitivity tests on three key parameters: the balance parameter α, the muta- tion rate, and the population size. These interconnected strategies enable PSIO to maintain a dynamic bal- ance between exploration and exploitation, reducing the likelihood of premature convergence - a common challenge in complex optimization problems. Keywords: algorithm; balance; chlorophyll; convergence; diversification; exploration; intensification; optimization; photosynthesis; population; problems; psio; search; solution
Overlapping Domain Decomposition Methods for Noncoercive Hamilton-Jacobi-Bellman Equation by Chebbah, Samar; Haiour, Mohamed; Madi, Sofiane (2025) - The extended system satisfies the following equations:max 1≤i≤n (B̃iζ − G i(ζ)) Math, 18 (2) (2025), 6070 11 of 20 By subtracting these two equations and considering the decomposition Bi = A i+ µI, we obtain: (Bi − µI)(ζ+ − ζ−) = 0 ⇔ A i(ζ+ − ζ−) = 0. Keywords: decomposition; domain; haiour; max; solution
Asymptotic Solutions to a Singularly Perturbed Partial Integro-Differential Equation with a Rapidly Oscillating Right-Hand Side by Begaidarov, Muminbek ; Bibulova, Dana; Kalimbetov, Burkhan (2025) - Math, 18 (4) (2025), 6488 13 of 20 ≤ c0k0 x∫ x0 ||w(ζ, ε)||dζ + c0k1 x∫ x0 ζ∫ x0 ||w(s, ε)||dsdζ+ + X0 ε c0||Φ(x, ε)||C[x0,X]×[0,T ] ≤ c0k0 x∫ x0 ||w(s, ε)||ds+ +c0k1 x∫ x0 x∫ x0 ||w(s, ε)||dsdζ + c0X0 ε ||Φ(x, ε)||C[x0,X]×[0,T ] ≤ ≤ c0k0 x∫ x0 ||w(s, ε)||ds+ c0k1 X∫ x0 x∫ x0 ||w(s, ε)||dsdζ+ + c0X0 ε ||Φ(x, ε)||C[x0,X]×[0,T ] ≤ (c0k0 + c0k1X0) x∫ x0 ||w(s, ε)||ds+ + c0X0 ε ||Φ(x, ε)||C[x0,X]×[0,T ] where X0 = X − x0, ||K(x, t, s)||C[x0,X]×[0,T ] = k0, ||∂K(x,t,s) ∂x ||C[x0,X]×[0,T ] = k1. ∂u ∂τj − λ1(x)u− x∫ x0 K(x, t, s)u(s, t, ψ(s)ε , ε)ds = h1(x, t)+ +h2(x, t)e τ2σ, u(x0, t, 0, ε) = y0(t), ( (x, t) ∈ Keywords: differential; equation; kalimbetov; problem; solution

Equation

A complete Classification of Lienard equation by Zeghdoudi, Halim; Bouchahed, Lahsen; Dridi, Raouf (2013) - =−2 f fx , fx x = 0 and g 6= 0 x − 2 f fx x 2 � 2 fx 3 f , B =− λ f fx , fx x x x = − f fx 3 fx x Keywords: equation;  
Characterization Theorems for Scale Invariance Property of Insurance Premium Calculation Principles by Pratsiovytyi, Mykola; Drozdenko, Vitaliy (2014) - (29) In the case of scale invariant mean value premium principle equation (29) can be rewritten as v(Θπm.v.[X ε p]) = pv(Θε) + (1− p)v(Θ). 2. Mean Value Premium Principle The following theorem describes necessary and sufficient conditions under which mean value premium calculation principle possesses scale invariance property. Keywords: equation; � �
On the Solutions of the Diophantine Equation $p^x +(p+4k)^y=z^2$ for Prime Pairs $p$ and $p+4k$ by Mina, Renz Jimwel Silva; Bacani, Jerico Bravo (2021) - Lastly, we study the solutions of Diophantine equations of the form px + (p+ 4k)y = z2, k ≥ 2 (3) where p and p+ 4k are both primes. Acu, Burshtein, Dockan, Neres, Rabago, Sroysang, and Suvarnamani are among the mathematicians who studied Diophantine equations of the form ax + by = z2 (cf. Keywords: equation
On the Diophantine Equation Mp^x + (Mq + 1)^y = z^2 by Gayo, Jr., William Sobredo; Bacani, Jerico Bravo (2021) - On the number of solutions of Diophantine equations x2−D = pn. More on Diophantine equations of type px + qy = z2. Keywords: equation
Definite integral of a hyperbolic quotient function expressed in terms of the Lerch function by Reynolds, Robert; Stauffer, Allan (2021) - Use equation (21) and set m = β = 1 and simplify. Next using equation (2) and replace y by log(a), k by k − 1 and multiply both sides by − iπ 2c2 and simplifying to get R. Reynolds, A. Stauffer / Eur. Keywords: equation; use
A Note on the Definite Integral of the Lerch Function by Reynolds, Robert; Stauffer, Allan (2021) - = − log(2) (13) Proof. This transform is then used to derive definite integrals in terms of fundamental constants, elementary and special functions. Keywords: equation
Definite Integral of Exponential Polynomial and Hyperbolic Function in terms of the Incomplete Gamma Function by Reynolds, Robert; Stauffer, Allan (2021) - Use equation (14) and set k = 0 and simplify. Use equation (14) and set a = 1 and simplify. Keywords: equation; integral
A Note on the Infinite Sum of the Lerch function by Reynolds, Robert; Stauffer, Allan (2022) - 2020 Mathematics Subject Classifications: 30E20, 33-01, 33-03, 33-04, 33-33B Key Words and Phrases: Lerch function, incomplete gamma function, Catalan’s constant, Apréy’s constant 1. Introduction Infinite sums of special functions have been studied in the works of [1, 5, 6, 10, 13]. Keywords: equation; function; n=1; simplify
Definite Integrals Involving Logarithmic Powers, Binomials and Polynomials Expressed in terms of the Lerch Function by Reynolds, Robert; Stauffer, Allan (2022) - x2 − 1 dx, (1) which has a closed form solution in terms of the Lerch function. x2 − 1 dx = 1 2 iπ ( logk(a)− 2(iπ)keiπmΦ ( −eimπ,−k, 1− i log(a) π )) , (9) where −1 < ℜ(m) < 1. 8. Keywords: equation
On the Partial Differential Equations with Non-Constant Coefficients and Convolution Method by Kilicman, Adem; Eltayeb, Hassan (2009) - Now consider the equations (5) and (11) have solutions F(x , t) and K(x , t) respectively, then we can easily check whether F(x , t) ∗ ∗K(x , t) is a solution for a similar type of wave equation. Now by taking double Laplace transform for the equation (11) and single Laplace transform for initial conditions, the solution of equation (11) given by u(x , t) = L−1 s L−1 p      sH1(p) � s2 − p2 � − pG1(s) � s2 − p2 � + pH1(p)−H1(0) � s2 − p2 � − sG1(s)− G1(0) � s2 − p2 � + F(p, s) � s2 − p2 � Ψ(p, s)      (12) provided the inverse double Laplace transform exist. Keywords: equation
Numerical Study of Two Dimensional Steady Incompressible Newtonian Laminar Flow of Blood Through Constricted Artery by Tsetimi, Jonathan; Mamadu, Ebimene James (2022) - The results obtained reveal alterations in blood flow due to presence of stenosis in arterial wall and the implications are discussed. It describes the physical laws that govern blood flow in the blood vessels. Keywords: blood; equation; flow; velocity
Exact Solution of Burger's Equation Using Tensor Product Technique by Al-sharif, Sharifa Naem; Aljarrah, Ameera ; Almefleh, Hassan (2022) - Now, Ψ′ = et = Ψ, then equation (2) becomes Φ⊗Ψ+Φ′ ⊗Ψ Math, 15 (4) (2022), 1444-1454 1451 Ψ ′ Ψ = 1− f∫ dΨ Ψ = ∫ (1− f)dt ln |Ψ| = ∫ (1− f)dt Ψ = e ∫ (1−f)dt. To verify equation (5), set Φ = ex = Φ′ = Φ′′ and Ψ = e ∫ (1−f)dt and Ψ′ = (1−f)e ∫ (1−f)dt = (1 − f)Ψ, then u = Φ ⊗ Ψ, ux = Φ′ ⊗ Ψ Keywords: equation
Analytical Solution of Vertically Integrated Equations of a Confined Aquifer in two-dimension using Finite Volume method by Itoua-Tsele , Cordy Jourvel; Ouassissou, Antoine Filankembo (2023) - Gw-pinn: A deep learning algorithm for solving groundwater flow equations. [10] proposed a mathematical model to represent the transition of groundwater flow from con- fined to unconfined aquifers, specifically the classical differential operator that is based on the rate of change is replaced by a non-conventional one including the differential operator that can represent processes following the power law to capture the memory effect, after which the numerical analysis was carried out using the Caputo fractional operator, and numerical solutions were obtained. Keywords: aquifer; equation; flow; groundwater; head; volume
Bifurcation and Exact Traveling Wave Solutions for the Nonlinear Klein-Gordon Equation by Arab, Meraa (2023) - This paper focuses on the construction of traveling wave solutions to the nonlinear Klein–Gordon equation by employing the qualitative theory of planar dynamical systems. Traveling wave solution Applying the traveling wave transformation ξ = x− ωt, u = φ(ξ) (2) to Eq. Keywords: equation; nonlinear; orbits; periodic; phase; solutions; system; wave
The Spectrum of a Certain Large Block Matrix by Edris Rawashdeh; Heba Adel Abdelkarim; Eman Rawshdeh (2024) - = d∗k+1 = −d∗k+1) for all k = 1, 2, . . = d∗k+1 = −d∗k+1) for all k = 1, 2, . . Keywords: equation; matrix
Conservation Laws and Symmetry Multi-Reductions of Two (2 + 1)-Dimensional Equations: The Zakharov-Kuznetsov (ZK) Equation and a Nonlinear Wave Equation by Kakuli, Molahlehi Charles; Sinkala, Winter; Masemola, Phetogo (2025) - We obtain four nontrivial conserved vectors T1 = ( T t 1, T x 1 , T y 1 ) , T2 = ( T t 2, T x 2 , T y 2 ) , T3 = ( T t 3, T x 3 , T y 3 ) , T4 = ( T t 4, T x 4 , T y 4 ) , (4.9) where T t i , T x i , T y i , i = 1, . . . Reduction via X = X5 We obtain the first reduction of the conservation law T4 by writing it in canonical variables determined from writing the associated symmetry X = X5 in the form X = ∂ ∂q . Keywords: conservation; equation; reduction; symmetries; symmetry; t r; t t; t y
On the Study of Bi-Univalent Functions Defined by the Generalized S\u{a}l\u{a}gean Differential Operator by Al-Rawashdeh, Waleed (2024) - In this paper, we make use of the generalized Sălăgean differential operator to define a novel class of bi-univalent functions that is associated with the generalized hyperbolic sine function in the open unit disk D. In this paper, as an application of the Sălăgean operator, we introduce a new class of bi-univalent functions and discuss certain characteristic properties of this generalized function class. Keywords: class; equation; following; functions
An Application of Legendre Polynomials to Bi-Bazilevic Functions associated with q-Ruscheweyh Operator by Al-Rawashdeh, Waleed (2025) - This operator is introduced with the aim of generalizing the class of qanalogue of the Ruscheweyh operator within the set of univalent functions. In 1933, Fekete and Szegö [19] established the upper bound of the expression |a3−λa22| for univalent functions f , where the 0 ≤ λ ≤ 1. Keywords: class; cos; equation; following; functions; operator; polynomials; rαq
Quantization of Dissipative Anisotropic Harmonic Oscillators by Al-khamiseh, Bashar M. ; M. Alawaideh, Yazen; Issaadi, Hayat ; Muhammad Bilal; Abbas, Shajar ; Ghannam, Hala ; Baleanu, Dumitru (2025) - All methods yielded consistent results, demonstrating the model’s robustness and its significance for understanding dissipative quantum systems. The quantum Bateman method has also been extensively studied for dissipative systems, offering valuable insights [3– 5]. Keywords: dissipative; energy; equation; oscillator; quantization; quantum; systems
Harvesting Mixed, Homoclinic Breather, M-Shaped, and Other Wave Profiles of the Heisenberg Ferromagnet-Type Akbota Equation by Ceesay, Baboucarr; Baber, Muhammad Z.; Ahmed, Nauman; Jawaz, Muhammad; Macías-Díaz, Jorge E.; Gallegos, Armando (2025) - We use the Hirota bilinear technique to investigate wave solutions to the Heisenberg ferromagnetic- type Akbota problem arising in surface geometry. The investigation obtained a variety of wave solutions such as periodic lump waves, periodic cross-kink waves, homoclinic breather waves, M-shaped waves, and mixed waves, proving the universality of the method. Keywords: = √; bω1 −; c √; equation; exp; plot; solutions; v6 =; wave; σ √; − √; √ aθ(2−; √ bk2; √ d; √ −abθ2
Statistical Inference on Type II Topp Leone Generalized Inverted Exponential Distribution with Some Applications on Real Data by Alsaiary, Zakeia Amer; Al-Jadani, Sarah (2025) - (vi) The α̂, bias and MSEs values for Bayes estimates of E loss function under Jeffery’s prior and E loss function with (d = 1) under Quasi prior are very similar. (iv) The α̂, bias and MSEs values for Bayes estimates of E loss function under Jeffery’s prior and E loss function with (d = 1) under Quasi prior are very similar. Keywords: distribution; equation; function; loss
Qualitative Study on Finite Volume Method for Solving Linear and Nonlinear Partial Differential Equations by Saeed, Abdulkafi Mohammed; Alfawaz, Thekra Abdullah Fayez (2025) - Furthermore, WENO schemes are capable of achieving high-order accuracy (third, fifth, or even higher) in smooth regions, making them highly attractive for problems requiring high precision. WENO schemes have gained more attention than Essentially Non-Oscillatory (ENO) schemes, both in algorithm development and applications. Keywords: differencing; equation; error; numerical; scheme; volume
Analyzing Approximate and Exact Wave Solutions of Optical Fibres in the Time-fractional Estevez-Mansfield-Clarkson Equation by Yasmeen, Bushra; Ahmad, Khalil; Fatima, Nahid (2025) - The proposed method entails transforming nonlinear fractional partial differential equations into nonlinear ordinary differential equations. Introduction In applied science, engineering, and mathematics, as well as in the modeling of a va- riety of physical nonlinear phenomena, nonlinear fractional partial differential equations (NFPDEs) are essential [1], [2] . Keywords: equation; nonlinear; solutions; w k
Hybridization of Neural Nets and Genetic Algorithms to Compute the Boundary Control for Controlled Heat Equation by Tomar, Nutan Kumar; Sukavanam, N; Singh, K P (2011) - The exact solution of the above problem is given in [2] as follows: The (optimal) control function is πexp(2π2ν t) sin(πx); for 0< x < 1; y = 0,1 and πexp(2π2ν t) sin(πy); for 0< y < 1; x = 0,1 and the temperature ω being defined by ω(x , y, t) = πexp(2π2ν t)(sin(πx)+ sin(πy)) The controlled semilinear heat equation, with boundary control, in Q is ∂ ω(x , t) ∂ t = c2∆ω(x , t) + Keywords: boundary; control; equation; heat; network
Abundant Explicit Non-Traveling Wave Solutions to the $(3 + 1)$-Dimensional Nonlinear Evolution Equation Using a Generalized Variable Separation Method by Alsallami, Shami; Alkinidri, Mohammed (2025) - Non-traveling wave solutions allow us to characterize more complex natural phenom- ena across various scientific fields, which may not be easily analyzed using soliton solutions. 2020 Mathematics Subject Classifications: 35Q51, 35C05, 37K40 Key Words and Phrases: Non-traveling wave solutions, Generalized variable separation tech- nique, evolution equation, Wave solutions, Symbolic computation 1. Keywords: equation; f1(z; nonlinear; solutions; wave
Symmetries and Novel Exact Solutions for $ (2+1) $-D QZK Equation via Lie-Symmetry and Kudryashov-Auxiliary Method by Gaber, Ahmed; M. Younis, Tawfik ; F. Alharbi, Mona (2025) - − q − 2q −m2r − 2m2r + 2rm+ rm) pm[1 + csc (k(x−m1) + h(y −m2))] . − q − 2q −m2r − 2m2r + 2rm+ rm) pm[1 + csch (kt+ h(y −m2x))] . Keywords: equation; gaber; solutions
Asymptotics Solutions of a Singularly Perturbed Integro-Differential Fractional Order Derivative Equation with Rapidly Oscillating In-homogeneity by Bobodzhanov , Abdukhafiz; Kalimbetov, Burkhan; Turekhanov, Kassymkhan (2025) - e 1 ε s∫ t0 θ(α−1)λ1(θ)dθ ∣∣∣∣∣∣ s=t s=t0 − − t∫ t0 ∂ ∂s ( K(t, s)z1(s) s(α−1)λ1(s) ) e 1 ε s∫ t0 λ2(θ)dθ ∣∣∣∣∣∣ s=t s=t0 − t∫ t0 ∂ ∂s ( K(t, s)z2(s) λ2(s) ) e 1 ε s∫ t0 λ2(θ)dθ ds − = ε K(t, t)z2(t) λ2(t) e 1 ε t∫ t0 λ2(θ)dθ − K(t, t0)z2(t0) λ2(t0) − −ε t∫ t0 ∂ ∂s ( K(t, s)z2(s) λ2(s) ) Keywords: differential; equation; k(t; problem
Deducing Trigonometric Functions from Differential Equations: An Educational Perspective by Khan, Sameen Ahmed; Kankarej, Manisha; Khan, Mohammad Nazrul Islam (2025) - In this Section, we deduced the basic properties of the trigonometric functions, sinx and cosx starting with the second-order linear differential equation y′′ + y = 0, using the qualitative properties of differential equations (essentially the uniqueness of the solutions). If y = s(x), then y′ = c(x) and c2(x) + s2(x) = C. Using the initial conditions, s(0) = 0 and c(0) = 1, we have C = 1. Keywords: differential; equation; functions; khan; s(x; solutions; theorem
Numerical Solution of the Intuitionistic Fuzzy Complex Heat Equation with Intuitionistic Complex Dirichlet Boundary Conditions via the Explicit Finite Difference Method by Alkouri, Abd Ulazeez; Damrah, Sadeq; Zureigat , Hamzeh; Al-Ogilat , Osama; Hussein, Eman (2025) - Math, 18 (3) (2025), 6232 2 of 15 Key Words and Phrases: Finite difference methods, complex, fuzzy numbers, Intuitionistic fuzzy sets, complex fuzzy numbers, fuzzy heat equations 1. Numerical solution of fuzzy heat equation with two different fuzzifications. Keywords: cif; equation; heat; j(ξ; t;β
Generalized SWAP and iSWAP and Solutions to the Yang-Baxter Equation in All Dimensions by Pourkia, Arash (2025) - Math, 18 (3) (2025), 6344 9 of 14 (αSWAP)S =  eiα1 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ eiαd ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ eiαd2−d+1 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ eiαd2  =  x11 ∗ ∗ ∗ ∗ ∗ ∗ ∗ xdd ⊗  y11 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ydd  =  x11y11 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ x11ydd ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ xddy11 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ xddydd  This completes the proof. Below, we illustrate this argument by highlighting the relevant entries with boxes: αSWAP =  eiα1 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ 0 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ 0 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ eiαd2  =  x11 ∗ ∗ ∗ ∗ ∗ ∗ ∗ xdd ⊗  y11 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ydd  =  x11y11 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ x11ydd ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ xddy11 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ xddydd  For (αSWAP)S, a similar argument (illustrated below with matrices and boxed entries) shows that assuming (αSWAP)S = X ⊗ Y leads to the equality eiα1eiαd2 = eiαdeiαd2−d+1 . Keywords: baxter; equation; gates; quantum; yang; αswap; ∗ ∗
Innovative Solitary Wave Solutions for the (3+1)-Dimensional Boussinesq Kadomtsev-Petviashvili-Type Equation Derived via the Improved Modified Extended Tanh-Function Method by W. Mohammed, Wael ; Khalifa, Abeer; Alshammari, Hijyah ; Ahmed, Hamdy M. ; S. Algolam, Mohamed ; Elbarougy, Reda ; Ahmed, Karim (2025) - Several traveling wave and soliton solutions are derived and discussed. Construction of soliton solutions and periodic solutions of the boussinesq equa- tion by the modified decomposition method. Keywords: equation; soliton; solutions; ℵz −; − ωt
Random Exact Solutions for the Stochastic Korteweg-de Vries Equation by Alshuhail, Altaf ; Hassan, Taher S.; Algolam, Mohamed; Ahmed, Athar I.; Mohammed, Wael W. (2025) - Unlike traditional wave solutions that disperse and dissipate over time, singular solitons have the remarkable feature of maintaining their form and amplitude as they propagate through a medium. Backlund transformations and soliton solutions for the kdv6 equation. Keywords: equation; solutions

System

Single-Input Control Systems on the Euclidean Group SE(2) by Adams, Ross M.; Biggs, Rory; Remsing, Claudiu C. (2012) - Introduction In recent decades, attention has been drawn to invariant control systems evolving on ma- trix Lie groups of low dimension. A category of control systems. Keywords: control; lie; system
Competition Among Manufacturers in Technological Innovation in the Market with Delayed Information by JSS, SilvÃ©rio Dos Santos; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Torresan, Paulo; Torresan, Paulo; Torresan, Paulo; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Torresan, Paulo; Torresan, Paulo; Torresan, Paulo; Azevedo, Katia A. G.; Torresan, Paulo; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Torresan, Paulo; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Torresan, Paulo; Torresan, Paulo; Azevedo, Katia A. G.; Torresan, Paulo; Torresan, Paulo; Torresan, Paulo; Torresan, Paulo; Azevedo, Katia A. G.; Torresan, Paulo; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Torresan, Paulo; Torresan, Paulo; Torresan, Paulo; Torresan, Paulo; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Torresan, Paulo; Azevedo, Katia A. G.; Torresan, Paulo; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Torresan, Paulo; Torresan, Paulo; Torresan, Paulo; Torresan, Paulo; Azevedo, Katia A. G.; Torresan, Paulo; Torresan, Paulo; Torresan, Paulo; Torresan, Paulo; Torresan, Paulo; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Torresan, Paulo; Azevedo, Katia A. G.; Torresan, Paulo; Torresan, Paulo; Torresan, Paulo; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Torresan, Paulo; Torresan, Paulo; Torresan, Paulo; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Torresan, Paulo; Azevedo, Katia A. G.; Torresan, Paulo; Torresan, Paulo; Azevedo, Katia A. G.; Torresan, Paulo; Torresan, Paulo; Azevedo, Katia A. G.; Torresan, Paulo; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Azevedo, Katia A. G.; Torresan, Paulo; Azevedo, Katia A. G.; Torresan, Paulo; Torresan, Paulo; Azevedo, Katia A. G. (2014) - = 2x y − d y + be−σx[x sinσy − y cosσy] + ae−r x sin r y = 0. − y cosσy ≥ 0 for (x , y) ∈ S2. Keywords: system
Modeling, Simulation and Performance Analysis of a Flexible Production System by Boualem, Mohamed; Cherfaou, Mouloud; Bouchentouf, Amina Angelika; Aissani, Djamil (2015) - In some situations there may indeed be an infinite supply of work; in production systems, the supply of parts for processing at an expensive machine may be controlled and not allowed to exhaust. 2010 Mathematics Subject Classifications: 60K25, 68M20, 90B22 Key Words and Phrases: Queueing models; flexible production systems; modeling; simulation; stabil- ity. Keywords: class; customers; network; stability; station; system
Optimal reliability allocation for redundancy series-parallel systems by Abed, Saad Abbas; Udriste, Constantin; Tevy, Ionel (2017) - The original results include: (i) submersion of a ”series-parallel system” into a ”series system”, (ii) detailed analyse of a series-parallel system whose components of each subsystem have the same reliability; (iii) designing series-parallel systems by similarities with other engineering problems; (iv) dualities between reliability systems and electric circuits. System reliability and mean life can be increased by additional means by applying redun- dancy at various levels. Keywords: reliability; series; system
New derived systems of Hideâ€™s coupled dynamo model by Allahem, Ali (2017) - The system where N = 2 is given by the following set of nonlinear ordinary differential equations [7]: ẋ1 = mx2y1 − x1 − βz1, ẏ1 = α(1−mx2x1)− κy1, ż1 = x1 − λz1. = zy, ẏ = 1− xz, ż = xy, If we consider those solution for which x = z and perform the substitution u = x = z, then we get the following system u̇ = zu, ẏ = 1− u2, (16) These equations are well-known which are called the Bullard model dynamo [2]. Keywords: system
On Flows Spectrum on Closed Trio of Contours with Uniform Load by Buslaev, Alexander Pavlovich; Tatashev, Alexander Gennadjevich; Yashina, Marina Victorovna (2018) - Thus, if the cluster velocity is not equal to 1, then the system approaches to one of the two states ( l, 12 , α30 ) , 0 ≤ α30 ≤ 1, Fig.1, or ( α10, 1 2 , 1 2 + l ) , 0 ≤ α10 ≤ 1, Fig.2, up to a shift, during a finite time 0,5 0,50,5 0 0 0 l 0,5 - l γ0γ -0 l Figure 1: System state l, 1/2, α30 0,5 0,50,5 0 0 0 α 0 1 - l 0,5 + l α 0 -l Figure 2: System state α10, 1/2, 1/2 + l 2.4. Depending on the value of cluster length l we have 1) Keywords: state; system; time; α3,0
Impact Optimization of Battery Energy Storage System in Microgrid Operation by Adjei, Bernard; Donkoh, Elvis K.; Otoo, Dominic; Owusu-Ansah, Emmanuel De-Graft Johnson; Mahama, Francois (2020) - Reliability-constrained optimal sizing of energy storage system in a microgrid. We will be neglecting the possibility of cost savings because from our initial solution, the amount of PV power sold was zero (0). Keywords: battery; cost; grid; microgrid; power; storage; system
On General Properties of Degenerate Systems of Second Order Partial Differential Equations of Hypergeometric Type by Issenova, Akkenzhe; Tasmambetov, Zhaksylyk; Rajabov, Nusrat (2021) - Peculiarities of building the solution of Horn type system consisting of equations. Especially, it is little known about related systems with Whittaker type system. Keywords: solutions; system; variables
The Discrete Lyapunov Equation of The Orthogonal Matrix in Semiring by Gregoria Ariyanti; Sari, Ana Easti Rahayu Maya (2023) - 3. Results and discussion The problem of discrete Lyapunov equations over semirings is limited to orthogonal matrices. Let discrete Lyapunov equation over semiring AXAT − X + Q = 0 with A ∈ Mn×n(S), Q ∈ Mn×n(S). Keywords: kronecker; linear; lyapunov; semiring; system
Analysis of Novel 4D Rabinovich-Fabrikant Continuous Dynamical System with Coexistence Attractors by aziz, Maysoon M; Arif, Ghassan E.; Ahmad, Ahmad T. (2023) - Characteristic equation The Jacobian matrix of new system (1), at equilibrium point E0(0, 0, 0, 0) is: 0.077 −1 0 0 1 0.077 0 0 0 0 −0.2 4 0 0 −0.2 4  It’s characteristic equation λ4 − 3.954λ3 + 0.791129λ2 − 3.6993302λ − 0.8047432 = 0. Math, 16 (3) (2023), 1991-2004 1995 (a) (b) Figure 1: The wave-form of new system (1): (1a)x− t, (1b)z − t. 3.3.2. Keywords: aziz; control; lyapunov; new; synchronization; system
On controlling, Vibration Performance and Energy Transfer of an Offshore Wind Turbine Tower System via PPF Controller by Alsaadi, Ateq; Salah Hamed, Yasser (2023) - The results also be compared to previous research that has been published. 2020 Mathematics Subject Classifications: 34A34, 34C15, 34C23, 34C25, 34D20, 34E13, 37N15, 70B05, 70K05, 70K40, 70K42, 70K50 Key Words and Phrases: Offshore wind turbine system, Energy transfer, Vibration control, Stability, positive position feedback control 1. [0] B. Fitzgerald , S. Sarkar and A. Staino, “Improved reliability of wind turbine towers with active tuned mass dampers (ATMDs)” Journal of Sound and Vibration 419 (2018) 103–122. Keywords: control; response; system; turbine; wind
Integral Resonant Controller for Suppressing Car’s Oscillations and Eliminating its Inherent Jump Phenomenon by Kandil, Ali; Hamed, Y. S. (2023) - Applied nonlinear control. Nonlinear integral resonant controller for vibration reduction in nonlinear systems. Keywords: amplitude; car; control; force; irc; kkc; motion; response; system
$D$-Stability Analysis of Structured Matrices Appearing in First and Second Order Economy Models by Bakery, Awad A.; Rehman, Mutti-Ur; Alshabhi, Salah H.; Alshehri, Mohammed N.; Mohammed, Mustafa M.; Mahgoub, Hala S.; Magzoub, Mona; Hamed, Sakeena E. M.; Taha, Khdija O. (2025) - Furthermore, new results are established on interconnections between structured stable matrices, structured D-stable matrices, and µ-values. The novel results on structured stable matrices, and structured D-stable matrices corresponding to first order dynamical systems are analyzed in section 3. Keywords: ain; iin o; matrices; matrix; o o; o p22; p11 o; stability; system; µ-values
The Asymmetric Periodically Forced Van Der Pol Oscillator by Alraddadi, Ibrahim (2025) - Moreover, Guckenheimer et al. observed that there can be can be chaotic attractors for return map F (13) by analysing the behaviour associated with canard trajectories [10]. = 1 τκ (γk sin(2πωt)− β − y) ẏ = α τκ (y − y3 3 + x) (2) which is a slow-fast system if α ≫ 1 . Keywords: der; figure; map; oscillator; pol; return; system; van
Steady-State Performance Evaluation of an MX/G(a, b)/1 Queue with Low-Batch Service, Multiple Vacations and Uninterrupted Server Renovation by S., Karpagam; N, Aarthy; Gupta, Gopal Kumar (2025) - Several researchers have studied bulk service systems with multiple vacations. - Function of cumulative distribution for bulk service times. R(.) Keywords: a−1∑; batch; bulk; m =; queue; queueing; server; service; system; time
A Comparative Study on the Impact of Infection on the Stability of Eco-epidemiological Models by Hassan, Kawa (2025) - The eigenvalue in the i-direction is λ2 = s−3 − wp−3 − d3, and for: J ′ 13 = s−3 (n2p − 3 (c2+2s−3 ) G2 3 − e ) −n2s − 3 G3 mn2p − 3 (c1−(s−3 )2) G2 3 0  , we have: tr(J ′ 13) = s−3 ( n2p − 3 (c2 + 2s−3 ) G2 3 − e ) , det(J ′ 13) Hence, λ2 = s−3 − wp−3 − d3 < 0. Keywords: holling; predator; prey; response; system; type
Exponential Stability of Volterra Integro-Dynamic Sylvester Matrix System on Time Scales by Chintamaneni , Harisha; Bhogapurapu, Venkata Appa Rao; Ayyalappagari, Sreenivasulu (2025) - Stability and controllability of VID Sylvester matrix systems have also been extensively studied. In this paper, we deals with exponential stability of VID Sylvester matrix system of the following form{ Y ∆(ι) = A(ι)Y (ι) + Y (ι)B(ι) + ∫ ι 0 Keywords: matrix; scales; stability; system; time
Finite-Time Scaled Consensus in Hybrid Multi-Agent Systems via Conjugate Gradient Methods by Donganont, Mana; Intawichai, Siriwan ; Phongchan , Saranya (2025) - To ensure accessibility for readers less familiar with hybrid consensus systems or conjugate gradient methods, we provide comprehensive nu- merical simulations in Section 4. Main results This section presents the main theoretical contributions of the paper, focusing on finite- time scaled consensus in hybrid multi-agent systems (HMAS). Keywords: agent; cgm; consensus; finite; hybrid; matrix; protocol; scaled; system; time
Optimal Trajectories for Drones with Limited Observability Constraints by Ajami, Alain; Sawma, Jean; Gauthier, Jean-Paul; El Maalouf, Joseph (2025) - 2020 Mathematics Subject Classifications: 49J15, 93C95, 93B07 Key Words and Phrases: Control system, Dynamic output stabilization, Asymptotic stability 1. Dynamic output stabi- lization of control systems: An unobservable kinematic drone model. Keywords: control; drone; minimum; observer; stabilization; system; target; time
On the Dynamics of Particular Discrete Quadratic Systems with Potential Absence of Equilibria: Standard Euler versus Nonstandard Mickens Discretizations by Ansori, Moch. Fandi; Khoerul Fata, Hafidh; Ashar, Nurcahya Yulian; Herdiana, Ratna; Saleh, Khairul (2025) - These results enrich the study of discrete chaotic systems and highlight the advantages of nonstandard discretization. An efficient nonstandard finite differ- ence scheme for a class of fractional chaotic systems. Keywords: dynamics; equilibrium; nonstandard; parameter; scheme; stability; system
Bi-Metric Structures and Their Applications in Bitopological Contexts by Alsoboh, Abdullah ; Oudetallah, Jamal ; Amourah, Ala; Al-Naimi, Raja’a ; Al Hatmi, Mohammed ; Audeh, Wasim ; Almalkawi, Ahmad ; Sasa, Tala (2025) - If (X,ϕ1) and (X,ϕ2) are both separable metric spaces, then (X,Ψ,⊕) forms bi-separable bi-metric system. For bi-complete bi-metric system (X,Ψ,⊕) with Ψ(x, y) = (ϕ1(x, y), ϕ2(x, y)) and ⊕ implementing component-wise addition, consider mapping T : X → X satisfying: Ψ(T (x), T (y)) ≤comp (λ1 · ϕ1(x, y), λ2 · ϕ2(x, y)) for all x, y ∈ X and constants λ1, λ2 ∈ Keywords: metric; spaces; system; topology
Frequency Locking and Bifurcation Analysis in Asymmetrically Forced Van der Pol-DuffingModel of Glacial Cycles by Alraddadi, Ibrahim; Almuaddi, Saad M. (2025) - Figures 6(a) through 6(c) illustrate the saddle-node bifurcation of the return map as system parameters are varied. [9] established the theoretical framework for under- standing folded singularities and canard trajectories in forced van der Pol systems, while Ashwin et al. (2018) Keywords: der; forcing; frequency; locking; parameter; pol; return; system; van
Center Bifurcation for the Smallest Bimolecular Mass-Action System by Salih, Rizgar (2025) - − 4534b1 − 1969c1 − 855d1). K is the sum of the diagonal minors of (2) and K = k4 (k3 − k1 − k2), • Keywords: bifurcation; center; equilibrium; point; system
Bifurcations, Hidden Attractors, and Chaos in a Nonlinear Three-Dimensional System by Fata, Hafidh Khoerul; Ashar, Nurcahya Yulian (2025) - Among the many forms of chaotic systems, a particularly interesting subclass is the three-dimensional system with quadratic nonlinearity and no equilibrium The Kaplan-Yorke dimension quantifies the degree of chaos in the system, and for chaotic systems, the dimension is often non-integer. Keywords: bifurcation; chaos; dynamics; equilibrium; lyapunov; system

Time

On Energy Waves via Airy Functions in Time-Domain by Eroglu, Emre; Isik, Ozlem (2016) - = �q ε−1 0 �∇⊥ψm × z � ,± q µ−1 0 =− q µ−1 0 ∂c t en(z, t) � #»z ×∇⊥φn(r) � , Hzm(r, z, t) Keywords: domain; energy; time
Sir Clive W.J. Granger Memorial Special Issue on Econometrics: An Introduction by Castle, Jennifer L.; Hendry, David F. (2017) - Perspectives on Econometrics and Applied Economics: A Tribute to Sir Clive Granger. The ET interview: Professor Clive Granger. Keywords: clive; granger; hendry; research; series; time
Clive W.J. Granger and Cointegration by Castle, Jennifer L.; Hendry, David F. (2017) - [24] R. F. Engle and C. W. J. Granger. [32] J. Gonzalo and C. W. J. Granger. Keywords: cointegration; correction; econometrics; economic; granger; hendry; i(1; journal; models; series; time; variables
Long Memory and Fractional Differencing: Revisiting Clive W. J. Granger's Contributions and Further Developments by Ito, Ryoko (2017) - Since component models consisting of short memory processes tend to be easier to estimate and interpret than fractionally integrated models, the former became a very popular mode of long memory models. Break detection in long memory time series is an active area of research today. Keywords: cointegration; econometrics; granger; journal; memory; models; processes; series; time; volatility
Spectra of Local Cluster Flows on Open Chain of Contours by Buslaev, Alexander Pavlovich; Tatashev, Alexander G (2018) - The average value of clusters velocities is called the average velocity of system clusters in time. In this paper, it has been shown that, in the case of open chain, the spectrum of cluster velocity and mode periodicity contains only one component. Keywords: cluster; node; time
Some Results on Blow-up Phenomenon for Nonlinear Porous Medium Equations with Weighted Source by Di, Huafei; Chen, Lin; Song, Zefang (2020) - Furthermore, from the choice of ε1 and ε2, it is easy to see that ε1(1+ε2)n (m+1)(n−2) = 1. Inserting (3.4)-(3.6) into (3.3), it follows that ϕ′(t) ≤ −(m+ 1) ∫ Ω |∇um|2dx+ (m+ 1)C3(l + 1) m+ l + 1 |Ω| + ut −4um = a(x)f(u), x ∈ Ω, t > 0, (1.1) u(x, t) = 0 or ∂u ∂ν = 0, x ∈ ∂Ω, t > 0, (1.2) u(x, 0) = g(x) ≥ 0, x ∈ Ω, (1.3) where m > 1 and Ω ⊂ Rn (n ≥ 3) is a smooth bounded domain, ν is the outward normal vector, g(x) is a continuous nonnegative function and satisfies the compatible condition. Keywords: blow; m+1; time
Developing Just-In-Time and Network Flow Models For Urban Snow Removal Problem by Bandpey, Zeinab; Tannouri, Ahlam; Brown, Isabelle Kemajou; Nkwanta, Asamoah (2021) - The research implemented in [2] covers how route assignments can improve the efficiency of snow removal problem. In urban areas, there is a critical need for efficient methods for snow removal while considering the impact on the transportation infrastructure of a city. Keywords: cost; flow; jit; l ≤; problem; removal; snow; time; transportation; truck; xijl
Infinite Iterative Processes: The Tennis Ball Problem by Weller, Kirk; Stenger, Cindy; Dubinsky, Ed; Vidakovic, Draga (2007) - Here, there are three coordinations of infinite processes. This has always been a feature of any fully developed process conception, but is particularly important in the case of infinite processes where there is no last step. Keywords: audrey; balls; bin; infinite; iterative; number; problem; process; processes; sam; students; time
The Mohanad Transforms and Their Applications for Solving Systems of Differential Equations by Saadeh, Rania; Alshawabkeh, Al-anoud; Khalil, Raed; A. Abdoon, Mohamed; Taha , Nidal; Khalid Almutairi, Dalal (2024) - − λ1M {C1(t)}+ λ2M {C2(t)} = 0, M {C ′ 3(t)} − λ2M {C2(t)} = 0.  (44) Operating M.T. to (44) and using the initial conditions (42) ζM {C1(t)} λ2M {C2(t)} − λ1M {C1(t)} = 0, ζM {C3(t)} − ζ2C3(0)− λ2M {C2(t)} = 0.  (45) Simplifying the system (45), we obtain (ζ + λ1)M {C1(t)} = ζ2α, (ζ + λ2)M {C2(t)} Keywords: chemical; differential; equations; m.t; sec−1; time; transform
Analysis of Stability, D-Stability, and Pseudospectra in Economic Modeling by Rehman, Mutti-Ur; Hamed, Sakeena E. M.; Taha, Nidal E. ; Mustafa, Arafa O.; Dilmurodov, Khurshidbek; Mahgoub, Hala S.; Magzoub, Mona ; Bashir, Runda A. A.; Mohammed, Mustafa M.; Bakery, Awad A. (2025) - In [22], the most general general relationships between performance and robustness of dynamical system, and special type of matrix stabilities, that is, D stability and diagonal stability were studied and analyzed. We have made use of Eigtool to visualize the pseudo-spectrum of structured matrices across the dynamical systems. Keywords: matrix; singular; stability; stable; time; values; −a)−1b
Numerical Simulation of Cutting Transport in a Drilling Operation by using TVD RKDG scheme with WENO Limiters by Khan, Ilyas; Rehman, Asad; Mehmood, Shahid; Zia, Saqib; Koh, Wei Sin (2025) - Case 5: t = 4000 s, mass rate = 4 kg/s, plotting of cuttings mass rate out vs time. 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Time [s] 0 0.5 1 1.5 2 2.5 3 3.5 4 C ut tin g M as sr at e ou t [ kg /s ] 25 boxes 50 boxes Figure 33: Case 5: t = 4000 s, mass rate = 4 kg/s, plotting of cuttings mass rate out vs time. Keywords: case; concentration; cuttings; depth; figure; mass; numerical; rate; time
Numerical Simulation of the Ripa Model using the Upwind CE/SE Scheme by Zia, Saqib; Rehman, Asad; Majeed, Samina; Ghaffari, Abuzar; Yasmeen, Shagufta ; Koh, Wei Sin ; Khan, Ilyas (2025) - Comparison of upwind CESE with simple CE/SE scheme at time t = 12. scheme captures sharp discontinuities better and has similar accuracy to other schemes from the literature. Kinetic flux vector splitting schemes for the radiation hydrodynamical equations. Keywords: equations; n−1/2; scheme; time; upwind
A Spatiotemporal Framework for Malaria Control Integrating Exposure Heterogeneity and Optimal Strategy Deployment by Abbas, Nadeem; Shatanawi, Wasfi; Zanib, Syeda Alishwa (2025) - − ϕM EF − (m1 +m3)ϵF EF ] + Ξ9[−(m1 +m3)ϵF IF + ϕM EF ]. (5.39) Where (Ξi), i = 1, 2, . . . HM , (5.33) dRM dt = ηMEht + δMHM − ϵMRM − ωMRM , (5.34) dSF dt = λF −m3 ( αMβMSF IM TF + αMβMRMSF TF ) − (m1 +m3)ϵFSF , (5.35) dEF dt = m3 ( αMβMSF IM TF + αMβMRMSF TF ) Keywords: control; control control; humans; m2 0; malaria; time; tio; transmission; zanib
Mathematical Modeling and Genetic Algorithm-Based Hyperheuristic Optimization for Quality of Service and Load Balancing in Cloud Communication Networks by Danach, Kassem ; Aly, Wael Hosny Fouad; Haddad, Samir (2025) - RR assigns tasks cyclically without considering task size or server load, leading to potential inefficiencies. Deep reinforcement learning for cloud load balancing. Keywords: allocation; aly; balancing; cloud; cloud computing; computing; framework; gahoqos; heuristic; latency; load; min; optimization; performance; qos; resource; server; service; task; time
Simulating Arterial Blood Flow Using Finite Volume Conservation Element and Solution Element Scheme by Zia, Saqib; Qandeel, Aqsa; Rehman, Asad; Ahmed, Sidrah ; Ahmed, Munshooor; Koh, Wei Sin (2025) - [23] H. Tao, R. Husam, J. J. Dheyaa, K. S. Pradeep, F-H. A. Ali, H. A. H. Abbas, F. H. Dheyaa, M. Hiba, H. I. Ameer, and S. S. S. Narinderjit. Well-balanced discontinuous galerkin method and finite volume weno scheme based on hydrostatic reconstruction for blood flow model in arteries. Keywords: blood; flow; journal; k j; numerical; scheme; time
Threshold-Based Nonlinear Protocols for Scaled Edge Consensus under Input Saturation Constraints by Donganont, Mana; Witthayarat, Uamporn; Intawichai, Siriwan; Phongchan, Saranya (2025) - The edge counterpart, scaled edge consensus, is comparatively recent: Park et al. (2) The network is said to achieve scaled edge consensus if there exists a scalar λ ∈ R satisfying lim t→∞ Z(t) Keywords: activation; consensus; control; dispersion; donganont; edge; gain; quasi; saturation; scaled; threshold; time; z(t

Function

Hankel's Transform and Rieman's Hypothesis by Rusev, Peter (2010) - Indeed, suppose the Hankel transform with kernel w1/2Jα(w), α > −1 of the function (5) is of the form (6) with function F in the class G(1−θ), 1/2 ≤ θ < 1, i.e. (4) holds for z = x ∈ (0,∞). A necessary and sufficient condition for validity of Rieman’s hypothesis is given in terms of the growth of Hankel’s transform of a function closely related to the classical ζ-function. Keywords: function
Spectrum of Periodically Correlated Fields by Dehay, Dominique; Hurd, Harry; Makagon, Andrzej (2014) - In this case G = , K = {kT : k $ !}, the quotient group G/K can be identified with [0, T ) with addition modulo T , the mapping ı is defined as ı(t) = KX , s+ (T1, 0), t+ (T1, 0) - = KX , s+ (0, T2), t+ (0, T2) - , 0 < T1, T2 <3, then X is strongly K-PC with K = {(k1T1, k2, T2) : Keywords: field; function; measure
Perfect Morse Function on SO(n) by Solgun, Mehmet (2016) - Then, the Morse polynomial of f is defined to be Pf (t) = n ∑ k=0 µk tk (13) where µk is the number of critical points of f of index k. The same argument is also true for degenerate critical points. Keywords: function
C-Support Vector Classification the Estimation of the MS Subgroups Classification with Selected Kernels and Parameters by Karaca, Yeliz; Hayta, Åžengul; Karabudak, Rana (2016) - Table 6: C-SVC Kernel Parameters Kernel Type LINEAR POLY RBF SIGMOID Degree(poly) 1.00 2.00 1.00 3.00 Gamma in kernel function (poly/rbf/sigmoid) 0 Coef in kernel function 0 Tolerance of termination criteria (eps) 0.001 C (Complexity Cost) 1 Compute probability estimates 1 Use shrinking heuristics 1 Data normalization 1 As to (Radial Basis Function) Kernel, in the study Gaussian kernel type has been used. Many different practices have been applied for parameter values with Gamma in kernel function, Coef in kernel function, Tolerance of termination criteria, Complexity cost, Compute probability estimates, Use shrinking heuristics, and Data normalization. Keywords: classification; data; disability; edss; function; karaca; kernel; linear; patients; set; study
Flocking of Multi-agents in Constrained Environments by Sharma, Bibhya Nand; Vanualailai, Jito; Chand, Utesh (2009) - The Lyapunov-based control scheme requires the design of target attractive func- tions and obstacle avoidance functions. Therefore, we construct obstacle avoidance functions that basically measure the dis- tances between the ith boid and obstacles in the workspace. Keywords: boid; control; formation; function; vanualailai
New Subclasses of Analytic Function Associated with q-Difference Operator by Frasin, Basem; Ramachandran, C; Soupramanien, T. (2017) - Mohammed and Darus [12] studied approximation and geometric properties of these q-operators in some subclasses of analytic functions in compact disk. Applications to analytic functions defined by using fractional calculus operators and convolution During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance. Keywords: function
Regularized SVM Classification with a new Complexity-Driven Stochastic Optimizer by Howe, J. Andrew; Bozdgoan, Hamparsum (2016) - Assuming they meet Mercer’s conditions, kernel functions correspond to a nonlinear map into a higher dimensional feature space F and then taking the dot product in this space. While kernel functions execute a non-intuitive process of dimensional inflation, the fre- quent superior performance of analysis with kernels is well documented in a variety of meth- ods (KDA, KPCA, KLR, . . . ). Keywords: analysis; bozdogan; classification; data; function; icom; kernel; � �
Some new Hermite-Hadamard Type Conformable Fractional Integral Inequalities for Twice Differentiable MT_(r;g,m,\varphi)-preinvex Functions by Fundo, Akli; Kashuri, Artion; Ramosaco, Miftar; Liko, Rozana (2017) - In the present paper, the notion of MT(r;g,m,ϕ)-preinvex function is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving MT(r;g,m,ϕ)-preinvex functions are given. Motivated by these results, in Section 2, the notion of MT(r;g,m,ϕ)-preinvex function is introduced and some new integral inequalities for the left-hand side of (3) involving MT(r;g,m,ϕ)-preinvex functions are given. Keywords: function; g(t
The Generalized Artin Primitive Root Conjecture by Carella, N. A. (2018) - Key Words and Phrases: Primitive root, Generalized primitive root 1. The basic properties of primitive root are explicated in [1], [30], et cetera. Keywords: function; log; mod; root
Computing mu-values for Representations of Symmetric Groups in Engineering Systems by Rehman, Mutti-Ur; Anwar, M. Fazeel (2018) - The obtained bounds for SSV for above matrix M when the perturbation structure takes the form, ∆B = {diag(∆1) : ∆1 ∈ C3,3}, are as follows. The obtained bounds of SSV for above given matrix M when the perturbation set takes the form, ∆B = {diag(∆1) : ∆1 ∈ C3,3}, are as follows. Keywords: algorithm; bounds; function; matrix; mussv; perturbation
Geostatistical Analysis with Copula-based Models of Madograms, Correlograms and Variograms by Ouoba, Fabrice; Diakarya, Barro; Talkibing, Hay Yoba (2019) - The major contribution of this paper is to propose new models of geostatistical depen- dence tools by using copula functions. Let CF be the copula underlying a stochastic process Z = {Z(s1), . . . Keywords: copula; function; f−1z
Linear Combination and Reliability of Generalized Logistic Random Variables by Ozelim, Luan Carlos de Sena Monteiro; Rathie, Pushpa Narayan (2019) - In the present paper, generalized logistic random variables are studied. In the present paper, the linear com- bination of generalized logistic random variables with different location, scale and shape parameters is given, in a compact form, in terms of the H-function. Keywords: distribution; function; reliability; variables
Density and Risk Function of the Circular Kernel Study by Njamen Njomen, Didier Alain; Yayebga, Hubert Clovis (2019) - The second part deals with the estimation of kernel density function. Some asymptotic properties of kernel estimators of a density function in case of censored data. Keywords: data; density; estimator; function; kernel; mean; risk
Using Fractal Calculus to Express Electric Potential and Electric Field in Terms of Staircase and Characteristic Functions by Delfan, Nasibeh; Pishkoo, Amir; Azhini, Mahdi; Darus, Maslina (2020) - We solve the problem with Cantor set fractal charge distribution while for other kind of discrete fractal distri- butions this work can be continue in future. Distributed charge Q on Cantor set describe it as charge density function. Keywords: charge; fractal; function; iteration; sαc2
Coefficients Characterization of Entire Harmonic Functions in Terms of Norm of Gradients at Origin in R^n, nâ‰¥ 3 by Kumar, Devendra; Vishnoi, Rajeev Kumar (2020) - Coefficient characterizations of generalized order, lower order and generalized type of entire harmonic function having the spherical harmonic expansion throughout a neighborhood of the origin in Rn have been obtained in terms of norm of gradients at origin. [18] of entire harmonic functions in terms of norm of gradient at origin . Keywords: function; lim; sup
Further Approximations on Durrmeyer Modification of Szasz-Mirakjan Operators by Yadav, Rishikesh; Meher, Ramakanta; Mishra, Vishnu Narayan (2020) - Such type of properties have been studied by researchers using various operators (see [4, 5, 17–19]). Table 1: Convergence estimations of the operators B∗n(g;x) to the function g(x) x ↓, un = n→ at n=10 at n=50 at n=100 at n=200 at n=250 at n=500 at n=1000 0.1 0.202522 0.0156053 0.0069326 0.00326665 0.00258244 0.00126086 0.000622967 0.5 3.82396 0.325365 0.148479 0.0710035 0.0563036 0.0276615 0.0137104 0.9 27.2622 2.13631 0.969982 0.462837 0.366865 0.180094 0.0892291 1.0 42.1618 3.22439 1.46137 0.696735 0.552174 0.270979 0.134238 1.5 310.724 20.8491 9.3538 4.43876 3.51461 1.72172 0.852162 2.0 1888.96 110.236 48.9145 23.0939 18.2677 8.93151 4.4164 2.5 10237.6 516.742 226.689 106.464 84.1292 41.0503 20.2783 R. Yadav, R. Meher, V. N. Mishra / Eur. Keywords: function; operators
Radon Measure-valued Solutions for Nonlinear Strongly Degenerate Parabolic Equations with Measure Data by Nkombo, Quincy Stevene; Li, Fengquan (2021) - = ∫ T 0 u(·, t)(Et)dt where Et = {x ∈ Ω/(x, t) ∈ E} (c) there exists a constant C > 0 such that ess sup t∈(0,T ) ‖ u(·, t) ‖M(Ω)≤ C. In the following, we will use the notation ‖ u ‖L∞((0,T ),M(Ω))= ess sup t∈(0,T ) ‖ u(·, t) ‖M(Ω) . There holds 1 τ ∫ t+τ t 〈u(s), ρ〉Ω ds− 〈u0, ρ〉Ω = ∫ T 0 ητ (s)ds ∫ Ω ψ(ur)∆ρdx+ ∫ T 0 ητ (s) ∫ Ω ρdµ. Since ητ (s) → χ(0,t] for every s ∈ (0, T ) as τ → 0 Keywords: equations; function; lim; measure; problem; radon; set
Extremal Copulas and Tail Dependence in Modeling Stochastic Financial Risk by Mallam, Hassane Abba; Moutari, Natatou Dodo; Diakarya, Barro; Bisso, Saley (2021) - C of the random vector U = [F1(X1), ..., Fn(Xn)]. ;Xn is a sequence of random variables with common distribution F , then the excess variable {Yj = Xj − u/Xj > u}; Nu = card{k/Xk > u} which is governed by the law Fu (conditional distribution of the unknown continuous distribution function F with respect to the threshold u), converges asymptotically towards a non-degenerate law. Keywords: copula; dependence; function; f−1; tail; uh+1
A Note on an Octuple Integral in terms of the Lerch Function by Reynolds, Robert; Stauffer, Allan (2022) - Introduction The octuple integral derived in this manuscript is given by ∫ R8 + (rs) m−1 2 (r + s)−m/2(tz)− m 2 −1(t+ z) m+1 2 (uv)− m 2 − 1 2 (u+ v)m/2(xy)m/2(x+ y) 1 2 (−m−1)e−p(r+u+x+z)−q(s+t+v+y) logk ( a √ rs √ t+ z √ u+ v √ xy √ r + s √ tz √ uv √ x+ y ) dxdydzdrdsdtdudv (1) where the parameters k, a ∈ C, Re(p, q) > 0 are general complex numbers with −1/2 ≥ Re(m) ≥ −1. Using equation (2) we replace y by (3)log ( a √ rs √ t+ z √ u+ v √ xy √ r + s √ tz √ uv √ x+ y ) then multiply by both sides by (4)(rs) m−1 2 Keywords: function; integral
A Triple Integral Involving the Struve Function Hv(t) Expressed in terms of the Hurwitz-Lerch Zeta Function by Reynolds, Robert; Stauffer, Allan (2022) - Introduction In this paper we derive the triple definite integral given by (1) ∫ ∞ 0 ∫ ∞ 0 ∫ ∞ 0 y1−mtm−v−1x−m+2v+1HHHv(t)e −bx2−cy2 logk ( at xy ) dxdydt ∗Corresponding author. y1−mtm−v−1x−m+2v+1HHHv(t)e −bx2−cy2 logk ( at xy ) dxdydt = 1 2πi ∫ ∞ 0 ∫ ∞ 0 ∫ ∞ 0 ∫ C aww−k−1y−m−w+1HHHv(t) e−bx2−cy2tm−v+w−1x−m+2v−w+1dwdxdydt = 1 2πi ∫ C ∫ ∞ 0 ∫ ∞ 0 ∫ ∞ 0 aww−k−1y−m−w+1HHHv(t) e−bx2−cy2tm−v+w−1x−m+2v−w+1dxdydtdw = 1 2πi ∫ C πaww−k−1c m+w 2 −12m−v+w−3 sec ( 1 2 π(m+ w) ) b m+w 2 −v−1dw from equation (13.2) on page 392 in [8] and equation (3.326.2) in [2] where −1 < Re(w + m) < 0 and Re(w + m) < Re(v) + 3/2, Re(b) > 0, Re(c) Keywords: function; ∫ ∞
A New Sushila Distribution: Properties and Applications by Boonthiem, Somchit; Moumeesri, Adisak ; Klongdee, Watcharin; Ieosanurak, Weenakorn (2022) - In this paper, we introduce a new continuous distribution mixing exponential and gamma distributions, called new Sushila distribution. We define new Sushila distribution and its properties in Section 2. Keywords: distribution; function; new; sushila; θ α
Neural Network of Multivariate Square Rational Bernstein Operators with Positive Integer Parameter by Ibtihal.J.M; Mohammad, Ali J. (2022) - = O(n−(α−ε)m), as n −→ ∞ for function f ∈ Lip(β), 0<ε<α. □ I.J. Mohammad, A.J. Mohammad / Eur. integral bernstein type of neural network operators. Keywords: function
On Gaussian Fibonacci Functions with Periodicity by Mohamed Salih, Hariwan Fadhil (2023) - In this work, Gaussian Fibonacci functions with the use of the (ultimately) periodicity and exponential Gaussian Fibonacci functions are also discussed. Especially, by giving a non- negative real valued function, several exponential Gaussian Fibonacci functions are attained. 2020 Mathematics Subject Classifications: 11B39, 11B99 Key Words and Phrases: Gaussian Fibonacci functions, Gaussian (ultimately) periodic, Fibonacci functions 1. Introduction Fibonacci numbers have many applications in different disciplines such as in mathe- matics, philosophy, physics, art, architecture etc, where can be found in [2, 3, 7]. Keywords: fibonacci; function; gaussian
Generalized Core Functions of Maximum Entropy Theory of Ecology by Corcino, Cristina; Corcino, Roberto Bagsarsa; Picardal, Jay (2024) - (30) Setting (30) equal to zero and solve for R(n, ϵ), 0 = − ( 1 + q 1− q − q 1− q Rq−1 ) + α0 + α1q(n− µq,1)R q−1 + α2q(nϵ− µq,2)R q−1 C. Corcino, R. Corcino, J. Picardal / Eur. Through illustrative examples, the paper provided sample probability functions for the q-Spatial structure function, showcasing how these generalized formulations can be applied in practical scenarios. Keywords: entropy; function; n=1; structure
On $\psi$ gs-Functions in Bitopological Spaces by Tutanes, Lezel Mernilo (2024) - Noiri and Popa in [7] studied some properties of weakly open functions in DOI: https://doi.org/10.29020/nybg.ejpam.v17i3.5208 Email address: lezeltutanes@buksu.edu.ph (L.M. Tutanes) https://www.ejpam.com 2173 © 2024 EJPAM Some properties of weakly open functions in bitopologcal spaces. Keywords: function; j)-ψgs; set
Some Results of Conformable Fourier Transforms by Rachid, Bahloul ; My Soufiane, Rechdaoui ; Abdeljawad, Thabet; Abdalla, Bahaaeldin (2024) - = ∫ t 0 sα−1f(s) ds, t ∈ = −2n−1α2n sin(2αtα + nπ 2 ), (πα) 1 α < t < ( 3π2α) 1 α and for t ∈ Keywords: function; periodic; t α; tα α; α α
Statistical Inference Based on Censored Data of Entropy for Lomax Distribution by Ahmed, Samah M. ; Ismail, Gamal (2025) - [4] S M Sunoj and P G Sankaran, Quantile based entropy function. [31] M Ahsanullah, Record values of Lomax distribution. Keywords: adaptive; data; distribution; entropy; function; i=1; loss; progressive; type
Flux at Infinity of Subharmonic Functions on $\mathbb{R}^2$ by Amulya Smyrna C; N. Nathiya (2025) - There is also a theorem in (Brelot [2]), by using a series representation for harmonic functions defined outside a compact set in R2, it states that given a harmonic function h outside a compact set in R2, there exists a harmonic function H on R2 such that |h−H| is bounded if and only if the flux at infinity of h is 0. Total measures of subharmonic functions and least harmonic majorants Proposition 3. Keywords: function; harmonic; infinity; measure; set; subharmonic
Subordinate Average Structures on Random Walks by M. Surya Priya; N. Nathiya (2025) - If (−∆ ′ )s ≥ (−∆ ′ )p, then s ≥ p on N . so that s ≥ p on N . Keywords: -average; -superaverage; function
A New Bivariate Transmuted Family of Distributions: Properties and Application by Alsalafi, Amani; Shahbaz, Saman ; Al-Turk, Lutfiah (2025) - However, in many situations, the jointly modeling of two variables is neces- sary, making bivariate distributions essential. Bivariate distributions also play a critical role, particularly in modeling extreme events. Keywords: cubic; distribution; family; function
A New Method for Generating Continuous Distributions with Applications by Morad Ahmad; Amleh, Mohammad Abdel-Moniem (2025) - Assume that Y1, Y2, ...., Yn is a random sample from α − RE distribution, the corre- sponding likelihood function is: L(α, θ, yi) For this, we generate random samples of α − RE distribution by considering the true values of θ and α to be 1.5 and 2, respectively. Keywords: distribution; function
Novel Types of Supra Functions Inspired by Supra $\epsilon$-Open Sets by Abd El-latif, Alaa M.; Abu-Gdairi, Radwan; Azzam , Abd elfattah; Gharib , Fatouh ; Mohammed Alhassan Attaalfadeel, Husham ; Abdelfattah, Walid ; M. Shaaban, Shaaban ; Aldawood, Mohamed (2025) - The concept of supra open sets, which take into account the fundamental components of supra topology (abbreviated, STS), was introduced by Mashhour et al. They then used their previously defined category of supra open sets to study new kinds of operators called supra ϵ-interior (closure, accumulation, exterior, and boundary, respectively). Keywords: function; soft; supra
A Class of Reduced Bias Estimators of Distortion Risk Measures under Dependence Serials with Heavy-Tailed Marginals by Deme, El Hadji; Agbrabatt, Aminetou; Barry, Mamadou Aliou; Ahmedou, Sidiya; El Waled, Khalil (2025) - The first part ( n k s )−γ Q(1 − k/n) in the right side of (18) is exactly estimated by the Weissman’s type estimator Q̂ (K) k (1 − s) and defined in (12). − γ 1 β − γ  gβ(k/n)Xn−k,n H2 = γ 1 β − γ ( Xn−k,n Q(1− k/n) − 1 ) gβ(k/n)Q(1− k/n) H3 = γ 1 β − γ gβ(k/n)Q(1− k/n)− ∫ ∞ Q(1−k/n) gβ(F (x))dx H4 = Ân,k(ρ̂ )( 1 β − γ̂ (K∆̂∗ opt ) n,k )( 1− βγ̂ (K∆̂∗ opt ) n,k − βρ̂ )gβ(k/n) Xn−k,n. Under assumptions and for all n large enough, we have from (23), √ k ( γ̂ (K∆̂∗ opt ) k Keywords: distortion; estimator; function; risk; value
Generalized Extended Confluent, Whittaker $k$-functions and Their Properties by Haider Shah, Syed Ali ; Shah, Mujahid Hussain ; Vivas-Cortez, Miguel ; Mubeen, Shahid; Rahman, Gauhar (2025) - We also obtain Riemann-Liouville fractional integral and Riemann-Liouville k-fractional integral of these new generalized extended Whittaker k-function. In [34], Panwar and Rai introduced Whittaker k-function and investigated the fractional integral of Whittaker k-function. Keywords: function; hypergeometric; whittaker
Generous Roman Domination Subdivision Number in Graph by Hamja, Jamil; Sheikholeslami, Seyed Mahmoud; Esmaeili, Mina; Volkmann, Lutz; Aniversario, Imelda; Bugo, Lucille (2025) - These findings not only extended the appli- cability of generous Roman domination to broader classes of graphs, but also established meaningful links between classical domination parameters and this new variant. [12, 13] demonstrate the rapid development of generous Roman domination as a promising research direction. Keywords: domination; function; grd; weight
Some New Weighted Results for the Hardy Operator on Variable-Exponent λ-Central Morrey Space by Asim, Muhammad ; Suwais, Khaled ; Mlaiki, Nabil (2025) - Function spaces with variable exponents: an introduction. [46] If M is weakly bounded on a Banach function space Y, i.e, ∥χ{Mf>λ}∥Y ≤ λ−1∥f∥Y, (3) where λ > 0 and f ∈ Y, then sup 1 |B| ∥χB∥Y∥χB∥Y′ < +∞. (4) Now we define weighted Banach function space and explain some of their properties. Keywords: exponent; function; k=−∞; spaces; variable; wp1
Statistical Inference for the Epanechnikov-Burr XII Distribution with Simulation and Case Studies by Odat, Naser; Hazaymeh, Ayman ; Bataihah, Anwar; Hatamleh, Raed; Abu Qamar, Majdoleen; Melhem, Alaa (2025) - 2020 Mathematics Subject Classifications: 60E05, 62-07 Key Words and Phrases: Burr XII distribution, epanechnikov, maximum likelihood, moment, moment generating function 1. = E(etX) does not exist for the Epanechnikov–Burr XII distribution when t > 0 due to its heavy-tailed nature. Keywords: burr; distribution; ebd; function; xii
Global Weighted $L^2$ $\dbar$-solvability on Noncompact Pseudoconvex Complex Lie Groups by Al-Abdallah, Abdel Rahman (2025) - Iterating this over an exhausting sequence of levels, we obtain an exhaustion G = ⋃ j∈N Ωj by smoothly bounded strictly pseudocon- vex domains Ωj ⋐ G, and smooth psh functions φj on Ωj such that supΩj−1 |φj such that each metric ball Bj := Bω(e, rj) (centered at the identity e ∈ G) is relatively compact in U1 and that 5Bj (the ball of radius 5rj) is still contained in U1. Keywords: function; lie; psh
The G-Rank-Mapped Transmuted Fréchet Weibull Distribution under Cubic Model: Mathematical Theory, Computational Statistics, and Sustainability Data Analysis by Imliyangba, Imliyangba; Abouelenein, Mohamed; Das, Bhanita; Chettri, Seema; Baruah, Bhupen; Jyoti Hazarika, Partha; Eliwa, Mohamed (2025) - Figure 5: Distribution function of CRTFW distribution for selected values of λ1 and λ2. Similarly, Figures 4 and 5 show the pdf and cdf of CRTFW distribution for different values of λ1 and λ2. Keywords: crtfw; crtfw distribution; data; distribution; fréchet; function; weibull; weibull distribution
Mathieu-type Series for the aleph-function Occuring in Fokker-Planck Equation by Saxena, Ram K.; Pogany, Tibor K (2010) - [24], how- ever the notation and complete definition is presented here in the following manner in terms of the Mellin–Barnes type integrals [also see 25]: ℵ[z] = ℵ m,n pi ,qi,τi ;r [z] = ℵ m,n pi ,qi ,τi;r � z �� (a j,A j)1,n, . . . = 1, in (1) the definition of following I–function [21] is recovered: I[z] = ℵ m,n pi ,qi ,1;r[z] = ℵ m,n pi ,qi ,1;r � z �� (a j ,A j)1,n, . . . Keywords: function; � �
Asymptotic Expansion of n-dimensional Faxen-type Integrals by Paris, Richard Bruce (2010) - [1] N G Bakhoom, Asymptotic expansions of the function Fk(x) [2] B L J Braaksma, Asymptotic expansions and analytic continuations for a class of Barnes- integrals, Compos. Keywords: algebraic; arg; expansion; function

Space

On Some Properties of Weak Soft Axioms by Hussain, Sabir (2017) - Let (X, τ,A) be a soft topological space over X and eG, eH are two distinct soft points in X̃A. If there exist soft disjoint soft semi-open sets (F1, A) and (F2, A) such that eG∈̃(F1, A), eH ∈̃(F2, A), then (X, τ,A) is called soft semi-T2-space. Since (X, τ,A) is soft semi-T2-space and eG and eH are distinct soft points in X̃A, then there exist soft disjoint soft semi-open sets (G1, A) and (G2, A) such that eG∈̃(G1, A) and eH ∈̃(G2, A). Keywords: semi; set; space
Simpler Proof of the Ringrose's Characterization of Compact Operators by Shukurov, Aydin (2015) - The aim of this note is to give short, simpler and elementary proof of one characterization of compact operators via orthonormal sequences, which, hopefully will make this fact more accessible to nonspecialists and to a wide audience (especially to students). Key Words and Phrases: orthonormal sequence and orthonormal bases in Hilbert space, Ringrose’s characterization of compact operators, linear operators, compact operators 1. Keywords: hilbert; operator; space
C-Tychonoff and L-Tychonoff Topological Spaces by ALZahrani, Samirah (2018) - Let Z be a Tychonoff space and let f : X −→ Z be a bijective function such that the restriction f|K : K −→ f(K) is a home- omorphism for each compact subspace K ⊆ X. Let h : Y −→ X be a homeomorphism. If X is C-Tychonoff and f : X −→ Y is a witness of the C-Tychonoffness of X, then f may not be continuous. Keywords: space; subspace; tychonoff
Soft Hypervector Space and Fuzzy Soft Hypervector Space by Ranjbar-Yanehsari, Esmail; Asghari-Larimi, Mohsen; Ameri, Reza (2019) - Then (i) (f,A)0 u (g,B)0 v (h, c)0 (ii) fc(0) = gc(0)⇒ (f,A)0 u (g,B)0 = (h,C)0, ∀c ∈ A ∩B. 5. Image and pre-image of fuzzy soft hypervector space In this section, the theorem of homomorphic image and homomorphic pre-image of fuzzy soft hypervector spaces are studied. Soft hypervector spaces and fuzzy soft hypervector spaces EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 12, No. 1, 2019, 118-134 ISSN 1307-5543 – www.ejpam.com Published by New York Business Global Soft hypervector spaces and fuzzy soft hypervector spaces Esmail Ranjbar-Yanehsari1, Mohsen Asghari-Larimi1,∗, Reza Ameri2 1 Department of Mathematics, Golestan University, Gorgan, Iran 2 Department of Mathematics, University of Tehran, Tehran, Iran Abstract. Keywords: hypervector; let; space
Product-Normed Linear Spaces by Barnes, Benedict; Adjei, I. A.; Amponsah, S. K.; Harris, E. (2018) - The authors in [5] and [6] independently extended the linear normed space to quasi- normed linear space. Conclusion In a nutshell, we have introduced the product-normed linear space and product-semi- normed linear space (product-semi-Banch space) which are endowed with some functional space. Keywords: linear; normed; product; space
Curvature Inequalities for Submanifolds of S-space From by Rehman, Najma Abdul (2019) - − k + 3s− 4 4 (2s− 2ms)− 3 4 (k − 1) ‖ PX ‖2 which proves the required result. + 1 2 2n+s∑ r=m+1 [ (hr11 + · · ·+ hrmm)2 + (hr11 − hr22 − · · · − hrmm)2 ] + 2 2n+s∑ r=m+1 ∑ iKeywords: space
New Topology on Omega Algebra by Alqahtani, Mesfer Hayyan; Ozel, Cenap; Alshammari, Ibtesam (2020) - Aω ×Aω −→ Aω, Then for all a1, a2, a3 ∈ A, the following axioms are satisfied: (i) a1 ⊕ a2 = a1 or a2; (ii) a1 ⊕ ω = a1 = ω ⊕ a1; M. Alqahtani, C. Özel, I. Alshammari / Eur. If there exist a γ1 ∈ I where Sγ1 = Aω, then ⋃ γ∈I Sγ = Aω ∈ τω. Keywords: inverse; omega; proof; space
Results on C2-paracompactness by Alzumi, Hala; Kalantan, Lutfi; Saeed, Maha Mohammed (2021) - Let Y and Y ′ be T2 paracompact spaces, f : X −→ Y and f ′ : A C-paracompact is a topological space X associated with a paracompact space Y and a bijective function f : X −→ Y satisfying that f �A: A −→ f(A) is a homeomorphism for each compact subspace Keywords: paracompact; space
New Topologies between the Usual Topology and the Half-disc by Alghamdi, Nadiah; Kalantan, Lutfi Nooruddin (2021) - ⟨a, b⟩• ⟨a, b⟩ ∈ K, Ur(⟨a, b⟩) ⟨a, 0⟩ •◦ ◦ ⟨a, 0⟩ ∈ L, Ur(⟨a, 0⟩) ⟨a, 0⟩ •◦ ◦ ⟨a, 0⟩ ∈ L, Cr(⟨a, 0⟩) 1. ⊆ D if ⟨u, 0⟩ ∈ A or Cδ′(⟨u, 0⟩) ⊆ D, if ⟨u, 0⟩ ∈ L \ A. Keywords: space; uah
Some Properties of Weak Separation Axioms in Coc-Compact Sets by AbuShaheen, Fuad A (2022) - U and p ∈ U with y ∈ X − {p, x}. Then coc-A∨ = ∪{F : X − F ∈ τk : F ⊆ A}, if there is no coc-closed set contains in A, then coc-A∨ = φ. Keywords: coc; space
Results about P-Normality by Kalantan, Lutfi ; Mansouri, Mai (2022) - A topological spaceX is called P -normal if there exist a normal space Y and a bijective function f : X −→ Y such that the restriction f|A : A −→ f(A) is a homeomorphism for each paracompact subspace A topological space X is called P -normal if there exist a normal space Y and a bijective function f : X −→ Y such that the restriction f|A : A −→ f(A) is a homeomorphism for each paracompact subspace Keywords: -normal; space
C-Almost Normality and L-Almost Normality by Alqurashi, Wafa; Thabit, Sadeq (2022) - Since X is compact space which is neither almost regular, almost normal nor Hausdorff, we conclude: X is neither C-almost regular, C-almost normal, epi-regular nor epi-almost normal. X is also Hausdorff space, which is neither Urysohn, regular, mildly normal, compact, paracompact nor epi-mildly normal Keywords: compact; epi; example; space; topology
Epi-completely Regular Topological Spaces by AlShammari, Ibtesam Eid (2022) - A note of quasi-normal spaces. [30, Example 15], and the either-or-topology [30, Example 17], are normal compact spaces, which are neither epi-completely-regular, epi-regular nor epi-normal. Keywords: epi; example; hausdorff; space; topology
Results about C-κ-normality and C-mild normality by Kalantan, Lutfi; Alawadi, Alyaa; Thabit, Sadeq (2023) - Let X and Y be minimal Hausdorff spaces, if X and Y are κ-normal spaces then X Since (X ,τ ) and (Y ,τ ′ ) are nearly compact Hausdorff spaces, we get (X,τ s) and (Y ,τ ′s) are Hausdorff compact spaces [20], and (X,τ s) × (Y ,τ ′s) is a T2 compact topological space which is coarser than the topology on X ×Y . Keywords: hausdorff; normality; space
Inner Products on Discrete Morrey Spaces by Jakfar, Muhammad; Manuharawati, Manuharawati; Lukito, Agung; Fiangga, Shofan (2023) - For each n ∈ N, take u = p and λ(n) = ( 1 k 1 p+ 1 n ) with λk(n) To show that the inclusion is strict, we need to find λ = (λk)k∈Z such that ∥λ∥mv,2 < ∞ but ∥λ∥mu,p = ∞. Choose u = p and λ = (λk)k∈Z with λk Keywords: space
Submaximality on Bigeneralized Topological Spaces by Farhat, Yasser ; Krishnan, Muthumari; Subramanian, Vadakasi; M. R. Ahmadi Zand (2023) - In section 4, we define the notion (s, v)⋆-bigeneralized submaximal space and the re- lationship between (s, v) and (s, v)⋆ bigeneralized submaximal space is proven. With the results given in the mentioned sections, it is possible to easily check whether a given space is (s, v) or (s, v)⋆ or (s, v)⋆⋆ bigeneralized submaximal space or not, is obtain some tricks to check in a (s, v) ((s, v)⋆ and (s, v)⋆⋆) bigeneralized submaximal space, a given set is (v, s)-nowhere dense or not, are given the necessary conditions for check whether a given space is submaximal space or not. Keywords: space
Locally Compact Spaces with Defects by Zailai, Mohmmad (2023) - We denote by X• the set of points of X which do not have compact neighborhoods. A T1 space X is a space with defects of type local compactness, l.c.w.d., if all points have compact neighborhoods except for some points. Keywords: space
CC-Tychonoffness, CCT3 and CC-Almost Regularity by Thabit, Sadeq; Alqurashi, wafa (2023) - Note that: CC-regularity does not imply CC-complete regularity, CCT3 does not imply CC-Tychonoff and CC-almost regularity does not imply CC-almost complete regularity. Math, 16 (2) (2023), 1260-1273 1268 Similarly, every T1 CC-regular Fréchet (resp. Keywords: cct3; resp; space; tychonoff
Strong Coproximinality in Bochner $L^p$-Spaces and in Köthe Spaces by Jawdat, Jamila (2023) - Math, 16 (3) (2023), 1543-1551 1547 Hence, for any y ∈ G, we have ||g(t)− y|| = ||g(t)− h(t) + h(t)− y|| ≤ ||g(t)− h(t)||+ ||h(t)− y|| < ||f(t)− y||+ δ′/µ(T ), ∀y ∈ G, a.e. t ∈ T. Finally, taking δ = δ′/µ(T ), we get, g(t) ∈ RG(f(t), δ), for a.e. t ∈ T. Remark 1. ||f(t)− h(t)||+ δ, ∀h ∈ L1(µ,G), a.e. t ∈ T. Hence, we get∫ T ||g(t)− h(t)||dt < ∫ T ||f(t)− h(t)||dt+ δ · µ(T ), ∀h ∈ L1(µ,G). Keywords: coproximinal; space
Nuclearity of a Class of Vector-valued Sequence Spaces by Sidaty, Mohamed Ahmed (2023) - Dual space of certain vector sequence spaces. Reflexivity and AK-property of certain vector sequence spaces. Keywords: sequence; space; λ(e
The SL(2,R) Group Representations on Spaces of Holomorphic Functions on the Unit Disc by Alghamdi, Amjad (2023) - = {( a b c d ) : ad− bc = 1, a, b, c, d ∈ R } . Math, 16 (4) (2023), 2348-2367 2349 A = {( α 0 0 α−1 ) : α > 0 } , N = {( 1 x 0 1 ) : x ∈ R } . Keywords: space; su(1
Separation Axioms via $F$-open Sets by Baloush, Malouh; Noiri, T. ; Talafha, M. ; dzul-Kifli3, S. Che (2024) - For F -open sets of X, the following properties hold: (1) The finite union of F -open sets is F -open, (2) The finite intersection of F -open sets is F -open. Keywords: space
A new Outlook on Omega Closed Functions in Bitopological Spaces and Related Aspects by Atoom, Ali; Qoqazeh, Hamza ; M Alholi, Maryam ; ALmuhur, Eman ; Hussein, Eman ; A. Owledat, Anas ; A. Al-Nana, Abeer (2024) - Consider- ing (G, υ1 , υ2) is pair−paracompact H ˜ has pair−open locally finite parallel refinement de- clare that:Q ˜ = {QD : D ∈ Ω1 } ⋃ {Q∗ D : D ∈ Ω2 }, where {QD : D ∈ Ω1 } is υ1-locally fi- nite paracompact of Hg,and {Q∗ D : D ∈ Ω2} is υ2-locally finite paracompact of H \ g , Ω = Ω1 ⋃ Ω2.Let L1 = {Υ−1(QD) Let (D,κ1 , κ2), (G, υ1 , υ2) be any bitopological spaces,(D,κ1 , κ2) be a pair−Lindel .. of space and (G, υ1 , υ2) be a P̋−space then the projection function π : (D ×G, κ1 × υ1 , κ2 × υ2) Keywords: space
New Results on Difference Paracompactness in Topological Spaces by Alrababah, Rahmeh ; Amourah, Ala; Jamal Salah; Reyaz Ahmad; Ali A. Atoom (2024) - It is a significant type of topological spaces that retain compactness while benefiting from paracompactness, which is considered a generalisation of compact spaces. 2020 Mathematics Subject Classifications: 54B05, 54B10, 54C05, 54D05, 54D10, 54D30, 54E55 Key Words and Phrases: Topological spaces, Paracompact spaces, D−paracompact spaces, Countably D−paracompact spaces ∗Corresponding author. Keywords: d−cover; d−paracompact; refinement; space; w,ϑ
Bounded $q$-variation Functions in Spaces with Indefinite Metric by Villa, Osmin Ferrer; Mart´ınez, Jos´e Naranjo (2025) - Functions of bounded variation in Krein spaces This section presents the fundamental theory of bounded variation functions in Krein spaces, which were introduced by Ferrer, Naranjo and Guzmán [4] Let (K = K+ ˙[+]K−, [·, ·]) be a Krein space and let f : [a, b]→ K a strongly of bounded variation function in [a, b] on (K = K+ ˙[+]K−), suppose that c in (a, b), then f is strongly of bounded variation in [a, c] and in [c, b] on (K = K+ ˙[+]K−). Keywords: krein; space; variation
Some Rigidity Theorems of Closed Geodesic Polygons and Spherical Curves in Metric Spaces with Curvature Bounded Below by Phokaew, Chanpen ; Sama-ae, Areeyuth (2024) - We will start by describing a triangle in metric space with curvature bounded below whose convex hull is isometric to a comparison triangle’s convex hull in model space RK . [1–5, 13] introduced lower and upper curvature bounds on metric spaces without Riemannian structure, which extended concepts to arbitrary spaces. Keywords: space
Necessary and Sufficient Conditions for the Equivalence of Statistical, Ideal, and Standard Convergence in G-Metric Spaces by Manuharawati, Manuharawati; Jakfar, Muhammad; Hamzah, Ahmad Taufik (2025) - Statistical convergence in g-metric spaces. Fixed point theorems in g-metric spaces. Keywords: sequence; space
Fixed Point Results for Enriched Interpolative Type Multivalued Contractions via a Simulation Function by Gangwar, Amit ; Rawatb, Shivam ; Aydi, Hassen ; Aljohani, Sarah; Mlaiki, Nabil (2025) - [0, 1] and x, y ∈ U , the next inequality holds: ρ(u,W (x, y;λ)) Math, 18 (2) (2025), 5792 11 of 16 Example 2. Let U = [0, 1] be equipped with the Euclidean metric ρ(x, v) = |x − v|, for each x, y ∈ U , and T : Keywords: metric; space; yn+1
Pretopological Spaces Induced by Rough Sets and Their Applications by Azzam, Abd El-Fattah; Mareay, Roshdey; Abd-Elhamed, Gehad M. ; Aldawood, M. ; Ali, Manal E. (2025) - Rough pretopological approximation space This section introduces the application of pretopological space in rough approximation space. Conclusion This paper used the pretopological concepts to generate rough approximation space. Keywords: approximation; rough; set; space
Some Characterizations of Quasi-Curves in Galilean 3-Space by Elsharkawy, Ayman; Noha Elsharkawy (2025) - Quasi-position vector curves in Galilean 4-space. 2020 Mathematics Subject Classifications: 51A05, 53A35 Key Words and Phrases: Quasi-frame, Galilean 3-space, quasi-normal curves, quasi-rectifying curves, quasi-osculating curves. Keywords: curve; elsharkawy; frame; quasi; space
On The Distinctive Bi-generations That are Arising Three Frameworks for Maximal and Minimal Bitopologies spaces, Their Relationship to Bitopological Spaces, and Their Respective Applications by Atoom, Ali; Al-Otaibi, Mutaib ; Qoqazeh, Hamza ; AlKhawaldeh, AL-Faroq Omar (2025) - Assume that (Z, ϑ1, ϑ2) is pairwise compact closed spaces and not pairwise minimal compact closed space, then there is ϑ / 1 ≤ ϑ1 and ϑ / 2 ≤ ϑ2 and (Z, ϑ / 1, ϑ / 2) is pairwise compact closed space. Whenever (Z, ϑ1, ϑ2) be pairwise compact compact closed space and (N,ϑ1, ϑ2) ⊂ (Z, ϑ1, ϑ2), then (N,ϑ1, ϑ2) is pairwise compact when and only when (N,ϑ1, ϑ2) is pairwise closed in (Z, ϑ1, ϑ2). Keywords: compact; pairwise; pairwise lindelöf; space
G-Compact Spaces Characterized by the Intersection of Countable Neighborhoods by Shatnawi, Mutaz ; Oudetallah, Jamal ; Bataiha, Anwar ; Amourah, Ala; Alsoboh, Abdullah; Sasa, Tala (2025) - In this research, we introduce and analyze the concepts ofG-compactness, G-Lindelöfness, and G-countably compactness within the framework of topological spaces, which are characterized by more rigorous conditions compared to those governing compact and Lindelöf spaces. This relationship enables metric spaces to exemplify topological spaces, facilitating the investigation of concepts such as continuity and convergence see [3]. Keywords: compactness; finite; set; space
Existence and Uniqueness of Fixed Points in $MR-Metric$ Spaces and Their Applications by Malkawi, Abed Al-Rahman (2025) - This study explores MR-metric spaces, which generalize the classical metric space framework to encompass a wider array of applications. This paper investigates fixed-point theorems within MR-metric spaces, an extension of standard metric spaces, emphasizing the existence and uniqueness of fixed points for continu- ous mappings S : X → X, where X is a closed, bounded, and convex subset of a Banach space (E, ∥ · ∥). Keywords: metric; point; space
A Study on $(\textit{c}, \textit{d})$ $\mathcal{IF}$-$Q$ Uniform $\mathtt{Ir}^{*}$ Centred Structure Compactification by S, Thirukumaran ; G K, Revathi (2025) - IF −Q uniform Ir∗ centred structure space PX and let G be a (c,d) IF −Q uniform Ir∗ centred structure space PX . Keywords: ir∗; ir∗ structure; space; structure; uniform
Iterative Approaches to Multiple Fixed Points in Generalized Metric Spaces by Alzubaidi, Yassin (2025) - We combine the concept of having multiple fixed points for a mapping with the ap- proach of obtaining these points through iterative methods. This enables us to establish our main result: the existence of multiple fixed points that can be iteratively obtained for generalized contraction mappings satisfying specific conditions. Keywords: metric; space
Separation Axioms in Quadri-Partition Neutrosophic Soft Topological Spaces by Saeed, Maha Mohammed ; Hatamleh, Raed Hatamleh2; El-latif, Alaa M. Abd ; Al-Husban, Abdallah ; Fujita, Takaaki ; Armada, Cris L. ; Andleeb, Rabia ; Khattak, Arif Mehmood (2025) - 2020 Mathematics Subject Classifications: 54A05 Key Words and Phrases: Neutrosophic soft set, quadri-partitioned neutrosophic soft set, quadri-partitioned neutrosophic soft topological space, quadri-partitioned neutrosophic soft sep- aration axioms. [7] introduced hybrid set which is known as neutrosophic soft set and defined some definitions and operations. Keywords: neutrosophic; quadri; set; sets; space
Various Types of Supra $epsilon$-separation Axioms and Relationships by Aldawood, Mohamed; Abd El-latif, Alaa M.; Aldwoah , Khaled; Azzam , Abd elfattah; Hasnaoui , Abdelhalim ; Elashiry, Mostafa; M. Attaalfadeel, Husham ; Elkordy, Enas (2025) - The definition of supra soft topological space was introduced by El-Sheikh et al. Supra gen- eralized closed soft sets with respect to an soft ideal in supra soft topological spaces. Keywords: sets; soft; space; supra
Supra Regularity and Supra Normality Inspired by Supra-$\epsilon$-Open Sets by Aldawood, Mohamed; Abd El-latif, Alaa M.; Aldwoah , Khaled; Azzam , Abd elfattah; Hasnaoui , Abdelhalim ; Elashiry, Mostafa; Elkordy, Enas ; Mohammed Alhassan Attaalfadeel, Husham (2025) - [43] established the definition of supra soft topological space. Supra gen- eralized closed soft sets with respect to an soft ideal in supra soft topological spaces. Keywords: sets; soft; space; supra; supra-ϵ-t2
Revisiting Best Proximity Results of Relatively Meir-Keeler Condensing Operators in Hyperconvex Spaces by Gabeleh, Moosa; Markin, Jack; Aphane, Maggie (2025) - Since TRp ∈ G and TRq ∈ H, we have Rp = TRp and Rq = TRq. We first prove that if (G,H) is a nonempty, compact and hyperconvex pair of subsets of a hyperconvex metric space (M, d), then every cyclic relatively u-continuous mapping T defined on G ∪H has a best proximity point. Keywords: hyperconvex; nonempty; pair; space; theorem
Novel Results on D-Soft Compact Spaces by Oudetallah, Jamal ; Almalkawi, Ahmad ; Alrababah, Rahmeh ; Amourah, Ala; Alsoboh, Abdullah ; Al Mashraf, Khaled ; Sasa, Tala (2025) - [31] on soft submaximal and soft door spaces, Saleh and Salih [32] on c-continuity and c-compact spaces via soft sets, Al- Mufarrij and Al-Ghour [33] on regular-closed functions between soft topological spaces, and Alshammari et al. Basic Principles and Primary Notions In this section, we present the main concepts and results that we employed in our study in the theory of soft sets in soft topological spaces. Keywords: compact; cover; set; sets; space
Collectionwise Pre-Normality in Topological Spaces by thabit, Sadeq; Alawadi, Alyaa; Noaman, Rafiqa (2025) - (2) for any discrete family {Fs}s∈S of closed sets in X, there exists a discrete family {Us}s∈S of g⋆-pre-open sets in X such that Fs ⊆ p int(Us) for each s ∈ S. (3) for any discrete family {Fs}s∈S of closed sets in X, there exists a discrete family {Us}s∈S of g-pre-open sets in X such that Fs ⊆ p int(Us) for each s ∈ S. (4) for any discrete family {Fs}s∈S of closed sets in X, there exists a discrete family {Us}s∈S of πg-pre-open sets in X such that Fs ⊆ p int(Us) for each s ∈ S. Proof. Math, 18 (4) (2025), 6597 9 of 15 (2) for any discrete family {Fs}s∈S of g-closed sets in X, there exists a discrete family {Us}s∈S of pre-open sets in X such that p cl(Fs) ⊆ Us for each s ∈ S. (3) for any discrete family {Fs}s∈S of g-closed sets in X, there exists a discrete family {Us}s∈S of g⋆-pre-open sets in X such that p cl(Fs) ⊆ p int(Us) for each s ∈ S. (4) for any discrete family {Fs}s∈S of g-closed sets in X, there exists a discrete family {Us}s∈S of g-pre-open sets in X such that p cl(Fs) ⊆ p int(Us) for each s ∈ S. (5) for any discrete family {Fs}s∈S of g-closed sets in X, there exists a discrete family {Us}s∈S of πg-pre-open sets in X such that p cl(Fs) ⊆ p int(Us) for each s ∈ S. Proof. Keywords: collectionwise; family; pre; space
Some Convergence Results for the Solution of New Type of Variational Inequalities Associated with Generalized Pseudo-Monotone Mappings in Complete CAT (0) Spaces by Rashid, Maliha ; Kalsoom, Amna ; Masood, Nida; Aloqaily, Ahmad; Mlaiki, Nabil (2025) - One of the numerical methods for solving variational inequality problems (VIP’s) is known as projection method [9–11] which is further expanded to gradient, extragradient and subgradient methods (see, e.g., [12–25] and the references therein). [11], introduced an extragradient method in finite dimensional Euclidean space to obtain solution of variational inequality problem under the mapping of mono- tone and Lipschitz continuous. Keywords: inequality; lemma; space; −−→; −−−→; −−−−→; −−−−−→
The Ordered Implicit Relations: Fixed Point Problems and Applications by Anam Arif; Muhammad Nazam; Ahmad, Hijaz; Alraddadi, Ibrahim Alraddadi; Xu, Changjin; Waleed Mohammed Abdelfattah (2025) - By (J2), there exists T ∈ B(E , E) along with ∥T ∥1 < 1, s ≥ 1, so that R(f1, f2) ⪯ 1 s T (R(f0, f1)) ⪯ T (R(f0, f1)) and R(f2, f3) ⪯ 1 s T (R(f1, f2)) ⪯ T (R(f1, f2)). 1 and R(f1, f2) ⪯ 1 s T (R(f0, f1)) ⪯ T (R(f0, f1)) and R(f2, f3) ⪯ 1 s T (R(f1, f2)) ⪯ T (R(f1, f2)). Keywords: cone; metric; point; r(ϑ; space
Minimal Generators for the Rees Algebra of Rational Space Curves of Type (1,1,d-2) by Wang, Haohao; Hoffman, J. William; Jia, Xiaohong; Goldman, Rong (2010) - − y( w z )3( y x )2] = x2z4 − y3w3; x3z2r ′i ( w z , y x ) = x3z2[z − y( w z )2( y x )3] = x3z3 − y4w2; x4zr ′i ( w z , y x ) − y t, and transform the singular point to (0,0,0,1). Keywords: curve; generators; singular; space; w z; y t; y x; y z; z x; − y

Equations

Canonical Reduction of the Self-Dual Yang Mills Equations to Complex Ginzburg-Landau Equations and Exact Solutions by Shehata, Abdel Rahman M.; Al-Zaidy, Jammel F. (2017) - The classical solutions to nonlinear field equations give us insight into the bound state behavior of field theories, particular interest are new class of classical solutions of the Yang Mills equations. The paper is organized as follows: On one hand the reduction of Yang-Mills theory to cGL equation , and exact solutions are presented in sections 2 and 3 respectively. Keywords: equations; gauge; mills; physics; solutions; yang
Global Estimation of the Cauchy Problem Solutions' and Blow up the Navier-Stokes Equation by Durmagambetov, Asset (2017) - c2 0 ∫ R3 ∫ R3 q̃(k + p)q̃(p− k′) (|p|2 − |k|2 − i0) dk + .... A(k, k′) = c0Q(k, k′) + Qf = ∫ S2 Q(k, θ ′ , θ)f(k, θ ′ )dθ ′ , T+ Q f = ∫ ∞ 0 ∫ S2 Q(k, θ ′ , θ)f(k, θ ′ )dθ ′ |k|2 − s2 − i0 s2ds, f = f(k, θ ′ ), Q(k, θ ′ , θ) Keywords: equations; functions; navier; phase; problem; proof; theorem
A Novel Power Series Method for Solving Second Order Partial Differential Equations by Kurulay, Muhammet; Bayram, Mustafa (2009) - In this article, a new approach is proposed to solve partial differential equation. Chen and Ho [7] proposed methods to Solving partial differential equations by two-dimensional differential transform method. Keywords: differential; equations
Analytical Study for Certain Ordinary Differential Equations with Variable Coefficients via GÎ±-Transform by Prasertsang, Patarawadee; Sattaso, Supaknaree; Nonlaopon, Kamsing; Kim, Hwajoon (2021) - 2020 Mathematics Subject Classifications: 34A25, 34A26, 44A05 Key Words and Phrases: Laplace transform, Sumudu transform, Elzaki transform, Gα-transform, Ordinary differential equation 1. In 2010, H. Eltayeb and A. Kilicman [14] introduced some relationships between Sumudu transform and Laplace transform. Keywords: differential; equations; laplace; sumudu; transform
Applications of Double Fuzzy Sumudu Adomain Decompositon Method for Two-dimensional Volterra Fuzzy Integral Equations by F. Alidema, Artan (2022) - Introduction An important branch in fuzzy mathematics is the topics of fuzzy integral equations. The problems posed in the study of fuzzy integral equations are: existence and unique- ness, boundedness of the solutions Keywords: equations; integral; sumudu; transform
Mathematical Eigenfunctions Analysis for 2nd Kind of Fredholm Integral equations by Al-Taee, Lamiaa Hazim ; Fawze, Ahmed A. Mohammed (2023) - Fredholm integral equation is one of the most important integral equations, and researchers look to the basis of integral equations as a transformation of some points over given vector space that have specific criteria by making use of certain specified operators to other points located in the same space The current paper is a trial to investigate the Eigen functions appears through math- ematical treatment of 2nd kind of Fredholm integral equations by making use a new developed an Inverse Iterative Numerical Scheme (IINS). Keywords: equations; mathematics; numerical
Oscillatory Behavior of Higher-Order Differential Equations with Delay Terms by Balatta, Shoura Ahmed; Ismail, Eddie Shahril; Hashim, Ishak; Bataineh, Ahmad Sami; Momani, Shaher (2023) - [22] Yan J. R. Oscillation theorems for second order linear differential equations with damping. [10] Elabbasy E. M. On the oscillation of nonlinear second order differential equations. Keywords: differential; equations; i=1; order; oscillation
Some Families of Differential Equations for Multivariate Hybrid Special Polynomials Associated with Frobenius-Genocchi Polynomials by Wani, Shahid Ahmad; Patil, Shivtej ; Ramirez, William; Hernandez, Juan (2025) - = η1 GEF n (η1, η2, η3, · · · , ηm;λ)+2n η2 GEF n−1(η1, η2, η3, · · · , ηm;λ) +3n(n−1) η3GEF n−2(η1, η2, η3, · · · , ηm;λ)+· · ·+n(n−1) · · · (n−m+1)mηm GEF n−m(η1, η2, η3, · · · , ηm;λ) = ( η1 − n+1 2(1−λ) ) GEF n (η1, η2, η3, · · · , ηm;λ) + 2nη2 GEF n−1(η1, η2, η3, · · · , ηm;λ) +3n(n− 1)η3 GEF n−2(η1, η2, η3, · · · , ηm;λ) + · · ·+ n(n− 1)(n− 2) · · · (n−m+ 1) ηm GEF n−m(η1, η2, η3, · · · , ηm;λ)− 1 1−λ n+1∑ k=2 ( n+1 k ) GEF n−k+1(η1, η2, η3, · · · , ηm;λ) Keywords: equations; gef; polynomials; ηm;λ
Advancing Solutions for Fractional Differential Equations: Integrating the Sawi Transform with Iterative Methods by Saadeh, Rania ; Al-Wadi, Alaa ; Qazza, Ahmad (2025) - This paper presents a powerful approach to solving fractional differential equations by combining the Sawi transform with iterative methods, particularly the Sawi iterative method. We begin by reviewing the fundamental properties and theoretical aspects of the Sawi transform, demonstrating its effectiveness in simplifying and solving fractional differential equations. Keywords: differential; equations
Fourth-Order Differential Equations: Asymptotic andOscillatory Behaviors of Solutions by Almutairi, Alanoud (2025) - By Lemma 4, we see (11) holds and from Lemma 1 with U = σ (η) , V = (p− 1) εη2/ ( 2 (κ (η)µ (η))1/(p−1) ) and η = ζ, we get ζ ′ (η) ≤ −ϱ (η) + ( 2 εη2 )(p−1) κ (η)µ (η) (σ (η))(p−1)+1 pp . Lemma 1 is used with U = σ∗ (η) , V = 1/ς (η) , p = 2 and η = w, We obtainThe formula is ζ ′ (η) ≤ −ϱ∗ (η) + 1 4 ς (η) (σ∗ (η))2 . Keywords: differential; equations; p−1
Fourth Order Functional Differential Equations of Neutral Type: Enhanced Oscillation Theorems by Muhsin, Waed ; Almarri, Barakah ; Jazmati, Mohammad S. ; Moaaz, Osama ; Elabbasy, Elmetwally M. (2025) - We concentrate only on those solutions of (1) that satisfy sup{|x (u) | : u ≥ U} > 0, for all U ≥ u0, i.e., it is a nontrivial solution. Moreover, as (Ω (u) /I123 (u)) ′ ≤ 0 and κ(2t) (u) ≤ u, we have Ω ( κ(2t) Keywords: differential; equations; order; oscillation
Sixteenth-Order Steffensen-Ostrowski Approach for Nonlinear Problems with Applications in Celestial, Predator-Prey and Neural Activation by Akram, Saima; Riaz, Muhammad Bilal; Akram, Faiza; Amir, Fouzia; Khalid, Hareem; Sobirovich, Dexkanov Suxrob (2025) - k j − y j)(k j − t j)(k j −ζ j)(ζ j − z j) + (t j −ζ j)(t j − k j)(t j − y j)g(z j) (z j − t j)(z j −ζ j)(z j − k j)(z j − y j) + g(t j) (t j −ζ j) + g(t j) (t j − k j) + g(t j) (t j − y j) + g(t j) (t j − z j) . Consider an analytic function E : C2 → C in the vicinity of (0,0), with λ = g(z j) g(y j) = O(e2 j) and µ = g(y j) g(k j) = O(e j). − k j)−g[z j,k j,k j](y j − k j) z j − y j , a3 = g[z j,k j,k j]−g[y j,k j,k j] z j − y j , b4 = (g[y j,k j,k j](S3 −S2)+g[z j,k j,k j](S3 +S1)+g[w j,k j,k j](S2 −S1)) −S2 1S2 +S1S2 2 +S2 1S3 −S2 2S3 −S1S2 3 +S2S2 3 , b3 = (g[y j,k j,k j](S2 2 −S2 3)+g[z j,k j,k j](S2 3 −S2 1)+g[w j,k j,k j](S2 1 −S2 2)) Keywords: convergence; equations; g(k j; iterative; j −; j −ζ; j)(t j; k j; methods; order; t j; u j; w j; y j; z j; − k; − t; − y; − z
Hamilton-Jacobi Framework for Nonholonomic Dynamics by Nawafleh, Khaled (2025) - Now substituting equation (100) in constraint equation (85) we get: ẏ = sinφ, (103) Inserting equation (97) into equation (103) and integrating the result equation∫ ẏdt = ∫ sin(α1t+ β1)dt , (104) we find y(t) According to equations (25) and (26), equation (27) can be expressed as: θ̈ = −ẍ cosφ− ÿ sinφ. Keywords: equations; hamilton; nonholonomic; sinφ
On Qualitative Properties of $L_\Theta$-Solutions for Coupled Systems of Hadamard-Type Fractional Integral Equations in Banach Spaces by Metwali, Mohamed; Alsallami, Shami A. M. (2025) - = ( T1y(t), T2x(t) ) , t ∈ J, where T1y = h1 + Ff1 ( Λ1(y), U1(y) ) , T2x = h2 + Ff2 ( Λ2(x), U2(x) ) , M. Metwali, S. Alsallami / Eur. J × R × R → R be continuous in x and y for almost all t and measurable in t ∈ J . Keywords: equations; integral; spaces; γ(β; χd∥θ
New Multi-step Collocation Methods for Non-standard Volterra Integral Equations by Thabbah, Hayder Abdullah ; Darania, Parviz; Pishbin, Saeed (2025) - [εz,1, εz,2, ..., εz,m]T , (19) and matrices Ān+1 = diag(ā1n+1, ..., ā m n+1), (20) (B (z) n+1)j,k =  ∫ 1 0 K̂z(tn+1,j , s)Lk(s)ds, z = r, ..., n, ∫ cj 0 K̂z(tn+1,j , s)Lk(1 + s)ds, z = n+ 1, (21) (C (z) n+1)j,i =  ∫ 1 0 K̂z(tn+1,j , s)L̂i(s)ds, z = r, ..., n, ∫ cj 0 K̂z(tn+1,j , s)L̂i(1 + s)ds, z = n+ 1, (22) and (D (z) n+1)j,i =  ∫ 1 0 K̂z(tn+1,j , s)L̃i(s)ds, z = r, ..., n, ∫ Keywords: equations; integral; step
Investigation of the Asymptotic and Monotonic Properties of Solutions of Functional Differential Equations with Multiple Delays and a Damping Term by Aloraini, Sarah ; Almohaimeed, Ahmed S. ; Moaaz, Osama (2025) - du = ∞; (2) (H3) p, h, qi ∈ C ([s0,∞), [0,∞)) , for i = 1, 2, ..., n, 0 ≤ p(s) ≤ p0 < 1, where p0 is a constant, and qi does not vanish identically on any half-line of the form [t∗,∞), t∗ ≥ t0; (H4) τ, ηi ∈ C([s0,∞),R), τ(s) ≤ s, ηi(s) s, lims→∞ τ (s) = ∞, and lims→∞ ηi (s) = ∞, for i = 1, 2, ..., n. Based on a solution to (1), we consider a real-valued function x ∈ C ([s∗,∞) ,R) , s∗ ≥ s0, where z, r (z′)κ ∈ C1 ([s∗,∞) ,R), and x fulfills (1) on [s∗,∞). Keywords: differential; equations; order

Sets

A note on "Î²-Open Sets and Ideals in Topological Spaces"[European Journal of Pure and Applied Mathematics 6 (2019) 893{903] by Hosny, Mona (2019) - If there exists an open set U such that U ⊆ A ⊆ cl(int(cl(U))), then A is β-open set. In [2, 12], the concept of semi-open sets with respect to an ideal was investigated. Keywords: sets
A View on Connectedness and Compactness in Fuzzy Soft Bitopological Spaces by Sayed, Abdelhamied Farrag (2021) - Fuzzy soft set in topological space further studied by Roy [27]. [27] A fuzzy soft topology τ over (X,E) is a family of fuzzy soft sets over (X,E) satisfying the following properties: (i) 0̃E , 1̃E ∈ τ , (ii) if fA, gB ∈ τ, then fA∩̃gB ∈ τ , (iii) if fAα ∈τ for all α ∈ ∆ an index set, then ⋃̃ α∈∆fAα ∈ τ. Keywords: sets
On m-I-Continuous Multifunctions by Noiri, Takashi; Popa, Valeriu (2022) - [21] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Introduction Semi-open sets, pre-open sets, α-open sets, b-open sets and β-open sets play an impor- tant role in the research of generalizations of continuity for functions and multifunctions. Keywords: sets
Weakly (Λ, sp)-continuous Multifunctions by Boonpok, Chawalit; Viriyapong, Chokchai (2022) - A multifunction F : (X, τ) → (Y, σ) is said to be weakly (Λ, sp)-continuous if, for each x ∈ X and each (Λ, sp)-open sets V1, V2 of Y such that F (x) ∈ V + 1 ∩V − 2 , there exists a (Λ, sp)-open set U of X containing x such that F (U) ⊆ V (Λ,sp) 1 and F (z)∩V (Λ,sp) 2 6= ∅ for every z ∈ U . [F+(V (Λ,sp) 1 )∩F−(V (Λ,sp) 2 )](Λ,sp) for every (Λ, sp)-open sets V1, V2 of Y ; (3) [F−([K1](Λ,sp)) ∪ F+([K2](Λ,sp))] (Λ,sp) ⊆ F−(K1) ∪ F+(K2) for every (Λ, sp)-closed sets K1,K2 of Y ; C. Boonpok, C. Viriyapong / Eur. Keywords: sets; sp)-open
On b-open Sets via Infra Soft Topological Spaces by Abu-Gdairi, Radwan ; Al-Shamiri, Mohammed M. Ali; Saleh, Salem Ali Mohammed ; Al-shami, Tareq (2022) - Introduction Molodtsov [62] proposed the idea of soft set (S-set) as a new mathematical tool to deal with vagueness. Soft sets combined with fuzzy sets and rough sets: a tentative approach. Keywords: set; sets; shami
Hesitant Fuzzy Compactness and Hesitant Fuzzy Regularity in Hesitant Fuzzy Topological Spaces by Swaminathan, A.; Ozel, Cenap; AlShammari, Ibtesam Eid (2023) - Math, 16 (3) (2023), 1381-1388 1382 The following terminologies, “hesitant fuzzy minimal open set, hesitant fuzzy maximal open set, hesitant fuzzy mean open set,hesitant fuzzy clopen set, hesitant fuzzy cut-point space, hesitant fuzzy connected topological space,hesitant fuzzy disconnected topologi- cal space and hesitant fuzzy topological space”are respectively abbreviated as “HFMIO, HFMAO, HFMEO, HFCLO, HFCS, HFCTS,HFDTS and HFTS.” 2. [10] V. Torra, Hesitant fuzzy sets. Keywords: set; sets
AI-Assisted Wearable Devices for Promoting Human Health and Strength Using Complex Interval-Valued Picture Fuzzy Soft Relations by Hatamleh, Raed ; Al-Husban, Abdullah ; Zubair, Sulima Ahmed Mohammed ; Elamin, Mawahib ; Saeed, Maha Mohammed ; Abdolmaleki, Eisa ; Fujita, Takaaki ; Nordo, Giorgio ; Khattak, Arif Mehmood (2025) - Let τ be the collection of complex interval valued picture fuzzy soft sets over X, then τ is said to be a complex interval valued picture fuzzy soft topology (TST) on X The union of any number of members of complex interval valued picture fuzzy soft sets in τ belongs to τ , (iii) The intersection of any two complex interval valued picture fuzzy soft sets in τ belongs to τ . Keywords: fitness; interval; let; membership; picture; set; sets; ϋ1; ϋ2; ϋ3
Exploring $\beta$-Basic Rough Sets and Their Applications in Medicine by El-Bably, M. K. ; Abu-Gdairi , R. ; Fleifel, K. K. ; El-Gayar , M. A. (2024) - Subset neighborhood rough sets. The proposed contributions introduce a novel approach for constructing topological rough sets (βb-rough sets) that do not rely on the induced topologies. Keywords: sets
Applications of the Supra Soft SD-Closure Operator to Soft Connectedness and Compactness by Abd El-latif, Alaa M.; Abu Gdairi, Radwan; Azzam, Abdelfattah; A. Aldwoah, Khaled; Aldawood, Mohamed; M. Shaaban, Shaaban (2025) - Several concrete applications on soft sets have been introduced in rough set models [8], medical sciences A family of soft sets Ψ = {(Cϵ,∆) : ϵ ∈ ε} is claimed to be a supra soft open cover, if all of the members of Ψ are supra open soft sets. . Keywords: lindelöf; sets; soft; ssts
Neutrosophic Hypersoft Topological Framework for Agricultural Decision-Making by Kaviyarasu, M. ; Rajeshwari, M. ; Alqahtani, Mohammed (2025) - AlHij- jawi introduced possibility neutrosophic hypersoft sets to expand the practical reach of neutrosophic sets for complex multi-attribute thinking under various uncertainty condi- tions [18]. It is clear that the values of the null set and absolute set in neutrosophic sets are equal to the values of the null set and absolute set in neutrosophic hypersoft sets. Keywords: decision; hypersoft; let; making; neutrosophic; s1,γ1; s2,γ2; set; sets; topology
Supra E-open Sets: Features, Operators and Applications by Abd El-latif, Alaa M.; Radwan, Radwan Abu-Gdairi; Azzam , Abd elfattah; Mohammed Alhassan Attaalfadeel, Husham ; M. Shaaban, Shaaban ; M. Aldawood; Aldwoah , Khaled (2025) - Utilizing our recently introduced category of supra open sets, we define new kinds of operators called supra ϵ-interior (closure, accumulation, exterior, and boundary, respectively). [13], presented the notion of supra open sets which consider the basic building blocks of supra topology ((abbreviated, STS)). Keywords: sets; soft; supra
Applications of Weighted Tangent Similarity Measure of Picture Hesitant Fuzzy Sets by Al Qarni, Noura; Alshehri, Noura Omair; Alghamdi, Rania (2025) - A combination of fuzzy similarity measures and fuzzy entropy measures for supervised feature selection. Similarity measures play a crucial role in numerous fuzzy set applications, including decision-making, pattern recognition, and medical diagnosis. Keywords: measure; membership; picture; sets; similarity; ωtsm
Independent Neighborhood Polynomial of the Direct and Corona Products of Trees by Abdulcarim, Normalah Sharief; Dagondon, Susan C. (2025) - Not all graphs have independent neighborhood set. Then the independent neighborhood polynomial of G of order m is Ni(G, x) = m∑ j=ηi(G) ni(G, j)xj , where ni(G, j) is the number of independent neighborhood sets of G of cardinality j and ηi(G) is the minimum cardinality of an independent neighborhood set which is called the independent neighborhood number of G. Example 4. Keywords: neighborhood; sets
A New Approach to Vague Soft Rough Topological Spaces by Hatamleh, Raed ; Alqawaqneh, Haitham ; Nasir Odat2 Odat, Nasir Odat; Al-Husban, Abdallah ; Khattak, Arif Mehmood; M. Abd El-latif, Alaa ; Abdelfattah, Walid ; Elashiry, M. I. ; Hasnaoui, Abdelhalim (2025) - To enhance understanding of this study, numerous examples are provided. 2020 Mathematics Subject Classifications: 03E72, 06E25, 54A40, 54H05 Key Words and Phrases: Rough sets, vague soft rough sets, vague soft rough topology. The layout of this paper is systematized as follows, Section 2, implies some basic defini- tions including soft set, rough set, vague soft sets and some operations on vague soft sets which are necessary for the up-coming section. Keywords: apr; sets; vague
Fermatean Double-Valued Neutrosophic Soft Topological Spaces by Hatamleh, Raed ; Odat, Nasir ; Abujabal, Hamza Ali ; khan, Faria ; Khattak, Arif Mehmood; M. Abd El-latif, Alaa ; M. Attaalfadeel, Husham M. ; Hasnaoui, Abdelhalim (2025) - 2020 Mathematics Subject Classifications: 54A05 Key Words and Phrases: Fuzzy set, Fermatean fuzzy soft set, neutrosophic soft set, Fermatean double valued neutrosophic soft set, Fermatean double valued neutrosophic soft union, Fermatean double valued neutrosophic soft intersection, AND operator, OR operator, Fermatean double valued neutrosophic soft topological space ∗Corresponding author. [16], neutrosophic soft sets Keywords: 0.9⟩; neutrosophic; set; sets; vol; ⟨x1; ⟨x2; ⟨x3
Separation Axioms Beyond T2: Novel Properties and Interactions in Non-Regular Spaces by Oudetallah, Jamal; Audeh, Wasim ; Al-Labadi, Manal ; Al-Naimi , Raja’a ; Batiha, Iqbal; Amourah, Ala; Sasa, Tala (2025) - This result reveals the deep connection between separation properties of point sets and function spaces, demonstrating how the structure of continuous function algebras determines topological space properties, as extensively studied by Gillman and Jerison Our investigation yields several new characterizations of such spaces using tools from general topology, set theory, and functional analysis. Keywords: hausdorff; separation; sets; spaces
An Extended TOPSIS Technique in Cubic Vague Soft Set Relations with its Application in Renewable Energy Sources by Masadeh, Esraa ; Alhazaymeh, Khaleed ; Al-shboul, Abedallah ; Abdelfattah, Waleed Mohammed ; Zulqarnain, Rana Muhammad ; Siddique, Imran ; Ahmad, Hijaz (2025) - In this work, we address multi-criteria decision-making (MCDM) problems under high uncertainty by developing an extended Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) within the framework of cubic vague soft set relations (CVSSR). We develop a new theoretical framework for cubic vague soft set relations (CVSSR), introducing rigorous definitions, properties, and proofs that generalize classical vague and cubic soft set structures. Keywords: 0.50]⟩; cubic; cvss; decision; energy; f(f̃; g̃,bv; making; relation ℜ; set; sets; topsis; vague
Correlation Measure for Quadri-Partitioned Neutrosophic Refined Sets and its Application in Medical Diagnosis by A. Azzam, A.; Alreshidi, B. ; Aldawood, M; M. Awad, Mohamed; Abdelhalim Hasnaoui; Ahmed Abu-Tahon, Medhat ; M. Abdel-Mageed, Ahmad. ; Khattak, Arif Mehmood (2025) - 10, which displays the t-SNE view of patient disease correlations. Math, 18 (4) (2025), 7168 20 of 26 Figure 12 The three patient profiles (P1, P2, and P3) are projected into three non-linear components, similarity patterns in their correlation patterns, in Fig. 13, which displays a 3D t-SNE depiction of patient disease correlations. Keywords: cluster; correlation; j ê; neutrosophic; patient; sets

Distribution

Transmuted Weibull Distribution: A Generalization of theWeibull Probability Distribution by Aryal, Gokarna R.; Tsokos, Chris P. (2011) - η σ y η−1 η exp(−y) � 1−λ+ 2λexp � −y �� 1+λexp � −y �� j−1 × � 1− exp � −y �� j−1 exp � −(n− j)y �� 1−λ+λexp � −y ��n− j , where, y = � x σ �η Therefore, the pdf of the largest order statistic X(n) is given by fX(n) (x) = nη σ � x σ �η−1 exp � − � x σ �η�� 1−λ+ 2λexp � − � x σ �η�� × � 1+λexp � − � x σ �η��n−1� 1− exp � − � x σ �η��n−1 and the pdf of the smallest order statistic X(1) is given by fX(1) (x) = nη σ � x σ �η−1 exp � − � x σ �η�� 1−λ+ 2λexp � − � x σ �η�� × � exp � − � x σ �η�§ 1−λ+λexp � − � x σ ��ª�n−1 . = � 1− exp � − � x σ �η�� 1+λexp � − � x σ �η�� . Keywords: distribution; exp �; weibull; η �; σ �; − �; � x; � −; � �
Transmuted Modified Weibull Distribution: A Generalization of the Modified Weibull Probability Distribution by Khan, Muhammad Shuaib; King, Robert (2013) - Math, 6 (2013), 66-88 67 This article defined the family of transmuted modified Weibull distributions. For the minimum and maximum order statistic of the four parameters transmuted modified Weibull distribution have different life time distributions when its parameters are changed. Keywords: distribution; order; weibull; −ηtβ
Empirical Likelihood Ratio Based Goodness-of-Fit Test for Generalized Lambda Distribution by Ning, Wei (2014) - f j − 1), (5) where η is a lagrange multiplier. We then will apply maximum empirical likelihood method to estimate the numerator. Keywords: data; distribution; gld; i=1; likelihood; log; test
Exponentiated Transmuted Modified Weibull Distribution by Pal, Manisha; Tiensuwan, Montip (2015) - Discussion In this paper, we introduce a new generalization of the Weibull distribution called expo- nentiated transmuted modified Weibull distribution and discuss its intrinsic properties. Transmuted modified Weibull distribution: A Generalization of the Modified Weibull Probability Distribution. Keywords: distribution; p(−αt; weibull
Nonlinear Least Squares Estimation of the Shifted Gompertz Distribution by Markovic, Darija; Jukic, Dragan (2017) - 2010 Mathematics Subject Classifications: 65D10, 65C20, 62J02 Key Words and Phrases: Shifted Gompertz distribution, nonlinear least squares, least squares estimate, lp-norm estimate, existence problem 1. Therefore, in other words, under the assumptions of the theorem, the LS estimate exists if and only if there is at least one shifted Gompertz distribution which is in an LS sense as good as or better than the best exponential distribution. Keywords: distribution; gompertz
Topp-Leone Inverse Weibull Distribution: Theory and Application by Abbas, Salman; Taqi, Syed Ali; Mustafa, Fakhar; Murtaza, Maryam; Shahbaz, Muhammad Qaiser (2017) - [10] discussed moments of order statistics of Inverse Weibull distribution and obtained BLUE (best linear unbiased estimator) for both location and scale parameters. Aleem [12] worked on the product, ratio, and single moments of lower record values of Inverse Weibull distribution. Keywords: distribution; inverse; tliw; weibull
Transmuted Modified Weibull distribution: Properties and Application by Khan, Muhammad Shuaib; King, Robert; Hudson, Irene L. (2018) - Modified Weibull distribution. 2. Transmuted Modified Weibull Distribution The transmuted modified Weibull distribution (TMWD) was recently proposed by Khan and King Keywords: distribution; exp; weibull
On Concomitants of Dual Generalized Order Statistics for a Bivariate Inverse Exponential Distribution by Shahbaz, Saman Hanif; Shahbaz, Muhammad Qaiser (2018) - In this section we have derived the joint distribution of the concomitants of the dgos for bivariate inverse exponential distribution given in (9). 5. Conclusions and Recommendations In this paper we have obtained the distribution of concomitants and joint distribu- tion of two concomitants of dual generalized order statistics when a sample is available from bivariate inverse exponential distributions. Keywords: concomitants; distribution
Cubic Transmuted Uniform Distribution: An Alternative to Beta and Kumaraswamy Distributions by Rahman, Md. Mahabubur; Al-Zahrani, Bander; Shahbaz, Saman Hanif; Shahbaz, Muhammad Qaiser (2019) - Parameters (−0.25) (−0.75) (−1.00) (0.25) (0.75) (1.00) 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 x F( x) Parameters (−0.25) (−0.75) (−1.00) (0.25) (0.75) (1.00) Figure 2: Density and Distribution Functions Plots for Proposed CTU Distribution. We will give the rth moment of proposed CTU distribution in the following theorem. Keywords: ctu; distribution; family
A Note on the (Weighted) Bivariate Poisson Distribution by Bidounga, R.; Batsindila Nganga, P. C.; NiÃ©rÃ©, L.; MizÃ¨re, D. (2021) - Math, 14 (1) (2021), 192-203 193 Several authors have studied bivariate Poisson distributions, in particular Berkhout & Plug [4] and Lakshminarayana et al. The structure of bivariate Poisson distribution. Keywords: distribution; poisson; poisson distribution
The Bivariate Extended Poisson Distribution of Type 1 by Rufin, Bidounda; Diafouka, Michel Koukouatikissa; Miz Ìel Ìe Kitoti, R Ìeolie Foxie; Miz`ere, Dominique (2021) - e−θ1 )( β1 θ y1 − 1 ) β−1 1  1− e−θ1( β1 θ1 y1 − 1 ) e−θ1  δ0(y1) × ∑ y2 ( θ y2 2 y2! e−θ2 )( β2 θ y2 − 1 ) Math, 14 (4) (2021), 1517-1529 1523 α ( e−y1 − c1 )∑ y2 ( θ y2 2 y2! e−θ2 )( β2 θ y2 − 1 ) Keywords: distribution; poisson
An Approach of Estimating the Value at Risk of Heavy-tailed Distribution using Copulas by Korotimi, Ou´edraogo; Diakarya, Barro (2022) - Copulas and conditional distribution function The conditional quantile estimation based on copulas is based on quantile regression and the asymptotic distribution of this estimator has been proven to be Gaussian (see Noh et al In this study, we consider a random vector X = (X1;X2; ...;Xm)T of dimension m with joint distribution function F and marginal distribution function F1; ...;Fm. Keywords: conditional; copula; distribution; quantile
Analysis and Mathematical Modeling for Flood Surveillance from Rainfall by Extreme Value Theory for Agriculture in Phitsanulok Province, Thailand by Deetae, Natthinee (2022) - Analysis of the generalized Pareto distribution The estimate of generalized Pareto distribution in Table 7 indicates the results of the GPD modeling on extreme rainfall data in Phitsanulok province using the threshold ap- proach. 2020 Mathematics Subject Classifications: 60G70, 62G32 Key Words and Phrases: Extreme values theory, Generalized extreme values distribution, Generalized Pareto distribution, Return level, Maximum likelihood estimation, Rainfall 1. Keywords: data; distribution; maximum; rainfall; return; value
Numerical Assessment of Symmetric Wedge Water-entry Impact Using OpenFOAM by Ibrahim, Basar; Zekri, Hussein (2022) - Numerical assessment of turbulence effect on forces, spray parameters, and secondary impact in wedge water entry problem using k-ε method. (a) (b) Figure 5: Predicted pressure contours during wedge water entry for the laminar case with all features included. Keywords: distribution; entry; figure; flow; gravity; numerical; pressure; surface; water; wedge
A New Class of Generalized Extreme Value Distribution and Application under Alpha Power Transformation Method by Khamrot, Pannawit; Deetae, Natthinee (2023) - Alpha power transformation generalized extreme value distribution A random variable X is said to have APTGEV distribution, denoted by G(µ, σ, ξ, α), with location parameter µ, shape parameter σ, and scale parameter ξ, α, if the PDF and CDF of X for x ≥ 0 and ξ ̸= 0 are given by G(x;µ, σ, ξ, α) The central moments (µk) of APTGEV distribution can be obtained from µk = E(X − µ′ 1) k = k∑ n=0 (−1)n ( k n ) (µ′ 1) nµ′ k−n. Keywords: aptgev; data; distribution; power; return; value
Second Order Transmuted Kumaraswamy Distribution and its Related Results by Tushar, Md. Tusharuzzaman; Rashedi, Khudhayr A. ; Alshammari, Tariq S. ; Rahman, Md. Mahabubur (2024) - Section 7 uses two actual applications from the real world to prove the dominant flexibility of CTKw distribution over comparable distributions. Now, by substituting the cdf of the Kumaraswamy distribution from equation (4) to the cdf of the second order transmutation map in equation (3 ), a continuous random variable X is said to have CTKw distribution if it has the following distributional form FCTKw (x; a, b, λ) = Keywords: b −; ctkw; data; distribution; kumaraswamy; log; xai
On the Bivariate Extension of the Extended Standard U-quadratic Distribution by Lakibul, Idzhar; Polestico, Daisy Lou L. ; Supe, Arnulfo P. (2024) - The joint probabil- ity and cumulative distribution functions of the derived distribution are obtained and it is observed that the said distribution can generate bivariate shape distributions with the following properties: (i) X and Y have bathtub shapes; (ii) X has a constant distribution and Y has a bathtub shape; and (iii) X has an inverted bathtub and Y has a bathtub shape. 2020 Mathematics Subject Classifications: 60E05, 62E10, 65C10 Key Words and Phrases: Standard U-quadratic distribution, Kumaraswamy distribution, Bi- variate distribution, Bivariate Pseudo Family, bathtub shape distribution ∗Corresponding author. Keywords: distribution
The Stochastic Transportation Problem with Imprecise Data using Lomax Distribution by Pulloru Bhavana; Priya, D. Kalpana (2024) - The terms for TP that are modelled under such circumstances are fuzzy transportation problems (FTP) and stochastic transportation problems (STP). An alternate method for finding more for less solution to fuzzy transportation problem with mixed constraints. Keywords: distribution; problem; transportation; xij
Order Statistics and Actuarial Measures from Powered Inverse Rayleigh Distribution by Khan, Izhar (2024) - Transmuted Rayleigh distribution. [20] obtained moments properties of PIR distribution based on dual generalized order statistics. Keywords: distribution; statistics
A New Method of Generating Truncated Bivariate Families of Distributions by Alsulami, Eftekhar; Al-Turk, Lutfiah; Shahbaz, Muhammad (2024) - (34) Again using the density and distribution functions of Burr distribution in Eq.18, the conditional distribution of X2 given X1 = x1 is fBTBB(x2|x1) In the next section we will study the bivariate truncated Burr family of distributions for baseline Burr distribution. Keywords: aβ2; bivariate; burr; distribution; xβ1; xβ2; −(α+1
On the Generalization of the Bivariate Extended Standard U-quadratic Distribution by Lakibul, Idzhar; Polestico, Daisy Lou L. ; Supe, Arnulfo P. (2025) - 2020 Mathematics Subject Classifications: 60E05, 62E10, 65C10 Key Words and Phrases: Standard U-quadratic distribution, Kumaraswamy distribution, Bi- variate distribution, Bivariate extended Standard U-quadratic Distribution, bathtub shape distri- bution ∗Corresponding author. For instance, the current study focuses on a specific class of bivariate distributions, and there may be alternative distribu- tions or estimation techniques that could provide additional benefits, particularly in cases with more complex dependence structures. Keywords: distribution
On the Generalized Version of the Extended Standard $U$-Quadratic Distribution by Lakibul, Idzhar; Polestico, Daisy Lou ; Supe , Arnulfo (2025) - Random numbers Generated from GeSU distribution of size N = 10000. It reveals that the ML estimates of the said distribution parameters is consistent for all parameters since the MSE decays toward zero. Keywords: distribution; esu
Survival Weighted Pareto Distribution: Order Statistics and Its Applications by Khan, Izhar; Mustafa, Abdelfattah (2025) - The h(t) of SWPD distribution decreasing depending on the shape parameter. (M. I. Khan), amelsayed@mans.edu.eg (A. Mustafa) https://www.ejpam.com 1 Keywords: distribution; khan; statistics
Bayesian Analysis of the Lomax-Power Rayleigh (T-X) Distribution by Ijaz, Muhammad; Khan, Naeem; Khan, Izhar; Mustafa, Ghulam; Alqifari, Hana N (2025) - A large number of problems have been tackle using Bayesian analysis under different probability distributions, for example, [9] discussed Bayesian analysis of for skew symmet- ric distribution, [10] explore Bayesian and non-Bayesian inference for Truncated Cauchy power Weibull-G class of distributions, [11] considered Lomax distribution with four loss functions, [12] discussed the Bayesian analysis of the Extended Lomax distribution. For example, recently a lot of new versions of the Lomax dis- tribution have been derived, e.g [1] derived X-Gamma Lomax distribution, [2] presented Inverse Power Lomax distribution, [3] discuss Lomax Power Rayleigh distribution. Keywords: bayesian; distribution; jeffery; lomax; loss; uniform
Advanced Censoring Schemes for Statistical Inference of Reliability in Engineering Contexts by Hassan, Amal S.; Abdalla, Gaber Sallam Salem ; Almetwally, Ehab M.; Elgarhy, Mohammed; Yousef, Manal M. (2025) - This study address this gap in an analysis of the multi-stress-strength model Υ = P (U < W < V ), in which stresses (U &V ) and strength (W ) are defined using the exponentiated Weibull distribution. Thus, the main driving force behind this can be summed up as follows: • Establish reliability inferences for Υ = P (U < W < V ), assuming that strength (W ) and two stresses (U and V ) have independent EWD with the same scale parameter. Keywords: bayesian; data; distribution; estimates; estimation; et al; ewd; hassan; j=1; reliability; strength
A Novel U-Statistic Test for Exponentiality Against EBUCL Reliability Class and Applied to Complete and Censored Data Across Various Risk Profiles by B. H. Etman, Walid ; F. Abouelenein, Mohamed; S. Eliwa, Mohamed ; El-morshedy, Mahmoud ; Roushdy, Noura ; M. EL-Sagheer, Rashad (2025) - Math, 18 (3) (2025), 6376 23 of 24 [14] M. A. W. Mahmoud and M. M. M. Mansour. [16] S. A. Qaid, S. E. Abu-Youssef, and M. M. M. Mansour. Keywords: data; distribution; test
Ranked Set Sampling-Based Statistical Inference for the Exponentiated Inverted Weibull Distribution and its Variants: Theory, Simulation and Data-Driven Analysis by Deka, Upama ; Das, Bhanita; Hazarika, Partha; Das, Jondeep; Eliwa, Mohamed; Abouelenein, Mohamed (2025) - This study investigates the estimation of parameters for the exponentiated inverted Weibull distribution using ranked set sampling and its specific forms, including extreme ranked set sampling and median ranked set sampling. Simulation Results This study carries out a simulation analysis to evaluate the performance of the maxi- mum likelihood estimators for the parameters β and θ of the EIWD using data collected through simple random sampling, ranked set sampling, extreme ranked set sampling, and median ranked set sampling methods. Keywords: data; distribution; erss; i=1; j=1; rss; sampling; set
Efficient Estimation via Record Ranked Set Sampling for Copula-Linked Bivariate Exponentiated Inverted Weibull Distributions by Deka, Upama; Das, Bhanita; Roushdy, Noura; Eliwa, Mohamed (2025) - The study of concomitants of record values (CRV) is a relatively recent yet important development in the field of ordered random variables. Parallel work by [21, 22] focused on the Fisher information contained in record values and their concomitants. Keywords: blue; concomitants; crrss; distribution; record; set; values
Neutrosophic Reliability Analysis Using the Kumaraswamy Distribution: A Robust Framework for Uncertain Data by Odat, Naser (2025) - Math, 18 (4) (2025), 7098 10 of 13 Figure 1: Coverage probability of neutrosophic reliability estimator for various sample sizes and parameter values. Figure 3: Convergence of neutrosophic reliability estimate to the true value with increasing sample size. Keywords: distribution; interval; neutrosophic; reliability; θl1; θu1
Convex Ordering of Random Variables and its Applications in Econometrics and Actuarial Science by Gupta, Arjun K.; Aziz, Mohammad A.S. (2010) - In this work, we discuss the use of lower convex order of random variables to approximate this distribution. The convex order is closed under mixtures: Let X, Y and Θ be random variables such that [X |Θ = θ] ≤cx Keywords: distribution; variables

Functions

Professor H. M. Srivastava: Man and Mathematician by Cangul, Ismail Naci (2010) - Having had hardly any formal education at the Primary School level, Professor Srivastava was admitted in 1946 into Grade 3 of the Government Higher Secondary School at Ballia at the age of 6 years after his successful performance in the mandatory written and oral entrance examinations. Professor Srivastava received his university education at the University of Allahabad where he completed his B. Sc. in 1957 and M. Sc. in 1959. Keywords: analysis; functions; number; professor; srivastava; theory; university
Casimirs and Lax Operators from the Structure of Lie algebras by Linton, Carol; Holderbaum, William; Biggs, James (2012) - 2010 Mathematics Subject Classifications: 17B45, 53D17, 17B63 Key Words and Phrases: Casimir invariants, Lax operators, structure constants, matrix Lie algebras, Poisson manifolds 1. The situation is easier when considering matrix Lie algebras with an imposed Lie-Poisson structure although a nondegenerate bi-linear form I is assumed in dually g - see equation (4). Keywords: e ∂; functions; h ∂; lie; ∂ p
Coefficient Problems in a Class of Functions with Bounded Turning Associated with Sine Function by Khan, Muhammad Ghaffar; Ahmad, Bakhtiar; Sokol, Janusz; Muhammad, Zubair; Mashwani, Wali Khan; Chinram, Ronnason; Petchkaew, Pattarawan (2021) - Utilizing (18) and (19), we may get∣∣a3 − ρa22∣∣ = ∣∣∣∣c26 − c21 12 − ρ 16 c21 ∣∣∣∣ . This gives ∣∣a3 − ρa22∣∣ = 1 6 ∣∣∣∣{c2 − (4 + 3ρ 8 ) c21 }∣∣∣∣ . Keywords: functions; hankel
Some Double Integrals Stemming from the Boltzmann Equation in the Kinetic Theory of Gasses by Srivastava, Hari M. (2022) - [16] H. M. Srivastava, Certain double integrals involving hypergeometric functions, Jñānābha Section A, 1: 1–10, 1971. (1) DOI: https://doi.org/10.29020/nybg.ejpam.v15i3.4429 Email addresses: harimsri@math.uvic.ca (H. M. Srivastava) https://www.ejpam.com 810 © 2022 EJPAM All rights reserved. Keywords: functions
The Cryptographic Properties of Von Neumann Cellular Automata by Martin del Rey, Angel; Burrieza, J. Escuadra; Iglesias, J.L. PÃ©rez; SÃ¡nchez, G. RodrÃguez; Dios, A. Queiruga; de la Villa Cuenca, A. (2010) - (* algebrai degree 4 *)ag[4℄={};Do[ aux=Append[IntegerDigits[k,2,15℄,1℄;AppendTo[ag[4℄,FromDigits[aux,2℄℄,{k,0,2^15-1}℄;(* algebrai degree 3 *)g={};Do[ aux1=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{1,0,0,0,0}℄℄,2℄;aux2=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{0,1,0,0,0}℄℄,2℄;aux3=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{0,0,1,0,0}℄℄,2℄;aux4=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{0,0,0,1,0}℄℄,2℄;aux5=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{1,1,0,0,0}℄℄,2℄;aux6=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{1,0,1,0,0}℄℄,2℄;aux7=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{1,0,0,1,0}℄℄,2℄;aux8=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{0,1,1,0,0}℄℄,2℄; REFERENCES 775aux9=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{0,1,0,1,0}℄℄,2℄;aux10=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{0,0,1,1,0}℄℄,2℄;aux11=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{1,1,1,0,0}℄℄,2℄;aux12=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{1,1,0,1,0}℄℄,2℄;aux13=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{1,0,1,1,0}℄℄,2℄;aux14=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{0,1,1,1,0}℄℄,2℄;aux15=FromDigits[Flatten[Append[IntegerDigits[k,2,11℄,{1,1,1,1,0}℄℄,2℄;Flatten[AppendTo[g,{aux1,aux2,aux3,aux4,aux5,aux6,aux7,aux8,aux9,aux10,aux11,aux12,aux13, aux14,aux15}℄℄,{k,0,2^11-1}℄;ag[3℄=Flatten[g℄;(* algebrai degree 1 *)ag[1℄={};Do[ aux16=FromDigits[Flatten[Reverse[Append[IntegerDigits[k,2,5℄,{0,0,0,0,0,0,0,0,0,0,0}℄℄℄,2℄;AppendTo[ag[1℄,aux16℄,{k,0,2^5-1}℄(* algebrai degree 2 *)total=Table[k,{k,0,2^16-1}℄;aux17=Union[ag[4℄,ag[3℄,ag[1℄,{0}℄;ag[2℄=Complement[total,aux17℄; • (* Definition of the derivative of a boolean fun tion *)der[w,b,x℄:=BitXor[f[IntegerDigits[w,2,16℄,x℄,f[IntegerDigits[w,2,16℄,BitXor[b,x℄℄℄; lass=NlBalGrad3[4℄;Nl4BalGrad3LK={};Do[ w= lass[[l℄℄;LK[w℄={};Do[ If[ Or[Table[der[w,IntegerDigits[i,2,4℄,IntegerDigits[j,2,4℄℄,{j,0,2^4-1}℄=={0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},Table[der[w,IntegerDigits[i,2,4℄,IntegerDigits[j,2,4℄℄,{j,0,2^4-1}℄=={1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}℄,AppendTo[LK[w℄,i℄℄,{i,0,2^4-1}℄;If[LK[w℄=={0},AppendTo[Nl4BalGrad3LK,w℄℄,{l,1,Length[ lass℄}℄; lass=NlBalGrad3[2℄;Nl2BalGrad3LK Keywords: algebraic; automata; cellular; degree; functions; properties; ℄ ℄
Toeplitz Determinants for the Class of Functions with Bounded Turning by Abdul Wahid, Nur Hazwani Aqilah; Mohamad, Daud; Kamarozzaman , Nur Maziah ; Ahamad Shahminan , Ainurraziqin (2022) - ([7]) Let p (z) ∈ P of the form p (z) = 1 + ∞∑ n=1 pnz n and µ ∈ C. Then |pn − µpkpn−k| ⩽ 2max {1, |2µ− 1|} , [25] considered Toeplitz determinants of starlike functions connected with the sine function, and Zulfiqar et al. Keywords: functions; tαδe
Coefficient Problems for Star-like Functions with Respect to Symmetric Conjugate Points Connected to the Sine Function by Mohamad, Daud; Abdul Wahid, Nur Hazwani Aqilah; Hasni, Nurul Natasya (2023) - − ( 1 8 ( k2 − 5 8 k1 2 ))2 = 1 64 ( 3 16 k1 4 − 10 16 k1 2k2 + 1 2 k1k3 − k2 2 + 5 4 k1 2k2 − 25 64 k1 4 ) − ( k1 4 )( 1 8 ( 2k2 − k1 2 )) + 1 3 ( k1 4 )3 ] = 1 128 ( 3k1 3 − 10k1k2 + 8k3 ) , (17) and γ4 = 1 2 [ 1 64 ( 8k4 + 3k1 2k2 − 2k2 2 − 8k1k3 ) − k1 4 ( 1 96 ( k1 3 − 9k1k2 + 12k3 )) Keywords: coefficients; functions
On the Number of Restricted One-to-One and Onto Functons Having Integral Coordinates by Latayada , Mary Joy R. (2023) - i, i ≤ n. To count the number of restricted onto functions f |Si , let us consider the following sequence of events: E1 : event of choosing a subset S1 of Nm such that |Si| = i. E2 : event of forming a restricted onto function f |Si : Nm −→ Nn. By Multiplication Principle, the number of such restricted one-to-one functions f |Si = f |Si−1∪{m+1} overall Si ⊆ Nm+1 is equal to |E1||E2| = Ŷ (i− 1,m)(m+ 2− i). Keywords: functions
Fekete-Szegö Functional of a Subclass of Bi-Univalent Functions Associated with Gegenbauer Polynomials by AlRawashdeh, Waleed (2024) - Univalent functions. Univalent functions. Keywords: class; functions; polynomials
A family of Analytic Functions Subordinate to Horadam Polynomials by AlRawashdeh, Waleed (2024) - Then for bx > 0 and for some ζ ∈ R, |a3 − ζa22| ≤ { bx 2B , if ζ ∈ [ζ1, ζ2] |2(pbx2+qa)BA2(γ+1)2−b2x2(K(γ+1)2+4ζB)| 4BA2(γ+1)2 , if ζ /∈ Solving for ζ we get: (γ + 1)2(2A2(pbx2 − bx+ qa)− b2x2K) 4Bb2x2 ≤ ζ ≤ (γ + 1)2(2A2(pbx2 + bx+ qa)− b2x2K) 4Bb2x2 Hence, inequality (17) becomes |a3 − ζa22| ≤  bx 2B , if ζ ∈ [ζ1, ζ2]∣∣∣∣pbx2+qa 2B − b2x2K 4BA2 − ζ ( bx A(γ+1) )2 ∣∣∣∣ , if ζ /∈ Keywords: class; functions; polynomials
Hankel and Toeplitz Determinants of Logarithmic Coefficients of Inverse Functions for the Subclass of Starlike Functions with Respect to Symmetric Conjugate Points by Abdul Wahid, Nur Hazwani Aqilah; Tumiran, Adawiyah; Timilehin Gideon Shaba (2024) - 2020 Mathematics Subject Classifications: 30C45, 30C50 Key Words and Phrases: Univalent functions, starlike functions, symmetric conjugate points, exponential function, inverse functions, coefficient estimates, logarithmic inverse coefficients, Han- kel determinant, Toeplitz determinant, subordination 1. Furthermore, a recent study has focused on the Hankel and Toeplitz determinants, which involve the use of logarithmic coefficients, but in the direction of inverse functions for some classes of univalent functions, for instance, [2, 11, 12, 18] may provide further insight into this. Keywords: coefficients; functions
A Specific Class of Harmonic Meromorphic Functions Associated with the Mittag-Leffler Transformation by Ahmed, Sarah ; Alsoboh, Abdullah; Darus, Maslina (2024) - This article uses the Mittag-Leffler transformation to explore a specific category of harmonic meromorphic functions. The main focus of this study is on harmonic meromorphic functions that can be represented by the Mittag- Leffler transformation. Keywords: functions; µ=1
Euler Polynomials and Bi-univalent Functions by Amourah, Ala; Jarwan, Dunia ; Salah, Jamal; Mohammed, M. J.; Meqdad, S. A. ; Anakira, Nidal (2024) - Our aim is to construct a new and comprehensive subclass of bi-univalent functions. Coefficient bounds and fekete-szegö problem for qualitative subclass of bi-univalent functions. Keywords: functions
Some New Applications of the Quantum Calculus for New Families of Sigmoid Activation Bi-univalent Functions Connected to Horadam Polynomials by Mishra, Nidhish Kumar ; Khan, Mohammad Faisal ; Lone, Showkat Ahmad (2024) - Using this newly defined q-analogous differential operator and Horadam polynomials, we introduce new subclasses of bi-univalent functions in D. An analytic function g ∈ A will be the bi-univalent in D, if both g and g−1 are univalent in D and the family of bi-univalent functions of the form (1) is represented by the symbol Σ. Keywords: functions; polynomials; q ψ(s; ψ(s
Bounds for Certain Determinants of Logarithmic Coefficients for the Class of Functions with Bounded Turning by Abdul Wahid, Nur Hazwani Aqilah; Amirnuddin, Ilya Qursiah; Mohammad Azmi, Nurul Izzah (2024) - [31–33] highlighted the importance of logarithmic coefficients for estimating the Tay- lor coefficients of univalent functions. The findings in this paper could inspire further research into determining upper bounds for Hankel, Toeplitz, and Vandermonde determinants with logarithmic coefficients as entries, particularly within other subclasses of univalent functions, while considering the inverse functions for G(α, δ). Keywords: coefficients; functions; hankel; tαδ
A Subclass of Bi-univalent Functions Defined by aSymmetric q-Derivative Operator and Gegenbauer Polynomials by Illafe, Mohamed; Mohd, Maisarah Haji ; Yousef, Feras ; Supramaniam, Shamani (2024) - (2) A function f is said to be bi-univalent in U if both f(z) and f−1(z) are univalent in U. Let Σ denote the class of bi-univalent functions in U given by (1). Two inclusive subfamilies of bi-univalent functions. Keywords: functions
A Family of Bi-Univalent Functions Defined by( p, q)-Derivative Operator Subordinate to a GeneralizedBivariate Fibonacci Polynomials by Basem Aref Frasin; Sondekola Rudra Swamy; Amourah, Ala; Jamal Salah; Ranjitha Hebbar Maheshwarappa (2024) - Math, 17 (4) (2024), 3801-3814 3803 The renowned Koebe theorem (see[25]) states that, each function ψ ∈ S has an inverse given by ψ−1(ω) = Ψ(ω) = ω − d2ω 2 + (2d22 − d3)ω 3 − (5d32 − 5d2d3 + d4)ω 4 + ... (3) satisfying ζ = ψ−1(ψ(ζ)) and ω = ψ(ψ−1(ω)), |ω| < r0(ψ), r0(ψ) ≥ 1/4, ζ, ω ∈ D. The notion of bi-univalent functions was first presented by Levin in his work Generalized bivariate fibonacci polynomial and two new subclasses of bi-univalent functions. Keywords: functions
Subfamilies of Bi-Univalent Functions Defined by Imaginary Error Functions Subordinate to Horadam Polynomials by Al-hawary, Tariq; Frasin, Basem Aref ; Amourah, Ala ; Salah, Jamal (2025) - = FΩ(s, r, u, y, t, τ), in which FΩ(s, r, u, y, t, τ) the family of functions L ∈ Ω and satisfying the below conditions (1− τ) EL(℘) ℘ + τ (EL(℘))′ ≺ Υ(y, ℘) + 1− s and (1− τ) EV (ϖ) ϖ + τ (EV (ϖ))′ ≺ Υ(y,ϖ) + 1− s, where ℘,ϖ ∈ Θ, τ ≥ 0, y ∈ R. T. Al-Hawary et al. / Eur. For λ = 0 and τ = 1, we have, FΩ(s, r, u, y, t, 1) = FΩ(s, r, u, y, t), in which FΩ(s, r, u, y, t) the family of functions L ∈ Ω and satisfying the below conditions and (EV (ϖ))′ ≺ Υ(y,ϖ) + 1− s, where ℘,ϖ ∈ Θ, y ∈ R. Example 3. Keywords: functions
Characterizations of Weakly Contra-$(\tau_1,\tau_2)$-continuous Functions by Kong-ied, Butsakorn ; Sompong, Supunnee ; Boonpok, Chawalit (2025) - Moreover, several characterizations and some properties concerning weakly contra- (τ1, τ2)-continuous functions are established. 2020 Mathematics Subject Classifications: 54C08, 54E55 Key Words and Phrases: τ1τ2-open set, weakly contra-(τ1, τ2)-continuous function 1. Keywords: functions; τ1τ2
Fekete-Szeg¨o Inequalities for a New Class of Bi-Univalent Functions Defined via the Mittag-Leffler Function by Al-Ityan, Mohammad ; Amourah, Ala; Alsoboh, Abdullah ; Anakira, Nidal ; Bani Raba'a, Mohammad ; Hammad, Suha ; Sasa, Tala (2025) - The subclass offers a robust frame- work for studying bi-univalent functions, particularly in relation to coefficient estimates, distortion theorems, and other central topics in geometric function theory. A class of bi-univalent functions in a leaf-like domain defined through subordination via q-calculus. Keywords: class; functions; γ(ג+; γ(ℶ
Coefficient Results on Certain Subclasses of Sakaguchi Type Bi-univalent Functions by Lee Chew Yee; Maslina Darus (2025) - Hence, the following conditions must be satisfied by function F ∈ A for its inverse map F−1 to exist: F−1(F(ξ)) 2020 Mathematics Subject Classifications: 30C10, 30C45, 30C50, 33C45 Key Words and Phrases: Analytic functions, bi-univalent functions, convolution, Gegenbauer polynomial, Einstein function, Sakaguchi type function, coefficient estimate, Fekete-Szegö 1. Keywords: functions
Vandermonde Determinant for the Generalized Bounded Turning Functions Associated with Gregory Coefficients by Abdul Wahid, Nur Hazwani Aqilah; Cik Soh, Shaharuddin (2025) - 2020 Mathematics Subject Classifications: 30C45, 30C50 Key Words and Phrases: Univalent functions, inverse functions, bounded turning functions, Gregory coefficients, Taylor coefficients, logarithmic coefficients, Vandermonde determinant 1. Introduction Let A denote the class of analytic functions f (z) that can be expressed as a Taylor series expansion in the open unit disk E = {z ∈ C : |z| < 1}, given by f (z) = z + ∞∑ n=2 anz n , z ∈ E. (1) We denote by S the subclass of A consisting of univalent functions in E. The inverse of a function f (z) ∈ S of the form (1) has a series expansion given by f−1 (w) = w + ∞∑ n=2 Anw n, |w| < r0 (f) , r0 (f) ≥ 1 4 , (2) ∗Corresponding author. Keywords: coefficients; functions; ταδ
Hankel Determinant of Analytical Functions Closely Tied to Bell Polynomials by Alnajar, Omar; Alshammari, K. Alshammari; Amourah, Ala; Darus, Maslina (2025) - Investigating new inclusive subclasses of bi-univalent functions linked to gregory numbers. Subfamilies of bi-univalent functions associated with the imaginary error function and subordinate to jacobi polynomials. Keywords: functions; −ξ2)+1
Some Conditions for Certain Two Families of Analytic Functions Associated with Touchard Polynomials by Al-hawary, Tariq; Frasin, Basem Aref; Cotˆırl˘a, Luminita-Ioana; Breaz, Daniel (2025) - An application of a binomial distribution series on certain analytic functions. An application of a poisson distribution series on certain analytic functions. Keywords: functions; ε=2
Representation of Bi-Univalent Functions to Lucas Balancing Polynomials with Geometric Properties and Coefficient Bounds by Thangamani, Stalin; Mohammed, Pshtiwan Othman; Devadoss, Jeno Francis ; Yousif, Majeed Ahmad; Arab, Meraa ; Baleanu, Dumitru (2025) - In this paper, we introduce and analyze a new subclass of bi-univalent functions defined in the open unit disk, associated with Lucas and Lucas balancing polynomials. The findings presented here are valuable for applications in geometric function theory and areas like fluid mechanics, conformal mappings, and engineering models where the analytic structure of bi-univalent functions plays a significant role. Keywords: 4(1; functions
Fekete-Szegö Inequality Estimate for Analytic Functions Using Salagean-Difference Operator and Leaf-Like Domain by Naik, Avaya; Sushree Chinmayee Sahoo (2025) - 2020 Mathematics Subject Classifications: 30C45 Key Words and Phrases: Analytic function, Univalent functions,Fekete-Szegö inequality,Leaf like domain 1. Introduction The theory of univalent functions, a cornerstone of geometric function theory, explores the properties of analytic functions that are injective in the open unit disk. Keywords: functions; operator; p(ζ; λh(ζ
Estimates for the Coefficients of Subclasses Defined by the q-Babalola Convolution Operator of Bi-Univalent Functions Subordinate to the q-Fibonacci Analogue by Almalkawi, Ahmad ; Alsoboh, Abdullah; Amourah, Ala ; Sasa, Tala (2025) - Central to q-calculus is the deformation parameter q ∈ (0, 1), which ensures convergence and structural integrity of function classes, particularly those defined by geometric proper- ties such as starlikeness and convexity. = ℓ1z 2 + ( ℓ2 − ℓ21 2 ) z2 2 + ( ℓ3 − ℓ1ℓ2 − ℓ31 4 ) z3 2 + · · · , (21) and Υ(φ(z); q) = 1 + p̃1 [ ℓ1z 2 + ( ℓ2 − ℓ21 2 ) Keywords: functions
On the Fractional q-Differintegral Operator for Subclasses of Bi-univalent Functions Subordinate to q-Ultraspherical Polynomials by Ahmed, Mamoon ; Alsoboh, Abdullah; Amourah, Ala ; Salah, Jamal (2025) - 2020 Mathematics Subject Classifications: 30A36, 30C45, 81P68, 11B37 Key Words and Phrases: Subordination; Ultraspherical Polynomial; q-Calculus; Analytic functions; Univalent functions; bi-univalent functions; Orthogonal polynomials; Carathéodory’s functions; Fekete-Szegö problem. In this paper, we introduce a novel class of bi-univalent functions using the fractional q-differintegral operator and q-Ultraspherical polynomials. Keywords: functions; polynomials
A Class of Bi-Univalent Functions Associated with Shell-Like Geometries and the q-Fibonacci Analogue by Alsoboh, Abdullah ; Amourah, Ala; Al-Maqbali, Abdullrahman ; Alnajar, Omar; Awad, Feras ; Sasa, Tala (2025) - = ℓ1z 2 + ( ℓ2 − ℓ21 2 ) z2 2 + ( ℓ3 − ℓ1ℓ2 − ℓ31 4 ) z3 2 + · · · , (17) A. Alsoboh et al. / Eur. Math, 18 (4) (2025), 6689 10 of 19 and Υ(φ(z); q) = 1 + p̂1 [ ℓ1z 2 + ( ℓ2 − ℓ21 2 ) z2 2 + ( ℓ3 − ℓ1ℓ2 − ℓ31 4 ) z3 2 + · · · ] + p̂2 [ ℓ1z 2 + ( ℓ2 − ℓ21 2 ) z2 2 + ( ℓ3 − ℓ1ℓ2 − ℓ31 4 ) z3 2 + · · · ]2 + p̂3 [ ℓ1z 2 + ( ℓ2 − ℓ21 2 ) Keywords: alsoboh; class; functions
Hankel Determinant Estimates for Bi-Bazilevič-Type Functions Involving q-Fibonacci Numbers by Alsoboh, Abdullah; Tayyah, Adel Salim ; Amourah, Ala ; Al-Maqbali, Abdullrahman A. ; Al Mashraf, Khaled ; Sasa, Tala (2025) - z2 2 + ( ℓ3 − ℓ1ℓ2 − ℓ31 4 ) z3 2 + · · · . z2 2 + ( ℓ3 − ℓ1ℓ2 − ℓ31 4 ) z3 2 + · · · ] + p2 [ ℓ1z 2 + · · · ]2 + p3 [ ℓ1z 2 + · · · ]3 + · · · = 1 + p1ℓ1 2 z + 1 2 [( ℓ2 − ℓ21 2 ) p1 + ℓ21 2 p2 ] z2 + 1 2 [( ℓ3 − ℓ1ℓ2 + ℓ31 4 ) p1 + ℓ1 ( ℓ2 − ℓ21 2 ) p2 + ℓ31 4 p3 ] z3 + · · · = 1 + ϑqℓ1 2 z + 1 2 [( ℓ2 − ℓ21 2 ) ϑq + (1 + 2q)ϑ2qℓ 2 1 2 ] z2 + 1 2 [( ℓ3 − ℓ1ℓ2 + ℓ31 4 ) ϑq + ℓ1 ( ℓ2 − ℓ21 2 ) (1 + 2q)ϑ2q + (1 + 3q)ϑ3qℓ 3 1 4 ] z3 + · · · (17) Similarly, there exists an analytic function ν, defined in D, such that |ν(ξ)| < 1 and p(ξ) = Υ(ν(ξ); q). Keywords: alsoboh; class; functions
Geometric Characterizations of Imaginary Error Functions in Subclasses of Spirallike Analytic Functions by Yousef, Feras ; Alholi, Maryam M ; Al-Hawary, Tariq (2025) - Error functions inequalities. The radius of starlikeness for error function. Keywords: functions; ϵ=2
On a Subclass of Starlike Functions related to Pascal and Poisson distributions by Algethami, Badriah; Lashin, Abdel Moneim; El-Emam, Fatma (2025) - An application of the distribution series for certain analytic function classes. Math, 18 (4) (2025), 7014 12 of 12 distribution series on certain analytic functions. Keywords: functions; m=2
A New Subclass of Bi-Univalent Functions Involving Bell and Meixner-Pollaczek Polynomials by Alnajar, Omar; Amourah, Ala; Alsoboh, Abdullah ; Khabour, Omar ; Al Hatmi, Mohammed Mattar ; Sasa, Tala (2025) - In this work, we present a novel subclass of bi-univalent functions defined by Meixner- Pollaczek and Bell polynomials. Building upon these classical families, several subclasses of bi-univalent functions have been constructed using orthogonal polynomials such as Chebyshev, Gegenbauer, and Horadam polynomials. Keywords: functions; polynomials; ϱ⅁(q̃
The Imaginary Error Function and New Classes of Bi-Univalent Functions Subordinate to Jacobi Polynomials by Alnajar, Omar ; Amourah, Ala ; Alsoboh, Abdullah; Khabour, Omar ; Al-Hatmi, Mohammed ; Al-Hawari, M. ; Sasa, Tala (2025) - A unique family of bi-univalent functions, commonly known as functions that are defined on the symmetric domain, is presented and investigated in this paper. 2020 Mathematics Subject Classifications: 30C45 Key Words and Phrases: Imaginary error function, jacobi polynomials, bi-univalent functions, fekete-szegö inequality, maclaurin series ∗Corresponding author. ∗Corresponding author. Keywords: +1 2(ℑ+; 2(ℑ+; 2)(t−; 3)(ℑ+; 8(ℑ+; functions; ℑ+1)(ℑ+2
A Study on Bi-Univalent Functions of Complex Order Arising from the q-Fibonacci Analogue by Alsoboh, Abdullah ; Amourah, Ala; Almashrafi, Khaled ; sasa, Tala (2025) - The results obtained in this investigation not only extend and generalize several previous contributions in the theory of bi-univalent functions, but also provide new insights into the interplay between bi-univalent function theory, the q-Fibonacci numbers and the shell-like geometries. Motivated by recent advances in q-calculus and its applications in geometric function theory, we construct and examine two distinct families of analytic bi-univalent functions. Keywords: functions
Analytic Subclass Conditions for Operators Involving the Generalized Imaginary Error Function by Alameer, Amerah; Al-hawary, Tariq; Frasin, Basem; Yousef, Feras (2025) - Error functions inequalities. The radius of starlikeness for error function. Keywords: functions
Coefficient Problems for Bi-Univalent Functions via $q$–Rabotnov Kernels and $q$–Fibonacci Subordination by Alsoboh, Abdullah; Almalkawi, Ahmad ; Amourah, Ala ; Al Mashrafi, Khalid; Sasa, Tala (2025) - Motivated by the interplay between q–calculus and geometric function theory, this paper introduces and investigates a new subclass of bi-univalent functions associated with shell- like domains generated through the q–Rabotnov function and the q–analogue of Fibonacci num- bers. These findings enrich the structural understanding of bi-univalent functions and suggest future directions involving operator theory, convolution structures, and further applications of q–calculus in complex analysis. Keywords: functions; γq(1 +; δ β
Quasi-Hadamard Product of Certain Meromorphic p-Valent Analytic Functions by Goyal, Som Prakash; Goswami, Pranay (2010) - 2000 [7] V. KUMAR, Hadamard product of certain starlike functions, J. Math. [12] T. SEKINE, On quasi-Hadamard products of p-valent functions with negative coefficients in: H. M. Srivastava and S. Owa (Editors), Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 317–328. 1989. Keywords: functions

Point

An Iterative Method for (AGDDV I P) in Hilbert Space and the Homology Theory to Study the (GDDCPn) in Riemannian n-manifolds in the Presence of Fixed Point Inclusion by Kumar Das, Prasanta (2011) - ≡ H. Let W be a maximal fixed point open set in X with respect to ∇F − T. Then, there exists a unique y0 such that y0 ∈ (∇F − T − 1X ) −1(0X ) and y0 solves the problem (GDDV IPn), that is, (∇F − T )(y0) ∈ (τ ∗(X )) ≡ H. Let W be a maximal fixed point open set in X with respect to ∇F − T. Then, there exists an unique y0 such that y0 ∈ (∇F − T − 1X ) −1(0X ) and y0 that solves the problem (GDDV C Pn), that is, (∇F − T )(y0) ∈ (τ ∗(X )) Keywords: point
Coincidence and Common Fixed Point Theorems in Gb-Cone Metric Spaces by Benchabane, Saadia; Djebali, Smail (2021) - REFERENCES 1365 (3) If in Corollary 1, we set F = R = S and f = I, then we obtain an extension of [11, Theorem 2.7]. (4) T = R and z = y in Theorem 2 leads to a generalization of [16, Theorem 2.1] with M = T . (5) Corollary 2 with F = R = S, f = I, and z = y is an extension of [2, Theorem 2.1, Theorem 2.5, Theorem 2.8]. Keywords: cone; metric; point; y3n+1
A Family of Optimal Cubic-Order Multiple-root Solvers and Their Dynamics by Kim, Hwajoon; Rathie, Arjun Kumar ; Geum, Young Hee (2023) - As the first example, we select the polynomial p1(z) = (z3 − z)4 with roots z = 0,±1 of multiplicity m = 4. = (z − A)m(z − B)m with the stability analysis of strange fixed points. Keywords: order; point; |ℑ(t)|
Numerical Assessment of Gravity for Sloshing in Tank Using OpenFOAM by Sabri, Dilheen; Zekri, Hussein (2022) - They also analyzed free surface, size of the wetted region, and the pressure distribution along the wetted region with and without gravity. Math, 15 (4) (2022), 2022-2031 2029 Figure 5: Free surface, with (blue dots) and without (black dots) gravity at t = 1.2 s. Figure 6: Free surface, with (blue dots) and without (black dots) gravity at t = 1.3 s. Figure 7: Pressure distribution, with (blue line) and without (black line) gravity at t = 1.2 s. is contributing to this impact and its parameters. Keywords: figure; gravity; point; pressure; sloshing; surface; tank
A Discrete Predator-prey Model with Allee and Refuge Effect by Kapcak, Sinan (2023) - Existence of the Fixed Points In this section, we analyse the existence of fixed points of discrete system (4). (a) Fixed points: P0, P1 (b) Fixed points: P0, P1, P + 1 (c) Fixed points: P0, P1, P + 0 (d) Fixed points: P0, P1, P + 2 , P+ 3 Figure 1: Four possible cases for existence of the fixed points. Keywords: point
On Common Fixed Point for Contractive Mappings in $p$-Pompeiu-Hausdorff Metric Spaces by Ekayanti, Arta; Marjono, Marjono; Muslikh, Mohamad; Fitri, Sa'adatul (2024) - 2020 Mathematics Subject Classifications: 47H10, 26E25 Key Words and Phrases: common fixed point, set-valued mappings, contractive mappings, partial metric spaces, p-Pompeiu-Hausdorff Metric Spaces 1. So, we obtain x ∈ Gm(x) and x ∈ Fn(x) for each m,n. It means x is common fixed point of Gm and Fn for every m and n. Keywords: metric; p(x; point
Determination of the Fixed Point of Lotka-Volterra Function by Osei Fokuo, Mary; Obeng-Denteh, William; Dontwi, Isaac Kwame; Mensah, Patrick Akwasi Anamuah (2024) - We then apply the idea and the definition of the theorem of fixed points and fixed point. 2020 Mathematics Subject Classifications: 54H25, 47H10, 54E35 Key Words and Phrases: Lotka-Volterra, fixed point, parameter, solution, function,contraction mapping, fixed point theorem 1. Keywords: point
Enhanced Results in Common and Coincidence FixedPoint Theory with Applications to Simulation Mappings by Majid, Nassar Aiman ; AL. Jumaili, Alaa; Ng , Zhen Chuan Ng ; Lee, See Keong Lee (2024) - Again, due to the triangle inequality yields∣∣S ( Txsk+1−1,Txsk+1−1,Txsk ) − S (Txsk ,Txsk ,Txsk+1) ∣∣ ≤ S ( Txsk+1−1,Txsk+1−1,Txsk+1 ) . − S ( Txsk−1,Txsk−1,Txsk+1−1 )∣∣ ≤ S ( Txsk+1 ,Txsk+1 ,Txsk+1−1 ) . Keywords: point
An Outreach Note on the Poincare Conjecture for Non-specialists by Otera, Daniele (2024) - Indeed, also real world mechanics or physics force us to move from dimension 2 to dimensions 3, 4 or higher. Whereas in the DIFF category (i.e. for differential manifolds) it is true in dimensions 1, 2, 3, 5 and 6, it is still open in dimension 4, whereas in the other cases it is generally false. Keywords: conjecture; curvature; dimension; manifold; point; sphere; surface
On the Family of Theorems on Metric Completeness by Park, Sehie (2024) - We list a large number of examples of metric fixed point theorems which follow from our principles. [21] S. Park, Improving many metric fixed point theorems, Letters Nonlinear Anal. Keywords: metric; point; theorem
New Proofs of Fixed Point Theorems on Quasi-metric Spaces by Park, Sehie (2025) - In the present paper, we give very simple proofs of fixed point theorems for various multimap classes in [40]. In Section 8, we give a few example of fixed point theorems which can not applicable our Theorem H. Finally, Section 9 is for epilogue. Keywords: d(x; metric; point; theorem
Maxwell Hybrid Nanofluid (Cu-Al2O3/Water) and (CuO-Ag/Water) Near a Stagnation Point above an Extending Sheet by Gaber, Ahmed; Mohamed, Mona; Moatimid, Galal (2025) - The numerical dual solution of stagnation point flow and melting heat transfer of Casson fluid induced by a stretching sheet was investigated [20]. Stagnation point flow is highly relevant in applications involving heat transfer and fluid dynamics near boundaries with localized forces or heat sources. 2.1. Keywords: flow; fluid; heat; hybrid; moatimid; mohamed; nanofluid; nanoparticles; point; sheet; stagnation; stretching; surface; temperature; thermal; transfer; velocity; water
Fixed Point Theorems in Controlled Rectangular Modular Metric Spaceswith Solution of Fractional Differential Equations by Ishtiaq, Umar; Saleem, Naeem; Farhan, Muhammad; Aphne, Maggie; Chowdhury, Mohammad Showkat Rahim (2025) - Fuzzy b-metric spaces: fixed point results for ψ-contraction correspondences and their application. 2020 Mathematics Subject Classifications: 47H10, 54H25 Key Words and Phrases: Controlled metric space, modular metric space, fixed point; existence and uniqueness, non-linear fractional differential equations 1. Keywords: point
Common Fixed Points of Asymptotically Regular Mappings in Convex Metric Spaces with Application by Khan, Abdul Rahim; Ugwunnadi, Godwin; Aphane, Maggie; Yousaf, Faizan ; Abbas, Amir (2025) - If E is a function on a metric space Q into itself, then the set O(E, e) := {Ene : n = 0, 1, 2, 3, · · · } is called the orbit of E at the point e ∈ Q. E is called orbitally continuous at p ∈ Q if for any sequence {qk} ⊂ O(E, q) for some q ∈ Q, limk→∞ qk = p entails that limk→∞Eqk = Ep. ([7],Theorem 2.2) Suppose that (Q, d) is a complete metric space, E and F are asymptotically regular self-mappings on Q satisfying the following condition: d(Eq, Fp) ≤ µd(q, p) + ν{d(q, Eq) + d(p, Fp)}, ∀q, p ∈ Q (2) where 0 ≤ µ < 1, 0 ≤ ν < ∞. Suppose further that E and F are either k-continuous for some k ≥ 1 or orbitally continuous. Keywords: point
Characterization and Application of Fixed Point Theorems for 3-Self Mappings in Generalized Metric Spaces by Noorwali, Maha; Hatamleh, Raed; Abubaker, Ahmad A.; Al-Husban, Abdallah ; Hamja, Jamil J.; Nordo, Giorgio; Fujita, Takaaki ; Khattak, Arif Mehmood (2025) - Fixed point theorems for contractive mappings were established by Huang et al. In [6], a graph was introduced to study fixed point theorems about Reich-type contractions in metric spaces. Keywords: ê1; ê2; ê3⋎+2; f3ê3⋎+2; g(ê3⋎+1; g(z; point; spaces
Exploring Fixed Point Theory in Quasi-Partial Metric Spaces: A Unified Approach with Applications in Integral Equations and Computational Sciences by Qawaqneh, Haitham Ali (2025) - Fixed point results for geraghty type generalized f-contraction for weak admissible mappings in metric-like spaces. New functions for fixed point results in metric spaces with some applications. Keywords: metric; point
Convergence and Fixed Points of Self-Mappings in MR-Metric Spaces: Theory and Applications by Malkawi, Abed Al-Rahman (2025) - Introduction This paper presents a comprehensive study on the convergence and fixed points of self-mappings in MR-metric spaces, a recently introduced generalization of metric spaces. These findings have significant implications for various fields, including optimization, machine learning, and numerical analysis, and provide a solid foundation for further research and applications in MR-metric spaces. Keywords: metric; point
Common Fixed Point Theorems for Mappings Satisfying implicit Relation in Bipolar metric Space} by Penumarthy Parvateesam, Murthy; Dhuri, Chandra Prakash ; RAMASWAMY, RAJAGOPALAN; Hyatt Khan, Khizar; Abdelnaby, Ola Ashour (2025) - = Y ⊆ X ∪ Y = T (X ∪ Y ). Let X = {C(a, b, d) : a, d ∈ R} and Y = {L(b, d) : d ∈ R}. Keywords: metric; point
Common Fixed Point Results in Double-Composed Cone Metric-Like Spaces for Some Generalized Rational Contractions with Applications by A. Hijab, Anas ; Shaakir, Laith; Aljohani, Sarah; Mlaik, Nabil Mlaik (2025) - Obviously, cone b-metric-like spaces are generalized to cone b-metric spaces, cone metric-like spaces, cone metric spaces and metric spaces, respectively, but the same is not true vice versa (see [17, 19, 21–25, 27]). 2020 Mathematics Subject Classifications: 47H10, 54E50, 54H25 Key Words and Phrases: Fixed point, Cone metric space, Double-controlled metric-like spaces, Double-composed cone metric spaces, Double-composed cone-metric-like spaces. Keywords: cone; lc(a; metric; point; spaces
Advances in Rational Contractions within Extended $b-$Metric Spaces and Their Applications by Qawaqneh, Haitham Ali; Al-Musannef, Gawhara ; Alsamir, Habes (2025) - Existence of fixed point results in orthogonal extended b-metric spaces with application. Fixed point results in metric-like spaces via σ-simulation functions. Keywords: point
Solving Systems of Monotone Variational Inclusion Problems with Multiple Output Sets in Banach Spaces by Abass, Hammed; Aphane, Maggie; Oyewole, Olawale Kazeem; Narain, Ojen; Mustafoyev, K. I. (2025) - − g(x) : x ∈ E}, x∗ ∈ E∗. Let the domain of g be denoted by domg = {x ∈ E : g(x) < +∞}, hence for any y ∈ E, we define the directional derivative of g at x in the direction of y by g0(x, y) = lim t→0+ g(x+ ty)− g(x) t . The graph of B denoted by G(B) = {(x, x∗) ∈ E × E∗ : x∗ ∈ Bx}. Keywords: banach; point; problem; spaces
Fixed Points of Mappings Contracting Perimeters of Polygons: A Geometric Generalization of Banach’s Principle by Nazam, Muhammad; Habiba, Umme; De la Sen, Manuel (2025) - (3) where x, l ∈ Z. Corollary 1. (Banach fixed point theorem) Let (Z, s) be a complete metric space, and let L : Z → Z be a contraction mapping, then it admits a fixed point. Fixed point theorem for mappings contracting perimeters of trian- gles. Keywords: point
Fixed Point Results on Interpolative Metric Spaces via Simulation Functions by Gulyaz Ozyurt, Selma; Alsahli, Ghaziyah (2025) - Math, 18 (2) (2025), 6282 2 of 13 to metric fixed points. https://doi.org/10.2298/FIL2422729K [8] E. Karapınar, Recent advances on metric fixed point theory: A review, Applied and Computational Mathematics an International Journal, 22(1), 3-30 (2023). Keywords: metric; point
On Rational-Type Contractive Mappings in Bi-Complex Valued Control Metric Spaces and Applications by Sarwar, Muhammad; Fatima, Nahid; Shah, Sayed Khayyam; Khan, Asad; Abodayeh, Kamaleldin (2025) - Let db be a (BCVMS) defined on S = {0, 1, 2} such that, db(0, 1) = db(1, 2) = Let db be a (BCVMS) defined on S = {0, 1, 2} such that, db(0, 1) = 60 + 60i2, db(1, 2) = Keywords: db(κ; metric; point
Fixed Point Theory in MR-Metric Spaces Fundamental Theorems and Applications to Integral Equations and Neutron Transport by Qawasmeh, Tariq; Malkawi, Abed Al-Rahman (2025) - Main Results This section presents the fundamental theorems that constitute the core contributions of our work in MR-metric spaces. By the Banach fixed-point theorem in MR-metric spaces (Theorem 1), T has a unique fixed point f∗ ∈ C([a, b]). Keywords: contraction; metric; point; spaces; theorem
MR-Metric Spaces: Theory and Applications in Weighted Graphs, Expander Graphs, and Fixed-Point Theorems by Malkawi, Abed Al-Rahman; Rabaiah, Ayat (2025) - The set-valued fixed point theory developed in Theorem 2.2, extending classical results [24] (iii) Applications in expander graph analysis through coupling time metrics (Theorem 2.3) This paper makes three principal contributions: • A constructive method for generating MR-metrics on weighted graphs via minimal spanning subtrees, with applications in network optimization (Section 3.1) • A fixed-point theory for set-valued contractions in MR-metric spaces, generalizing results from [25] • New bounds on coupling times in expander graphs using MR-metric analysis, im- proving upon previous work This paper introduces the concept of MR-metric spaces, a generalization of traditional metric spaces that operates on triples of points rather than pairs. Keywords: m(u; metric; point
Triple Fixed-Point Theorems: Generalized Analysis with AI/Crypto Applications by Noorwali, Maha ; Alqawaqneh , Haitham ; Tahir, Muhammad ; Khattak, Arif Mehmood; M. Abd El-latif, Alaa ; A. Aldwoah, Khaled ; L. Armada, Cris ; Hanna M. Mohammad, Nurijam ; J. Hamja, Jamil (2025) - − x3n+2 − x3n+3∥2 − α∥x3n − x3n+1 − x3n+2∥2 9: −β ∥x3n−x3n+1∥2∥x3n+1−x3n+2∥2∥x3n+2−x3n+3∥2 1+∥x3n+1−x3n+2∥2∥x3n+2−x3n+3∥2 10: if ∥x3n+3 − x3n∥ < ϵ then qa 11: break 12: end if 13: n← n+ 1 14: end while 15: return u← − x3n+3 − x3n+4∥2 M. Noorwali et al. / Eur. Keywords: contraction; convergence; mappings; metric; point; product; spaces; theorem
On Fixed Points in Complex Valued Controlled S-metric Spaces and an Application by Qawaqneh, Haitham; Chamoli, Divyanshu ; Rawat, Shivam; Aydi, Hassen; Bisht, Monika (2025) - The concept of complex valued metric spaces was introduced by Azam et al. Subsequently, numerous researchers have extended the concept of metric space by altering the metric function and weakening different conditions (see, for example, [9–14]). Keywords: metric; point; τω+1
Some Fixed Point Results for Monotone Multivalued and Integral Type Contractive Mappings by Batul, Samina ; Qawaqneh, Haitham Ali; Sikandar, Arbab ; Shehzad, Usman; Aydi, Hassen (2025) - 2020 Mathematics Subject Classifications: 47H10, 54H25, 54C60 Key Words and Phrases: Fixed point, Gb-metric space, monotone multivalued functions 1. By the definition of Gb-metric space, one has κ(Gb(u, u, w)) Keywords: g(t)dt; metric; point
MR-Metric Spaces: Theory, Applications, and Fixed-Point Theorems in Fuzzy and Measure-Theoretic Frameworks by Malkawi, Abed Al-Rahman; Rabaiah, Ayat (2025) - [10], offering a unified framework for uncer- tainty quantification. 2020 Mathematics Subject Classifications: 54E50, 47H10, 28E10, 26A33, 60B10 Key Words and Phrases: MR-metric spaces, fuzzy fixed points, Radon-Nikodym derivative, measure concentration, Hausdorff metric, neutrosophic sets 1. Examples and Applications Section 3 demonstrates the versatility of MR-metrics: (i) Medical Diagnosis: Fuzzy mappings F model symptom-diagnosis relations, with Theorem 1 guaranteeing unique fuzzy fixed points (e.g., COVID-19 diagnosis). (ii) Sensor Networks: Keywords: malkawi; metric; point; spaces
Fixed Point Theorems on Multiplicative Cone Bipolar Metric Space and Their Applications by Ramaswamy, Rajagopalan (2025) - Consider q0 ∈ B & ϑ0 ∈ F then for each ℓ ∈ N ∪ {0}, we define Sq2ℓ = ϑ2ℓ,Ωq2ℓ+1 = ϑ2ℓ+1,Sϑ2ℓ = q2ℓ+1,Ωϑ2ℓ+1 = q2ℓ+2. Let q0 ∈ B & ϑ0 ∈ F then for each ℓ ∈ N ∪ {0}, define Sq2ℓ = ϑ2ℓ,Ωq2ℓ+1 Keywords: point; α(q0; α(qℓ
Generalized Branciari Metrics: Fixed Point Results and Open Problems by Kostic, Aleksandar (2025) - As generally in metric fixed point theory, further research scope could be focused on proving analogues of standard metric fixed point theorems, or further generalization of the underlying structure of g.B.m.s. (or both). A. Kostić / Eur. J. Pure Appl. 3. Prove a version of fixed point theorem with “simulation functions” of Khojasteh et al. Keywords: point

Data

Estimation and Selection in Regression Clustering by Qian, Guoqi; Wu, Yuehua (2011) - It classifies the data into k clusters, which together satisfy two requirements of a partition: (i) each cluster must contain at least one object; (ii) each object must belong to exactly one cluster. The objective is to reconstruct the underlying structure (5) from the observed data by estimating the number of clusters k0 and then classifying the data and estimating the class- specific parameters accordingly. Keywords: clustering; clusters; data; number; regression
Data Fusion Using Weighted Likelihood by Guo, Pengfei; Wang, Xiaogang; Wu, Yuehua (2012) - By assumption (A5), we have E|C | = E �� n2∑ j=1 w2 j � l2 j(β)− l2 j(β0) � �� ≤ n2∑ j=1 w2 j E ��log f (y2 j ,β) f (y2 j ,β0) �� ≤ K n2∑ j=1 w2 j = K · n2o(n−1/2) → 0. By using a similar idea, we propose to choose likelihood weights by using the estimated pairwise likelihood ratio. Keywords: data; group; information; j=1; likelihood; wang; weights; wle
Performance of Linear Discriminant Analysis Using Different Robust Methods by Alrawashdeh, Mufda Jameel; Radwan, Taha Radwan; Abunawas, Kalid Abunawas (2018) - Robust estimators have been proposed to limit the effects of outlier observations, and certain methods have been pre- sented to overcome the outlier problem, such as the high breakdown criterion developed by Hawkins and McLachlan [11]. All the parameters must be estimated based on robust estimators to overcome the outlier problem, thereby requiring high-performance robust estimators. Keywords: algorithm; analysis; covariance; data; detmcd; estimator; fastmcd; fch; robust
Decomposing the Quantile Ratio Index with Applications to Australian Income and Wealth Data by Prendergast, Luke Anthony; Staudte, Robert G (2019) - Further, by examining the QRI estimates for the quartile partition, we found that all the change in inequality of incomes over the time period 2004 to 2014 can be attributed to the outer classes, with incomes inequality in the middle class remaining stagnant. Given that the QRI is a simple average of quantile inequality measures of the form R(p) = 1−Q(p/2)/Q(1− p/2), one for each 0 Keywords: data; estimates; income; inequality; partition; qri; quantile; table
Optimal Solution Properties of an Overdetermined System of Linear Equations by Novoselac, Vedran; Pavic, Zlatko (2019) - If k(l0) < 0, it follows from (21) that f1 is decreasing on 〈−∞, a(l0+1)〉 and increasing on 〈a(l0+1),∞〉, therefore the minimum of f1 is attained for x∗ = a(l0+1) V. Novoselac, Z. Pavić / Eur. Math, 12 (4) (2019), 1360-1370 1364 is convex and attains its global minimum on the set R, which is denoted by x∗ = mean(w, a) and called the weighted mean of the data. Keywords: data; i=1
Investigating the Association Between Carbon Dioxide (CO2) Emissions and Energy Consumption on the Economic Growth of Clusterized Countries in the World by Wardhani, Laksmi Prita; Rukmi, Alvida Mustika; Ardamayanti, Thaliah Fauz (2023) - Other countries that have also succeeded in increasing economic growth and reducing CO2 emissions are Malta and Gambia. We use a large volume of data related to CO2 emissions per capita and energy consumption per capita of each country in the world, so a clustering process is needed using the K-Means method, which divides the country into three cluster labels: high, medium, and low. Keywords: cluster; co2; consumption; countries; data; emissions; energy; energy consumption; gdp; low; medium; regression
Scientific Data Visualization with Shape Preserving C1 Rational Cubic Interpolation by Hussain, Malik Zawwar; Sarfraz, Muhammad; Hussain, Maria (2010) - , n− 1 in rational cubic function (1) to obtain positive curve through positive data. 3.1. Positive curve is produced in Figure 4 using positive curve data interpolation scheme developed in Section 3. Keywords: data; hussain
Portfolio Optimization Using CART and Genetic Algorithms by Baba, Cheibetta Ahmed ; Diongue, Abdou Ka (2025) - Alternatively, authors such as Konno, Konno and Yamazaki [3], and Zenios, Pang and Speranza [4], have suggested that portfolio risk should be calculated in linear rather than quadratic form, to create linear programming models for selecting an optimal portfolio, while incorporating asymmetrical risk criteria to simplify optimization. Indexing of financial series We suggest modeling financial asset time series by estimating local trends. Keywords: ahmed; algorithm; assets; baba; data; dionque; optimization; portfolio; risk; series; value; variance
Heptapartitioned Neutrosophic Soft Topological Spaces and Some Graphical Representation of Sternberg’s Triangular Theory of Love in terms of Heptapartitioned Neutrosophic Soft Sets with the Applications of Some Advanced Machine Learning Techniques by Saeed, Maha Mohammed ; Alqawaqneh, Haitham ; Alsahli, Ghaziyah ; Abd El-latif, Alaa M. ; Khan, Yahya ; Hamja, Jamil J; Armada, Cris L. ; Khattak, Arif Mehmood (2025) - Key Words and Phrases: Neutrosophic soft set, HPNS points, HPNSTS, HPNS p-open set, set, K-Means algorithm, machine learning techniques and Heatmaps. ∗Corresponding author. Next is heptapartitioned neutrosophic soft set weighted Euclidean distance: dλ(A,B) = Keywords: correlation; data; hpns; let; love; set; η)(s; ∂)c
An Enhanced Class of Estimators for the Population Mean Using Neutrosophic Statistics: A Case Study of the Islamabad Stock Exchange by Al-Marzouki, Sanaa ; Ahmad, Sohaib (2025) - A novel method for con- ducting neutrosophic analysis of variance has been introduced within the framework of neutrosophic data Aslam [30]. Further information on neutrosophic data is available in references Tahir et al. Keywords: cxn; data; estimators; mse; neutrosophic; values; ρyxn
Developing a Generalized Class of Estimators for Estimation of Population Mean using Neutrosophic Approach by Al-Marzouki, Sanaa ; Ahmad, Sohaib (2025) - Making use of neutrosophic data, we propose a generalized class of estimators for the population mean under simple random sampling. A novel method of analyzing neutrosophic data via analysis of variance was introduced [30]. Keywords: ahmad; data; estimators; mean; neutrosophic; statistics
Sparse Cells, Inflated Odds: Bias Reduction Methods for Complex Survey Data with an Application to Hygiene Availability by Mohammed, Zakariya; Mohammed, Sanaa; Salih, Mohyaldein; Ibrahim, Myada; Hamed, Omer ; Osman, Ola; Satty, Ali (2025) - [16], who extended Bayesian hierar- chical approaches for sparse survey data, have provided important theoretical groundwork. Complex survey designs, such as UNICEF’s Multiple Indicator Cluster Surveys (MICS), often generate sparse cells across strata, leading to inflated odds ratios (ORs), wide confidence in- tervals (CIs), and convergence failures in survey-weighted logistic regression (SLR). Keywords: bias; data; firth; fplr; household; regression; slr; states; sudan; survey

Matrix

2-D Reversible Cellular Automata with Nearest and Prolonged Next Nearest Neighborhoods under Periodic Boundary by Åžiap, Irfan; Akin, Hasan; Oguz, Selman (2017) - (1) to all cells of the first row of information matrix 5×5, then we obtain the first block row of rule matrix TR and next apply the rule R to all the cells of the second row of information matrix 5× 5, we obtain the second block row of rule matrix TR. Next, we relate the transformation Ψ with rule matrix TR. Keywords: e t; matrix; m−3; rule
Commutative Law for the Multiplication of Matrices as Viewed in Terms of Hankel's Principle by Kobayashi, Yukio (2014) - The disagreement of b′(a′x) and (b′a′)x is due to the multiplication of the 1× n matrix b′ and the 1×1 matrix a′x in the order violating the rule of matrix multiplication. Taking this view, “the principle of the permanence of form and its transition” also holds for the commutative law for matrix multiplication. Keywords: matrix; multiplication
Observations on Some Special Matrices and Polynomials by El-Mikkawy, Moawwad E A; Atlan, Faiz (2015) - Math, 8 (2015), 135-151 147 Hence n # k= j c(n, k)S(k# 1, j # 1) =(n# j)! ! n# 1 j # 1 2 =(n# 1)n# j ! (i # 1)!(n# i)! Keywords: matrix
Solving Bi-matrix Games with Pay-offs of Triangular In-tuitionistic Fuzzy Numbers by Seikh, Mijanur Rahaman; Nayak, Prasun Kumar; Pal, Madhumangal (2015) - These two classes of fuzzy bi-matrix games are referred as bi-matrix games with I-fuzzy goals and bi-matrix games with I-fuzzy pay-off. In the following, we shall often call a two-person bi-matrix game with pay-offs of TIFNs as intuitionistic fuzzy bi-matrix game, denoted byáI FBG = (SI ,SI I , Ã, B̃). Keywords: games; matrix; non
Identifiability and Minimality in Rational Models by Pestano-Gabino, Celina; GonzÃ¡lez-ConcepciÃ³n, ConcepciÃ³n; Gil-FariÃ±a, MarÃa Candelaria (2010) - In particular, two specific problems arise when considering rational matrix models: i) identifiability, especially when a unique representation for a pair of minimum orders (m.o.) does not exist; and ii) exchangeable models, particularly when several pairs of m.o. 2. Rational Models in Multivariate Time Series We are interested in studying if a process X t , a k-vector of random variables, conforms to certain rational matrix models, for instance VARMA or STFE models. Keywords: m.d; matrix; models; property; series; table
On Identities for Sequences of Binomial Sums with the Terms of Sequences {u_kn} and {v_kn} by Omur, Nese; Åžener, Cemile Duygu (2017) - A−1 )n = n∑ t=0 ( n t )( ckvk + 2 )t ( c2k(−q)k+1 − ckvk − 1 )n−t A−(n−t). Writing 4λ ( qk(−1)k+1c2k − ckvk − 1 ) to each side of (3), we write λc2k ( v2k − 4 (−q)k )2 = ( λ+ ( qk(−1)k+1c2k − ckvk − 1 ))2 . Keywords: c2k(−q)k; ckvk; matrix
Optimized Cramerâ€™s Rule in WZ Factorization and Applications by Babarinsa, Olayiwola; Sofi, Azfi Zaidi Mohammad; Ibrahim, Mohd Asrul Hery; Kamarulhaili, Hailiz (2020) - The matrix norms and performance time of WZ factorization together with LU factorization are analyzed using sparse matrices on MATLAB via AMD and Intel processor to deduce that the optimized Cramer’s rule in the factoriza- tion algorithm yields accurate results than LU factorization and conventional WZ factorization. 2020 Mathematics Subject Classifications: 65F05, 65F35, 15A23 Key Words and Phrases: WZ factorization, LU factorization, Linear systems, Cramer’s rule, MATLAB 1. Keywords: e r; e t; factorization; matlab; matrix; z(k−1
Spectral Dichotomy Methods of a Matrix with respect to the General Equation of the Parabola by Traoré, Seydou; Mouhamadou, Dosso (2022) - − A has no eigenvalues on the parabola with equation 2p (p 2 − x )2 = (y − pb)2 with p > 0 • Output variables: P̃ and H̃ P̃ being the projector on the right subspace of zIn−A associated with the eigenvalues outside the parabola and the matrix H̃ whose norm gives the dichotomy criterion. If |z| > αAd + 1 αAd with the conditions (36) we have ∥∥∥∥Az ∥∥∥∥ < 1. Which leads to (zIn −A)−1 = 1 z (In − A z )−1 = 1 z +∞∑ k=0 Ak zk S. Traoré, M. Dosso / Eur. Keywords: + √; eigenvalues; matrix; − √; √ p; 
New bounds for the Eigenvalues of Matrix Polynomials by Burqan, Aliaa; Dbabesh, Hamdan; Qazza, Ahmad; Khandaqji, Mona (2023) - REFERENCES 817 Finally, applying Lemma 4 to get w (H) ≤ w (S) ≤ 1 2 ( w (S11) + w (S22) + w (S33) + √ w2(S11)+}|S12∥2 + ∥S13∥2 + √ w2(S22)+}∥S21∥2 + ∥S23∥2 ++ √ w2(S33)+}∥S31∥2 + ∥S32∥2 Thus, w(H) ≤ 1 2 ξ + 2 cos2 ( π mn− 3 ) + 1 + √ ξ2 + ( 1 2 ( α+ η + √ (α− η)2 + 4β2 ))2 + τ2 + 2 + √ 5 4 + √( 2 cos2 ( π mn− 3 ) + 1 )2 + ( 1 2 ( α+ η + √ (α− η)2 + 4β2 ))2 + µ + √√√√(2 + √ 5 4 )2 + τ2 + µ. Conclusion We have established new effective bounds for the eigenvalues of matrix polynomials by employing the similarity of matrices and matrix inequalities including the numerical radius, spectral radius and matrix norms. Then w(T ) ≤ 1 2 n∑ k=1 w(Tkk) + √√√√√w2(Tkk) Keywords: matrix; radius; w(t
The Linear Algebra of (r, β)-Stirling Matrices by Engalan, Genevieve B.; Latayada, Mary Joy (2023) - βt+ r βt+ β + r βt+ 2β + r βt+ 3β + r (βt+ r)2 (βt+ β + r)2 (βt+ 2β + r)2 (βt+ 3β + r)2 (βt+ r)3 (βt+ β + r)3 (βt+ 2β + r)3 (βt+ 3β + r)3  = Vβ,r 4 (t). 2.4. − s]S(β,s)(4) =  1 0 0 0 r − s 1 0 0 (r − s)2 2(r − s) 1 0 (r − s)3 3(r − s)2 3(r − s) 1   1 0 0 0 s 1 0 0 s2 β + 2s 1 0 s3 β2 + 3βs+ 3s2 3β + 3s 1  =  1 0 0 0 r 1 0 0 −1 + 2r + (r − 1)2 b+ 2r 1 0 −2 + 3r + 3 (r − 1)2 + (r − 1)3 b2 + 3b+ 6r − 3 + 3b (r − 1) + 3 (r − 1)2 3b+ 3r 1  =  1 0 0 0 r 1 0 0 r2 β + 2r 1 0 r3 β2 + 3βr + 3r2 3β + 3r 1  = S(β,r)(4) Proposition 3. Let Pn[r] and S2(n)[β] be the n×n Pascal matrix and Stirling matrix of the second kind. Keywords: matrix; βt+
Proposal for a Generalized Convolution to Mitigate Heat Generation in Convolutional Neural Networks by Kim, Hwajoon; Kang, Byeongjae; Yeun, Sunyoung; Lim, Eunyoung (2025) - In this deep learning method, generalized convolution applies convolution only to spe-82 cific nodes and does not require pooling work. Without47 further mention, sp, sc, ss and si refer to pooling size, convolution size, stride size, and48 image size, respectively.49 A matrix B is called a submatrix of A if B ⊂ A and satisfies the conditions of a matrix.50 51 H. Kim et al. / Eur. Keywords: cnn; convolution; generalized; matrix; pooling
Impulsive Protocols for Scaled Consensus in Edge-Dynamic Multi-Agent Systems by Donganont, Siriluk ; Witthayarat, Uamporn ; Donganont, Mana (2025) - The burgeoning interest in edge dynamics has inspired a new wave of research aimed at solving edge consensus problems under dynamic topologies. Figure 1: The communication net work G ∪ G′. In order to solve edge consensus problems, we first transform the graph G∪G′ to its line graph, using the same methodology as [14], denoted by L(G ∪ G′), as shown in Figure 2. Keywords: agent; consensus; donganont; edge; matrix; scaled; systems
A Key Exchange Protocol based on the Twin Conjugacy Search Problem over Tropical Algebra by Begum, A. Kashifa ; Muthukumaran, V.; Govindan, Vediyappan; Byeon, Haewon (2025) - Analysis of a key exchange protocol based on tropical matrix algebra. ∃ an unique n × n matrix E ∈ Mn(Rmin),∋ P ⊗ E = E ⊗ P = P , where E =  0 ∞ . . . Keywords: algebra; key; matrix; problem; protocol; tropical
Stability, D-Stability, Strong D-Stability of Positive Linear Time-invariant Systems with Applications by ur Rehman, Mutti; Alzabut , Jehad; Phulpoto, Amanullah; Tounsi, Mohamed; Al Naimi, Raja (2025) - Matrix diagonal stability in systems and computation. The numerical testing supports the spectrum analysis and ϵ- pseudospectrum of Metzler matrices. Keywords: d1(a1; d2a2; da2; linear; matrices; matrix; metzler; stability; systems; γd−1
Common Riccati Stability and Time-Delay Systems by Algefary, Ali; Alqufari, Khulud (2025) - In the first part, we explore the connections between common Riccati stability for a family of matrix pairs U = {(Ai, Bi)}mi=1 and the concepts of common Lyapunov stability and common Schur stability. The results provide criteria for common Riccati stability, exploring its implications on Lyapunov and Schur stability across matrix families. Keywords: family; lyapunov; matrix; riccati; stability
Haar Wavelets and $D$-Stability of Lumped-Parameter Dynamical Systems by Siddiqua Mazhar ; Rehman, Mutti-Ur (2025) - Furthermore, our results are primiraly based on the analysis of interconnection between µ-theory and theory of matrix stability. Recent directions in matrix stability. Keywords: matrices; matrix; p t; singular; stability; −a⊗
A Characterization of Diagonal Solutions for a Class of Linear Matrix Inequality by Algefary, Ali; Alhumaidan, Tulin (2025) - Math, 18 (3) (2025), 6417 3 of 10 matrix, we write positive diagonal matrix since it is clear that a diagonal positive definite matrix has all its diagonal elements positive. We say that the triple (A1, A2, A3) admits a positive diagonal solution if there exist positive diagonal matrices P1, P2, P3 ∈ Rn×n such that the block matrix AT 1 P1 + P1A1 + P2 + P3 P1A2 P1A3 AT 2 P1 −P2 0 AT 3 P1 0 Keywords: matrix
Properties and Applications of Generalized Numerical Radius in Block Matrix Structures by Al-Naimi, Rajaa; Al-Labadi, Manal; Audeh, Wasim; Oudetallah, Jamal; Rehman, Mutti-Ur; Alangood, Dheyaa (2025) - The introduction of partial matrices of numerical radius w(1)(A) and w(2)(A), which provide new geometric insights into block matrix behavior. Additionally, we develop relationships with classical matrix parameters and establish structural theorems for block matrices. Keywords: block; matrix; numerical; radius
A Matrix Variate Skew Distribution by Akdemir, Deniz; Gupta, Arjun K. (2010) - Matrix variate distributions can be used to account for the dependence among individual vector observations. When we want to refer to the multivariate or matrix variate forms of these functions, we will use subindices to describe the dimensions. Keywords: j=1; matrix; skew

Order

Chio’s-like method for calculating the rectangular (non-square) determinants: Computer algorithm interpretation and comparison by Salihu, Armend; Marevci, Fahri (2021) - REFERENCES 450 In this regard, it has been observed an obvious advantage of the computational speed of rectangular determinants calculation with Algorithm 2.3 compared to Algorithm 1.1. In this paper, we present an approach for the calculation of rectangular determinants, where in addition to the mathematical formula, we also provide a computer algorithm for their calculation. Keywords: a12; a13; a21; algorithm; determinant; order; ∣∣∣∣; ∣∣∣∣a11
Finite Groups with Minimal CSS-subgroups by Heliel, A. A.; Hijazi, R. A.; Al-Shammari, S. M. (2021) - In [17], Shaalan proved that a group G is supersolvable if all subgroups of prime order p or of order 4 (if p = 2) of G are S-quasinormal in G. Later on, Wang Then G ∈ F if and only if G has a normal subgroup H such that G/H ∈ F and every subgroup of F ∗(H) of prime order p or of order 4 (if p = 2) is SS-quasinormal in G, where F ∗(H) is the generalized Fitting subgroup of H. Also, Wei et al. in [21] used the c-normality concept and obtained the same previous result. Keywords: order; subgroup
A General Family of Fifth-order Iterative Methods for Solving Nonlinear Equations by Zein, Ali (2023) - Then the computational order of convergence can be computed by using the formula p ≈ ln |(xn+1 − α)/(xn − α)| ln |(xn − α)/(xn−1 − α)| . − xn−1)/(xn−1 − xn−2)| . Keywords: f ′(xn; methods; order; ′(xn; ′(yn
A Linear Subdivision Scheme with Sixth-OrderPrecision and $C^{5}$ Smoothness by Sameer Alshammari, Fahad; Ashraf, Pakeeza; Mehmood, Saba; Akgul, Ali (2025) - Subdivision schemes are a crucial component of geometric modeling, widely applied in curve and surface design. Subdivision schemes in cagd. Keywords: approximation; order; scheme; smoothness; subdivision
On the Solution of Fractional Order Nonlinear Boundary Value Problems By Using Differential Transformation Method by Che Hussin, Che Haziqah; Kilicman, Adem (2011) - References [1] Aytac Arikoglu and I. Ozkol, Solution of boundary value problems for integro- differential equations by using differential transform method, Applied Mathematics and Computation, 168, pp. [4] N. Bildik, A. Konuralp, F.O. Bek and S. Kucukarslan, Solution of different type of the par- tial differential equation by differential transform method and Adomian’s decomposition method, Applied Mathematics and Computation, 172, pp. Keywords: differential; order
Burst Error Enumeration of m-Array Codes over Rings and Its Applications by Åžiap, Irfan (2010) - Note that the matrices E = � 1 0 1 1 1 1 � 2×3 and D =    1 0 1 0 1 0 1 0 1    3×3 are burst errors but they are not generic burst errors. Now, we shall make use of generic burst errors to determine all burst errors especially the number of burst errors. Keywords: burst; errors; order; polynomial; weight

Hop

Hop Independent Sets in Graphs by Hassan, Javier; Canoy, Jr., Sergio R. ; Aradais, Alkajim A. (2022) - Math, 15 (2) (2022), 467-477 475 The Cartesian product of graphs G and H, denoted by G�H, is the graph with vertex set V (G�H) Then C = ⋃ x∈S [{x} × Tx], where S ⊆ V (G) and Tx ⊆ V (H) for each x ∈ S, is a hop independent set of G�H if and only if the following conditions hold. Keywords: hop; set
Restrained Strong Resolving Hop Domination in Graphs by Abragan, Armalene; Rara, Helen (2022) - [8] The corona G ◦H of graphs G and H, is the graph obtained by taking one copy of G of order n and n copies of H, and then joining the ith vertex of G to every vertex of the ith copy of H. For every v ∈ V (G), denote by Hv the copy of H whose vertices are attached one by one to the vertex v. Subsequently, denote by v + Hv the subgraph of the corona G ◦H corresponding to the join ⟨{v}⟩+Hv, v ∈ V (G). ̸= ∅. Proof : Suppose S is a restrained resolving hop dominating set of G ◦ H. Keywords: hop; resolving; set
Locating Hop Sets in a Graph by Pagcu, Ethel Mae; Malacas, Gina; Canoy, Jr., Sergio (2022) - ∩ S. A set S ⊆ V (G) is strictly locating if it is locating and NG(u) ∩ S ̸= S for all u ∈ V (G) \ S. Locating Hop Sets in the Corona of Graphs The corona of two graphs G and H, denoted by G ◦ H, is the graph obtained by taking one copy of G of order n and n copies of H, and then joining the vertex vi of G to every vertex of the ith copy of H. For every v ∈ V (G), denote by Hv the copy of H whose vertices are joined or attached to the vertex v. Denote by v +Hv the subgraph of the corona G ◦H corresponding to the join ⟨{v}⟩+Hv. Keywords: hop; locating; set
Forcing Subsets of Connected Co-Independent Hop Domination in the Edge Corona and Lexicographic Product of Graphs by Calanza, Yves Dave; Rara, Helen (2022) - In this study, the forcing subsets of minimum connected co-independent hop dominat- ing sets in graphs are defined and established and some characterizations of forcing subsets of minimum connected co-independent hop dominating sets of graphs resulting from the edge corona and lexicographic product of two graphs are generated. 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Forcing subsets, connected co-independent hop, domination, co- independent set, edge corona, lexicographic product 1. Keywords: coi; forcing; hop; set; γch
Strong Resolving Hop Domination in Graphs by Mohamad, Jerson; Rara, Helen (2023) - x, y ∈ V (G) such that x ∈ WG where WG is a strong resolving set of G; (iv) Tx = V (H) for every x ∈ S with degG(x) = |V (G)| − 1. For (iii), let x, y ∈ V (G) such that xMMDy. Keywords: hop; resolving; set
Hop Italian Domination in Graphs by Canoy Jr, Sergio; Jamil, Ferdinand; Menchavez, Sheila (2023) - Since G is noncomplete, there exist u, v ∈ V (G) such thatdG(u, v) = 2. Observe that g = ({u}, V1 \ {u, v}, {v}) is a PNDI -function of G with ωG(g) = ωG(f). ■ It is worth noting that the family of graphs G for which γ2h(G) = γhI(G) Keywords: hop; set; γhi(g
Connected Roman Hop Dominating Functions in Graphs by Aradais, Alkajim; Cariaga, Jerry Boy; Canoy, Jr., Sergio (2025) - = 3 if and only if G = K1 and H = K2 (or H = K1 and G = K2) or G = K1 and H is a graph with at least one isolated vertex (or H = K1 and G is a graph with at least one isolated vertex). Math, 18 (1) (2025), 5648 10 of 13 For the converse, suppose G = Kn and let S be a gammach-set in G. Since S is a hop dominating set, V (Kn) Keywords: hop; γcrh(g
Legal Closed Hop Neighborhood Independent Sequences in Graphs by Hassan, Javier; Aripin , Farhadz; Bonsocan, Maria Andrea ; Pon, Kimberly Jane (2025) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Independent set, legal closed hop neighborhood independent sequence, legal closed hop neighborhood independence number, co-legal closed neighborhood independent sequence 1. Conclusion The concept of legal closed hop neighborhood independent sequence has been intro- duced and initially investigated in this study. Keywords: hop; lchni; neighborhood; sequence; set
L-Hop Independent Sequences in Graphs by Maharajul , Kaimar Jay ; Hassan, Javier; Laja, Ladznar S. (2025) - Legal hop independent sequences in graphs. The concept of an independent set is often studied in the context of maximum independent sets, which refers to the largest possible ∗Corresponding author. Keywords: hop; sequence
Super Hop Roman Domination in Graphs by Casinillo, Leomarich; Canoy, Jr., Sergio (2025) - Since vx ∈ E(G +H) for all x ∈ V (H), it follows that u ∈ V G 2 , w ∈ V G 1 ∪ V G 2 , dG(u, v) = 2, and N2 G(w)∩ V G 0 = {v}. Let f = (V0, V1, V2) be an RDF on G + H, and let V G i = Vi ∩ V (G) and V H i = Vi ∩ V (H) for i ∈ {0, 1, 2}. Keywords: hop; γshr(g

Problem

On the basisness in L_2(0,1) of the root functions in not strongly regular boundary value problems by Mamedov, Khanlar R.; Menken, Hamza (2008) - All eigenvalues of the boundary-value problem (1.1), (1.2), starting from some num- ber, are simple and form two infinite sequencesλk,1, λk,2, k = N,N+1, · · ·, whereN is a positive integer and λk,1 = −(2kπ)2 − q′(1)− q′(0) + 1∫ 0 q2(t)dt (4kπ)2 +O( 1 k3 ), (2.1) λk,2 = −(2kπ)2 + q′(1)− q′(0)− 1∫ 0 q2(t)dt (4kπ)2 +O( 1 k3 ), (2.2) and the corresponding eigenfunctions are of the form yk,1(x) [7] N. B. Kerimov, Kh. R. Mamedov, On the Riesz basis property of the root functions in certain regular boundary value problems,Math. Keywords: problem; q′(0; µk,1
On an Inverse Problem for Sturm-Liouville Equation by Karahan, Done; Mamedov, Khanlar (2017) - Physical applications of discontinuous Sturm-Liouville problem are given in [3]-[8]. [8] G. Freiling, V. Yurko: Inverse Sturm-Liouville problems and their applications, Nova Science Publishers, INC. (2008). Keywords: problem; ρ(x
Estimates for Resonant Frequencies Under Boundary Deformation in Multi-dimensional Space by Khelifi, Abdessatar; Shamma, Mohammed Nour (2010) - The properties of eigenvalue problems under shape deformation have been the subject of comprehensive studies [9, 22] and the area continues to carry great importance to this day [4, 7, 6, 8, 12, 13, 14, 15]. [4] O. P. Bruno and F. Reitich, Boundary-variation solution of eigenvalue problems for elliptic operators, J. Fourier Anal. Keywords: problem; theorem
The Problem of the Optimal Control with a Lower Coefficient for Weakly Nonlinear Wave Equation in the Mixed Problem by Ismayilova, Gunay (2020) - By a generalized solution of the problem (1), (2) for a given function v(x) ∈ V we mean a function u = u(x, t; v) from U such that for t = 0 it satisfies the condition u(x, 0) = u0(x) and the integral identity∫ Q [ −∂u ∂t ∂η ∂t + n∑ i=1 ∂u ∂xi ∂η ∂xi + vuη ] dxdt− ∫ Ω u1(x)η(x, 0)dx = ∫ Q f(x, t, u)ηdxdt (8) for all η = η(x, t) from U and are equal to zero for t = T . It is clear that, the identities∫ Q [ −∂um ∂t ∂η ∂t + n∑ i=1 ∂um ∂xi ∂η ∂xi + vmumη ] dxdt− − ∫ Ω u1(x)η(x, 0)dx = ∫ Q f(x, t, um)ηdxdt (11) are true for all η ∈ U which are equal to zero at t = T . Keywords: problem
Finite Rank Solution for Conformable Degenerate First-Order Abstract Cauchy Problem in Hilbert Spaces by Seddiki, Fakhruddeen; Al-horani, Mohammad; Khalil, Roshdi Rashid (2021) - [15] M. Abu Hammad, R. Khalil, Conformable fractional Heat differential equation, In- ternational Journal of pure and applied mathematics 94(2):215- 221, (2014). [22] M. Al Horani, M. Fabrizio, A. Favini, and H. Tanabe, Fractional Cauchy problems for infnite interval case, Discrete Continuous Dynamical Systems-S, 3(12):3285, (2020). Keywords: i=1; problem; 
On the Existence, Uniqueness and Application of the Finite Difference Method for Solving Cauchy-Dirichlet Problem by Ngoma, Diogene Vianney Pongui; Germain Nguimbi; Vital Delmas Mabonzo; Madzou, Bienaime Bervi Bamvi (2022) - Math, 15 (3) (2022), 1348-1362 1355 < Aλv, v >=  2v1 − v2 − v1 + 2v2 − v3 −v2 + 2v3 − v4 ... −vN−2 + 2vN−1 − vN −vN−1 + 2vN   v1 v2 v3 ... vN−1 vN  ; < Aλv, v >= (2v1−v2)v1+(−v1+2v2−v3)v2+(−v2+2v3−v4)v3+(−vN−2+2vN−1−vN )vN−1+(−vN−1+2vN )vN < Aλv, v >= N∑ i=1 [−vi−1 + 2vi − vi+1]vi < Aλv, v >= N∑ i=1 (−vi−1vi) + N∑ i=1 (2v2i ) + N∑ i=1 (−vi+1vi) or N∑ i=1 (−vi+1vi) = fi (36) therefore, −µ ∆x2 (ui+1 − 2ui − ui−1) + ci ∆x (ui+1 − ui) = fi (37) Keywords: cauchy; numerical; problem
Variative Problems in Teaching Mathematics by Aliyev, Samed Jahangir; Tahirov, Bahadur O.; Hashimova, Tarana A. (2022) - 2020 Mathematics Subject Classifications: 97G10, 97G30, 97G40 Key Words and Phrases: Variative problem, variation of problem conditions, multivariate problems. Such problems are called variative problem. Keywords: circle; problem; trapezoid
Simultaneous Identification of the Parameters in the Mathematical Model of Brain Tumor Growth Dynamics Under Treatment by Tatar, Salih; BenSalah, Mohamed ; Alamil, Maryam (2024) - Math, 17 (4) (2024), 2651-2675 2655 Here the inverse problem consists of simultaneously determining the treatment profile k(x, t) and the initial tumor cell density φ, by means of the time-integral measurements of tumor cell density (measured data) defined as follows: ϕ1 := ∫ T 0 ω1(t) c(x, t) dt and ϕ2 := ∫ T 0 ω2(t) c(x, t) dt, x ∈ B, (3) where ω1(t) and ω2(t) denote two distinct weight functions. We note that since time- integral measurements of tumor cell density do not typically reveal time-dependent profiles, we consider the function k(x, t) ∈ L∞(Q) in the following separable form: k(x, t) = α(x)β(t), (4) where α(x) ∈ L∞(B) represents the spatial component of the treatment profile k(x, t) and describes how the treatment efficacy varies across different spatial locations within the brain region. Keywords: cell; density; noise; parameter; problem; treatment; tumor
The Learning Skills and Level of Understanding of Grade 9 Students on a Mathematics Lesson on Sequences and Series by Luga, Mary Joy; Samson, Harold; Buan, Amelia ; Nabua, Edna ; Salazar, Douglas (2025) - Out of the 123 participants, 32.58% (or 44 par- ticipants) are in benchmark creative thinking skill level, 56.91% (or 70 participants) are M. J. Luga et al. / Eur. In the last few years, there has been a lot of emphasis and importance placed on open ended questions because they are designed in such a way as to uncover the level of student understanding (e.g., procedural vs. conceptual) and misconceptions of mathematical concepts. 2.2. Keywords: learners; level; problem; skills; solving; students; study; thinking; understanding
Inverse Boundary Value Problem for Fourth-Order Pseudo-Hyperbolic Equation with Nonlocal Integral Conditions of the Second Kind by Yashar, Mehreliyev; Mammedov, Anar (2025) - Problem Statement on Determining the Unknown Coefficient and the Constant Term In the rectangle ΠT = {(x, t) : 0 ≤ x ≤ 1, 0 ≤ t ≤ T} we will consider the following problem: ωtt(x, t)− ωttxx(x, t) + ωxxxx(x, t) Let us designate V 4,2(ΠT ) = {ω(x, t) : ω(x, t) ∈ C2(ΠT ), ωxxxx(x, t), ωttxx(x, t ∈ C(ΠT )}. Keywords: problem; ω(x
Finite Rank Solution for Conformable Second-Order Abstract Cauchy Problem in Hilbert Space by Odetallah, Huda; Abualhomos, Mayada ; Sasa, Tala ; Shaikh, lubaba ; Miri, Omniya (2025) - i (t) ∈ C(I), i = 1, 2, ..., n. Before analyzing the main problem, we establish the theoretical foundation using fundamental matrices. i (t) ∈ C(I), i = 1, 2, ..., n. Then, the problem has a unique solution. Keywords: i=1; problem
Multiple solutions of steady MHD flow of dilatant fluids by Zakia, Hammouch (2008) - f f ′′+ β(1− f ′2) +M(1− f ′) =−a f f ′′2. Keywords: flow; problem; solutions; ′′γ
An Inverse Problem for a Parabolic Equation with Nonlocal Boundary Conditions and Two-point Overdetermination by Azizbayov, Elvin Ibrahim; Safarova, Aynur (2025) - Nonlocal inverse problem for determination of time derivative coefficient in a second-order parabolic equation. 2020 Mathematics Subject Classifications: 35R30, 35K10, 35A09, 35A01, 35A02 Key Words and Phrases: Inverse problem, parabolic equation, nonlocal conditions, classical solution, existence, uniqueness 1. Keywords: a1(s; a1(τ; ds t∫; inverse; k a1(s; problem; λ2k; λ2k a1(s; − t∫
Solving Multi-Objective Resource Allocation Problem Using a Novel Optimization Approach: Genetic Algorithm with Hybrid Mutation by El-Shorbagy, M.A.; El-sisy, M.A. (2025) - Therefore, GA-HM represents an effective and efficient approach for solving multi-objective resource allocation problems. An effective ant colony optimization algorithm (aco) for multi-objective resource allocation problem (morap). Keywords: algorithm; allocation; morap; mutation; objective; optimization; problem; resource; shorbagy; solutions
Complex Analysis Methods Related an Optimization Problem with Complex Variables by Lai, Hang-Chin; Huang, Tone-Yau (2010) - = �∑k i=1λiRe � f (•,ηi) + (·) HAw1 �� × �∑k i=1λiRe � g(ξ,ηi)−α H Bw2 �� − �∑k i=1λiRe � f (ξ,ηi) +α HAw1 �� × �∑k i=1λiRe � g(•,ηi)− (·) HBw2 �� for •= (·, ·) ∈ Q ⊂ C2n. = ��E(|z|4)− 2 � E(|z|2) �2 − |E(z2)|2 �� E(|z|2)2 where E(·) stands for expectation, and |z|2 = z · z. Keywords: problem; � f; � ∑k; � �

Differential

Derivative Operators on Quantum (3) space with Two Parameters and Weyl algebra by Ozavsar, Muttalip; Yesilot, Gursel (2012) - = p−1d x y, yd y = d y y, ydz = p−nqmdz y (25) zd x = q−1d xz, zd y = pnq−md yz, zdz = dzz. x y + f22d y x , yd y = bd y y, ydz = h11dz y + h12d yz (15) zd x = g21d Keywords: algebra; differential; quantum
Relative differential K-theory by Elmrabty, Adnane; Maghfoul, Mohamed (2014) - The group of differential K-characters on a smooth compact manifold X is defined as the K-theoretic version of the group of Cheeger-Simons differential characters on X using the (M , E, f )-picture of Baum-Douglas for K-homology. In Section 2, we recall the definition of the group of differential K-characters and study some of its properties. Keywords: differential
Polynomial Integral Transform for Solving Differential Equations by Barnes, Benedict (2016) - =F(s) = ∫ ∞ 1 f (ln x). = sup 1≤x<∞ ∫ ∞ 1 | f (ln x).x−s−1|d x B( f (x))≤ sup 1≤x<∞ ∫ ∞ 1 | f (ln x)||x−s−1|d x B( f (x))≤M ∫ ∞ 1 | f (ln x)|d x , where M > 0. Keywords: differential; transform
Solutions of Different Types of the Linear and Nonlinear Higher-Order Boundary Value Problems by Differential Transformation Method by Hassan, I. H. Abdel-Halim; Erturk, Vedat Suat (2009) - =−1 2 , Y (4) = −1 8 , (5.12) where, according to Eq. (2.1), a = Y (1), b = y′′′(0) 3! = Y (3) and c = y(v)(0) 5! = Y (5). = Y (1), Y (5), a2 = y(iii)(0) 3! = Y (3), a3 = y(v)(0) 5! = Y (5), I. Abdel-Halim and V. Ertürk / Eur. Keywords: differential
Using $G_{\alpha}$-transform to Study Higher-order Differential Equations with Polynomial Coefficients by Sattaso, Supaknaree; Prasertsang, Patarawadee; Prasertsang, Torsak (2023) - Table 1 lists some of the transforms along with their definitions, and we use α to convert the Gα-transform as appropriate. Table 1: Some integral transform definitions Transform Definition Gα-Transform Laplace ∫∞ 0 e−τ/wf(τ)dτ α = 0 and 1/s = w Sumudu 1 w ∫∞ 0 e−τ/wf(τ)dτ n−1∏ s=l (m+ α− s) Y (l)(w) wm−n−l − m−1∑ k=0 n∏ L=1 (−m+ k + L)wα−m+k+L+1y(k)(0). Keywords: cons; differential; transform
A Numerical Solution for Nash Differential Games Based on the Runge Kutta 4th-order Method by Megahed, Abd El-Monem; M. Kamel, Nesreen ; M. Hanafy, I. ; A. Omar, Nora (2025) - For n = 0, x1 − x0 = h 6 Φ1(xn, λ1,n, λ2,n, t), |x1 − x0| = ∣∣∣∣h6Φ1(xn, λ1,n, λ2,n, t) ∣∣∣∣ , |x1 − x0| ≤ h 6 M1. = h [ λ1(t1 + K2λ1 2 )2 P1 (1− (x1 + h 2 )) − λ1(t1 + K2λ1 2 )λ2(t1 + K2λ1 2 ) P2 (x1 + h 2 )− ϕ1 ] , K4λ1 = hFλ1 (x1 + h, t1 +K3x) = h [ λ1(t1 +K3λ1) 2 P1 (1− (x1 + h)) − λ1(t1 +K3λ1)λ2(t1 +K3λ1) P2 (x1 + h)− ϕ1 ] . (45) λ1,2 = −h2ϕ1 + h6 6 [ (ϕ1) 2 P1 ( (1− x0) + 4(1− x0 − h 2 ) + (1− x0 − h) ) − ϕ1ϕ2 P2 ( x0 + 4(x0 + h 2 ) + (x0 + h) )] + ϕ1h 2 (46) A. A. Megahed et al. / Eur. Keywords: differential; firm

Metric

Harmonic and (Ï•, Ï•Â´)-holomorphic Maps on Some Generalization of Contact Metric Manifolds by Malek, Freshteh; Samanipour, Mahboobeh (2017) - It should be noted that these manifolds are not necessarily contact metric manifolds. 2010 Mathematics Subject Classifications: 53C40, 53C15, 53C25 Key Words and Phrases: Quasi contact metric manifold, Nearly Sasakian manifold, Quasi Kähler manifold, Holomorphic map, Contact metric manifold 1. Keywords: contact; manifolds; metric
Some Common Fixed Points of Six Mappings on G_b-metric Spaces Using (E.A) Property by Mustafa, Zead; Jaradat, M.M.M.; Aydi, Hassen; Alrhayyel, Ahmad (2018) - Different authors used (φ, ψ)-contractions to obtain common fixed point results in different spaces. 2010 Mathematics Subject Classifications: 47H10, 54H25 Key Words and Phrases: Complete Gb-metric space, Cauchy sequence, (φ, ψ)-contraction, (E.A) property, common fixed point, weakly compatible. Keywords: lim; metric; n→∞
Fixed Point Results in Metric-like Spaces via Sigma-simulation Functions. by Alsamir, Habes; Selmi Noorani, Mohd; Shatanawi, Wasfi; Aydi, Hassen; Akhadkulov, Habibulla; Qawaqneh, Haitham; Alanazi, Kareem (2019) - 2010 Mathematics Subject Classifications: 47H10, 54H25 Key Words and Phrases: Fixed point, metric-like space, simulation function, (α, β)-admissible mapping 1. We also establish the existence of fixed points for this class of mappings in metric-like spaces. Keywords: metric
Special Sequences on Generalized Metric Spaces by Farhat, Yasser ; Amel Souhail; Vigneswaran, Vadakasi; Krishnan, Muthumari (2022) - Cauchy sequence Bourbaki− Cauchy sequence / Theorem 11 provides an easy way to check, in a generalized metric space, whether a given sequence is Bourbaki-Cauchy or not. Cauchy sequence pseudo− Cauchy sequence / Keywords: metric; sequence
Metrical Fixed Point Results on \lowercase{b}-multiplicative metric spaces employing binary relaion by AlShammari, Ibtesam Eid; Ali, Shahbaz; Khan, Q.H.; Rashid, T.; Ozel, Cenap (2023) - 2020 Mathematics Subject Classifications: 47H10, 54H25,46J10 Key Words and Phrases: Multiplicative metric space, Binary relation, Relation theoretic con- tractions, Coincidence Points 1. [4] M. Özaşvar, A.C. Çevikel, Fixed points of multiplicative contraction mappings on multiplicative metric spaces, ArXiv : 1205.5131v1 [matn. Keywords: metric
Unique Fixed Point Results via Geraghty Type Contraction with Applications by Abodayeh, Kamaleldin; Rome, Badshah-e-; Nizam, Sidra; Sarwar, Muhammad (2025) - The idea of fixed point in fuzzy metric space (FWS̃) has been studied and explored by several authors. On some result in fuzzy metric space. Keywords: metric; ˆ κm; ζ ˙; ζ βpwµpκm´1,κm; ζqq; κm`1
Interpolative Contractions for $b$-metric Spaces and Their Applications by Babu, Dasari Ratna ; Koduru, Naga Koteswara Rao (2025) - Czerwik [5] developed the idea of b-metric space, often known as metric type space, as a generalization of metric space.. 2020 Mathematics Subject Classifications: 47H10, 54H25 Key Words and Phrases: Common fixed points, b-metric space, integral equation, functional equation 1. Keywords: metric
Enhanced Uncertainty Modeling through Neutrosophic MR-Metrics: A Unified Framework with Fuzzy Embedding and Contraction Principles by Malkawi, Abed Al-Rahman (2025) - A 3-tuple (Z, T , ∗) is a Fuzzy Metric Space if: • Z is a non-empty set, • ∗ is a continuous t-norm, • T : Z × Z × (0,∞) → [0, 1] satisfies: (i) T (υ, ξ, γ) = 1 ⇐⇒ υ = ξ, (ii) T (υ, ξ, γ) = T (ξ, υ, γ), (iii) T (υ, ξ, γ) ∗ T (ξ,ℑ, ρ) ≤ T (υ,ℑ, γ + ρ), (iv) limγ→∞ T (υ, ξ, γ) = 1. A. Malkawi / Eur. → [0, 1] satisfy: (N1) T (υ, ξ, γ) = 1 ⇐⇒ υ = ξ (Truth-Identity). Keywords: m(υ; metric
Contractive Operators Controlled by Simulation Functions in Fuzzy Metric Spaces with Transitive $\mathcal{K}$-Closed Binary Relations by Moussaoui, Abdelhamid; Pantović, Mirjana ; Radenović, Stojan (2025) - Math, 18 (3) (2025), 6486 3 of 18 For any s, t ∈ E, if (s, t) ∈ R, we say that s is related to t via R, often denoted sRt. The relation is antisymmetric if for all s, t ∈ E , the conditions sRt and tRs imply s = t. Additionally, R is complete if for every s, t ∈ E , the pair [s, t] belongs to R. Finally, given a self-mapping K : E → E , the relation R is said to be K-closed if whenever (s, t) ∈ R, it follows that (Ks,Kt) ∈ R for all s, t ∈ E . Keywords: metric; relation
Applications of MR-Metric Spaces in Measure Theory and Convergence Analysis by Malkawi, Abed Al-Rahman; Rabaiah, Ayat (2025) - h-simulation functions and ωb-distance mappings in the setting of gb-metric spaces and application. This paper investigates the role of MR-metric spaces in the fields of measure theory and convergence analysis. Keywords: m(υ; measure; metric; ξ,ℑ
Compactness and Separability in MR-Metric Spaces with Applications to Deep Learning by Malkawi, Abed Al-Rahman (2025) - This paper establishes fundamental topological properties of MR-metric spaces, a sig- nificant generalization of conventional metric spaces characterized by an R-scaled tetrahedral in- equality. 2020 Mathematics Subject Classifications: 54E35, 54D30, 54E50, 46Nxx, 68T07 Key Words and Phrases: MR-metric spaces, compactness, separability, paracompactness, deep learning, global optimization, quantum computing, neural networks, topological properties, fixed point theory 1. Keywords: metric
Extending F-Contraction Theory: Fixed Points in Triple-Controlled S-Metric Spaces by Azmi, Fatima M.; Ansari, Arsalan Hojjat; Petroudi, Seyyed Hossein Jafari (2025) - Our results significantly extend the classical (αs-F)-contraction framework by proving the exis- tence and uniqueness of fixed points under these generalized settings. 2020 Mathematics Subject Classifications: 47H10, 54H25 Key Words and Phrases: Fixed point, triple controlled S-metric type spaces, (αs, µs, (Q,h)− F)-contraction, S-metric spaces, pair (Q,h) upper class 1. Keywords: metric

Numerical

Numerical Finite-Difference Approximations of a Coupled Reaction-Diffusion System with Gradient Terms by Khalil, Manar; Hashim, Ishak ; Rasheed, Maan; Samat, Faieza ; Momani, Shaher (2024) - where F (δxU n i , V n i ) = (V n i )p1 − ∣∣∣∣Un i+1 − Un i−1 2h ∣∣∣∣q1 , G (δxV n i , Un i ) = (Un i ) p2 − ∣∣∣∣V n i+1 − V n i−1 2h ∣∣∣∣q2 . − Un i and envi = vni − V n i , where uni = u(xi, tn), v n i = v(xi, tn) and (Un i , V n i ) are a accurate and numerical solutions of a one-dimensional time-dependent coupled system of two PDEs, Consecutively. Keywords: blow; numerical; v n; ∥∥e0
Finite Difference Scheme for One-dimensional Coupled Parabolic System with Blow-up by Khalil, Manar; Hashim, Ishak ; Rasheed, Maan; Momani, Shaher (2025) - I − 1) where enui = uni − Un i , envi = vni − V n i , uni = u (xi, tn) , vni = v (xi, tn) is the exact solution of problem (1) Suppose that e0ui = 0, e0vi = 0 ∀i = 0, 1, . . Since (1− rn) ≥ 0, it follows that∥∥En+1 u ∥∥ ≤ (1− rn) ∥En u∥+ rn ∥En u∥+ L1kn ∣∣vnj − V n j ∣∣+ ∣∣∣Tn+1/2 ui ∣∣∣∥∥En+1 u ∥∥ ≤ ∥En u∥+ Lk ∥En v ∥+ ∣∣∣Tn+1/2 ui ∣∣∣ ≤ Cn ( k + h2 ) + kLCn ( k + h2 ) + C ( k + h2 ) ≤ (1 + kL)Cn ( k + h2 ) + C ( k + h2 ) Keywords: blow; numerical

Ideal

Singular Ideals of Ternary Semirings by Dutta, Tapan K.; Shum, Kar Ping; Mandal, Shobhan (2012) - M is called a right ternary semimodule over a ternary semiring S or simply a right ternary S-semimodule if there exists a mapping M × S × S −→ M (images to be denoted by ms1s2 for all m ∈ M and s1, s2 ∈ S) satisfying the following conditions: (i) (m1 +m2)s1s2 = m1s1s2 +m2s1s2 (ii) m1s1(s2 + s3) = m1s1s2 +m1s1s3 (iii) m1(s1 + s2)s3 = m1s1s3 +m1s2s3 (iv) (m1s1s2)s3s4 = m1(s1s2s3)s4 = m1s1(s2s3s4) (v) 0M s1s2 = 0M = m1s10S = m10Ss2 for all m1, m2 ∈ M and for all s1, s2, s3, s4 ∈ S. A left ternary S-semimodule can be similarly defined. As h1s3s ∈ H for all s ∈ S, h1s3s ∈ rS(s1as2) ∩ H for all s ∈ S. Now, h1s3s = 0 for all s ∈ S ⇒ s2h1s3st = 0 for all s, t ∈ S ⇒ S ⊆ rS(s2h1s3) i.e. rS(s2h1s3) = S. Now by condition (α) this implies that s2h1s3 = 0, a contradiction. Keywords: ideal; right; semiring; ternary; z(s
Weakly Special Radical Class and Special Radical Class of Ternary Semirings by Dutta, Tapan K.; Shum, Kar Ping; Mandal, Shobhan (2012) - Therefore, S ∈ S ′. Conversely, let S ∈ S ′ and S′ be a nonzero homomorphic image of S such that β(S′) Let S ∈ S and S′ be a nonzero homomorphic image of S. Keywords: class; ideal; semiring; ternary
On (m,n)-ideals of Left Almost Semigroups by Khan, Waqar; Yousafzai, Faisal; Khan, Madad (2016) - Note that a0 is defined as an operator element such that a0 y = y and za0 = z for any y, z ∈ S. 3. 0-Minimal (0, 2)-Bi-Ideals in Unitary LA -Semigroups If S is a unitary LA -semigroup, then it is easy to see that S2 = S, SA2 = A2S and A⊆ SA ∀A ⊆ S. Note that every right ideal of a unitary LA -semigroup S is a left ideal of S but the converse is not true in general. Here Am or An are suppressed if m= 0 or n= 0, that is A0S = S or SA0 = S. Note that if m= n= 1, then an (m, n)-ideal A of an LA -semigroup S is called a bi-ideal of S. If we take m = 0 or n = 0, then an (m, n)-ideal A of an LA -semigroup S becomes a left or a right ideal of S. An (m, n)-ideal A of an LA -semigroup S with zero is said to be 0-minimal if A 6= {0} and {0} is the only (m, n)-ideal of S properly contained in A. An LA -semigroup S with zero is said to be 0-(0,2)-bisimple if S2 6= {0} and {0} is the only proper (0,2)-bi-ideal of S. An LA -semigroup S with zero is said to be nilpotent if S l = {0} for some positive integer l. Let m, n be non-negative integers and S be an LA -semigroup. Keywords: -semigroup; ideal; sa2
On 2-absorbing primary ideals in commutative semirings by Sarohe, Poonam; Dubey, manish kant (2016) - (1) Let Sx be a weakly 2-absorbing primary ideal of S and r, s, t ∈ S with rst ∈ Sx . A nonempty subset I of a semiring S is called an ideal of S if a, b ∈ I and r ∈ S, a + b ∈ I and ra, ar ∈ I . Keywords: ideal; primary
Near Ideals in Near Semigroups by Bagirmaz, Nurettin (2018) - Finally, near image and near inverse image of near ideal are discussed. We introduced the notion of near ideal that our notion depends on the upper approximation and does not depend on the lower approximation. Keywords: ideal; near
Hypersemigroups and Fuzzy Hypersemigroups by Kehayopulu, Niovi (2017) - The aim is to show that the theory of hypersemigroups and the theory of fuzzy hyper- semigroups are parallel to each other, in the following sense: An hypersemigroup H is intra-regular, for example, if and only if A∩B ⊆ B∗A for every right ideal A and every left ideal B of H. And an hypersemigroup H is intra-regular if and only if f ∧g � g◦f for every fuzzy right ideal f and every fuzzy left ideal g of H. An hypersemigroup H is left quasi-regular if and only if A∩B ⊆ A ∗B for every ideal A and every nonempty subset B of H. And an hypersemigroup H is left quasi-regular if and only if f ∧ g � f ◦ g for every fuzzy ideal f and every fuzzy subset g of H. 2010 Mathematics Subject Classifications: AMS 20M99, 08A72 Key Words and Phrases: Hypersemigroup, right (left) ideal, bi-ideal, fuzzy right (left) ideal, fuzzy bi-ideal, regular, intra-regular, left (right) quasi-regular, semisimple 1. For two fuzzy subsets f and g of H, we denote by f ◦ g the fuzzy subset of H defined as follows: f ◦ g : H → [0, 1] a→  ∨ (y,z)∈Aa min{f(y), g(z)} Keywords: ideal
Almost Prime Ideal in Gamma Near Ring by Khan, Waheed Ahmad; Muhammad, Adnan; Taouti, Abdelghani; Maki, Jameel (2018) - 2010 Mathematics Subject Classifications: 13A05, 13A18, 12J20 Key Words and Phrases: Γ-near-rings, prime ideals, almost prime ideals. Introduction and Preliminaries Recently, the generalization of prime ideal i.e., almost prime ideal in commutative rings has been introduced and discussed by Srikant M. Bhatwadekar and Pramod K. Sharma ( See [3]). Keywords: ideal; prime
The Minimality and Maximality of n-ideals in n-ary Semigroups by Petchkaew, Pattarawan; Chinram, Ronnason (2018) - U = S r {a} and U is the unique maximal n-ideal of S. (4) S r U = {a ∈ S | f(Sn−1, a) = S} and U is the unique maximal n-ideal of S. Proof. U = S r {a} and U is the unique maximal n-ideal of S. (4) S r U = {a ∈ S | f(Sn−1, a) = S} and U is the unique maximal n-ideal of S. Proof. Keywords: ideal
On Hoehnke Ideal in Ordered Semigroups by Kehayopulu, Niovi (2018) - Since h ∈ S, s ∈ S\A and s /∈ (shS], we have h ∈ HA(S). They call a right ideal of S semiprime if it is proper and for any right ideal A of S, A2 ⊆ I implies Keywords: ha(s; ideal
An Application of le-semigroup Techniques to Semigroups, Î“-semigroups and to Hypersemigroups by Kehayopulu, Niovi (2019) - ∪A ∗ S ∪ S ∗A ∗ S], respectively; where for a subset B of S, the symbol (B] denotes the subset of S defined by {t ∈ S | t ≤ b for some b ∈ B}. Since a is a right ideal element of S, b ∈ S and aeb = (ae)b ≤ ab ≤ m, by hypothesis, we have a ≤ m or b ≤ m, thus m is weakly prime. Keywords: b ⊆m; ideal; prime; semigroup; ≤ m
Weakly Prime and Weakly Primary Ideals in Gamma Seminearrings by Khan, Waheed Ahmad; Taouti, Abdelghani; Karkain, Seema; Salami, Azar; Arif, Waqar (2019) - (1) If A is weakly prime ideal of R and B is a nonempty subset of R. Then, AΓB is a weakly prime ideal of R. (2) If A and B are weakly prime ideals of R, then AΓB is an ideal of R. Example 10. Let S = {0, 1, e, a, c} ⊆ R be a Γ-sub-seminearring of R with Γ = {1, α}.Clearly, in S the ideals I = {0, a} and J = {0, c} are weakly prime ideals but not prime. Keywords: ideal; prime
On Fuzzy Sets in Hypersemigroups by Kehayopulu, Niovi (2019) - By hypothesis, we have S = S ∗ b ⊆ S ∗A ⊆ Denote by I(u) the ideal of S generated by the element u of S and by L(u) the left ideal of S generated by u. For an hypersemigroup S and any u ∈ S, we have I(u) = u ∪ (S ∗ u) ∪ (u ∗ S) ∪ S ∗ u ∗ S and L(u) Keywords: ideal
Almost Bi-Î“-Ideals and Fuzzy Almost Bi-Î“-Ideals of Î“-Semigroups by Simuen, Anusorn; Abdullah, Saleem; Yonthanthum, Winita; Chinram, Ronnason (2020) - Bi-quasi ideals and fuzzy bi-ideals of Γ-semigroups. [19]) Let M and Γ be non-empty sets. Keywords: ideal
Bi-interior Ideal Elements in âˆ§e-semigroups by Kehayopulu, Niovi (2021) - If S is a ∧e-semigroup and b, t ∈ S such that tet∧ ete ≤ b ≤ t, then b is a bi-interior ideal element of S. (2) If S is an ∧e-semigroup and semilattice under ∨ at the same time and b, t ∈ S such that tet ∨ ete ≤ b ≤ t, then b is a bi-interior ideal element of S. Proof. We also have b ≤ beb ≤ (beb)e(beb) ≤ (be)(eb) and so b = (be)(eb). Keywords: element; ideal
On Gamma LA-Rings and Gamma LA-Semirings by Khan, Waheed Ahmad; Taouti, Abdelghani; Salami, Azar; Hussain, Zahid (2021) - Here we introduce the notion of weakly prime ideal in Γ-LA-rings. So I is a weakly prime ideal of R because every prime ideal is weakly prime ideal. Keywords: ideal; prime
Almost Bi-interior Ideal in Semigroups and Their Fuzzifications by Gaketem, Thiti (2022) - 2020 Mathematics Subject Classifications: 20M12, 06F05 Key Words and Phrases: bi-interior ideal, fuzzy bi-interior ideal, weakly bi-interior ideal, weakly fuzzy bi-interior ideal 1. Every quasi ideal is a bi-interior ideal of S. (5) The arbitrary intersection of bi-interior of S is also bi-interior ideal of S. (6) If M a bi-interior ideal of S, then MS and SM are bi-interior ideals of S. For any hi ∈ Keywords: ideal
On Interval Valued Fuzzy Bi-interior Ideals in Semigroups by Gaketem, Thiti; Prommai, Tanaphong (2023) - We have µ̃ ⊓ χ̃S ⊑ χ̃S ◦ µ̃ ◦ χ̃S ⊓ µ̃ ◦ χ̃S ◦ µ̃ and implies that µ̃ ⊑ χ̃S ◦ µ̃ ◦ χ̃S ⊓ µ̃ ◦ χ̃S ◦ Then S is regular if and only if µ̃ ⊓ λ̃⊆̃λ̃ ◦ µ̃ ◦ λ̃ ⊓ µ̃ ◦ λ̃ ◦ µ̃ for every IVF bi-interior ideal µ̃ and every IVF ideal λ̃ of S. REFERENCES 129 Proof. Keywords: ideal; ivf; χ̃s
Application of Bipolar Fuzzy Set to a Novel of Fuzzy Ideal in $\Gamma$-Semigroups by Khamrot, Pannawit ; Gaketem, Thiti (2023) - | k ∈ S}, where ξp : S → [0, 1] and ξn : S → [−1, 0]. | k ∈ S}. Keywords: ideal
Multi-polar Q-hesitant Fuzzy Soft Implicative and Positive Implicative Ideals in BCK/BCI-algebras. by Alshayea, Maryam (2024) - We draw inspiration from the extensive body of work on hesitant fuzzy sets [13, 18], Q-fuzzy soft sets [7], and multi-polar fuzzy sets [5]. For a subset A of P, a multi-polar Q- hesitant fuzzy soft set (S,A) is called multi-polar Q-hesitant fuzzy soft positive implicative ideal over B if the multi-polar Q-hesitant fuzzy set S[e] = {(α, q), µS[e] i(α, q)|α ∈ B, q ∈ Q} on B is a multi-polar Q-hesitant fuzzy soft positive implicative ideal of B. Example 2. Keywords: bck; hesitant; ideal
$\sigma$-Prime Spectrum of Almost Distributive Lattices by Noorbhasha, Rafi ; Bandaru, Ravikumar ; Iampan, Aiyared (2024) - If B = R, then R is called a complemented ADL. Hence, (a)∗ ∨ (a)∗∗ = R. We denote SpecR and MaxR as the sets of all prime ideals and maximal ideals of R, respectively. Keywords: ideal
The Connections of Strongest Fuzzy Γ-ideals on Ternary Γ-semigroups by Nakkhasen, Warud; Yangnok, Onnalin; Chaidet, Kewarin; Jantanan, Wichayaporn (2024) - Let T = {a, b, c} and Γ = T . Let T = {a, b, c} and Γ = T . Keywords: ideal; ternary
L-Convex Sublattice of an L-Lattice and Complement of an L-Set by Jain, Aparna ; Jahan, Iffat (2025) - Also, the authors effectively use the concept of order reversing involution on the lattice L of truth values to define complement of an L-set. The maximal and minimal elements of both the lattices L and M are denoted by 1 and 0 respectively. Keywords: ideal
On Length and Mean Fuzzy Ideals of Sheffer Stroke Hilbert Algebras by Rajesh, Neelamegarajan ; Oner, Tahsin ; Iampan, Aiyared; Senturk, Ibrahim (2025) - This paper presents a detailed exploration of Sheffer stroke Hilbert algebras, introduc- ing the innovative concepts of length fuzzy ideals and mean fuzzy ideals within an interval-valued fuzzy framework. Specifically, the study establishes critical relationships between length fuzzy ideals and mean fuzzy ideals, their hierarchical subsets, and their implications for algebraic consistency and computational logic. Keywords: f̃inf(p; ideal; inf; length
A Note on $k$-Ideals in Ternary Semirings by Khan, Arbaz Jehan ; Chinram, Ronnason; Petapirak, Montakarn (2025) - EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS 2025, Vol. 18, Issue 2, Article Number 6096 ISSN 1307-5543 – ejpam.com Published by New York Business Global A Note on k-Ideals in Ternary Semirings Arbaz Jehan Khan1, Montakarn Petapirak1, Ronnason Chinram1,∗ 1Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand Abstract. In this paper, we give some examples of k-ideals of ternary semirings. Keywords: ideal; ternary
On Quotient KS-semigroups Induced by Fuzzy KS-ideals by Sarapuddin, Hulsen; Vilela, Jocelyn (2025) - Since (z ∗ x) ∗ (z ∗ y) ≤ y ∗ x and (z ∗ y) ∗ (z ∗ x) ≤ x ∗ y, we have µ((z ∗ x) ∗ (z ∗ y)) ≥ µ(y ∗ x) > 0 and µ((z ∗ y) ∗ (z ∗ x)) ≥ µ(x ∗ y) > 0 by Lemma 1(i). = y ∗ (y ∗ x) for all x, y ∈ X, (ii) positive implicative if (x ∗ y) ∗ z = (x ∗ z) ∗ (y ∗ z), or equivalently, x ∗ y = (x ∗ y) ∗ y for all x, y, z ∈ X, (iii) implicative if x∗ (y ∗x) = x for all x, y ∈ X, or if it is both commutative and positive implicative. Keywords: ideal; semigroup; µ(x; ∗ x; ∗ y; ∗ z
Pure Ideals on Ordered Power Ternary Semigroups on Ternary Semihypergroups Induced by Posets by Nongmanee, Anak ; Jeenkaew, Kanruethai; Phattarachaleekul, Maliwan (2025) - Conclusion In this article, we introduced the notion of ordered power ternary semigroups on ternary semihypergroups induced by posets which is an extension of power ternary semigroup on ternary semihypergroups. Then, the ideas of ideals and pure ideals in ordered power ternary semigroups on ternary semihypergroups induced by posets are introduced. Keywords: ideal; ternary

Solutions

Solutions of Some Quadratic Diophantine Equations by Sibihi, Alanoud (2023) - Then u2k − P (t)v2k = (a0y(k−1)l−1xl−1 + x(k−1)l−1xl−1 + y(k−1)l−1xl−2) 2 −P (t)(a0y(k−1)l−1yl−1 + x(k−1)l−1yl−1 + y(k−1)l−1yl−2) 2 = (u1uk−1 + (a0u1 + α)vk−1) 2 − P (t)(v1uk−1 + (a0v1 + β)vk−1) 2 = u21u 2 k−1 + 2u1(a0u1 + α)uk−1vk−1 + (a0u1 + α)2v2k−1 −P (t)v21u 2 k−1 − 2P (t)(a0v1 + β)v1uk−1vk−1 − P (t)(a0v1 + β)2v2k−1 = (u21 − P (t)v21)u 2 k−1 − [ (P (t)(a0v1 + β)2 − (a0u1 + α)2 ] v2k−1 +2 [u1(a0u1 + α)− P (t)v1(a0v1 + β)]uk−1vk−1 Using the above lemma, we have (P (t)(a0v1 + β)2 − (a0u1 + α)2 = P (t)u21 − P (t)2v21 = P (t)(u21 − P (t)v21) = P (t) and u1(a0u1 + α)− P (t)v1(a0v1 + β) In [2], Tekcan consider the number of integer solutions of Diophantine equation E : x2 − (t2 − t)y2 − (4t − 2)x + (4t2 − 4t)y = 0 over Z, where t ≥ 2. Keywords: solutions
On the Periodicity Solutions of Five Systems of Rational Systems of Difference Equations of Order Five by AL-Juaid, J. G. (2024) - Figure (1) demonstrates the behavior of the solutions of the SDE Eq.(1) with T0 = 1, T−1 = 0.5, T−2 = 0.2, T−3 = 2, T−4 = 3, E0 = 0.1, E−1 = 0.5, E−2 = 1, E−3 = 0.2, and E−4 = 0.3. 3. Math, 17 (4) (2024), 3254-3267 3259 E8n−10 = g, E8n−9 = k, E8n−8 = f, E8n−7 = as m(−1 + as) , E8n−6 = fw g , E8n−5 = as k(1− as) . Keywords: enen−4; solutions; tntn−4
Random Wave Equation for the Stochastic Quantum Zakharov-Kuznetsov Equation and their Exact Solutions by Mohammed, Wael; Sidaoui, Rabeb ; Alshammary, Hijyah ; Algolam, Mohamed (2025) - In the end, by using the transformation we utilized, we may derive stochastic solutions to the SQZKE. Solitary solutions of Quantum Zakharov-Kuznets equations are a crucial area of research with far-reaching implications for our understanding of plasma waves in quantum systems. Keywords: solutions
New Abundant Optical Solutions for The Stochastic Heisenberg Ferromagnetic Equation Used in a Ferromagnet via Two Different Methods by Mohammed, Wael; Iqbal, Naveed; Alshammari, Hijyah ; Algolam, Mohamed (2025) - 2020 Mathematics Subject Classifications: 35A20, 60H15, 60H10, 83C15, 35Q51 Key Words and Phrases: White noise, stochastic solutions, Jacobi elliptic functions method, random variable coefficients 1. We provide some figures for different solutions with varying noise intensity ν. Keywords: solutions
Novel Quasi-Periodic Type Optical Solitons and the Formation of Fractal Structures in Non-integrable Nonlinear Helmholtz Equations with Phase Portraits and Chaotic Analysis by Suwais, Khaled ; Mlaiki, Nabil ; Barak, Shoaib ; Ali, Rashid (2025) - [20, 21], which is remarkably effective and reliable, is used here to de- rive and investigate a special class of optical soliton solutions for coupled NHEs. For the aimed NHEs, this research exploration presents and analyzes new types of optical soliton solutions in the shape of the exponential, hyperbolic, trigonometric and rational functions with the aid of unified approach. Keywords: soliton; solutions; µ2 =

Polynomials

On Multi Poly-Genocchi Polynomials with Parameters a, b and c by Corcino, Roberto Bagsarsa; Laurente, Mark; Vega, Mary Ann Ritzell (2020) - Similarly, when it comes to Genocchi polynomials, the most common thing is to establish relationship between Genocchi polynomials, Bernoulli polynomials and Euler polynomials Math, 13 (3) (2020), 444-458 445 ∞∑ n=0 Gn tn n! = 2t et + 1 , |t| < π. (3) The Bernoulli, Euler and Genocchi polynomials are defined via generating functions to be, respectively, ∞∑ n=0 Bn(x) Keywords: genocchi; n=0; polynomials
Asymptotic Approximations of Apostol-Genocchi Numbers and Polynomials by Corcino, Cristina Bordaje (2021) - 2020 Mathematics Subject Classifications: 11B68, 41A60 Key Words and Phrases: Asymptotic approximations, Genocchi polynomials, Bernoulli poly- nomials, Euler polynomials, Apostol-Bernoulli polynomials, Apostol-Euler polynomials, Apostol- Genocchi polynomials 1. [2] A. Bayad, Fourier expansions for Apostol-Bernoulli, Apostol- Euler and Apostol- Genocchi polynomials, Math Comp., 80 (2011), 2219–2221. Keywords: apostol; polynomials
Generalized Laguerre-Apostol-Frobenius-Type Poly-Genocchi Polynomials of Higher Order with Parameters a, b and c by Corcino, Roberto Bagsarsa; Corcino, Cristina (2022) - For instance, mixing with exponential polynomials yields the Genocchi polynomials and Genocchi polynomials of higher order, which are given as follows: ∞∑ n=0 Gn(x) 2020 Mathematics Subject Classifications: 11B68, 11B73, 05A15 Key Words and Phrases: Poly-Genocchi polynomials, Laguerre polynomials, Apostol polyno- mials, Frobenius numbers, polylogarithm function, Appell polynomials, Euler polynomials, Bernoulli polynomials 1. Keywords: polynomials
Degenerate Apostol-Frobenius-Type Poly-Genocchi Polynomials of Higher Order with Parameters $a$ and $b$ by Corcino, Roberto Bagsarsa; Corcino, Cristina (2023) - Genocchi polynomials of higher order, which are respectively defined as follows: ∞∑ n=0 Gn(x) Recently, a new variation of poly-Genocchi polynomials with pa- rameters a, b and c was defined in [17] by mixing the definitions of polylogarithm, Apostol- Genocchi polynomials and Frobenius polynomials, namely, the Apostol-Frobenius-type poly-Genocchi polynomials of higher order with parameters a, b and c. Keywords: genocchi; ĝ(k; polynomials; x;λ
Construction of Fourier Series Expansion of Apostol-Frobenius-Type Tangent and Genocchi Polynomials by Corcino, Roberto Bagsarsa; Corcino, Cristina; Casas, Karl Patrick; Elnar, Allan Roy; Maglasang, Gibson (2023) - We then find the other poles of the function fn(t) as follows: λe2t − u = 0 λe2t = u λ 2t = log u λ + 2kπi tk := t = log (u λ )1/2 + kπi, for k ∈ Z By Cauchy Residue Theorem, we have 1 2πi ∫ CN fn(t)dt = Res(f(t), t = 0) Math, 16 (2) (2023), 1005-1023 1012 = u− 1 u 2n e−ξπix (−πi)n+1 [∫ ∞ 0 e 1 2 πix eπix − e−2t e−(2ξ+1)ttndt + (−1)n+1 ∫ ∞ 0 e 1 2 πix e2t − eiπx e(2ξ+1)ttndt ] = u− 1 u 2n e−ξπix (−πi)n+1 [∫ ∞ 0 e−(2ξ+1)t e 1 2 πix − e−2t− 1 2 πix tndt + (−1)n+1 ∫ ∞ 0 e(2ξ+1)t e2t− 1 2 πix − e 1 2 πix tndt ] = u− 1 u 2n e−ξπix (−πi)n+1 [∫ ∞ 0 e−(2ξ+1)t e 1 2 πix − e−2t− 1 2 πix · ( e2t − eπix ) Keywords: polynomials
Adomian Modification Methods via Orthogonal Polynomials: A Comparative Study by AL-Mazmumy, Mariam ; Bakodah, Huda ; Alsulami, Aishah; Alzaid, Nawal (2024) - Adomian modification methods via orthogonal polynomials The present section gives some important modifications of the standard ADM that are based on the application of orthogonal polynomials. Therefore, in what follows, we have obtained series of Adomian modification methods via orthogonal polynomials. Keywords: g(x; modification; n=0; polynomials
Note on Irreducible Polynomials over $\mathbb{F}_q[X]$ by M. Sibih, Alanod (2024) - EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 17, No. 2, 2024, 721-724 ISSN 1307-5543 – ejpam.com Published by New York Business Global Note on irreducible polynomials over Fq[X] Alanod M. Sibih Department of Mathematics, Jamoum University College, Umm Al-Qura University, Holly Makkah 21955, Saudi Arabia Abstract. This article focuses on irreducible polynomials with coefficients in Fq[X], where over Fq is a finite field. Keywords: polynomials
Higher Order Bivariate Bell-Based Apostol-Frobenius-Type Poly-Genocchi Polynomials with Parameters a and b by Corcino, Roberto Bagsarsa; Corcino, Cristina (2024) - 2020 Mathematics Subject Classifications: 05A15, 11B68, 11B73, 26C05, 33B10 Key Words and Phrases: Genocchi polynomials, Bell polynomials, Apostol-Frobenius-Type poly-Genocchi polynomials, Bell-based Apostol-Frobenius-Type poly-Genocchi polynomials, Stir- ling numbers 1. (1.2) Mixing with the Apostol polynomials yields the Apostol-Genocchi polynomials, and Apostol- Genocchi polynomials of higher order, which are respectively defined as follows: ∞∑ n=0 Gn(x, λ) tn n! Keywords: polynomials; tn n; y;u
On Apostol-Type Multi Poly-Genocchi Polynomials with Parameters a,b, and c by Laurente, Mark P. ; Ababa, A.Z. D. (2025) - An Apostol-type of multi poly Genocchi polynomials with pa- rameters a, b and c is defined by ∞∑ n=0 G(k1,k2,k3,··· ,kr) n (x;λ, a, b, c) tn n! Conclusion In this paper, we define Apostol-type of multi poly Genocchi polynomials with param- eters a, b and c through the concept of multi-poly logarithm. Keywords: ,kr; n=0; polynomials
Threshold Changeable Secret Sharing (TCSS) via Skew Polynomials by Angga Wijaya; Intan Muchtadi Alamsyah; Aleams Barra (2024) - Consequently, secret sharing schemes involve two primary stages: share generation and secret reconstruction. Secret sharing schemes and noncommutative polynomial interpolation. Keywords: polynomials; secret; sharing; skew
The Monomiality Principle Applied to Extensions of Apostol-Type Hermite Polynomials by Díaz, Stiven; Ramírez , William; Cesarano, Clemente ; Hernández, Juan ; Perez Rodriguez, Escarlin Claribel (2025) - Some implicit summation formulas and symmetric iden- tities for the generalized Hermite–Euler polynomials. 2020 Mathematics Subject Classifications: 11B68, 11B83, 05A19 Key Words and Phrases: Appell-type polynomials, Bernoulli and Euler numbers and polyno- mials, Hermite polynomials, quasi-monomial 1. Keywords: apostol; euler; polynomials
Certain Properties of $\Delta_h$ Legendre Polynomials and Applications in Computer Modelling by Wani, Shahid Ahmad; Khan, Waseem Ahmad; Alqurashi, Taghreed; Dar, Javid Gani; Salcedo, Dxion (2025) - Legendre polynomials exhibit orthogonality with respect to the weight function e−u on [0,+∞), ensuring that the weighted integral of two polynomials with different degrees is zero. Widely applied in mathematics, physics, and engineering, Legendre polynomials are integral to solving the Schrödinger equation for spherically symmetric quantum systems, including the hydrogen atom. Keywords: n=0; polynomials; s[h]n; u h; v h
Some Irreducible Polynomials Over a Finite Field by Chandoul, Amara; Assiry, Abdallah (2025) - 2020 Mathematics Subject Classifications: 11A05, 11C08, 11T06, 11T55, 12E05 Key Words and Phrases: Polynomial, irreducible polynomial, finite field, divisibility, divisibility criteria 1. The theory of irreducible polynomials over finite fields is both rich and elegant, blending algebraic rigor with practical utility. Keywords: finite; polynomials
On r-Bell-Based Apostol-Frobenius-Type Poly-Euler Polynomials by Corcino, Roberto Bagsarsa; Corcino, Cristina; Paspasan, Rodin; Alambra, Ronald (2025) - [2] Agoh T., Convolution identities for Benoulli and Genocchi polynomials, Electronic J. Combin. 21 (2014), Article ID P1.65. [9] Araci, S., Sen, E., and Acikgoz, M., Theorems on Genocchi polynomials of higher order arising from Genocchi basis, Taiwanese J. Math. Keywords: polynomials
The Type 2 Degenerate Hermite-Based Apostol-Frobenius-type Poly-Genocchi Polynomials with Parameters a, b and c by Corcino, Roberto Bagsarsa; Corcino, Cristina (2025) - Some identities of degenerate genocchi polynomials. Moment representations of fully degenerate bernoulli and degenerate euler polynomials. Keywords: genocchi; polynomials
On the Irreducibility of Polynomials with Prime Power Shifts by Chandoul, Amara; Mansour, Saber (2025) - This generalizes and extends earlier work on the irreducibility of such polynomials. [3], we establish a unified framework for studying the irreducibility of such polynomials. Keywords: deg; f(x; polynomials
Some Properties and Characterizations of Δh-Truncated Exponential based Hermite Polynomials by Qawaqneh, Haitham; Ahmad Khan, Waseem; Aydi, Hassen; Wani, Shahid Ahmad; Jadhav, Prakash (2025) - Among these developments, two-variable special polynomials have emerged as highly potent tools, facilitating the derivation of efficient and elegant identities and offering path- ways to novel classes of special polynomials. Special polynomials and fractional calculus. Keywords: e(r)h; n=0; polynomials; ξ1 h; ξ2 h
Bivariate Kind of Generalized Laguerre-Based Appell Polynomials with Applications to Special Polynomials by Ahmad Khan, Waseem; Qawaqneh, Haitham; Aydi, Hassen (2025) - Motivated by these developments, we introduce a new generalize Laguerre-based Ap- pell polynomials PLRn(r1, r2, r3). The new generalization of Laguerre and Laguerre-based Appell polynomials This section of our research paper introduces the new generalization of three-variable Laguerre-based Appell polynomials, denoted as PLRn(r1, r2, r3). Keywords: appell; k=0; laguerre; n=0; polynomials; tn n
On Bell-based Frobenius-type Eulerian Polynomials and Their Applications by Manoj Sharma; Khan, Waseem Ahmad ; Ugur Duran; Mohd Farman Ali; Ashish Sharma; Anupma Kumari (2025) - = ( (1− µ)2 (e(µ−1)aζ − µ)(e(µ−1)bζ − µ) )α e2abσζ+ρ(eaζ−1)+ρ(ebζ−1), (57) A(ζ) Let B(ζ) = ( (1− µ)2 (e(µ−1)aζ − µ)(e(µ−1)bζ − µ) )α ( 1− ( −µebζ )a) ( 1− ( −µeaζ )b) (µeaζ + 1)(µebζ + 1) e2abσζ+ρ(eaζ−1)+ρ(ebζ−1). Keywords: polynomials; ρ;µ
A Comprehensive Study of Generalized Bivariate q-Laguerre Polynomials: Structural Properties and Applications by Qawaqneh, Haitham Ali; Khan, Waseem Ahmad ; Aydi, Hassen ; Duran, Ugur ; Ryoo, Cheon Seoung (2025) - m−1 − D̂−1 q,ξTqm,η, (48) or, equally M̂G2V qLP = ηT(η;m) ( − ∂q ∂qD̂ −1 q,ξ )m−1 Tq,ξ − D̂−1 q,ξ , (49) and P̂G2V qLP = −D̂q,ξξD̂q,ξ = − ∂q ∂qD̂ −1 q,ξ , (50) respectively. H. Qawaqneh et al. / Eur. [m]Lω,q(ξ, η)D̂q,ψ ψω [ω]q! = ∞∑ ω=0 η(− ∂q ∂qD̂ −1 q,ξ )m−1 T(η;m)Tq,ξ − D̂−1 q,ξ  Keywords: laguerre; polynomials; q(ξ
Integral Formulas for the Noncentral Tanny-Dowling Polynomials by Mangontarum, Mahid; Madid, Norlailah M.; Campong, Asnawi A. (2025) - 2020 Mathematics Subject Classifications: 11B83, 11B73 Key Words and Phrases: Geometric polynomial, exponential polynomial, noncentral Tanny- Dowling polynomial, noncentral Dowling polynomial 1. (20) The next theorem provides an integral representation of the noncentral Tanny-Dowling polynomials in terms of noncentral Dowling polynomials. Keywords: noncentral; polynomials
Exponential Bases of Cliffordian Polynomials in Fréchet Modules by Zayed, Mohra (2025) - Suppose that the elements {Qn,k} of the Clifford matrix of coefficients of the SBSMPs {Qn(x)} satisfy{ |Qn,k| ≤M bn−k n+1 αk, 0 ≤ k < n, M ≥ 1 Qn,n = αn, (12) where {αn} is a bounded sequence of positive numbers, k and b are finite positive numbers. Consider the SBSMPs {Qn(x)} for which Qn,k = { αn, k = n, bn−k n+1 αk, 0 ≤ k < n, (18) where αi = 1 i+1 for i = k, n. Keywords: base; clifford; polynomials; qn(x

Theorem

VoronoÃ¯ type congruences and its applications by Agoh, Takashi (2009) - = m ∑ i=1 (−1)i−1ni � m i � n ∑ j=1 (a j)m−i � a j n �i , (2.1) so that (am− 1)Sm(n)≡ mn n−1 ∑ j=1 (a j)m−1 � a j n � (mod n2). Since p - a and p−1 - m, we also have am ≡ am+c(p−1) (mod ps) for each c and am 6≡ 1 (mod p). Keywords: j=1; mod; theorem
The Ehresmann-Schein-Nambooripad Theorem and its Successors by Hollings, Christopher (2012) - Similarly, f ⊗ e = f ∧ e = e ∧ f , hence idempotents in Co commute with respect to ⊗. We show that eRCo is a left congruence. If e ≤ f , then, since e = d(e) = r(e), we have e| f = d(e)| f = e = f |r(e) Keywords: categories; category; definition; groupoid; inductive; inverse; lemma; restriction; restriction semigroups; semigroups; theorem
Morita Theory for Rings and Semigroups by Wang, Yan Hui; Shum, Kar Ping; Ren, Xue Ming (2017) - Let R and S be Morita equivalent rings with local units via inverse equivalences G : R-Mod→ S-Mod and H : S-Mod→ R-Mod. We now list from [3] two properties of Morita equivalent rings with local units. Keywords: equivalent; following; inverse; left; morita; morita equivalent; rings; semigroups; theorem; theory; units
Hardy Spaces on the Polydisk by Shrestha, Khim Raj (2016) - We will see below that for f ∈ H p(Dn), 1 ≤ p <∞, the non-tangential limit of fz j1 ,...,z jk exists at almost all points of the distinguished boundary of the section Dn z j1 ,...,z jk which is Tl and the function fz j1 ,...,z jk can be restored by the Poisson integral of this limit. Let f ∈ H p(Dn), 1≤ p <∞. Then fz j1 ,...,z jk ∈ H p(Dl). Keywords: theorem; � �
Three Approaches to Inverse Semigroups by Hollings, Christopher (2015) - 2010 Mathematics Subject Classifications: 01A60, 20-03, 20M18, 20L05 Key Words and Phrases: inverse semigroup (fundamental, E-unitary, proper), inductive groupoid, idempotent-separating congruence, Munn representation, E-unitary cover, minimum group congru- ence, maximum group image, P-semigroup, P-Theorem 1. The investigation of inverse semigroups by means of their corresponding inductive group- oids (on the history of which, I have already written in detail in [40]) goes back to the his- torical roots of the notion of an inverse semigroup. Keywords: congruence; ehresmann; groupoid; inverse; inverse semigroups; mcalister; munn; notion; partial; theorem
Aluthge Transformation of Quasi n-class Q and quasi n- class Q* Operators by Senthilkumar, D.; Parvatham, S. (2018) - If T is quasi n class Q operator T and S is unitary such that TS = ST then A = TS is also quasi n class Q operator. If T = U |T | is the polar decomposition of quasi n class Q operator T , then T is quasi n class Q operator. Keywords: class; class q; operator; quasi; theorem
On the Paper "On hyperideals of ordered semihypergroups" by ZeGu in Ital. J. Pure Appl. Math. by Kehayopulu, Niovi (2019) - Except of the fact that this is not enough to pass from ordered semigroup to ordered hypersemigroup (symbols like S ◦ b ◦S ◦S ◦ a ◦S have no sense) and that there is no reference to ordered semigroup on which it is based, this theorem is an immediate consequence of Theorem 23 in [10] and it is not new (see also the equivalence (1)⇔ (2) in Corollary 24 in [10] and the remark after that). There are also two results obtained from ordered semigroups just putting a “◦” instead of “·” (that isn’t a correct way to work), without reference to ordered semigroups on which the results on ordered hypersemigroups are based. Keywords: prime; theorem
Some Applications of Ptolemy's Theorem in Secondary School Mathematics by Aliyev, Samed Jahangir; Hamidova, Shalala A.; Abdullayeva, Goncha Z. (2020) - (4) Applying Ptolemy’s theorem to the rectangles ACA1C1 ,A1B1C1B ,ABCC1 ,ABCA1, respectively, we obtain AA1 · CC1 = AC ·A1C1 + AC1 · CA1, (5) A1C1 ·BB1 = BA1 ·B1C1 + A1B1 ·BC1, (6) AC ·BC1 = AB · CC1 + BC ·AC1, (7) AC ·BA1 = AB · CA1 + BC ·AA1. 2020 Mathematics Subject Classifications: 97G10, 97G40 Key Words and Phrases: Ptolemy’s theorem, inscribed rectangle, regular heptagon, inscribed hexagon. Keywords: theorem
On Eigenvectors of Nilpotent Lie Algebras of Linear Operators by Hirsch, Morris W; Robbin, Joel W. (2021) - If πA is a prime power in f [t] for each A ∈≫ then the following hold: (a) πA(t) = (t− rA) n, rA ∈ f (b) there is a basis putting ≫ in triangular form Assertion (a) is equivalent to πA having a root rA ∈ f . Assume that for all A ∈ there exists rA ∈ f such that πA(t) Keywords: lie; theorem
The Fuglede-Putnam Theorem and Quasinormality for Class p-wA(s, t) Operators by Rashid, Mohammad H.M.; Altaweel, Nifeen (2022) - Let S = T ∗ = R as in Example 2 and X = P be the orthogonal projection onto ker(S). Let T = R and L = P be the orthogonal projection onto ker(T ). Keywords: class; ker(t; operator; theorem; wa(s
A Novel Approach for Studying Pythagorean Triples Suitable for Students at all Educational Levels by Amato, Roberto (2024) - This paper seeks to showcase how a new approach can breathe new life into research within the traditional domain of Pythagorean triples, introducing innovative applications to in- vigorate the field. The new results and applications, along with those found in the Preliminary Results section, show how the field of Pythagorean triples is still interesting and stimulating to study, despite the centuries that have elapsed. 2020 Mathematics Subject Classifications: 11D61, 97F99, 97G99, 97H99, 97I99 Key Words and Phrases: Pythagorean triples, Diophantine equations, Algebric groups, Geometry 1. Keywords: pythagorean; theorem; triples
Riesz Inequality for Harmonic Quasiregular Mappings by Bajrami, Elver (2024) - In this paper, we generalize the Riesz theorem for harmonic quasiregular mappings for a special case (when p = 2) in the unit disc. Conclusion In this paper we generalize the Riesz theorem for harmonic quasiregular mappings for a special case in the unit disc. Keywords: quasiregular; theorem
From Anosov Closing Lemma to Global Data of Cohomological Nature by Laureano, Rosário D. (2024) - Analytic regularity of solutions of livsic cohomology equations and some applications to analytic conjugacy of hyperbolic dynamical systems. Such equations also arise naturally in celestial Mechanics and statistical mechanics (see, for instance, [2]). Keywords: hyperbolic; theorem
On the Closability of Class Totally Paranormal Operators by Rashid, Mohammad H.M.; Alnabulsi, Salam (2025) - On H = ker(T − µI)⊕ ker(T − µI)⊥, T − µI can be decomposed as T − µI = [ 0 T12 0 T22 − µI|ker(T−µI)⊥ ] , where T22 = P |ker(T−µI)⊥T |ker(T−µI)⊥ . T is called totally paranormal [22] if T − µI is paranormal for every µ ∈ C. That is, ∥(T − µI)x∥2 ≤∥∥(T − µI)2x ∥∥ ∥x∥ for all x ∈ X and µ ∈ C. Keywords: d(t; ker(t; operator; paranormal; ran(t; theorem; σ(t
Design and Analysis of Shortened Bose-Chaudhuri-Hocquenghem Codes for Efficient Data Transmission over the Eisenstein Fields by Sajjad, Muhammad; Asghar, Rida ; Abdalrahem, Mushtaq K. ; Rajab, Adnan Burhan ; Narayana, Mahesha; Junjua, Moin-ud-Din; AlQahtani, Salman A. (2025) - The work starts with the defi- nition of shortened BCH codes over the Eisenstein fields with the mention of generator polynomials and the study of certain algebraic characteristics. 2020 Mathematics Subject Classifications: 94B75, 11T71, 94A24, 68P30, 14G50, 94A05 Key Words and Phrases: Eisenstein field, Shortened BCH codes, Modified BMA ∗Corresponding author. ∗Corresponding author. Keywords: bch; codes; eisenstein; fields; polynomial; theorem; z2[ω
Product Difference Fibonacci Identities Revisited: Quaternionic Generalizations of Everman and Koshy by Demirtürk, Bahar; Topal, Nazim (2025) - Using the Binet formula and the relation αβ = −q, we have Un−1Un+1 − U2 n = (αn−1 − βn−1)(αn+1 − βn+1) (α − β)2 − (αn − βn)2 (α − β)2 = α2n + β2n − αn−1βn+1 − αn+1βn−1 (α − β)2 − α2n + β2n − 2αnβn (α − β)2 = −αn+1βn−1 − αn−1βn+1 + 2αnβn (α − β)2 = −(αβ)n−1 α2 + β2 − 2αβ (α − β)2 Using the Binet formula and αβ = −q, we have Un−rUn+r − U2 n = (αn−r − βn−r)(αn+r − βn+r) (α − β)2 − (αn − βn)2 (α − β)2 = α2n + β2n − αn−rβn+r − αn+rβn−r (α − β)2 − α2n + β2n − 2αnβn (α − β)2 = −αn+rβn−r − αn−rβn+r + 2αnβn (α − β)2 = −(αβ)n−r α2r + β2r − 2αrβr (α − β)2 = −(αβ)n−r ( αr − βr α − β )2 = −(αβ)n−r(Ur)2 = −(−q)n−rU2 r . Keywords: fibonacci; identities; lucas; numbers; quaternions; sequences; theorem; α −; β)2

Group

Counting Symmetries with Burnside's Lemma and Polya's Theorem by Nasseef, Md Taufiq (2016) - ={Y Y Y Y }Or b(Y Y Y R) = Or b(Y Y RY ) = {Y Y Y R, Y Y RY } Or b(Y Y RR) ={RRRR, Y RRR,RY RR,RRY Y, Y Y RR,RY Y Y, Y RY Y, Y Y Y Y } A((12)(34)) Keywords: cycle; group; number; y y
A Generalization of the Calderon Admissibility Condition by Arefijamaal, Ali Akbar; Mohammadzade, Mohammad (2015) - In this paper, we first review these results and then introduce a more general setting for admissible groups. Moreover, some necessary conditions are pro- vided for a class of admissible groups. Keywords: group
Cycles in the chamber homology for SL(2,F) by Aeal, Wemedh (2014) - Introduction Let F be a p-adic non-archimedean local field with p 6= 2 and G = SL(2, F). 2. Local Langlands Correspondence and Base Change Let F be a non-archimedean local field, and G = SL(2, F). Keywords: base; group; sl(2
Analyzing Group Theoretical Properties of Groups with Order 24 by GAP by Aslan, Ahmet Faruk; Odabas, Alper (2015) - Table 1: Group & Generator Properties Group T Type of Group NS Number of Subgroups Group N Name of Group NNS Number of Normal Subgroups GAP T Type of GAP FiG Generators of Fitting Subgroup GAP N GAP Name of Group FrG Generators of Frattini Subgroup Deg. Subgroup lattice of C3 × C8 Group T 24/15 Group N D8 × C3 GAP T 24/11 GAP N d8× c3 Deg. 24 Ab. Keywords: gap; group; subgroup; table
The Group of Units of Integral Group Rings of Extra-Special 2-Groups by Mello, Cristiane de (2017) - Therefore u can be written as an integral invertible matrix U = [uij ] , 1 ≤ i, j ≤ 4, where u11 = 2(α1 + α2 + α4 + α8) + 1, u12 = 2(−α5 + α7 + α9 − α10), u13 = 2(−α3 + α6 + α11 − α14), u14 = 2(α12 − α13 − α15 + α16), u21 = 2(α5 + α7 + α9 + α10), u22 = 2(α1 + α2 − α4 − α8) + 1, u23 = 2(α12 + α13 − α15 − α16), u24 = 2(−α3 + α6 − α11 + α14), u31 = 2(α3 + α6 + α11 + α14), u32 = 2(α12 − α13 + α15 − α16), u33 = 2(α1 − α2 + α4 − α8) + 1, u34 = 2(−α5 + α7 − α9 + α10), u41 = 2(α12 + α13 + α15 + α16), u42 = 2(α3 + α6 − α11 − α14), u43 = 2(α5 + α7 − α9 − α10), u44 = 2(α1 − α2 − α4 + α8) + 1. = −α5 + α7 − α9 + α10, X41 = α12 + α13 + α15 + α16, X42 = α3 + α6 − α11 − α14, X43 = α5 + α7 − α9 − α10, X44 = α1 − α2 − α4 + α8. Keywords: group; units
Soft Uni-Abel-Grassmann's Groups by Ullah, Aman; Karaaslan, Faruk; Ahmad, Imtiaz (2018) - [10] A. Sezer, A. O. Atagün, Soft groups and normalistic soft groups, Computers and Mathematics with Applications, 62(2), 685-698, 2011. They defined concept of soft groups. Keywords: group
A-paracompactness and Strongly A-screenability in Topological Groups by Maqbool, Muhammad Kashif; Yousaf, Awais; Bosan, Muhammad Siddique; Jafari, Saeid (2020) - In semi topological group (G, ∗, τ) having a closed A-paracompact (countably A-paracompact) subset N . In 1962, J. Kister proved some properties of compactness in topological groups Keywords: finite; group; paracompact; topological
An Application of Finite Groups to Hopf algebras by Al-Mutairi, Tahani; Al-shomrani, Mohammed Mosa (2021) - Math, 14 (3) (2021), 816-828 826 Finally, to show that (H, µ, λ,∆, ε, S) is an R-Hopf algebra, we define the antipode map S : H 7−→ H, for all g ∈ G, by S(g) = g−1 [8] A semisimple Hopf algebra H is nilpotent if the ascending central series K ⊆ Z1 ⊆ Z2 ⊆ .... satisfies Zm = H for some m > 1. Keywords: algebra; group; hopf
On the Aspects of Enriched Lattice-valued Topological Groups and Closure of Lattice-valued Subgroups by Ahsanullah, TMG; Al-Thukair, Fawzi (2021) - For (LG2), consider x, y ∈ G with x 6= e and y 6= e, then µ(x) ∗ µ(y) Now let x, y ∈ G and µ ∈ LH . Keywords: category; closure; group; subgroup
Some Properties of g-Groups by Caraquil, Joey A. ; Baldado, Michael Jr. Patula (2022) - 2020 Mathematics Subject Classifications: 08A05 Key Words and Phrases: g-group, g-subgroup, group, homomorphism, zero element 1. [1] where a new algebraic struc- ture called g-group was introduced. Keywords: group
Nonabelian Case of Hopf Galois Structures on Nonnormal Extensions of Degree pqw by Jamal, Baraa M; Alabdali, Ali (2023) - Hopf–Galois structures on Galois field extensions of degree pq. We look at Hopf Galois structures with square free pqw degree on separable field extensions (nonnormal) L/K. Where E/K is the normal closure of L/K, the group permutation of degree pqw is G = Gal(E/K). Keywords: group; hgss
Finite Minimal Simple Groups Non-satisfying the Basis Property by Al Khalaf, Ahmad; Taha, Iman (2023) - 2020 Mathematics Subject Classifications: 20M05, 03D40 Key Words and Phrases: Simple group, Minimal group, Group with the Basis Property 1. It should be mentioned that simple groups are not soluble groups, unless the simple groups with prime orders. Keywords: basis; basis property; group; property; psl(2
On the Isomorphism Problem for Central Extensions II by Snanou, Noureddine (2024) - So, putting G1 = G2 = Zp, σ = idG1 and ρ = idG2 in the preceding proposition, the groups Zp × ε Zp and Zp × mεε0 Zp are upper isomorphic. (1) for all x ∈ G1, and y ∈ G2. Lemma 3.2. Keywords: group
On The Representations and Characters of Quaternions Group Q8 by Labsir, Abdallah; Fanich, El Mokhtar (2024) - We are interested in studying the linear representations of the Quaternions group Q8 by determining it’s charater table and irreducible representations which allows us to construct some representations of degre 6 and 8 of Q8. 2020 Mathematics Subject Classifications: 20C15, 20C20, 20C30, 20G20 Key Words and Phrases: Irreducible representation, Character table, Quaternions group, Group Q8 1. Keywords: group; representation
Exploring the Associated Groups of Quasi-Free Groups by Alotaibi, Abdulaziz Mutlaq ; Aljamal, Khaled Mustafa (2024) - 2020 Mathematics Subject Classifications: 16U60, 20C05, 16S34, 20E06 Key Words and Phrases: Free groups, cyclic groups, quasi-free group, free product of groups and associated groups. In this paper we show that for every group G there exists a group denoted H(G) and is called the associated group of G satisfying some important properties that as application we show that if F is a quasi-free group and G is any group, then H(F )is trivial and H(F ∗ G) ≊ H(G), where a group is termed a quasi-free group if it is a free product of cyclic groups of any order. Keywords: group
On the Characterizations of Approach Groups by Ahsanullah, TMG; Al Thukair, Fawzi (2024) - × G =< {F × G|F ∈ F, G ∈ G} >, i.e., we have {F ×G|F ∈ F, G ∈ G} as a basis for F×G. For F,G ∈ F(X) Noting that m (F ×G) = {xy|x ∈ F, y ∈ G} = F ⊙G, we have {F ⊙G|F ∈ F, G ∈ G} as a basis for F⊙G. Similarly, we find {F−1|F ∈ F} as a basis for F−1, where F−1 = {x−1|x ∈ F}. Keywords: approach; f(x; group
A Comparative Analysis of Four Group Decision-Making Techniques: KEMIRA G-I, KEMIRA G-II, Lon-Zo, and MACASP by Nana, Naguiesmongho Christian; Metchebon Takougang, Stéphane Aimé; Batieno, T. Benoît Joseph (2024) - The evaluation that decision-makers give by consensus on alternative ak with regard to criterion j is gj(a k) and it is defined by equation (3): gj(a k) = L∑ l=1 wdl j .gdlj (ak), k = 1, · · · ,K, j = 1, · · · ,m. (3) The overall performance g(ak) of the alternative ak is obtained according to equation (4) : g(ak) The Lon-Zo and MACASP methods are often used for ranking problems, where al- ternatives are ranked from best to worst[11, 15]. Keywords: criteria; decision; group; kemira; kemira g; methods
The Superfluous Kernel Property in First Theorems on Generalized Hopficity through Hereditarily Hopfian Groups by Bouzendaga, Abderrahim; Abdelalim, Seddik; Elmouki, Ilias (2025) - In our present paper, we characterize generalized Hopfian groups within the category of Abelian groups, based on a series of results in the context of Hopfian hereditation. On generalized Hopfian divisible p−groups In this section, we characterize generalized Hopfian groups in the category of divisible p−groups. Keywords: finite; group; hopfian; subgroup
Note on the Affine Group Representations by Alghamdi, Amjad; Alqurashi, Taghreed (2025) - Po iss on int eg ra l Fourier transform Fourier transform Laplace transform Figure 1: Intertwining operators between affine group representations 4.1. • Quasi-regular representation on the real line. Keywords: affine; group; representation; transform; wavelet
On Some Subcategories of Probabilistic Convergence Groups by Ahsanullah, TMG; Al Thukair, Fawzi (2025) - We order this set by set inclusion and we denote for p ∈ S the point filter by [p] = {F ⊆ S : p ∈ F}. If F ∈ F(S) and G ∈ F(T ), then the filter on S × T generated by the sets of the form {F × G : F ∈ F, G ∈ G} is denoted by F × G. Keywords: category; e ∈; f ∈; f−1; g ∈; group; p ∈; q ∈; φ ∈; ∈ cφ; ∈ f(s; ∈ ∆+
On Finite Groups with Transfer Maps and Weak Closure by Alotaibi, Abdulaziz ; Al-Tahat, khalid; Aljamal, Khaled Mustafa (2025) - Then P g is another Sylow p-subgroup of G, so there exists x ∈ G such that P g = P x, or equivalently gx−1 ∈ NG(P ). This is the natural projection map that sends each element g ∈ G to its coset in the quotient group G/Ǵ. The transfer homomorphism v from G → G/Ǵ is defined as: v(g) Keywords: group

Flow

Interaction of Pulsatile Flow on the Peristaltic Motion of Couple Stress Fluid Through Porous Medium in a Flexible Channel by Kumar, S.Ravi; Prasad, R.Siva (2010) - [ψ0+ kei tψ̄0+ ε[ψ1+ kei tψ̄1] (16) Substituting (16) in (9) and equating the like powers of ε, the equations corresponding to the zeroth and first order steady components are RSψ0y y y y y y −ψ0y The equations related to zeroth and first order oscillatory terms are RSψ̄0y y y y y y − ψ̄0y y y y +σ 2ψ̄0y y = 0 (22) Keywords: flow; y y
Finite Element Simulation of Newtonian and Non-Newtonian Fluid through the Parallel Plates Affixed with Single Screen by Memon, Abid Ali; Memon, Muhammad Asif; Bhatti, Kaleemullah; Shaikh, Gul Muhammad (2020) - Math, 13 (1) (2020), 69-83 76 (a) n=0.7 (b) n=0.8 (c) n=0.9 Figure 6: Percent change in maximum flow rate against the Reynolds number for different values of n (a) n=0.7 (b) n=0.8 (c) n=0.9 Figure 7: Percent change in maximum pressure against the Reynolds number for different values of n (a) n=1.1 (b) n=1.2 (c) n=1.3 Figure 8: Maximum flow rate against the Reynolds number for different values of n M. A. Memon et al. / Eur. Percentage change in maximum flow rate against the Reynolds number for different values of n (a) n=1.1 (b) n=1.2 (c) n=1.3 Figure 11: Percentage change in maximum pressure against the Reynolds number for different values of n M. A. Memon et al. / Eur. Keywords: flow; flow rate; fluid; number; pressure; rate; reynolds; reynolds number
Analysis of Electro-MHD of Third Grade Fuid Flow Through Porous Channel by Padhi, Sukanya; Nayak, Itishree (2020) - EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 13, No. 5, 2020, 1270-1284 ISSN 1307-5543 – www.ejpam.com Published by New York Business Global Special Issue Dedicated to Professor Hari M. Srivastava On the Occasion of his 80th Birthday Analysis of Electro-MHD of third grade fluid flow through porous channel Sukanya Padhi1,∗, Itishree Nayak2 1,2 Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Odisha, India Abstract. [4] employed numerical inversion of Laplace transform to study some unsteady third grade fluid flows. Keywords: flow; fluid; grade; temperature; uj+1; velocity
Analytical Discussion and Sensitivity Analysis of Parameters of Magnetohydrodynamic Free Convective Flow in an Inclined Plate by Suganya, S. Thamizh; Balaganesan, P.; Rajendran, L.; Abukhaled, Marwan (2020) - Chemical reaction effects on MHD free convective flow past an inclined plate. Radiation and chemical reaction effects on MHD flow along a moving vertical porous plate. Keywords: effect; flow; heat; mhd; plate; velocity
The Force on a Magneto-spherical Particle Oscillating in a viscous Fluid Perpendicular to an Impermeable Planar Wall with Slippage by El-Sapa, Shreen (2022) - Many researchers work about magnetic fields with normal convection in a permeable medium that has various implementations in energy, thermal geology, petrol extraction such as Qian and Bau [4] proved that MHD flows due to the oscillating plate. [8] studied MHD flow over a moving plate in a rotating fluid with magnetic field, Hall currents and free stream velocity. Keywords: field; flow; fluid; force; frequency; journal; magnetic; oscillating; sapa; slip; sphere; wall
A Numerical Simulation of Convection and Conduction Heat Transfer for a Fluid in a Porous Medium by Algwauish, Ghanim M.; Hammodat, Alaa A.; Saleem, Hamsa D. (2023) - [9] explored the Dufour and thermal permeability impacts on the occasional free magnetic characteristics of heat flow passing via an unbounded vertical permeable layer. Conclusion The influence of mass and heat transfer on mixed convection fluid flow past a horizontal channel are investigated in the present study. Keywords: flow; hammodat; heat; number; temperature
The Numerical Solution of Stagnation Point Flow of Non-Newtonian Fluid and Heat Transfer over a Porous Medium under Effect of Thermal Radiation and Magnetic Field by Saleem, Hamsa D.; Al-Obaidi, Iman H.; Hammodat, Alaa A. (2023) - 2020 Mathematics Subject Classifications: 65Lxx, 65Mxx, 80Mxx Key Words and Phrases: Stagnation point flow, Heat transfer, Shrinking/stretching sheet, Skin Friction coefficient, Local Nusselt 1. Stagnation point flow of non –newtonian fluid and heat transfer over a stretching /shrinking sheet in a porous medium. Keywords: flow; fluid; heat; sheet; stagnation; stretching; transfer
Wardrop Optimal Networks by Kalampakas, Antonios (2024) - Math, 17 (4) (2024), 2448-2466 2449 control or coordination because individual users acting in their self-interest do not natu- rally lead to system optimal flows. We achieve this by providing a set of necessary and sufficient conditions for Wardrop optimal flows and using this characterization we investigate the main properties of Wardrop optimal networks. Keywords: equilibrium; flow; j(ϕj; network
Numerical Simulation for Obtaining Advanced Engineering Applications Through an Important Fluid Problem by Tedjani, Ali H. ; Khader, Mohamed M. (2025) - Specifically, increasing the porous parameter, magnetic number, heat generation parameter, and Ec tends to decrease the Nusselt number. Furthermore, the observed decrease in the Sherwood number values for increasing magnetic number, Casson parameter, thermal conductivity parameter, heat generation parameter, and Eckert num- ber, is accompanied by an increasing trend for the Sherwood number with the unsteadiness parameter, diffusion parameter, and chemical reaction parameter. Keywords: film; flow; fluid; heat; khader; m. m.; parameter
Impacts of Activation Energy and Modified Darcy Law on the Motion of Williamson Nanofluid over a Stretching Riga Sheet through Porous Medium by Saeed, Abdulkafi Mohammed; Eldabe , Nabil T. M.; Ismael, Aya M. ; Ali, Saeed Mohammed Salman (2025) - − s23 − s s24 ) , s28 = s26+s27, s29 = s25−s28, s30 = 1+ s6 + s29, s31 = − (1 + s3 + s20) , s32 = − (s1 + s19) , s33 = s2 + s24, s34 = s5 + s28, s35 = 2s32, s36 = 3 s18 ,s37 = s s33, s38 = s34 √ 1/k+ s23, s39 = ( 1+ s)s21, s40 = ( 1 + √ 1/k ) s22, M. El-dabe Nabil et al. / Eur. + Nt Nb θ′′ − Sc λ e−E (E +m) (w − 1) θ φ = 0 (13) With conditions f = 0, f ′ = 1, θ = 1, φ = 1, η = 0 f ′ = 0, θ = 0, φ = 0 η → ∞ (14) Where We =Γa 3 2 x√ ν is the Williamson parameter, k = k0a ν is the permeability parameter, M = π j0M0 8 ρf a2x is the modified Hermann number, s = √ π2ν l2a is the dimensionless parameter, Pr = µ0cf kc is the Prandtl number, Nb = τ0DB(Cw−C∞) Keywords: figure; flow; fluid; nanofluid; q =
Marangoni Convection in Hybrid Nanofluid Flow over a Disk by Omer, Abdoalrahman S.A. (2025) - In this work Marangoni convection problem is studied for hybrid nanofluids. Because of their improved thermal characteristics, hybrid nanofluids which are created by suspending nanoparticles of several materials inside a base fluid have become a fascinating field of study. Keywords: disk; flow; heat; hybrid; marangoni; nanofluid; nanoparticles; parameters; profile; stretching; surface; temperature; transfer
Numerical Investigation of MHD Flow of a Tangent Hyperbolic Fluid Through a Porous Medium with Viscous Dissipation, Soret, and Dufour Effects by K , Umamaheswara Rao; Sheri, Siva Reddy; Kallem, Srinivas Reddy ; Perli, Alfunsa Prathiba; Gollapalli, Shankar; Helal, Medhat M. ; Abdulaziz Ibrahim , Ismail (2025) - Numerical analysis of the effect of chemical reaction and heat source on mhd hyperbolic tangent fluid flow across a non-linear stretching sheet in a porous medium. Zero and nonzero normal fluxes of thermal radiative boundary layer flow of nanofluid over a radially stretched surface. Keywords: boundary; concentration; figure; flow; fluid; heat; hyperbolic; number; tangent; temperature
Effects of Volume Fraction and Chemical Reaction on Inclined MHD Two-Phase Biorheological Flow in a Porous Tumor Region: Heat and Mass Transfer with Soret Effect by Kumar, Devendra; Garvandha, Mahesh; Kumar, Sanjeev; Deo, Narendra (2025) - In the observation, significant changes are observed in blood flow transport. Ther- mal parameters on blood flow, heat stress, and concentration that help in tumor treatments are described using numerical outputs and depicted through graphs. Keywords: blood; chemical; drug; figure; flow; fluid; heat; number; parameter; transport; tumor; velocity; volume
Numerical Study of Nano-encapsulated Phase Change Materials on Non-Newtonian Nanofluid Flow over a Stretching Sheet by Deswita, Leli; Syamsudhuha, Syamsudhuha; Effendi, Rustam; Asral, Asral (2025) - Results indicate that embedding NEPCM particles within the power-law nanofluid significantly enhances heat transfer through latent heat absorption and re- lease, though it also increases wall shear stress. 2020 Mathematics Subject Classifications: 41A30, 76F12, 65M60, 65N12 Key Words and Phrases: Runge–Kutta method, NEPCM, phase change heat transfer, nanoflu- ids, boundary layer 1. Keywords: flow; fluid; heat; law; power; temperature; transfer
A Comprehensive Review of Thermophoresis Particle Effects on Convective Heat Transfer and Climate Change Implications: Study of the Combined Characteristics by Nabwey, Hossam A. ; Ashraf, Muhammad ; Rashad, A; Chamkha, Ali (2025) - Impact of thermophoretic convective heat transfer in porous medium In porous medium the momentum of thermophoretic particles due to convective heat transfer can alter the porosity and permeability in the porous medium region. In environmen- tal engineering the understanding of thermophoretic convective heat transfer is important to predict the motion of pollutant particles and particulate the matters in the atmosphere, especially in the existence of thermal gradients. Keywords: convection; deposition; effects; flow; heat; heat transfer; impact; journal; motion; nabwey; nanofluid; particles; temperature; thermophoretic; transfer

I=1

Some Univalence Conditions of a Certain General Integral Operator by Barbatu, Camelia; Breaz, Daniel (2020) - 2020 Mathematics Subject Classifications: 30C45 Key Words and Phrases: Integral operators, analytic and univalent functions, open unit disk, univalence conditions, Schwarz Lemma 1. Integral operators of Bazilvic type. Keywords: i=1
New Refinement of Niezgodaâ€™s Inequality with Applications to Ky Fan Inequality by Chanan, Sadia; Khan, Asif R. (2020) - Under the assumptions stated above it should be noted that m∑ j=1 aj − m−1∑ j=1 l−1∑ k=0 λk+1xij+k  ∈ J. The aim of this paper is to present new refinement of Theorem 3. By applying the convex function φ(x) = ln ( x 1−x ) for all x ∈ (0, 12 ], to the inequality (6), we get, ln ( ∑m j=1 aj − ∑m−1 j=1 ∑n i=1wixij 1− ∑m j=1 aj + ∑m−1 j=1 ∑n i=1wixij ) ≤ n∑ i=1 wi ln ( ∑m j=1 aj − ∑m−1 j=1 ∑l−1 Keywords: i=1; j=1; m−1∑
Markov Modeling of Battery Cell Behavior Taking into Account Pulsed Discharge Recovery by Konane, Victorien Fourtoua (2021) - N − 1 pN,N = p where 0 ≤ p < 1, q = 1 − p. = −q + (1− q)e−α(N−xt), x0 = N, which yields xt = N − 1 α ln ( eαqt − 1− q q (eαqt − 1) ) . Keywords: battery; capacity; i=1; j=1
Global Asymptotical Stability of Delayed Impulsive Neural Networks without Lipschitz Neuron Activations by Wu, Ailong; Zhang, Jine; Fu, Chaojin (2010) - Since 2 � � fi(zi(t, φ̃)) � � · � � f j(z j(t −τi j, φ̃)) � �≤ 1 r f 2 i (zi(t, φ̃))+ r f 2 j (z j(t −τi j, φ̃)) then we get V̇ (z(t, φ̃))≤ −2 n ∑ i=1 di fi(zi(t, φ̃))zi(t, φ̃) + 2 n ∑ i=1 n ∑ j=1 ai j fi(zi(t, φ̃)) · Given the vector ψ = (ψ1, · · · ,ψn) T ∈ Rn, ψ = max 1≤i≤n � �ψi � �. Keywords: i=1; j �; � +; � f; � x; � �
Stochastic Complexity, Histograms and Hypothesis Testing of Homogeneity by Qian, Guoqi (2009) - By Taylor expansion, ∑ ni,m>0 ni,m log ni,m nπi,m = ∑ ni,m>0 ni,m log � 1+ ni,m− nπi,m nπi,m � G. Qian / Eur. Math, 3 (2010), 51-80 72 = m ∑ i=1 log r̃i,m+ m ∑ i=1 ni,m log (n+m)πi,m ni,m+ 1 + m ∑ i=1 log nπi,m+ 1 ni,m+ 1 +m log(n+m)− m ∑ i=1 log(nπi,m+ 1). Keywords: i=1; i=1 ni; length; log; m log; nπi; r̃i; � �
New Criteria for Guaranteeing Oscillation of Second-Order Differential Equations with Several Delays by Aldosari, Faten (2025) - Assume that the series of functions {ϑn (t)}∞n=0 is defined as ϑn (t) = ∫ ∞ t (p− 1) / (b (s))1/(p−1) ϑ p (p−1) n−1 (s) ds+ ϑ0 (t) , t ≥ t0, n = 1, 2, 3, ..., (28) and ϑ0 (t) = ∫ ∞ t n∑ i=1 qi (t) (1− y (πi (t))) (p−1) B̂ (t) dt, t ≥ t0, where ϑn (t) ≤ ϑn+1 (t) , t ≥ t0. Keywords: i=1; p−1; t t
A Novel Fractional Integral of a Function via Polynomial $n$-Fractional $s$-Like Preinvexity by Nasir, Jamshed; Aydi, Hassen; Mansour, Saber (2025) - If we take ϱ = 1 and n = 1 and ς∗(b1, a1) = b1 − a1, in Corollary 4, then one can get the inequalities (5). b1 − a1 but there exist invex sets which are noticonvex (see [11]). Keywords: i=1; ς ϱ; ϱ k
Score sequences in oriented k-hypergraphs by Pirzada, Shariefuddin; Guofei, Zhou (2008) - Clearly, � �V1 � � = j, � �V2 � �= n− j . if p = 1. To see S(s+n , s−p ) satisfies (2.1), we only need to show for each j (p ≤ j ≤ n− 1), j ∑ i=1 si > j(k− 1) � n− 1 k− 1 � + k−1 ∑ i=1 (i− k) � j i �� n− j k− i � . Keywords: i=1; � n−; � �
Detecting of Rumours in Social Media via Neutrosophic Hesitance Distance Measures by Kaviyarasu, M. ; R. , Venitha; Alqahtani, Mohammed (2025) - [0, 1] with the condition for the collection of NFSs D1, D2, D3 ∈ D(B) i. 0 ≤ dH(D1, D2) ≤ 1, dH(D1, D2) = 0 ⇐⇒ D1 = D2. ii. Let D1 and D2 be two NFSs on B and then NF product of D1 and D2 is D1 ◦D2 defined by D1 ◦D2 = TD1(d) ◦ TD2(d) Keywords: dh(d1; distance; hesitance; i=1
Tensor Product of Spaces with Generalized 2-Inner Product by Moreno Arroyo, Luis Mario; Ferrer Villar, Osmin Oberto; Sierra Acosta, Arley Yessit (2025) - In this work, we introduce the notion of tensor product of spaces with a generalized 2-inner product (see Definition 5), and we establish several interesting properties (see Proposition 5), thereby generalizing the classical properties of the tensor product of inner product spaces. We also established the notion of the 2-tensor product of linear operators on spaces with a generalized 2-inner product (see Definition 9), and demonstrated that several well-known identities for operators in inner product spaces remain valid in this new structure (see Proposition 8). Keywords: i=1; product; spaces; tensor

Vertex

Certified Vertex Cover of a Graph by Hassan, Javier; Bonsocan, Maria Andrea O. ; Rasid, Regimar A. ; Sappari, Amil-Shab S. (2024) - We characterize certified vertex cover in these graphs and subsequently derive the simplified formulas for calculating the certified vertex cover number. Moreover, we present some bounds and properties of certified vertex cover. Keywords: cover; vertex
Super Vertex Cover of a Graph by Canoy, Jr., Sergio; Bonsocan, Maria Andrea O. ; Hassan, Javier; Mahistrado , Angelica Mae ; Bilar, Vergel T. (2025) - 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Vertex cover, super vertex cover, super vertex cover number 1. Motivated by the introduction of these several variants of the parameter, we introduce and initiate the study of super vertex cover of a graph. Keywords: cover; set; super; vertex
Optimal Placement of Phasor Measurement Units using k-PowerDomination Number in Grid Networks by Anitha, J. ; Manimegalai, R. ; Nithishkumar, S. ; Arthi, R. ; Govindan, Vediyappan; Donganont, Siriluk (2025) - [4] in exploring connected PD within graphs, with the NP-hardness of determining the domination number in connected graphs being firmly established. The paper focuses on identifying graphs where every vertex acts as its own power dominating set (PDS), contributing a list of such graphs. Keywords: algorithm; domination; graphs; node; power; set; vertex; vertices
2-Vertex Covering of a Graph by Hassan, Javier ; Canoy, Jr., Sergio; Gamorez, Anabel E. ; Ahmad, Eman C. ; Sappari , An-Nadzwie (2025) - Other studies on vertex cover and its variations can be found in [7], [8], [9], [10], [11], [12], and Conclusion The parameter 2-vertex cover, a variant of vertex cover, had been introduced and initially studied. Keywords: cover; set; vertex; β2(g
Perfect 2-Distance Zero Forcing in Graphs by Hassan, Javier; Hajim, Erwan; Mahistrado, Angelica Mae L. ; Alayka, Akrimal M. (2025) - The join of G and H, denoted by G+H is the graph with vertex set V (G+H) A particular variant of zero forcing called perfect co-zero forcing is defined to study the behavior of the perfect 2-distance zero forcing sets in the join of graphs. Keywords: distance; forcing; set; vertex
$2$-Path Geodetic Vertex Covering of a Graph by Tapeing, Aziz; Canoy Jr., Sergio (2025) - Assume first that G ∈ {K3,K3, P1 ∪ P2}. This new parameter naturally extends two existing concepts: 2-path geodetic set and vertex cover of a graph. Keywords: cover; path; set; vertex; vertex cover; β2pg(g

Stability

Robust Exponential Stability of Recurrent Neural Networks with Deviating Argument and Stochastic Disturbance by Mingxin, Zha; Wenxiao, Si; Tao, Xie (2020) - For t0 ≤ t ≤ t0 + 2ρ, from (1), we have E‖y(t)− x(t)‖2 = E‖ ∫ t t0 −A(y(s)− x(s)) Thus, considering (23) and (24), for t ≥ t0 − α+mρ, ‖y(t; t0, y0)‖ = ‖y(t; t0 + (m− 1)ρ, y(t0 + (m− 1)ρ; t0, y0))‖ ≤ exp(−ρτ)‖y(t0 + (m− 1)ρ; t0, y0)‖ ≤ exp(−mρτ)‖y0‖ Consequently, when t > t0−α+ρ, the positive integer m that satisfies t0−α+(m−1)ρ ≤ t ≤ t0 − α+mρ, ‖y(t; t0, y0)‖2 ≤ exp(−τ(t− t0))exp(τ(ρ− α))‖y0‖2 (25) Obviously, (25) also holds for t0 ≤ t ≤ t0 − α+ ρ. Keywords: stability
Mathematical Model for the Effect of Buoyancy Forces on the Stability of a Fluid Flow by Aziz, Maysoon (2023) - 1 cos (2S1) B4 = 1 32 S−5 1 1 1− 2 sin2 (2S1) F AE (−32S1A3A4 − 32S1A4A5 − 12S1A2A5 − 12S1A2A3 + 56 S1A3A5 + 4S1A3A5 −8S3 1A2A4 − 8S3 1A4A5 ) + ( 2S1A 2 2 − 60S3 1A 2 4 + 56 3 S3 1A 2 3 + 16S2 1A 2 4 −4S−1 1 A2 5 + 8S3 1A2A5 + 16S2 1A3A4+ 8S1A 2 5 − 16S1A2A5 ) sin (2S1) (16S1A2A5+ 136 3 S2 1A3A4 − 12A2A5 + 8A2 5 ) cos (2S1) + (64S1A3A4 − 48 S1A4A5 − 16S1A2A5 + 24S1 A2A3 + 72S1A3A5 + 16S1A3A5) sin 2 (2S1) + (76S1A4A5 − 126S1A3A4− 140S1A2A4 + 44 A3A5 − 44A4A5 + 6S1A3A5 + 64S3 1A3A4 − 16S3 1A2A3 ) sin (2S1) cos (2S1)− ( 232 3 S3 1A 2 4 − 136 3 S3 1A 2 3 − 96S2 1A 2 4 + 48S1A3A5 sin 2 (2S1) cos 2 (2S1) + (144S1A2A4 − 72S1A3A4+ 144S1A4A5+ 36A4A5 − 36A3A5) sin 3 (2S1) cos (2S1) ] . B2 = −B4 sin (2S1)− 1 8S F AE [ −4 3 A2A5 − ( 8A3A4 − 4S−1 1 A2A4− 2A2A3 − S−1 1 A2A5 cos (2S1) +A4A5 sin (2S1)− (A2A5 + 4S1A3A4+ 5−1A2A5 ) sin2 (2S1) + 10 3 A3A4 sin (2S1) cos (2S1) + ( 2S−1 1 A3A4+ 4S−1A4A5 + 2S−1A3A5 ) sin (2S1) cos 2 (2S1)+ 2S−1 1 A4A5 sin 2 (2S1) cos (2S1) ] M. M. Aziz / Eur. Keywords: 2s1η; aziz; cos; sin; stability; s−1
Periodic Solutions of Strongly Nonlinear Oscillators Using He’s Frequency Formulation by Ismail, Gamal; Moatimid, Galal; Yamani, Mohammed (2024) - The simplified HFF of nonlinear oscillators was presented and demonstrated [2]. It can be utilized for studying various categories of nonlinear oscillators. Keywords: frequency; g. m.; m. moatimid; nonlinear; npa; stability
Hyers-Ulam Stability of Fifth Order Linear Differential Equations by Bowmiya, S.; Balasubramanian, G.; Govindan, Vediyappan; Donganont, Mana ; Byeon, Haewon (2024) - If p2 = 0, then |Γ(x)− ϕ(x)| ≤∈ ep2x ∫ l x e−p2tdt |Γ(x)− ϕ(x)| ≤∈ e0x ∫ l x e−0tdt |Γ(x)− ϕ(x)| ≤∈ ∫ l x dt |Γ(x)− ϕ(x)| ≤∈ (l − x);x ∈ If p5 = 0, then |K(x)− L(x)| ≤ εep5x ∫ l x e−p5tdt |K(x)− L(x)| ≤ ε ∫ l x dt |K(x)− L(x)| ≤ (l − x);x ∈ Keywords: hyers; stability; ulam
Machine Learning for Smart Grid Stability: Enhancing Reliability in Renewable Energy Integration by Danach, Kassem ; Aly, Wael Hosny Fouad; Kanj, Hassan (2025) - To address the challenges in smart grid stability, this study seeks to answer the following key research questions: (i) How effectively can machine learning models predict grid stability in scenarios with renewable energy integration? (ii) This study explores the application of machine learning techniques to pre- dict and enhance smart grid stability, focusing on scenarios involving renewable energy integration. Keywords: aly; energy; frame; grid; grid stability; integration; kanj; learning; machine; models; performance; power; smart; snr; stability

Neutrosophic

Applications of Neutrosophic N -Structures in n-Ary Groupoids by Rattana, Amornrat; Chinram, Ronnason (2020) - Neutrosophic N -structures over UP-algebras. 2020 Mathematics Subject Classifications: 20N15, 03B80 Key Words and Phrases: neutrosophic N -structures, n-ary groupoids, neutrosophic n-ary N - subgroupoids, ε-neutrosophic n-ary N -subgroupoids. Keywords: neutrosophic
Introduction to Neutrosophic B-algebras by Jacobe, Danilo Oppus; Vilela, Jocelyn P. (2021) - = y ∗ x; (v) x Since S is a subalgebra of X, a∗c, a∗d, b ∗ c, b ∗ d ∈ S so that (a ∗ d∧ b ∗ c)∧ b ∗ d ∈ S. Keywords: neutrosophic
Key Characteristics of Quadri-Partitioned Neutrosophic Riemann integrals and Quadri-Partitioned Neutrosophic Soft Topological Spaces by Shihadeh, Abdallah ; Abualhomos, Mayada ; Abd El-latif, Alaa M.; Alhusban, Abdallah ; Shaaban, Shaaban M.; Arslan, Muhammad ; Khattak, Arif Mehmood (2025) - Math, 18 (2) (2025), 5839 28 of 54 Theorem 6. Let (F̃ ,Ω), (G̃,Ω), and (H̃,Ω) be quadripartitioned neutrosophic soft sets over key set X. Then, the following properties hold: (i) (F̃ ,Ω) ∪∼ [(G̃,Ω) ∪∼ (H̃,Ω)] [6] discussed the concept of simplified neutrosophic sets (SNSs), which are a sub-class of neutrosophic sets, and explored several aggregation operators. Keywords: g̃,ω; let; neutrosophic; quadri; set; theory; xθ(r1,r2,r3,r4; τqpnss
On Parameterized Time Neutrosophic Soft Set and its Aplication by Hazaymeh, Ayman; Bataihah, Anwar; Abu Qamar, Majdoleen ; Alodat, Naser ; Melhem, Alaa (2025) - 2020 Mathematics Subject Classifications: 03E72, 03B52, 68T37, 90B50 Key Words and Phrases: Neutrosophic set, soft set,time fuzzy soft set, neutrosophic soft set, parameterized time neutrosophic soft set, parameterized fuzzy soft set 1. Parameterized time neutrosophic soft set (PP-TNSS) This section provides of the definition of a parameterized time neutrosophic soft set (PP-TNSS) and give its basic properties. Keywords: a)n t; neutrosophic; set; ⟨0.1; ⟨0.4; ⟨0.5
Direct Product of Complex Neutrosophic Subrings by Mateen, Muhamad Haris; Hoskova-Mayerova, Sarka; Alnefaie, Kholood; Smarandache, Florentin (2025) - 2020 Mathematics Subject Classifications: 13E15, 08A72, 03E72 Key Words and Phrases: Complex neutrosophic subring, level subsets of complex neutrosophic subrings, product of complex neutrosophic subrings 1. We expand this idea to talk about the abstraction of level subsets of complex neutrosophic sets and look into the basic algebraic properties of this event. Keywords: neutrosophic; set
A Combined Study of Continuities and Boundedness in Neutrosophic Pseudo-Normed Linear Spaces by Pandiselvi, M. ; Jeyaraman, M. ; Akram, M. (2025) - ρ1(ϖ − ϑ, φ) ≤ δ ⇒ ρ2(Υ(ϖ)−Υ(ϑ), φ) ≤ δ ς1(ϖ − ϑ, φ) ≤ δ ⇒ ς2(Υ(ϖ)−Υ(ϑ), φ) ≤ δ. η1(ϖ,φ) ≥ δ ⇒ η2(Υ(ϖ), φ) ≥ δ, ρ1(ϖ,φ) ≤ δ ⇒ ρ2(Υ(ϖ), φ) ≤ δ and ς1(ϖ,φ) ≤ δ ⇒ ς2(Υ(ϖ), φ) ≤ δ. γ ≥ δ.γ + δ ∥(ϖ −ϖ0)∥, by taking ϵ = γ. ⇒ γ γ+∥(ϖ−ϖ0)∥ ≥ δ ⇒ η(ϖ −ϖ0, γ) ≥ δ. ρ(Υ(ϖ)−Υ(ϖ0), ϵ) ≤ δ ∥Υ(ϖ)−Υ(ϖ0)∥ ϵ+ ∥Υ(ϖ)−Υ(ϖ0)∥ ≤ δ ⇒ ∥∥∥ ϖ3 1+ϖ − ϖ3 0 1+ϖ0 ∥∥∥ ϵ+ ∥∥∥ ϖ3 1+ϖ − ϖ3 0 1+ϖ0 ∥∥∥ ≤ δ ∥∥ϖ3 +ϖ0ϖ 3 −ϖ3 0 −ϖξ30 ∥∥ ϵ ∥(1 +ϖ)(1 +ϖ0)|+ ∥∥ϖ3 +ϖ0ϖ3 −ϖ3 0 −ϖξ30 ∥∥ ≤ δ∥∥(ϖ −ϖ0)(ϖ 2 +ϖξ0 +ϖ2 0) +ϖξ0(ϖ +ϖ0)(ϖ −ϖ0) ∥∥ ϵ ∥1 +ϖ +ϖ0 +ϖξ0∥+ ∥∥(ϖ Keywords: neutrosophic
An Approach to Closure and Kernel Defined through $N$-points by Sanabria, José ; Rosas, Ennis; Granados, Carlos (2025) - [10] Let (X, τ) be a N -topological space and N ∈ N (X). = {N ∈ N (X) : Υ(N c) = N c} is a N -topology on X and Υ is the N -closure in the N -topological space (X, τ(Υ)). Keywords: neutrosophic
Neutrosophic Bi-ideals in INK algebras by Remala, Mounikalakshmi; Tamma, Eswar Lal; Bhargavi, Yella (2025) - To model this selection process logically, we apply the concept of neutrosophic Bi-ideal in INK-algebra, which allows us to evaluate whether removing a less important factor still results in a valid and trustworthy decision. The literature works of Fuzzy sub algebras and fuzzy K-ideals in INK-algebras, fuzzy p-ideal in INK-algebra, Fuzzy translation of INK-ideal of INK-algebras also they proposed On intuitionistic fuzzy INK-ideals of INK-algebras, Direct product of intuitionistic fuzzy K-ideals of INK-algebras, Intuitionistic fuzzy translation on INK-algebra and also they have discussed neutosophic set in INK-algebra, neutrosophic h-ideal in INK-algebra have discussed by Kaviyarasu and Indhira, [3–7] and homomorphism and anti-homomorphism of neutrosophic INK-algebras have done by Mounikalakshmi, Eswarlal, Venkata Kalyani and Aiyred Iampan [8]. Keywords: ink; neutrosophic

Spaces

Some Properties of Fuzzy Supra Soft Topological Spaces by Abd El-latif, Alaa (2019) - A family Ψ = {uiE : i∈Λ} of fuzzy soft sets is said to be a fuzzy supra open soft cover, if each member of Ψ is fuzzy supra open soft set. 2010 Mathematics Subject Classifications: 54A40, 06D72, 54D30, 03E72 Key Words and Phrases: Fuzzy soft set, Fuzzy supra soft topological space, Fuzzy supra soft continuous mapping, Fuzzy supra soft compactness 1. Keywords: f−1; set; spaces; supra; topological
Köthe Dual of Some Vector-valued Sequence Spaces by Sidaty, Mohamed Ahmed (2024) - = B(α, t) = ⟨a, αt⟩, for α = (αn)n ∈ λ and t ∈ E, where B ∈ I(λ × E) is the integral bilinear form on λ× E corresponding to fa. Math, 17 (1) (2024), 171-179 174 Let a ∈ E′, M ∈ M with a ∈ M and x = (xn)n ∈ B. Then,∣∣∣∣∣ 〈 a, ∞∑ n=1 αnxn 〉∣∣∣∣∣ = ∣∣∣∣∣ ∞∑ n=1 αna(xn) ∣∣∣∣∣ ≤ ∞∑ n=1 |αna(xn)| ≤ εM (x). Keywords: spaces; λ(e
Volterra-Composition Operators Acting on $S^{p}$ Spaces and Weighted Zygmund Spaces by Al-Rawashdeh, Waleed (2024) - In this paper, we characterize the boundedness and compactness of the Volterra-type composition operators that act between Sp spaces and weighted Zygmund spaces. Boundedness and Compactness of Iφg In this section, we characterize the boundedness and compactness of the operator Iφg acting between Sp spaces and weighted Zygmund spaces Zµ. Keywords: spaces
Fixed Points for Generalized Contractions in $b$-Gauge Spaces and Applications by Nisse, Khadidja ; Qawaqneh, Haitham; Al-Musannef, Gawhara ; Alsamir, Habes ; Beloul, Said (2025) - Suppose that the following condition holds ˜(C2) ∀x, y ∈ E with x ̸= y, there exists N = N(x, y) ∈ N∗ and (apx,y)Np=0 ⊂ E such that: (i) a0x,y = x, aNx,y = y, and αν(a p−1 x,y , a p x,y) ≥ 1, ∀p = 1, ..., N,∀ν ∈ N ; (ii) N∑ p=1 spdwi(ν)(a p−1 x,y , a p x,y) ≤Ms,ν(x, y) < Moreover, for all x, y, z ∈ E and for every t ∈ K ∈ K, by means of Young’s inequality, we get: |x(t)− y(t)|2 ≤ (|x(t)− z(t)|+ |z(t)− y(t)|)2 ≤ 2 ( |x(t)− z(t)|2 + |z(t)− y(t)|2 ) K. Nisse et al. / Eur. Keywords: spaces
Grand Variable Herz-Morrey Type Besove Spaces and Triebel-Lizorkin Spaces by Sultan, Mehvish; Sultan, Babar; Popa, Ioan-Lucian (2025) - If d > 0 and λ− d/2 < 0, then we get I4 ≲ sup ϵ>0 sup L⩽0,L∈Z 2−Lλ ϵθ L∑ k=−∞ ∞∑ i=L+3 2 dq(1+ϵ)(k−i) 2  i∑ m=−∞ 2η(0)mq(1+ϵ) ∥∥∥∥∥∥∥  ∞∑ j=1 |gj |r  1 r 1m ∥∥∥∥∥∥∥ q(1+ϵ) p(·)   1 q(1+ϵ) ≲ sup ϵ>0 sup L⩽0,L∈Z 2−Lλ { ϵθ L∑ k=−∞ ∞∑ i=L+3 2 dq(1+ϵ)(k−i) 2 · 2iq(1+ϵ)λE q(1+ϵ) f } 1 q(1+ϵ) M. Sultan, B. Sultan, I-L. Popa / Eur. Math, 18 (3) (2025), 6274 26 of 33 If l ∈ N, p0 = r ∈ (n/a,< min {p−, κ}) , N > max{0,−s}+a and ω := N+s−d/r > 0, then we get (∫ 2 1 ∣∣∣2ls (Φ∗ 2−lg ) a (x) ∣∣∣κ dt t )r/κ ≲ ∑ k∈l+N0 2−ωr|l−k|2krsM Keywords: 2−lλ; j=1; mk̇; q(1+ϵ; spaces; sultan; sup; η(·),q),θ; ∥∥∥∥∥∥∥; ∥∥∥∥∥∥∥ 
Almost, Weakly and Nearly Lindel¨of Ideal Topological Spaces by Almuhur, Eman; Al-labadi, Manal ; Suleiman, Enoch; Khan, Nazneen ; Samei, Mohammad Esmael (2025) - In 1996, Santoro and Cammaroto [9] presented the concept of weakly Lindelöf spaces (SL). Since any open cover has a countable subcover if X is Lindelöf ideal space, this trivially satisfies the nearly Lindelöf condition, making any Lindelöf ideal space nearly Lindelöf Keywords: lindelöf; modulo; modulo j; spaces
Equivalence and Stability of Compactness in Operator Spaces over the Non-Commutative Torus by Ali, Mortada S.; Elamin, Abd Elmotaleb ; Mohammed, Ibtisam (2025) - While the classical theory of compact operators focuses on spaces of functions and matrices, the study of non-commutative operator algebras presents an intriguing new context for this theory. This study bridges these two notions and demonstrates the stability of compactness under multi-fold tensor products, which is an important feature describing the structure of non-commutative operator spaces Keywords: compactness; hilbert; operator; quantum; spaces; theory
Hyers-Ulam Stability of Generalized Quartic Mapping in non-Archimedean $(n,\beta)$-normed spaces by Gowri Senthil; Donganont, Siriluk ; S. Karthick; Balaanandhan Radhakrishnan; Tamilvanan, Kandhasamy (2025) - Consequences and Illustrative Example in Qp Corollaries and Examples Corollary 4.1 (Classical Non-Archimedean Case) Let E and F be non-Archimedean normed spaces, i.e., (n, β)-normed spaces with n = 1, β = 1. Generalizations of banach and kannan mappings in non-archimedean spaces. Keywords: spaces; νn−1
Some New Boundedness Results for Variable Marcinkiewicz Fractional Integral Operator on Herz-Morrey-Hardy Spaces by Sultan, Babar; Hussain, Amjad; Sultan, Mehvish; Popa, Ioan-Lucian (2025) - − v − n s (ii) − n q1∞ − v − n s < α∞ < n q′1∞ − v − n s . − ln |h1 − h2| , |h1 − h2| ≤ 1 2 , h1, h2 ∈ E, (1.3) where C(p) > 0. Keywords: herz; m0<0,m0∈z; m0∑; spaces; sultan; sup; |λi|u

Transform

Littlewood-Paley g-function and Radon Transform on the Heisenberg Group by Fang, Zheng; He, Jianxun (2018) - The research of Radon transform has made important influence due to its wide applications to partial differential equations, X-ray technology, radio astronomy and so on. The combination of Radon transform and wavelet transform has proved to be very useful both in pure mathematics and applied science. Keywords: radon; transform
A Generalization of Integral Transform by Barnes, Benedict; Sebil, C.; Quaye, A. (2018) - In this paper, the generalization of integral transform (GIT) of the function G{f(t)} is introduced for solving both the differential and interodifferential equations. Introduction The role of integral transforms has been increasingly recognized in the scientific world. Keywords: transform
Hankel Transform of (q,r)-Dowling Numbers by Corcino, Roberto B.; Latayada, Mary Joy Regidor; Vega, Mary Ann Ritzell P. (2019) - Reindexing the double sum, we get ∑ φ∈TAr (k,n−k) ωA(φ) = n∑ j=k ( n j ) q−nr2([r2]q) n−j ∑ ϕ∈B̄j−k ∏ c∈ϕ ω∗(|c|) where B̄j−k is the set of all tableaux ϕ with j − k columns of weights ω∗(ji) , s}, and φ2 be a tableau with n− k − j columns whose lengths are in the set {s+ 1, s+ 2, . . Keywords: hankel; k]q; numbers; transform
Bessel type transform associated with Titchmarshâ€™s Theorem by Waphare, Balasaheb Bhagaji; Sindhe, Yashoda S. (2021) - 2020 Mathematics Subject Classifications: 42A38, 42B37 Key Words and Phrases: Bessel operator, Bessel transform, Bessel generalized translation 1. i.e. ja−b−1 2 (t) = 2 a−b−1 2 Γ ( a−b+1 2 ) Ja−b−1 2 (t) t a−b−1 2 , where Jν is Bessel function of the first kind with ν = a−b−1 2 and Γ(x) is the Gamma function (see [1]). Keywords: bessel; transform
Decomposition of the Unitary Representation of $SL_{2}(\mathbb{R})$ on the Upper Half Plane into Irreducible Components by Alabbad, Fatimah (2024) - It is less known that there are related actions of SL2(R) on dual and double numbers which have the form z = x+ ιy, ι2 = 0 or ι2 = 1, correspondingly. A generic cycle [9], § 4.2 is the set of points (u, v) ∈ R2 defined for all values of σ by the equation k(u2 − σv2)− 2lu− 2nv +m = 0. (1) This equation is represented by a point (k, l, n,m) from a projective space P3, since for a scaling factor λ ̸= 0, the point (λk, λl, λn, λm) defines an equation equivalent to (1). Keywords: formula; representation; transform
Double Laplace-Sawi Transform by Al-Momani, Monther; Jaradat, Ali; Abughazale, Baha (2025) - 2020 Mathematics Subject Classifications: 44A05, 44A10 Key Words and Phrases: Laplace transform, Sawi transform, Double integral transform, Laplace-Sawi transform 1. Double Sawi Transform: Theory and Applications to Boundary Values Problems. Keywords: transform
The Double ARA-Sawi Transform by Abu Awwad, Raed; Al-Momani, Monther; Jaradat, Ali; Abughazaleh, Baha'; Al-Natoor, Ahmad (2025) - A new integral transform: ARA transform and its properties and applications. Double Sawi Transform: Theory and Applications to Boundary Values Problems. Keywords: transform
The Double Sumudu-Sawi Transform by Abu Awwad, Raed; Al-Momani, Monther; Abughazaleh, Baha'; Jaradat, Ali; Farah, Abdulkarim (2025) - Convolution Theorem of DS-SWT Let F (ξ, χ) represent the Heaviside unit step function, which is defined as follows: F (ξ − u, χ− v) = { 1, ξ > u and χ > v 0, otherwise We have SξWχ(h(ξ − u, χ− v)F (ξ − u, χ− v)) Keywords: transform
Modified Laplace-type Transform and Its Properties by Ege, Inci (2025) - 2020 Mathematics Subject Classifications: 44A10, 44A20, 34A25, 44A05 Key Words and Phrases: Laplace transform, Laplace-type integral transform, modified degen- erate Gamma function, integral equation 1. Then the integral G∗ α,λ{f(t)} = uα ∫ ∞ 0 (1 + λ)− t uλ f(t) dt (7) is said to be the modified Laplace-type transform G∗ α,λ of f(t) provided that the integral in (7) exists. Keywords: laplace; ln(1; transform
On the Degenerate Sadik Transform by Mohamadali, Jamilon; Abdulcarim, Normalah S. (2025) - [( (1 + λ(R)) −uα λ +2 −uα + 2λ − (1 + λ(R)) −uα λ +1 −uα + λ ) − ( (1) −uα λ +2 −uα + 2λ − (1) −uα λ +1 −uα + λ )] = 1 uβλ − ( 1 −uα + 2λ − 1 −uα + λ ) for −uα λ + 2 < 0 = 1 uβλ ( 1 uα − 2λ − 1 uα − λ ) = u−β (uα − 2λ)(uα − λ) . The degenerate Sadik transform of the function f(t) = t is given by Sλ{t} = u−β (uα − 2λ)(uα − λ) , for −uα λ + 2 < 0. (11) Proof. Keywords: degenerate; transform

Optimization

A hybridization of the Hestenes-Stiefel and Dai-Yuan Conjugate Gradient Methods by Laylani, Yoksal; Khudhur, Hisham M.; Nori, Edrees M.; Abbo, Khalil K. (2023) - A survey of nonlinear conjugate gradient methods. Hybrid conjugate gradient method The traditional numerator conjugate gradient methods ∥gk+1∥2 in relation to the up- date parameter βk (FR, DY, CD) Keywords: gradient; optimization; ytk

Ring

Skew Polynomial Rings over Weak sigma-rigid Rings and sigma(*)-rings by Bhat, Vijay; Kumari, Neetu; Gosani, Smarti (2013) - Krempa in [9] introduced σ-rigid rings; Kwak in [10] introduced σ(∗)-rings and Ouyang in [14] introduced weak σ-rigid rings, where σ is an endomorphism of ring R. These rings are related to 2-primal rings. Key Words and Phrases: Automorphism, σ(∗)-ring, weak σ-rigid ring, 2-primal ring 1. Keywords: ring
Skew-Laurent Rings over $\sigma(*)$-rings by Bhat, Vijay (2014) - We note that the condition that P ∈ Min.Spec(O(R)) implies that P ∩ R ∈ Min.Spec(R) can not be ignored as follows: Let R = Q×Q. Let σ : R→ R be defined by σ((a, b)) Skew Polynomial Rings Let R be a ring, σ be an endomorphism of R and δ a σ-derivation of R. Recall that δ is an additive map δ : R→ R such that δ(ab) = δ(a)σ(b) + aδ(b), for all a, b ∈ R. Example 3. Keywords: ring
Transparency of Polynomial Ring Over a Commutative Noetherian Ring by Bhat, Vijay Kumar; Chib, Kiran (2015) - R[x;σ,δ] is Noetherian ring by Hilbert Basis Theorem, namely Theorem (1.12) of Goodearl and Warfield Ring extensions and their quotient rings, East-West Journal of Mathematics, 9(1), 25-30. 2007. Keywords: ring
Weak PS-rings over Skew Hurwitz Series by Farahat, Mohamed A.; Al-Bogamy, Salha T. (2018) - Math, 11 (1) (2018), 244-259 250 Lemma 2. Let R be an NI-ring, L a maximal right ideal in R and R = R /nil (R) . Thus a = 0 which implies that `R ( L ) = (0) and we conclude that R = R /nil (R) is a right PS-ring. Case (2): Assume that NR(L) Keywords: left; right; ring; ring r
Generalization of Schur's Lemma in Ring Representations on Modules over a Commutative Ring by Hijriati, Na'imah; Wahyuni, Sri; Wijayanti, Indah Emilia (2018) - Further- more, this representation µ of ring R on module M is called an f -representation of R and M is called an f -representation module of R. Note that prefix f in ”f -representation” depends on a ring homomorphism f : R→ S we choose. From the previous paragraph, we have been knowing that the f -representation module of ring R is a module over R-algebra S. Keywords: module; ring
On Weak Graded Rings II by Al-Subaie, Najla SH.; Al-shomrani, Mohammed Mosa (2019) - If rk = 0, for some k ∈ K and r ∈ R, then there is an element k′ ∈ K such that k′r = 0. (ii) For r ∈ R and k ∈ K, there are elements r′ ∈ R and k′ ∈ K such that k′r = r′k. Keywords: ring
Near Ring Multiplications on a Modified Near Module Over a Near Ring by Ramakrishna, A. V.; Prasanna, T.V.N.; Lakshmi, D.V. (2021) - 2020 Mathematics Subject Classifications: 16Y30 Key Words and Phrases: Near ring, near module, semilinear map 1. Near ring Multiplication On a Modified Near Module Keywords: module; near; ring
Ore Extension Rings Satisfy the Weak PS-Rings by Farahat, Mohamed; Al-Bogamy, Salha (2021) - Given a module MR, an endomorphism α : R −→ R and an α- derivation δ : R −→ R. We say that MR is α-compatible if for each m ∈M and r ∈ R, we have mr = 0⇔ mα(r) = 0. Let R be a ring with identity 1 and α an endomorphism of R. Then a map δ : R −→ R is called an α-derivation of R if δ (a+ b) = δ (a) + δ (b) and δ (ab) = δ (a) b+ α (a) δ (b) , for all a, b ∈ R. We denote by A = R Keywords: nil; ring
Derivations in Differentially δ-prime Rings by Taha, Iman; Masri, Rohaidah ; Alkhalaf, Ahmad; Tarmizi, Rawdah (2022) - 2020 Mathematics Subject Classifications: 16N60, 16W25 Key Words and Phrases: Derivation, prime ring, δ-prime ring, δ-ideal. In particular, we prove that if R is a δ-prime ring with charR 6= 2 and I is a nonzero δ-ideal of R, where 0 6= δ ∈ D, c ∈ R and [c, δ(c)] in the center of R, then R is commutative. Keywords: prime; ring
Involution t–Clean Rings with Applications by Ahmad, Shaimaa; AL-Neima, Mohammed; Ali, Ahmed; Mahmood, Raida (2022) - This class called involution t-clean rings, which is a generalization of invo-clean rings and subclass of clean rings. 2020 Mathematics Subject Classifications: 16E50, 16U99, 05C25 Key Words and Phrases: Clean ring, invo-clean ring, tripotent element, Hosoya polynomial, Wiener index 1. Keywords: clean; invo; ring
Strongly 2-Nil Clean Rings with Units of Order Two by M.Salim, Renas; Shuker, Nazar (2023) - Let n ∈ Nil(R), then n = Σ1−Σ2+u, implies Σ1 − Σ2 = n − u, since n − u ∈ U(R), according to Proposition 3(3), (Σ1 − Σ2) 2 = 1. = (Σ1 − Σ2) 4 + (Σ1 − Σ2) 3 − (Σ1 − Σ2) 2 + (Σ1 − Σ2) 3 + (Σ1 − Σ2) 2 − (Σ1 − Σ2)− (Σ1 − Σ2) 2 − (Σ1 − Σ2) + 1 = (Σ1 − Σ2) 2 + (Σ1 − Σ2)− (Σ1 − Σ2) 2 + (Σ1 − Σ2) + (Σ1 − Σ2) 2 − (Σ1 − Σ2)− (Σ1 − Σ2) 2 − (Σ1 − Σ2) + 1 = 1. R. T. M.Salim, N. H. Shuker / Eur. Keywords: ring
The Reflexive Condition on Skew Monoid Rings by Ali, Eltiyeb (2023) - =  nil(R) R R · · · R 0 nil(R) R · · · R 0 0 nil(R) · · · R ... ... ... . . . 2020 Mathematics Subject Classifications: 16S34, 16S36, 20M25 Key Words and Phrases: Left APP -ring, skew monoid ring R ∗M , quasi Armendariz ring, σ-skew strongly M -nil-reflexive ring 1. Keywords: monoid; nil(r; reflexive; ring; skew
Generalized Reflexive Structures Properties of Crossed Products Type by Ali, Eltiyeb (2023) - [23], for each j and k, there exist dj , ek ∈ R and regular s, t ∈ R such that u−1bj = djs −1 REFERENCES 2167 and (vs)−1ck = ekt −1. In particular, if M = (N ∪ {0},+) and both f and ω are trivial, then R is strongly CM -reflexive if and only if R is strongly reflexive. Keywords: -reflexive; monoid; ring
Extending Abelian Rings: A Generalized Approach by Saad, Muhammad; Zailaee, Majed (2024) - On idempotent reflexive rings. An idempotent of a ring R is considered central if it is both left and right semicentral, and the set of central idempotents is denoted B(R) = Sl(R)∩Sr(R). Keywords: abelian; central; idempotent; ring; ring r
Exploring Ideals: An Analysis Through Rough Set Theory with Examples by Prakash, Anand ; Shukla, Rahul (2025) - Kuroki has conducted research on rough ideals in semigroups [11]. We also explore the concept of rough ideals, offering a precise definition to facilitate understanding. Keywords: ideals; ring; set; theory; z12
NJ-Abelian Rings: an Abelian-Like Approach by Saad, Muhammad; Abdelwahab, Samia (2025) - For rings R and S, letM and N be (R,S)-bimodule and (S,R)-bimodule, respectively. The next examples show that the classes of NJ-abelian rings and abelian rings are independent. Keywords: abelian; j(r; n(r; proposition; ring
Ore Extensions over Weak (Sigma)-rigid Rings and (sigma(*))-rings by Bhat, Vijay Kumar (2010) - 2000 Mathematics Subject Classifications: 16S36, 16P40, 16P50, 16U20,16W25 Key Words and Phrases: Automorphism, σ(∗)-ring, weak σ-rigid ring, 2-primal ring 1. We also discuss skew polynomial rings over weak σ-rigid rings. Keywords: ring
On the Structure of Commutative Rings with ${\bf {p_1}^{k_1}\cdots {p_n}^{k_n} Zero-Divisors by Behboodi, Mahmood; Beyranvand, R. (2010) - pn kn zero-divisors it suffices to deal with local rings with pi ti zero-divisors where that 1 ≤ i ≤ n and 0 ≤ t i ≤ ki , and henceforth we focus on rings R with |Z(R)| = pk where p is a prime number and k ≥ 1. In Section 3, first we characterize commutative rings R with |Z(R)|= pk where 1≤ k ≤ 7. Keywords: ring

Fluid

Peristaltic Flow of Newtonian Nanofluid Through Inclined Annulus Cylinder by Abdellateef, Ahmed Ibrahim; Syed, Zahoor ul haque Ishaque (2016) - We choose a cylindrical coordinate system (r ′, z′), where z′-axis lies along the centerline of the inner and outer tubes and r ′ is the distance measured radially. The problem has been studied in cylindrical coordinate system (r ′, z′), radial, and axial coordinates respectively, introducing a wave frame (r ′, z′) moving with velocity C away from the fixed frame (R′, Z ′) by the transformations. Keywords: fluid; ∂ r; ∂ z
Twice Order Slip on the Flows of Fractionalized MHD Viscoelastic Fluid by Jamil, Muhammad; Ahmed, Israr (2019) - [17] presented the exact analytical solutions in terms of generalized G and R functions for fractionalized Maxwell fluid flow because of oscillating and regularly quickening plate and examined that velocity is the function of frequency of oscillating plate, increasing for cosine and decreasing for sine oscillations. Twice order slip in fractional Maxwell fluid using Caputo operator is numerically analyzed by Aman Keywords: + i+j+k; fluid; j ∞∑; k ∞∑; y√ ν; θ1√ ν; ν ∞∑; −l,0),(1 +; −θ2 ν; ∞∑ i=0; ∣∣∣∣(1+i−j,0),(1 +
The Axisymmetric Migration of an Aerosol Particle Embedded in a Brinkmann Medium of a Couple Stress Fluid with Slip Regime by El-Sapa, Shreen; A. Almoneef ‎, Areej (2022) - Additionally, the theory of couple stress fluid flow introduces nonlin- ear terms in the relationship between shear stresses and velocity gradients. Couple stress fluid flow due to slow steady oscillations of a permeable sphere. Keywords: cot; couple; fluid; sin; slip; stress; α2a; θ r
Heat Transfer and Magnetohydrodynamic Nanofluid Flow Caused by a Stretching Sheet Heated Convectively: Numerical Investigation by Adel, Mohamed; Khader, M. M.; Babatin, M. M.; Alraddadi, I. ; Alaidrous, A. ; Ismail, G. M. (2025) - DOI: https://doi.org/10.29020/nybg.ejpam.v18i1.5502 Email addresses: m.adel@iu.edu.sa and adel@sci.cu.edu.eg (M. Adel), mmkhader@imamu.edu.sa (M. M. Khader), mmbabatin@imamu.edu.sa (M. M. Babatin), ialraddadi@iu.edu.sa (I. Alraddadi), aaaidrous@uqu.edu.sa (A. Alaidrous), gamalm2010@yahoo.com (G. M. Ismail) https://www.ejpam.com 1 [16] M. M. Khader and M. M. Babatin. Keywords: concentration; fluid; heat; nanofluid; parameter; temperature; transfer; θ(η; ϕ(η
Thermal and Concentration Analysis of Mucociliary Johnson-Segalman Fluid Flow in Chronic Obstructive Pulmonary Disease by Alaidrous, Amel; Ashraf, Hameed (2025) - We use respectively the k = A and k = P in the superscript to repre- sent the ACL and PCL. (55) for k = P yield respectively the ACL and PCL velocities. Keywords: acl; airway; ashraf; concentration; dxp0; fluid; mucus; pcl; temperature; velocity

Algorithm

A Modified AES-512 Bits Algorithm for Data Encryption by Owusu Bempah , Kwame ; Baah Gyamfi, Kwasi; Boateng, Francis Ohene; Owusu-Mensah, Isaac (2024) - This paper therefore focuses on developing a new AES-512 bits symmetric encryption algorithm through modification of the conventional AES-128 algorithm to be used purposefully in the classroom for document transfer. Further, in [1], a 4D teserract symmetric block was redesigned to be of good territory for the manufacture of encryption keys, and four rounds and other sub rounds are engaged to shift the teserract to be able to randomly produce some of the encryption keys. Keywords: algorithm; encryption
Double Inertial Krasnosel'skii-Mann-Type Method for Approximating Fixed Point of Nonexpansive Mappings by Akuchu, Besheng George; Ezeafulukwe, Uzoamaka; Aphane, Maggie; Ugwunnadi, Godwin; Asanya, Chukwuebuka Malachi (2024) - − bn||2 ≤ αn(1− αn)||T cn − bn||2 ≤ [||an − p||2 − ||an+1 − p||2] +[||an−1 − p||2 − ||an − p||2]. [ ∥an − p∥2 + tn(∥an−1 − p∥2 − ∥an − p∥2) −tn(1− tn)∥an − an−1∥2 ] +αn [ ∥an − p∥2 + rn(∥an−1 − p∥2 − ∥an − p∥2) −rn(1− rn)∥an − an−1∥2∥2 ] − αn(1− αn)||T cn − bn||2. Keywords: algorithm; inertial; nonexpansive; p||2
Efficient Viscosity Algorithms for Solving the Split Equality Fixed-Point Problem by Mohammed, Lawan; Kilicman, Adem; Bamanga, D. (2025) - (iv) Directed if ∥T1y − z∥2 ≤ ∥y − z∥2 − ∥T1y − y∥2,∀y ∈ H1 and z ∈ Fix(T1). Similarly, lim sup n→∞ ∥zn − U2zn∥ = 0. (23) On the other hand, ∥A1yn −A2zn∥2 = ⟨A1yn −A2zn,A1yn −A2zn⟩ = ⟨A1yn −A2zn,A1yn −A1y⟩+ ⟨A2zn −A1yn,A2zn −A2z⟩ , = ⟨A∗ 1(A1yn −A2zn), yn − y⟩+ ⟨A∗ 2(A2zn −A1yn), zn − z⟩ ≤∥A∗ 1(A1yn −A2zn) + (yn − U1yn)− (yn − U1yn)∥∥yn − y∥∥ + ∥A∗ 2(A2zn −A1yn) + (zn − U2zn)− (zn − U2zn)∥∥zn − z∥ ≤∥A∗ 1(A1yn −A2zn)− (yn − U1yn)∥∥yn − y∥ + ∥yn − U1yn∥∥yn − y∥ + ∥A∗ 2(A2zn −A1yn)− (zn − U2zn)∥∥zn − z∥ + ∥zn Keywords: 1(a1yn; algorithm; y∥2; z∥2
Fixed Point Techniques for Graph-Based Mappings with Image Recovery Approach by Panma, Sayan; Suparatulatorn, Raweerote; Chaobankoh, Tanadon (2025) - ∥xn − x∗∥2 + 2|βn|∥xn − xn−1∥∥dn − x∗∥ − (1− σi n)η i n(1− µi n)µ i n∥dn − Jidn∥2. Now, for any i = 1, 2, . . . , N, from Proposition 1, we have the inequalities: ∥Jicin − x∗∥2 ≤ ∥cin − x∗∥2 = ∥(1− µi n)dn + µi nJidn − x∗∥2 = ∥(1− µi n)(dn − x∗) + µi n(Jidn − x∗)∥2 = (1− µi n)∥dn − x∗∥2 + µi n∥Jidn − x∗∥2 − (1− µi n)µ i n∥dn − Jidn∥2 ≤ (1− µi n)∥dn − x∗∥2 + µi n∥dn − x∗∥2 − (1− µi n)µ i n∥dn − Jidn∥2 = ∥dn − x∗∥2 − (1− µi n)µ i n∥dn − Jidn∥2, and ∥Jibin − x∗∥2 ≤ Keywords: algorithm; gmsd; − x∗∥2

Disease

Modelling and Simulating a Transmission of COVID-19 Disease: Niger Republic Case by Oumarou, Abba Mahamane; Bisso, Saley (2020) - On the definition and compu- tation of the basic reproduction ratio r0 in the model of infectious disease in hetero- geneous populations. Pλ = (µ+ λ)(λ5 + a1λ 4 + a2λ 3 + a3λ 2 + a4λ+ a5), (17) with: a1 = 5µ+ µ1 + α+ α1 + α2 + γ + θ1 + θ2 + θd > 0, (18) a2 = (µ+α)(µ+α1 +α2) + (2µ+α+α1 +α2)(2µ+ γ + θ1 + θ2) + (2µ+α+α1 +α2)× (µ+ µ1 + θd) + (µ+ γ)(µ+ θ1 + θ2) + (2µ+ γ + θ1 + θ2)(µ+ µ1 + θd) + αβ > 0 (19) a3 = (µ+α)(µ+α1 +α2)(2µ+γ+θ1 +θ2)+(µ+α)(µ+α1 +α2)(µ+µ1 +θd)+(µ+γ)× (µ+θ1 +θ2)(2µ+α+α1 +α2)+(2µ+α+α1 +α2)(2µ+γ+θ1 +θ2)(µ+µ1 +θd)+(µ+γ)× (µ+ θ1 + θ2)(µ+ µ1 + θd) + αβ(3µ+ µ1 + γ + θ1 + θ2 + θd − α1 − 1) > 0 (20) a4 = (µ+ α)(µ+ α1 + α2)(µ+ γ)(µ+ θ1 + θ2) + (µ+ α)(µ+ α1 + α2)(µ+ µ1 + θd)× (2µ+γ+θ1+θ2)+(µ+γ)(µ+θ1+θ2)(µ+µ1+θd)(2µ+α+α1+α2)+αβ(µ+θ1+θ2)(µ+µ1+θd) + αβ(2µ+ µ1 + θ1 + θ2 + θd)(µ+ γ)− αβθ2α2 − αβα1(2µ+ µ1 + θ1 + θ2 + θd) − αβ(2µ+ µ1 + γ + θd) > 0 (21) A. M. Oumarou, S. Bisso / Eur. Keywords: disease; figure
Estimating the Basic Reproductive Number of COVID-19 Cases in Ghana by Otoo, Dominic; Donkoh, Elvis Kobina; Kessie, Justice Amenyo (2021) - They are called disease compartments if the individuals therein are infected, and nondisease compartment if the vice versa is the case. Let x = (x1, ..., xn)T ∈ Rm and y = (y1, ..., ym)T ∈ Rn represent the populations in disease compartments and nondisease compartments, respectively; F = (F1, ...,Fn)T and V = (V1, ...,Vn)T, where Fi represents the rate of new infections in the ith disease compartment; and Vi represents the transition terms, for example, death and recovery in the ith disease compartment. Keywords: compartment; covid-19; disease; individuals; number; rate; reproductive; transmission
Stochastic Dynamics of Epidemic Models with Resource Constraints: Extinction and Ergodicity by Amalraj, J. Leo ; Balamurugan, Manivannan ; Avinash, N.; Shukla, Pankaj ; Rajesh, M. V.; Govindan, Vediyappan; Donganont, Siriluk (2025) - Unlike clas- sical deterministic models that exhibit backward and Hopf bifurcations, stochastic models incorpo- rating white noise perturbations capture more realistic outbreak scenarios by smoothing transitions and expanding extinction regions. In epidemiology, stochastic models enhance the understanding of irregular epidemic patterns, such as those observed in COVID-19, by accounting for demographic noise and environmental disturbances Keywords: disease; epidemic; lim; models; stochastic

Σ1σ2

Upper and Lower almost Weak (Ï„1, Ï„2)-continuity by Boonpok, Chawalit; Viriyapong, Chokchai (2021) - Preliminaries Throughout the present paper, spaces (X, τ1, τ2) and (Y, σ1, σ2) (or simply X and Y ) always mean bitopological spaces on which no separation axioms are assumed unless explicitly stated. A subset A of a bitopological space (X, τ1, τ2) is called τ1τ2-semi-open [5] (resp. Keywords: σ1σ2; τ1τ2
On Weakly $(\tau_1,\tau_2)$-continuous Functions by Boonpok, Chawalit; Klanarong, Chalongchai (2024) - [10] introduced the concept of weakly continuous functions. Furthermore, several characterizations of weakly (τ1, τ2)-continuous functions are discussed. Keywords: cl(v; σ1σ2; τ1τ2
Weakly quasi $(\tau_1,\tau_2)$-continuous multifunctions by Pue-on, Prapart ; Sompong, Supannee ; Boonpok, Chawalit (2024) - = (τ1, τ2)-sInt(F +(Y − σ1σ2-Int(σ1σ2-Cl(V1))) ∩ F−(Y − σ1σ2-Int(σ1σ2-Cl(V2)))) ⊆ (τ1, τ2)-sInt(F +(Y − V1) ∩ F−(Y − V2)) EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 17, No. 3, 2024, 1553-1564 ISSN 1307-5543 – ejpam.com Published by New York Business Global Weakly quasi (τ1, τ2)-continuous multifunctions Prapart Pue-on1, Supannee Sompong2, Chawalit Boonpok1,∗ 1 Mathematics and Applied Mathematics Research Unit, Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham, 44150, Thailand 2 Department of Mathematics and Statistics, Faculty of Science and Technology, Sakon Nakhon Rajbhat University, Sakon Nakhon, 47000, Thailand Abstract. Keywords: cl(v2; σ1σ2
Upper and lower $s$-$(\tau_1,\tau_2)p$-continuous multifunctions by Viriyapong, Nongluk ; Sompong, Supannee ; Boonpok, Chawalit (2024) - A multifunction F : (X, τ1, τ2) → (Y, σ1, σ2) is said to be upper s-(τ1, τ2)p- continuous if for x ∈ X and each σ1σ2-open set V of Y containing F (x) and having σ1σ2-connected complement, there exists a (τ1, τ2)p-open set U of X containing x such that F (U) ⊆ V . For a multifunction F : (X, τ1, τ2) → (Y, σ1, σ2), the following properties are equivalent: (1) F is upper s-(τ1, τ2)p-continuous; (2) F+(V ) is (τ1, τ2)p-open in X for every σ1σ2-open set V of Y having σ1σ2-connected complement; N. Viriyapong, S. Sompong, C. Boonpok / Eur. Keywords: σ1σ2; τ2)p
Rarely $s$-$(\tau_1,\tau_2)p$-continuous Multifunctions by Kong-ied, Butsakorn ; Sompong, Supunnee ; Boonpok, Chawalit (2025) - European Journal of Pure and Applied Mathematics, 15(2):626–634, 2022. European Journal of Pure and Applied Mathematics, 15(3):1180–1188, 2022. Keywords: σ1σ2; τ2)p
Quasi $\theta(\tau_1,\tau_2)$-continuity for Multifunctions by Pue-on, Prapart ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - This paper presents new classes of multifunctions called upper quasi θ(τ1, τ2)-continuous multifunctions and lower quasi θ(τ1, τ2)-continuous multifunctions. Furthermore, several charac- terizations and some properties concerning upper quasi θ(τ1, τ2)-continuous multifunctions and lower quasi θ(τ1, τ2)-continuous multifunctions are established. Keywords: cl(v; θ(τ1; σ1σ2
Upper and Lower Weakly $s$-$(\tau_1,\tau_2)$-continuous Multifunctions by Pue-on, Prapart ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - A bitopological space (X, τ1, τ2) is said to be strongly s-(τ1, τ2)-normal if for every disjoint τ1τ2-closed sets F and K of X, there exist τ1τ2-open sets U and V having τ1τ2-connected complements such that F ⊆ U , K ⊆ V and τ1τ2-Cl(U) ∩ τ1τ2-Cl(V ) A bitopological space (X, τ1, τ2) is said to be s-(τ1, τ2)-normal if for each disjoint τ1τ2-closed sets F and K of X, there exist τ1τ2-open sets U and V having τ1τ2- connected complements such that F ⊆ U , K ⊆ V and U ∩ V = ∅. Theorem 14. Keywords: σ1σ2; τ1τ2; τ2)-continuous
Upper and Lower Quasi $\theta\tau^\star(\sigma_1,\sigma_2)$-continuity by Srisarakham, Napassanan ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - More- over, several characterizations and some properties concerning upper quasi θτ⋆(σ1, σ2)-continuous multifunctions and lower quasi θτ⋆(σ1, σ2)-continuous multifunctions are considered. We also investigate several characterizations of upper quasi θτ⋆(σ1, σ2)-continuous multifunctions and lower quasi θτ⋆(σ1, σ2)-continuous multifunctions. 2. Keywords: cl(v; set; σ1σ2
Weak Forms of $\mu(\sigma_1,\sigma_2)$-continuity for Multifunctions by Chiangpradit, Monchaya ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - In this section, we introduce the concepts of upper weakly µ(σ1, σ2)-continuous mul- tifunctions and lower weakly µ(σ1, σ2)-continuous multifunctions. For a multifunction F : (X,µ) → (Y, σ1, σ2) such that F (x) is a σ1σ2- regular σ1σ2-paracompact set of Y for each point x ∈ X, the following properties are equivalent: (1) F is upper µ(σ1, σ2)-continuous; (2) F is upper almost µ(σ1, σ2)-continuous; (3) F is upper weakly µ(σ1, σ2)-continuous. Keywords: set; σ1σ2

Algebra

Koszul Duality for Multigraded Algebras by Hawwa, F. T.; Hoffman, J. William; Wang, Haohao (2012) - = M for p = 0 and zero otherwise. = M for all i. The case when i = 0 is trivial since F0G(M) Keywords: algebra
(-1)-weak amenability of Unitized Banach Algebras by Valadkhani, Arezou; Hosseinioun, Alireza (2016) - Let A be a Banach algebra and A′′ be its second dual, for each a, b ∈ A, f ∈ A′ and F, G ∈ A′′ we define f · a, a · f and F · f , f · F ∈ A′ by f · a(b) = f (a · b), a · f (b) = f (b · a) F · f (a) =F( f · a), f · F(a) = F(a · f ). = δλ1 (F), for F ∈ A′′ (Note that since A#′ = A′ ⊕Ce′, λ0 ∈ A′ and α0 ∈ C are unique and H1(A′′,A#′) = H1(A′′#,A#′) Keywords: algebra; a′′; banach
States on Pseudo-BCI Algebras by Xin, Xiao Long; Li, Yi Jun; Fu, Yu Long (2017) - Moreover by Proposition 12, y ∗ x ∈ V (0) and so 0 ◦ (y ∗ x) = 0, and (y ◦ (y ∗ x)) ∗ y = (y ∗ y) ◦ (y ∗ x) = 0 ◦ (y ∗ x) = 0. y = y ◦ (y ∗x) ≤ x. Keywords: algebra; bci; pseudo
Linear Essential Spectrum Compressors by Outouzzalt, Hassan (2017) - Let ϕ : A→ B be a surjective up to inessential elements linear map, and consider the following statements. Let ϕ : A→ B be a surjective up to inessential elements linear map, and consider the following statements. Keywords: algebra; fredholm; linear; spectrum
The DG Poisson Adjoint Action and its Application by Li, Xiaojie; Hu, Xianguo; Lv, Jiafeng; Wang, Xingting (2019) - REFERENCES 23 [4] A. S. Cattaneo, D. Fiorenza and R. Longoni, Graded Poisson algebras, Encyclope- dia Math. Math, 12 (1) (2019), 14-24 15 given the definition of a DG Poisson Hopf algebra A, and discussed the structures for the universal enveloping algebra of A. Considering the importance of DG Poisson Hopf algebras and DG Poisson modules, our aim in this paper is to study the DG Poisson adjoint action on M , where M is a DG Poisson modules over a DG Poisson Hopf algebras A. Keywords: algebra; dg poisson; poisson
On B-ideals in a Topological B-Algebra by Belleza, Katrina Eusebio; Vilela, Jocelyn (2020) - Suppose x ∗ y ∈ U ∈ τ . Suppose x ∗ y ∈ U(x ∗ y) where x, y ∈ X. By Theorem 10, there exists G ∈ K such that G[[x ∗ y]] ⊆ U(x ∗ y). Keywords: algebra
On the E-infinity Algebras by Mohamed, Alaa Hassan; Abo Quota, Samar Abd-Elbaset (2021) - The exact triangle sequence, M f−→ N −→ Cf −→ ∑ M prompts a triangulation of the derived category, for a map f :M−→ N . The functor, Mod∞A −→ ComcB∞(A),M −→ B∞M exists. Keywords: algebra; category; definition; infinity; morphisms
Soft Hyper-GR Algebra by Engcot, Mark Kenneth; Petalcorin, Gaudencio Jr. (2022) - Let S = F (0) = F (1) = {0, 1}. Let A = H and let F : A → P (H) be the set-valued function defined as follows: F (a) = ⋃ B⊂H,aR̊B⇔x⊛0≪B B, where B ⊂ H and define a relation R̊ such that aR̊B if and only if x⊛ 0 ≪ B and a ∈ A. Then F (0) = F (1) = F (2) = {0, 1, 2} = H. Keywords: algebra; hyper; let
Algebras Satisfying Polynomial Identity of Degree Six that are Principal Train by Kabré, Daouda; Conseibo, André (2023) - For x = e + x0 + xλ + xλ̄, we have x2 = e + 2λxλ + 2λ̄xλ̄, x 3 = e − 3xλ − 3xλ̄, x 4 = e− 2λxλ − 2λ̄xλ̄, x 5 = e+ (2λ+ 3)xλ + (2λ̄+ 3)xλ̄. The algebra A is a principal train algebra of rank 4, with principal train polynomial X(X − 1)(X − λ1)(X − λ2) where λ1 and λ2 different and different from 1 2 , if and only if: 1) Keywords: algebra; train
On the Self-injectivity and CM-free of an Artin Algebra with Radical Cubic Zero by Laaraj, Mounir; Abdelalim, Seddik (2024) - An important invariant in our subject is the radical square of the projective cover of the first syzygy of each simple A-module and each Gorenstein-projective A-module that we consider here to be 0, so by a formula characterizing the calculation of the radical of syzygy of an indecomposable A-module of Lowey length 2, that is to say from the square radical 0, we will extend this calculation to a Gorenstein-projective A-module and by char- acterization of the latter, we construct a family (Si)i∈J of simple A-modules non-projective and Gorenstein-projective and the family (Pi)i∈J of projective modules such that each Pi is associated to Si. An A-module M in mod(A) is said Gorenstein-projective provided that there is a totally acyclic complex (P⋆) of projective modules such that its 0-th cocycle Z0(P⋆) is isomorphic to M . Keywords: algebra; gorenstein; module; projective
One Resolution of the Conjecture between the Projective Dimension of a Simple Module S of an Artinian Ring on Zero Radical’s Cube and the First Bifunctor Extension on S by Laaraj, Mounir; Abdelalim, Seddik; Elmouki, Ilias (2024) - Here are the calculations of the projective resolutions of simple modules (S(i))1≤i≤5, 0 −→ P (3)⊕ P (4) −→ P (2)2 −→ P (1) −→ S(1) −→ 0 REFERENCES 1867 0 −→ P (3)⊕ P (4) −→ P (2) −→ S(2) −→ 0 0 −→ P (5) −→ P (3) −→ S(3) −→ 0 0 −→ P (5) −→ P (4) −→ S(4) −→ 0 0 −→ P (5) −→ P (4) −→ S(5) −→ 0 = 0 because S(1) is an injective module and we have, 0 −→ P (5) −→ P (4) −→ P (2) −→ P (1) −→ S(1) −→ 0 which implies that pd(S) = 3 7.2. Keywords: algebra; conjecture; module; projective
Topological Homomorphisms in a Topological Dual B-Algebra by Nuñez, Rashin; Fuentes, Katrina (2025) - [x′]J ∈ W} = {[x′]S ∈ X/S | x′ ∈ Ψ−1(W )} = {Φ(x′) ∈ X/S | x′ ∈ Ψ−1(W )} = Φ(Ψ−1(W )) Let [a]S , [b]S ∈ X/S and W be a neighborhood of [a]S ∗ [b]S . Keywords: algebra
Implicative and Positive Implicative Ideals of Neutrosophic INK-algebras by Mounikalakshmi, Remala ; Tamma, Eswarlal ; Uppuluri, Venkata Kalyani ; Iampan, Aiyared; T. (2025) - [11] studied the idea of fuzzy implicative ideals and constructed a fuzzy characteristic implicative ideal in BCK-algebras. [12] introduced the concept of fuzzy implicative ideals in BL-algebras, and they state several properties of it. Keywords: algebra; implicative; ink
A Topological Structure on d-algebras by Abdulqader, Maha; Khalaf, Alias B. (2025) - If W is an open set not containing 0, then for each distinct elements ζ, η ∈ W with ζ ⊙ η ∈ W there exist two disjoint b-open sets containing ζ and η. Proof. For each subset M of a Tbd-algebra W and any element ζ ∈ W, the following statements are true: (i) Clb(M)⊙ ζ ⊆ Cl(M ⊙ ζ). Keywords: algebra
On Edge Q-algebras by Anantayasethi, Ananya; Saengsura, Kittisak; Susanti, Yeni; Sarasit, Napaporn (2025) - Then we obtain the following Cayley table: x1 x2 x3 … xi−1 xi xi+1 … xn x1 x1 x1 x1 … x1 x1 x1 … x1 x2 x2 x1 x1 ∨ x2 … We explore some properties of edge Q-algebras. Keywords: algebra; edge
Group-Derived and Non-Group-Derived Dual $BG$-Algebra by Chan, Clive Martin; Fuentes, Katrina (2025) - So, x ◦ y = x−1 ∗ y for any x, y from a group (X, ∗, 1) where 1 is the identity element. Define the binary operation “∗” as x ∗ y = y ◦ x for all x, y ∈ X. Keywords: algebra; y ◦

Rate

European Call Option under Stochastic Interest Rate in a Fractional Brownian Motion with Transaction Cost by Sumalpong, Felipe Jr Raypan; Lauron, Eric G. (2024) - This paper deals on the valuation of European call option price in a stochastic environ- ment by employing three factors which are the stochastic model of the asset value, the stochastic interest rate and the transaction cost. If the number of assets traded during the time interval [t, dt] is v, then E[|v|] = √ 2 π (dt)H (( ∂2V ∂X2 )2 σ2XX 2(t) + ( ∂2V ∂r∂X )2 σ2r + 2ρσXσrX(t) ∂2V ∂X2 ∂2V ∂r∂X ) 1 2 where V (t) is the option price, X(t) is the market price of the asset at time t, r(t) is the interest rate that follows the fractional Hull-White model with Hurst parameter H, σX is the volatility of the asset price, σr is the volatility of the interest rate and ρ is the correlation coefficient between the interest rate and the asset price. Keywords: interest; price; rate; ∂2v

Numbers

On Some Properties of Liouville Numbers in the non-Archimedean Case by Menken, Hamza; Asan, Abdulkadir (2013) - Let � an � be a sequence of p-adic integers such that νp � an � < νp � an+1 � (1) for every n, and νp � an+1 � ≥ n1+ε (2) for fixed ε > 0 and n> n0 (ε). Then, 0< � �α− Sn � � 1 n p = � � � � � ∞ ∑ i=1 an+i � � � � � 1 n p = h max n � �an+1 � � p , � �an+2 � � p , . . . Keywords: liouville; numbers; sn �; � �
Application of Probabilistic Method on Daehee Sequences by Liu, Chang; Bao, Wuyungaowa (2018) - Similarly, D̂ (k) n = D̂ (k) n,1 are higher-order Daehee numbers of the second kind, D̂n,ξ = D̂ (1) n,ξ are twisted Daehee numbers of the second kind, and D̂n = D̂ (1) n,1 are Daehee numbers of the second kind. (1) In special case, when x = 0, D (k) n,ξ = D (k) n,ξ(0) are called twisted Daehee numbers of order k. Keywords: numbers
Some Theorems on Tauber's Generalized Stirling, Lah and Bell Numbers by Corcino, Roberto Bagsarsa; Corcino, Cristina Bordaje; Rama, Gladys Jane (2019) - Tauber’s generalized Stirling numbers of the first and second kind satisfy the following orthogonality relation for a given sequence of polynomials Qk(x, n), n∑ m=s C m k,nD s k,m = n∑ m=s D m k,nC s k,m = δsn = { 0, if n 6= s 1, if n = s where k = 1, 2. R. Corcino, C. Corcino, G. Rama / Eur. (28) Substitute (28) into (4), then Qk(x, n) = n∑ m=0 C m k,nx m = n∑ m=0 C m k,n m∑ s=0 D s k,mQk(x, s) = n∑ m=0 m∑ s=0 C m k,nD s k,mQk(x, s) = n∑ s=0 { n∑ m=s C m k,nD s k,m } Qk(x, s). Keywords: n(m+; numbers
The r-Dowling Numbers and Matrices Containing r-Whitney Numbers of the Second Kind and Lah Numbers by Corcino, Roberto Bagsarsa; Montero, Charles; Montero, Maribeth; Ontolan, Jay (2019) - Now, we can rewrite the sum in (21) as Gn,β,r = S0 + S1 + S2 + . . These formulas imply two matrix relations involving r-Dowling numbers, r-Whitney numbers of the second, r-Whitney-Lah numbers and Lah numbers. Keywords: numbers; r[n; whitney
On Weak Projectivity in Arithmetic by Burgin, Mark (2019) - Abstract prearithmetics with weak projectivity relations for addition form the category AAWP where objects are abstract prearithmetics and morphisms are weak projectivity relations between additions. Abstract prearithmetics with weak monoprojectivity relations for addition form the category AAWMP where objects are abstract prearithmetics and morphisms are weak monoprojectivity relations between additions. Keywords: abstract; addition; multiplication; numbers; operation; prearithmetic; projective; projectivity; proposition; respect
Hankel Transform of the Second Form (q,r)-Dowling Numbers by Corcino, Roberto Bagsarsa; Ontolan, Jay; Rama, Gladys Jane (2019) - = 0, which implies dn,q = Fr,q([x]nq hn,q(x, a, r,m)) In [14], the authors have also tried to derive the Hankel transform of the sequence of q-analogue of (r, β)-Bell numbers. Keywords: hankel; numbers; q(x
Generalized Norlund and Norlund-type Means of Sequences of Fuzzy Numbers by Pattanaik, Pradosh Kumar; Paikray, Susanta Kumar; Jena, Bidu Bhusan (2020) - In this article we study some properties of generalized Nörlund and Nörlund-type means of sequences of fuzzy real numbers. We establish necessary and sufficient conditions for our purposed methods to transform convergent sequences of fuzzy real numbers into convergent sequences of fuzzy real numbers which also preserve the limit. Keywords: numbers
Explicit Formulas for the First Form (q,r)-Dowling Numbers and (q,r)-Whitney-Lah Numbers by Corcino, Roberto Bagsarsa; Ontolan, Jay; Lobrigas, Maria Rowena (2021) - Math, 14 (1) (2021), 65-81 77 = 1 qr+nm ([t]q − [r + nm]q) n∑ k=0 wm,r[n, k]q[t] k q = 1 qr+nm ( n∑ k=0 wm,r[n, k]q[t] k+1 q − n∑ k=0 [r + nm]qwm,r[n, k]q[t] k q ) = 1 qr+nm ( n+1∑ k=0 wm,r[n, k − 1]q[t] k q − n+1∑ k=0 [r + nm]qwm,r[n, k]q[t] k q ) = n+1∑ k=0 1 qr+nm (wm,r[n, k − 1]q − In this paper, a q-analogue of r-Whitney-Lah numbers, also known as (q, r)-Whitney- Lah number, denoted by Lm,r[n, k]q is defined using the triangular recurrence relation. Keywords: k]q; numbers; r[n
On Salem Formal Power Series by Dammak, Oussama ; Mansour, Saber (2022) - The set of the so called, Pisot numbers, is usually denoted by S, it is denoted by T , the set of Salem numbers. Math, 15 (3) (2022), 1321-1330 1322 while Salem numbers are referred to as T−numbers. Keywords: numbers; pisot; salem
A Pegagogical Study of Geometric Relations between the Sums of Cubic Integer Numbers and the Sums of Square Integer Numbers with the Sums of Odd Numbers by Kobayashi, Yukio (2022) - The formula n∑ k=1 k3 = ( n∑ k=1 k )2 can be proved pictorially by expressing square numbers as sums of consecutive odd numbers, with slightly different diagrams from those of well-known pictorial proofs The relationship between the sum of square numbers and that of triangular numbers can pictorially be shown by expressing the square numbers as sums of consecutive odd numbers. Keywords: numbers
Using the Sum of Triangular Numbers as the most Fundamental Number of Combinations Found using Heuristic Methods by Kobayashi, Yukio (2022) - Triangular numbers The relationship between the sum of natural numbers and triangular numbers ex- pressed by (17) and (18), respectively, indicates the number of combinations, n+2C3. Square numbers The sum of natural numbers and of triangular numbers can be explained in terms of combinatorics; thus, (20) suggests that the sum of square numbers can also be implied by combinatorics, and a diagram corresponding to Figure 1 can be drawn as shown in Figure 7. Keywords: numbers; triangular
On Divisibility Property of Type 2 $(p,q)$-Analogue of $r$-Whitney Numbers of the Second Kind by Corcino, Roberto Bagsarsa; Corcino, Cristina B. (2023) - )Wm,r[n, k − 1; t]p,q + [mk + r]p,qp mt−kmq−kr−m(k2)Wm,r[n, k; t]p,q. Applying (6) consequently gives W ∗ m,r[n+ 1, k; t]p,q = W ∗ m,r[n, k − 1; t]p,q + Preliminary Results This section provides a brief discussion on some relations that are necessary in deriving the divisibility property of the type 2 (p, q)-analogue of the r-Whitney numbers of the second kind W ∗ m,r[n, k; t]p,q. Multiplying both sides of the recurrence relation in (5) by q−kr−m(k2) yields q−kr−m(k2)Wm,r[n+ 1, k; t]p,q = q−kr−m(k2)qm(k−1)+rWm,r[n, k − 1; t]p,q + q−kr−m(k2)[mk + r]p,qp mt−kmWm,r[n, k; t]p,q q−kr−m(k2)Wm,r[n+ 1, k; t]p,q = q−(k−1)r−m(k−1 2 Keywords: numbers; r[n; t]p
Some Identities on λ-Analogues of Lah Numbers and Lah-Bell Polynomials by Kim, Dae San ; Kim, Taekyun; Kim, Hyekyung ; Kwon, Jongkyum (2024) - (48) Replacing t by 1 λ(1− e−λt) in (42) and using (9), we get 1 k! 1 λk ( eλt − 1 )k ert = ∞∑ m=k Lr,λ(m, k) 1 m! ( e−λt − 1 −λ )m (49) = ∞∑ m=k Lr,λ(m, k) ∞∑ n=m { n m } −λ tn n! J. Kwon et al. / Eur. Keywords: k=0; numbers; λ(x
An Invitation to Proofs Without Words by Alsina, Claudio; Nelsen, Roger B. (2009) - We begin with some theorems and proofs about the simplest figurate numbers: triangular numbers and squares. Sums of powers of 9 are triangular numbers, i.e., for all n≥ 0, 1+ 9+ 92 + . . Keywords: aaa; figure; numbers
Some Properties of the Non-central Stirling Numbers of the Second Kind with Complex Parameters by Arlan, Erwin; Montero, Maribeth (2025) - 2020 Mathematics Subject Classifications: 05A15, 05A18, 30C15 Key Words and Phrases: Classical Stirling numbers, Non-central Stirling numbers, Complex numbers 1. Thus, following the work of Flajolet and Prodinger, it is interesting if we could extend non-central Stirling numbers of the second kind to complex arguments. Keywords: numbers
Generalized Hyperharmonic Sum via Euler's Transform by Manulat, Kristen Vera; Corcino, Roberto Bagsarsa (2025) - In this paper, we present and prove a novel expression for binomial sums involving generalized hyperharmonic numbers. Building upon this foundation, the present paper aims to derive and prove a new expression for binomial sums involving generalized hyperharmonic numbers, utilizing the Euler-type transformation approach outlined in [14]. Keywords: j=0; k=0; numbers; n∑ k=0; r−k
Integral Representations of Generalizations of Pell Num-bers and their Companion Numbers by Nilsrakoo, Weerayuth; Nilsrakoo, Achariya (2025) - Since ∆2 k = k2 + 4k − 4 = k2 + 4(k − 1) > 0 for k ≥ 2, this equation has two roots, r1 = k + ∆k 2 = σk and r2 = k − ∆k 2 = (k − ∆k) − k = 0. (4) Keywords: nilsrakoo; numbers; pell

Τ1τ2

Upper and Lower Near $(\tau_1,\tau_2)$-continuity by Thongmoon, Montri ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - Furthermore, several characterizations and some properties concerning (τ1, τ2)δ-semicontinuous multifunctions, almost weakly (τ1, τ2)-continuous mul- tifunctions, weakly quasi (Λ, sp)-continuous multifunctions, ⋆-continuous multifunctions, β(⋆)-continuous multifunctions, α-⋆-continuous multifunctions, almost α-⋆-continuous mul- tifunctions, almost quasi ⋆-continuous multifunctions, weakly α-⋆-continuous multifunc- tions, sβ(⋆)-continuous multifunctions, weakly sβ(⋆)-continuous multifunctions, θ(⋆)-quasi continuous multifunctions, almost ı⋆-continuous multifunctions, weakly (Λ, sp)-continuous multifunctions, α(Λ, sp)-continuous multifunctions, almost α(Λ, sp)-continuous multifunc- tions, weakly α(Λ, sp)-continuous multifunctions, almost β(Λ, sp)-continuous multifunc- tions, slightly (Λ, sp)-continuous multifunctions, (τ1, τ2)-continuous multifunctions, al- most (τ1, τ2)-continuous multifunctions, weakly (τ1, τ2)-continuous multifunctions, weakly quasi (τ1, τ2)-continuous multifunctions, almost quasi (τ1, τ2)-continuous multifunctions, c- (τ1, τ2)-continuous multifunctions, c-quasi (τ1, τ2)-continuous multifunctions and s-(τ1, τ2)p- continuous multifunctions were established in [5], [28], [62], [3], [7], [17], [24], [6], [21], [20], Preliminaries Throughout the present paper, spaces (X, τ1, τ2) and (Y, σ1, σ2) (or simply X and Y ) always mean bitopological spaces on which no separation axioms are assumed unless explicitly stated. Keywords: τ1τ2
Upper and Lower Contra-$(\tau_1,\tau_2)$-continuity by Viriyapong, Nongluk ; Sama-Ae, Areeyuth ; Boonpok, Chawalit (2025) - Journal of Advanced Research in Pure Mathematics, 2(1):11–25, 2010. This paper presents new classes of multifunctions between bitopological spaces, namely upper contra-(τ1, τ2)-continuous multifunctions and lower contra-(τ1, τ2)-continuous multifunctions. Keywords: τ1τ2; τ2)-continuous

Decision

Multi-Criteria Decision Making for Determining Critical Success Factors in Achieving Top University Graduation by Assi, Peter Nga ; Bassey, Edet Effiong ; Atsu, Jeremiah Ugeh; Ibok, Ekpenyong Effiong; Nnaji, Emeka Samuel ; Ugbe, Bernard Azinu; Amadigwe, Samuel Chukwudike (2024) - The study discovered prominent themes supportive of student success including having a future orientation, persistence, and strong executive functioning skills such as time management and organization, were listed as CSFs for undergraduate students to reach their goals while attending university. It is hoped that the results from this study will assist researchers and post-secondary personnel in better understanding the important factors for student success and provide the framework for further in-depth exploration. Keywords: b c; c.i; c.r; csfs; decision; factors; grade; level; priority; pv =; students; success; sum; λmax
Bipolar Neutrosophic Aczel-Alsina Aggregation for Effective Group Decision-Making by Fahmi, Aliya; Khan, Aziz; Abdeljawad, Thabet; D. K. Almutairi, D. K. Almutairi; muhammad kashif Siddhu, muhammad kashif Siddhu (2025) - [−e − ( n∑ P =1 λ(−InH− P )Λ ) 1 Λ , −(1 − e − ( n∑ P =1 λ(−In(1−L− P ))Λ ) 1 Λ ), −(1 − e − ( n∑ P =1 λ(−In(1−S− P ))Λ ) 1 Λ )  Step 4 Computing the score function Q(a) = 1 6 ( H + + 1 − L + + 1 − S + + 1 + H − − L − − S − ) Step 5: Find the ranking. Math, 18 (2) (2025), 5824 8 of 43 (P ) P1 ⊕ P2 =  [1 − e−(−In(1−L+ 1 ))Λ+(−In(1−L+ 2 ))Λ) 1 Λ , 1 − e−(−InM+ 1 )Λ+(−InM+ 2 )Λ) 1 Λ , 1 − e−(−InN+ 1 )Λ+(−InN+ 2 )Λ) 1 Λ ] [−(1 − e − ( −InL − 1 )Λ+(−InL − 2 )Λ ) 1 Λ ), −(1 − e − ( −In(1−M − 1 )) Keywords: bipolar; decision; e −; fahmi; l −; making; n∑ p; p =; ξ −; − −; − ; − ; ; 
An Exponential Intuitionistic Fuzzy Framework for Sustainable Supplier Selection in Industrial Management by Kaviyarasu, M. ; a-Ioana Cotˆırla, Luminit,a-Ioana Cotˆırla; Breaz, Daniel; M.Rajeshwari (2025) - If X is a universe discourse and ς̃∗ be any particular element of X. The intuitionistic FS A∗ defined on X is a collection of ordered pairs, A∗ = {(ς̃∗, µA∗(ς̃∗), λA∗(ς̃∗)) If X is a universe discourse and ς̃∗ be any particular element of X. The EIFS EA∗ defined on X is a collection of ordered pairs, EA∗ = {( ς̃∗, µA∗(ς̃∗)e −aµA∗ (ς̃∗), λA∗(ς̃∗)e −aλA∗ (ς̃∗) ) Keywords: decision; ea∗; eb∗; µa∗(ς̃∗)e; ς̃∗; ς̃∗1; ς̃∗2; ς̃∗3; −aµa∗; −aµb∗; −aλa∗
Performance Assessment of Logistics Ports Using Order Theory: A Case Study of Egyptian Ports by Ibrahim Alharbi, Luai ; Badr, Elsayed ; Badr, Moaz ; Rabie, Aya (2025) - Because of their interpretability and sim- plicity, these “AHP + ranking” combinations continue to dominate port studies and in- fluence how researchers define criteria and assess port performance [3]. A crucial first step in increasing port productivity, improving service delivery and guar- anteeing greater integration with neighboring sectors is the accurate and scientific assessment of port performance. Keywords: ahp; analysis; approach; criteria; decision; evaluation; lapos; logistics; mcda; performance; port; study

Log

Generalization of Dunkl Dini Lipschitz Functions by El Ouadih, Salah; Daher, Radouan (2017) - The Dunkl kernel El on Rd × Rd has been introduced by C. F. Dunkl in [4]. We consider the weight function wl(x) = ∏ ζ∈R+ | < ζ, x > |2l(α), x ∈ Rd, where wl is W-invariant and homogeneous of degree 2γ where γ = γ(R) Keywords: dunkl; log
Extremes, Extremal Index Estimation, Records, Moment Problem for the Pseudo-Lindley Distribution and Applications by Lo, Gane Samb; Ngom, Modou; Diallo, Moumouni (2020) - u)− log log(1/u)) + θ−1K(u) (7) with K(u) In the part (b), we want to share that we do not need any other condition on top of k(n)/n → 0 to have the central limit theorem if F−1 is reduced to F−1∗ (1− u) = γ log u− C(γ) log log(1/u), u ∈]0, 1[, C(γ) ≥ 1. (12) Keywords: log; log(1
The Double Laplace Transform Expressed in terms of the Lerch Transcendent by Reynolds, Robert; Stauffer, Allan (2021) - Introduction In this paper we derive the double Laplace transform given by (1) ∫ ∞ 0 ∫ ∞ 0 xp−1yn−p−1 logk ( bx y ) e−(sx)n−(ty)ndxdy where the parameters a, k s and t are general complex numbers, n > Re(p) and Re(p) > 0. ∫ ∞ 0 ∫ ∞ 0 xp−1yn−p−1e−x n−yn log ( x y ) dxdy = − π2 cot (πp n ) csc (πp n ) Keywords: log; ∫ ∞
Note on a Stieltjes Transform in terms of the Lerch Function by Reynolds, Robert; Stauffer, Allan (2021) - x−p2x3 1 4π log ( p2+q2 p2 ) x tan−1(bx) (a2+x2)2 πb 4a(ab+1) log(β+µx2) γ+x2 π log( √ β+ √ γ √ µ)√ γ log(a2+b2x2) c2+g2x2 π log ( ag+bc g ) cg log(a2+b2x2) c2−g2x2 − iπ log ( − i(bc+iag) − log ( q2x2 + 1 ) γ + x2 dx Keywords: log
Definite Integral of Power and Algebraic Functions in terms of the Lerch Function by Reynolds, Robert; Stauffer, Allan (2021) - − iπ logk(a) Table of Definite Integrals In this section we use Eq (9) to derive a Table of definite integrals in terms of funda- mental constants and special functions. The additional Contour Integral Using Eq (2) and replacing y by using log(a) and multiply by πi to get (8) iπ logk(a) k! = 1 2πi ∫ C iπaww−k−1dw R. Reynolds, A. Stauffer / Eur. Keywords: bx bx+1; bx+1; log
Definite Integral of Logarithmic Power and Square Root Algebraic Functions Expressed in terms of the Lerch Function by Reynolds, Robert; Stauffer, Allan (2021) - Conclusion In this paper, we have derived a method for expressing definite integrals in terms of Special functions using our contour integration method. Definite integral in terms of the Lerch function Theorem 1. Keywords: log
A Quadruple Integral Involving the Legendre Function Pn(x) of the First Kind: Derivation and Evaluation by Reynolds, Robert; Stauffer, Allan (2022) - ∫ 1 0 ∫ 1 0 ∫ 1 0 ∫ 1 0 xm−1Pv(x) log −m ( 1 t ) log 1 2 (m−v−1) ( 1 y ) log m+v 2 ( 1 z ) logk ax √ log ( 1 y )√ log ( 1 z ) log ( 1 t ) The Hurwitz-Lerch zeta Function The Hurwitz-Lerch zeta function (25.14) in [1] has a series representation given by Φ(z, s, v) = ∞∑ n=0 (v + n)−szn (4) where |z|< 1, v ̸= 0,−1, .. and is continued analytically by its integral representation given by Φ(z, s, v) = 1 Γ(s) ∫ ∞ 0 ts−1e−vt 1− ze−t dt = 1 Γ(s) ∫ ∞ 0 ts−1e−(v−1)t et − z dt (5) where Re(v) > 0, and either |z|≤ 1, z ̸= 1, Re(s) > 0, or z = 1, Re(s) > 1. 4.2. Keywords: log
Second Order Expansions for Extreme Quantiles of Burr Distributions and Asymptotic Theory of Record Values by Diallo, Moumouni ; Ngom, Modou; Dembele , Soumaila; Lo, Gane Samb (2023) - Math, 16 (1) (2023), 609-656 637 Figure 2: γ < 0 : Burr I and Burr IV = − log r + log u+ log ( 1 + r + 1 2r u+O(u2) ) . − F−1(1− u) = c(1 + a(u))u−γ exp (∫ 1 u ℓ(t) t dt ) . Keywords: burr; log; log r; record; u r; values
Strongly Geodesic Log-Preinvex Functions by Saleh, Wedad; Lakhdari, Abdelghani; Meftah, Badereddine (2024) - ∀µ1, µ2 ∈ ϑ. Form (7), we have ξ(µ2) ≥ ξ(µ1) exp { dµ1ξγµ1,µ2 ξ(µ1) + ε∥η(µ2, µ1)(ς)∥2 } ,∀µ1, µ2 ∈ ϑ. By interchanging the roles of µ1 and µ2 in the inequality above, we also obtain: ξ(µ1) ≥ ξ(µ2) Keywords: geodesic; log; preinvex
The Effect of Variation in the Order of the Beurling Zeta Function in the Strip (0, 1) on the Upper Bound of Nₚ(x) by amen, zhwan; Al-Maamori, Faez; Fattah Hama, mudhafar (2025) - = li(x) +O(xe−k √ log x) for some k > 0, where li(x) = ∫ x 2 dt log t (iii) In 2006, Diamond, Montogomery and Vorhauer [18] showed that Landau’s result is best possiblre. So, we get exp [( 1 + t100(1−σ) 3 2 ) (log t) 2 3 ] ≤ t 1 2( 1 + t100(1−σ) 3 2 ) (log t) 2 3 ≤ log t 1 2( 1 + e100(1−σ) 3 2 log t ) ≤ 1 2 (log t) 1 3 e100(1−σ) 3 2 log t ≤ 1 + e100(1−σ) 3 2 log t ≤ 1 2 (log t) 1 3 so e100(1−σ) 3 2 log t ≤ 1 2 (log t) 1 3 log ( e100(1−σ) 3 2 log t ) ≤ log ( 1 2 (log t) 1 3 ) 100(1− σ) 3 2 log t ≤ log( 1 2 ) + log ( (log t) 1 3 ) (1− σ) 3 2 ≤ log 1 2 + 1 3 log log t 100 log t log ( e100(1−σ) 3 2 log t ) ≤ log ( 1 2 (log t) 1 3 ) 100(1− σ) 3 2 log t ≤ log( 1 2 ) + log ( (log t) 1 3 ) (1− σ) 3 2 ≤ log 1 2 + 1 3 log log t 100 log t Z. M. Amen, F. A. Al-Maamori, M. F. Hama / Eur. Keywords: beurling; log; log log; log t

Class

On Neat Reducts of Reducts of Cylindric Algebras by Ahmed, Tarek Sayed (2010) - Given a structure M and a tuple ā, we often write, with a slight abuse of notation, ā ∈ M instead of ā ∈ mM , where m is the arity of the tuple ā. By (2), choose j ∈ ω ∼ 3 so that Rdd f Rd3C j, j+m+n−4 is a non-representable Df3. Keywords: ahmed; algebras; class; cylindric; finite; logic
Structural and Spectral Properties of k-Quasi Class Q(N) and k-Quasi Class Q*(N) Operators by Lohaj, Shqipe (2022) - we write the spectrum of T, the r(T ) is the spectral radius of operator T which is defined by r(T ) The σa(T ) is the approximate point spectrum of operator T and it is proved that if λ ∈ σa(T ), then there exist the sequence (xn), such as ∥xn∥ = 1 and ∥(T − λI)xn∥ → 0, n → ∞. The null operator and the identity on H will be denoted by O and I, respectively. Keywords: class; k−quasi; k−quasi class; operator; q(n
Modeling and Multi-objective Optimal Control of Thedynamics of Counterterrorism in the Sahel Region in Africa by Pooda, Mathieu; Simpore , Yacouba; Traore , Oumar (2024) - Math, 17 (2) (2024), 870-904 896 dλ9 dt = −w5 + (λ9 − λ1)γ8 + (λ1 − λ5)c1π1 C(N −D) N2 + (λ1 − λ4)c1α1 C(C +A+ V ) (C + I)2 + (λ8 − λ1)c4α2 BC (C + I)2 +(λ2 − λ5)c1π5 R(N −D) N2 + (λ2 − λ9)c5ω3 R(R+A+ V +B) (R+ I)2 + (λ8 − λ2)c4ω4 BR (R+ I)2 +(λ3 − λ5)c1π3 A(N −D) N2 + (λ8 − λ3)c4ν3 BA I2 + (λ3 − λ9)c5ω2 A(A+ V +B) I2 + λ3ζ1 A(A+ V ) I2 +(λ4 − λ5)c1π2 V (N −D) N2 + λ4ζ2 V (A+ V ) I2 + (λ5 − λ6)c2β2 S ( N − (E + F + T ) ) N2 +(λ6 − λ7)c3β3 E ( N − (F + T ) ) N2 + (λ10 − λ7)τ1 F (A+ V ) (F + I)2 + (λ7 − λ10)c5β4 F (N − T ) N2 − λ7ζ3 F (A+ V ) (F + I)2 +(λ8 − λ10)c4θ2 PB (P + I)2 + (λ8 − λ5)c1π4 B(N −D) N2 + (λ8 − λ9)c5ω1 B(A+ V +B) I2 − λ8ζ4 B(A+ V ) I2 +(λ10 − λ8)τ2 B(A+ V ) I2 + (λ10 − λ9)c5θ1 P (P +A+ V +B) (P + I)2 + (λ9 − λ10)τ3 (A+ V )(A+ V +B) I2 +λ9 + (λ10 − λ5)c1π6 P (N −B) N2 + λ9ζ5 (A+ V )(A+ V +B) I2 dλ10 dt = −w6 + (λ10 − λ1)γ5 + (λ5 − λ1)c1π1 DC N2 + (λ5 − λ2)c1π5 DR N2 + (λ5 − λ3)c1π3 DA N2 + (λ5 − λ4)c1π2 DV N2 +(λ5 − λ8)c1π4 DB N2 + (λ10 − λ5)c1π6 D(N − P ) N2 + (λ6 − λ5)c2β2 S(E + F + T ) N2 + (λ7 − λ6)c3β3 E(F + T ) N2 +(λ9 − λ7)c5β4 TF N2 + (λ10 − λ8)c4θ2 BI (P + I)2 + (λ10 − λ9)c5θ1 TI (P + I)2 + λ10µ+ λ10η with transversality conditions λi(Tf ) Math, 17 (2) (2024), 870-904 878 dN dt = Λ− µN − δ1V − δ2A− δ3B − δ4T − δ5F − ηP Since A, V,B, T, F, P are positive functions and using the positivity of the functions δ1, δ2, δ3, δ4, δ5, given that the constants ζ1, ζ2, ζ3, ζ4, ζ5 and η are strictly positive as well, we get: dN dt ≤ Λ− µN Then d dt ( N − Λ µ ) ≤ −µ ( N − Λ µ ) Keywords: + b; + t; + v; + ω1; c +; class; e +; evolution; f +; i2 +; n +; n2 +; subpopulation; t n; t t; v f; λ5 −
A Generalization of the Concept of Cointegration to Harmonizable and Class (KF) Processes by Joyeux, Roselyne (2010) - This would be the case, for example, of non-stationary processes generated by nonlinear systems which co-move according to a linear adjustment process. In this paper we consider a class of processes which are non-stationary and includes the class of stationary processes as a subset. Keywords: class; harmonizable; processes; stationary

Table

An Indicator of One's Life Satisfaction by Saaty, Thomas L.; Zoffer, H. J.; Wei, Lirong (2018) - Many au- thors have discussed various dimensions of life satisfaction in a wide variety of situations. [4] conducted research on measures of life satisfaction for evaluation of the quality of life inventory. Keywords: comparisons; hierarchy; life; pairwise; people; saaty; satisfaction; subcriteria; table
Computational Analysis of Reverse Degree-Based Topological Indices in Hex-Derived Networks by Alsatami, Khalid A. ; Ali, Haidar; Ali, Bilal; Ali, Parvez (2024) - In chemical graph theory, topological indices are used to quantify various chemical properties of molecules. Topological indices are connected to numerous physicochemical prop- erties, such as vapor pressure, stability, and elastic energy. Keywords: hex; index; indices; table

Analysis

A Novel RGB Image Encryption Scheme using Operations on Residue Classes of Eisenstein Integers Z[ω]π by Sajjad, Muhammad; Alqwaifly, Nawaf A. (2025) - Among these, image encryption using algebraic structures and number theory has emerged as a promising area, especially for multimedia and medical imaging, where traditional schemes fail to meet performance or security thresholds. In image encryption, Eisenstein integers offer a promising basis for constructing substitution boxes, defining modular transformations, and encoding image pixels with non-standard algebraic operations, thereby increasing entropy and resistance to statistical analysis. Keywords: alqwaifly; analysis; boxes; classes; eisenstein; eisenstein integers; encryption; image; image encryption; integers; original; pixel; residue; rgb; sajjad; security; values

Series

Jordan-Hölder Theorem for Multigroups by Ejegwa, Paul Augustine ; Kausar, Nasreen; Musa Adeku Ibrahim; Cagin, Tonguc (2025) - Math, 18 (2) (2025), 5889 6 of 13 Table 2: Submultigroups of D based on Case (iii) Submultigroups and their structures D0 = {1}, D1 = {1, d2}, D2 = D̂1 = {1, d, d2, d3}, D̂2 = {1, 1, d, d2, d3}, D̂3 = {1, 1, d, d, d2, d2, d3, d3}, D̂4 = {1, 1, 1, d, d2, d3}, D̂5 = {1, 1, 1, d, d, d2, d2, d3, d3}, D̂6 = {1, 1, 1, d, d, d2, d2, d2, d3, d3}, D̂7 = {1, 1, 1, 1, d, d2, d3}, D̂8 = {1, 1, 1, 1, d, d, d2, d2, d3, d3}, D̂9 = D = {1, 1, 1, 1, d, d, d2, d2, d2, d3, d3}, Ḋ1 = {1, 1}, Ḋ2 = {1, 1, 1}, Ḋ3 = {1, 1, 1, 1}, Ḋ4 = {1, 1, d2}, Ḋ5 = {1, 1, d2, d2}, Ḋ6 = {1, 1, 1, d2}, Ḋ7 = {1, 1, 1, d2, d2}, Ḋ8 = {1, 1, 1, d2, d2, d2}, Ḋ9 = {1, 1, 1, 1, d2}, Ḋ10 Math, 18 (2) (2025), 5889 7 of 13 Table 4: Submultigroups of E based on Case (iii) Submultigroups and their structures E0 = {ρ0}, Ê1 = E1 = {ρ0, ρ1, ρ2}, Ê2 = {ρ0, ρ0, ρ1, ρ2}, Ê3 = {ρ0, ρ0, ρ1, ρ1, ρ2, ρ2}, Ê4 = {ρ0, ρ0, ρ0, ρ1, ρ2}, Ê5 = E = {ρ0, ρ0, ρ0, ρ1, ρ1, ρ2, ρ2}, Ė1 = {ρ0, ρ0}, Ė2 = {ρ0, ρ0, ρ0} Here, E0, Ê1, Ė1, Ė2 and Ê5 are trivial, and Ê2–Ê4 are proper non-trivial normal submultigroups of E without a maximal non-trivial normal submultigroup of E since either Keywords: multigroup; series; submultigroups
On Jordan-Hölder Theorem under Intuitionistic Fuzzy Groups by Paul Augustine Ejegwa; Kausar, Nasreen; Cagin, Tonguc (2025) - 2020 Mathematics Subject Classifications: 03F55, 06D72, 08A72 Key Words and Phrases: Intuitionistic fuzzy groups, Intuitionistic fuzzy subgroups, simple intuitionistic fuzzy groups, maximal normal intuitionistic fuzzy subgroups, normal series for intu- itionistic fuzzy groups, composition series for intuitionistic fuzzy groups 1. Hence, this paper defines simple intuitionistic fuzzy groups, maximal normal intuitionistic fuzzy subgroups, normal series for intuitionistic fuzzy groups, and composition series for intuitionistic fuzzy groups with illustrations. Keywords: series

Operator

Some Spectral Properties of the Generalized Difference Operator (Delta)v by Akhmedov, Ali M.; El-Shabrawy, Saad R. (2012) - = � y ∈ X : y = T x , x ∈ X . Also, if x0 6= 0 then we can easily see that � �xk � �≥ � �x0 � � , for all k ≥ 1, A. Akhmedov, S. El-Shabrawy / Eur. Keywords: operator; sequence; spectrum; � �
On the Elementary Solution for the Partial Differential Operator $\circledcirc_c^{k}$ Related to the Wave Equation by Bupasiri, Sudprathai (2018) - = f(x), where f is generalized function and u(x) is unknown function for x ∈ Rn. 2010 Mathematics Subject Classifications: 46F10 Key Words and Phrases: Elementary solution, Dirac-delta distribution, Temper distribution 1. In particular, we obtain (−1)kRe−2,1(v) ∗G(x) = M2,1(u) is an elementary solution of the wave operator defined by (10) where u = t2 − x21 − x22 − · · · − x2n−1. Keywords: operator
On the Bessel Operator $\odot_{B}^{t}$ Related to the Bessel-Helmholtz and Bessel Klein-Gordon Operator by Bupasiri, Sudprathai (2018) - (8) Moreover for m = 0, then we obtain Bessel diamond operator and defined by (1). 2010 Mathematics Subject Classifications: 46F10 Key Words and Phrases: Bessel Helmholtz operator, Bessel Klein-Gordon operator, Bessel diamond operator 1. Keywords: operator
Univalence of New General Integral Operator Defined by the Ruscheweyh Type q-Difference Operator by Elhaddad, Suhila; Aldweby, Huda; Darus, Maslina (2020) - If f ∈ A satisfies 1− |z|2<(%) <(%) ∣∣∣∣∣zf ′′ (z) f ′(z) ∣∣∣∣∣ ≤ 1, z ∈ U, then the operator f%(z) = { % ∫ z 0 t%−1f ′ (t)dt } 1 % , is belonging to S. S. Elhaddad, H. Aldweby, M. Darus / Eur. If f ∈ A satisfies ∣∣∣∣∣c|z|2% + (1− |z|2%)zf ′′ (z) %f ′(z) ∣∣∣∣∣ ≤ 1, z ∈ U, then the operator f%(z) Keywords: operator
On the Operator âŠ•k,m Related to the Wave Equation and Laplacian by Bupasiri, Sudprathai (2021) - Thus, equation (7) can be written as ⊕km = ( � +m2 )k (4+m2 )k ( L1 +m2 )k ( L2 +m2 )k = ( L2 +m2 )k ( L1 +m2 )k (4+m2 )k ( � +m2 )k (15) and from (7) with q = m = 0 and k = 1, we obtain Laplace operator of p-dimension ⊕0 = 44 p, where 4p = ∂2 ∂x21 + ∂2 ∂x22 + · · ·+ ∂2 ∂x2p . At first we study the fundamental solution of the operator ⊕k m and after that, we apply such the fundamental solution to solve for the solution of the equation ⊕k mu(x) = f(x), where f(x) is generalized function and u(x) is unknown function for x ∈ Rn. 2020 Mathematics Subject Classifications: 46F10 Key Words and Phrases: Wave equation, Laplace operator, Ultra-hyperbolic operator 1. Keywords: operator
On M−quasi Paranormal Operators by Hamiti, Valdete Rexhëbeqaj; Gjonbalaj, Qefsere Doko (2022) - we write the spectrum of T, the r(T ) is the spectral radius of operator T which is defined by r(T ) The σa(T ) is the approximate point spectrum of operator T and it is proved that if λ ∈ σa(T ), then exists sequence (xn), where ∥xn∥ = 1 and ∥(T − λI)xn∥ → 0, n → +∞ (see [6]). Keywords: m−quasi; operator; paranormal
Results of Semigroup of Linear Operators Generating a General Class of Semilinear Initial Value Problems by Saka-Balogun, Olaide ; Oyelami, Funmilayo; Akinyele, Akinola Yussuff; Omosowon, Jude (2023) - ∥∞ and let {T (t); t ∈ R+} ⊆ L(X) be defined by [T (t)f ](s) = f(t+ s) For each f ∈ X and each t, s ∈ R+, one may easily verify that {T (t); t ∈ R+} satisfies Examples 1 and 2 above. Keywords: linear; operator; semigroup
Some Properties of (M,k)-quasi Paranormal Operators on Hilbert Spaces by Rexhëbeqaj Hamiti, Valdete ; Makolli, Shkumbin (2024) - If S ∈ L(H) is unitarily equivalent to operator T, then S is a (M,k)−quasi paranormal operator. If T ∈ L(H) is a regular (M,k)−quasi paranormal operator, then the ap- proximate point spectrum of operator T lies in the disc σa(T ) ⊆ {λ ∈ C : 1√ M∥T−k−1∥ · √ ∥T k+1∥ · ∥T k−1∥ ≤ |λ| ≤ ∥T∥}. Keywords: k)−quasi; operator; paranormal

Vertices

Inverse Domination in X-Trees and Sibling Trees by Shalini, V.; Rajasingh, Indra (2024) - In either case, the number of dominated vertices is 7. A result on inverse domination number of some classes of Hypertrees is also included. Keywords: domination; inverse; set; vertices
Computing Metric and Connected Metric Dimension of Some Graphs by Elrokh, Ashraf; S. Almotairi, Eman; Mostafa, Hoda (2025) - 2020 Mathematics Subject Classifications: 05C78, 05C15 Key Words and Phrases: Algebraic Graph, metric basis, resolving set, metric dimensions, Connected metric dimensions, Algorithm, Network security, Edge Computing 1. Connected metric dimension of C4 ⊙ C5. Keywords: ui1; vertices
Property HyperGraphs and Property SuperHyperGraphs for Data Analysis by Fujita, Takaaki; Smarandache, Florentin (2025) - Group venues by field: FML = {VConfA, VConfB}, FTheory = {VJournalC} ∈ P2(V0), with V (2) = {FML, FTheory} and µ(FML, fieldName) = “Machine Learning”, µ(FML, hIndex) = 120, µ(FTheory, fieldName) = “Theory”, µ(FTheory, hIndex) = 85. Σ = {FOLLOWS, RATED, HAS_GENRE}, K = {type, name, age, city, title, year, rating, date}, S = N ∪ R ∪ Strings. Keywords: definition; e(n; fujita; hypergraph; level; property; set; smarandache; superhypergraph; vertices

Index

Computing Discrete Adriatic Indices of Probabilistic Neural Network by Deepika, T; Lokesha, V. (2020) - Adriatic indices are also part of topological indices, mainly it is classified into two namely extended variables and discrete adriatic indices, especially, discrete adriatic indices are analyzed on the testing sets provided by the International Academy of Mathematical Chemistry (IAMC) and it has been shown that they have good presaging substances in many compacts. Prologue and Provocation In this work peculiar attention is compensated to Adriatic indices that have been de- fined by D. Vukičević and M. Gasperov. Keywords: index
Semi-Total Point Graph of Neighbourhood Edge Corona Graph OF $G$ and $H$ by Agustin, Ika Hesti; Maragadam, A. S.; Dafik; Lokesha, V.; Manjunath, M. (2023) - Here we concentrated on topological indices involving the number of vertices, the number of edges and the maximum and minimum vertex degree. Key Words and Phrases: Semi-Total point Graph, Corona Product of Graphs, Neighborhood Edge Corona Graph, Lower and Upper Bounds of Topological indices. Keywords: dg(2; dh +; index; δg(2
Kernel Estimation of the Quintile Share Ratio index of Inequality for Heavy-tailed Income distributions by Modou Kebe; Deme, El Hadji; Tchilabalo Abozou Kpanzou; Manou-Abi, Solym Mawaki; Ebrima Sisawo (2023) - − k/n, Un,k,2 ( Q (K) n,k ) := ∫ 1 1−k/n Q (K) n,k (s)ds = (k/n)Xn−k,n 1 − γ̂ (K) n,k . with Qn(·) (respectively, Q (K) n,k is the empirical estimator (respectively, the Weissman’s type estimator) of the quantile function Q(·) and k = k(n) is a sequence of integers satis- fying k → ∞, k/n → 0 and as n → ∞. To simplify the proof, we need the following preliminary results whose proofs are given after this one. − Un,k,1(Q, β) L(Q,α) } (k/n)1/2Xn−k,n d = Wn,α,1 + oP(1), (19) as n → ∞, where Wn,α,1 := − ∫ 1−k/n 0 Bn(s)dQ(s) L(Q,α) (k/n)1/2Q(1 − k/n) . Keywords: estimator; index; k n; l(q; n d; opt; ∆̂∗
Topological Characterization of Hexagonal Network and Non-Kekulean Benzenoid Hydrocarbon by Kanj, Hassan; Iqbal, Hifza; Aftab, Muhammad Haroon; Raza, Hasnain; Jebreen, Kamel; Sowaity, Mohammed Issa (2023) - Zagreb connection indices provide better correlation coefficient then the classical Zagreb indices. Over the decades numerous structural topological descriptors have been defined, keeping in view the importance and applications of these structures we have defined Zagreb connection indices for hexagonal network and non-kekulean benzenoid hydrocarbon. Keywords: connection; index; indices; topological; zagreb
Graphical Invariants for some Transformed Networks by Ali, Nawaf; Khalifa, Tarek; Iqbal, Hifza; Aftab, Muhammad Haroon; Jebreen, Kamel; Jamil, Humira; Kanj, Hassan (2024) - Babujee et al. worked on topological indices and new graph structures [4]. There are thousands of topological indices developed over the decades in the field of chem- ical graph theory. Keywords: + dψ; dθ +; index; indices
Topological Characterization for Triangular, Regular Triangular Oxides and Silicates Networks by Khalifa, Tarek; Ali, Nawaf; Rafaqat, Muhammad ; Aftab, Muhammad Haroon; Kanj, Hassan; Alakkoumi, Mouhammad; Jebreen, Kamel (2024) - = 3 2 a2b4 + 3 4 (r − 1)a4b4 + (r − 2)a4b6 + ((r − 3)2 + (r − 3)) 4 a6b6 SaSb(f(a, b)) Zagreb indices and multiplicative zagreb indices of eulerian graphs. Keywords: aftab; b=1; index; triangular; zagreb
Bounds of Geodetic-Wiener Index on Spirocyclic Graphs by Artes Jr., Rosalio; Gobithaasan, Rudrusamy; Hasni, Roslan; Jafari Rad, Nader (2025) - It suffices to show the bounds of Wiener index in terms Harary index and use Lemma 2 together with Theorem 1. Applying Theorem 2 and the proof of Theorem 8 on the bounds of Wiener index with multiplicatively weighted Harary index yields the following corollary. Keywords: d(u; index; wiener

Temperature

Seebeck Effect on a Magneto-thermoelastic Long Solid Cylinder with Temperature-dependent Thermal Conductivity by Zenkour, Ashraf M.; Abouelregal, A. E.; Alnefaie, K. A.; Abu-Hamdeh, N. H. (2017) - The remaining constitutive equations of Duhamel-Neumann are given by σij = µ (ui,j + uj,i) Then, ur = u (r, t) and uϕ = uz = 0. Components of strain tensor eij are given as err = ∂u ∂r , eϕϕ = u r , ezz = erz = ezϕ = erϕ = 0. (10) Keywords: conductivity; cylinder; field; magnetic; temperature; zenkour
Detecting Warming Trends and Climate Regime Transitions Using Satellite-Derived Temperature Data in Northeast India by Lochan Bora, Shyam; Bharali, Sulaxana ; Bhuyan, Kalyan ; Das, Jayanta; Hazarika, Partha; Eliwa, Mohamed; Sallam Abdalla, Gaber ; Abouelenein, Mohamed (2025) - Together, these grid points offer a robust foundation for analyzing temperature trends and regime shifts across Northeast India’s diverse climate zones, providing insights that can support localized climate risk assessment and adaptation planning. Similar pat- terns have been observed in other studies focusing on elevation and urban influence on temperature trends Keywords: change; climate; india; ita; mean; monsoon; northeast; slope; stations; temperature; trends; warming; year

J=1

The Smoothness of Schrodinger Operator with Electromagnetic Potential by Saleem, Yahea Hashem; Shubber, Hadeel Ali (2019) - Thus Ψ(t, x) satisfies the equation ∂Ψ ∂t = ∑n j=1 1 2 (i∂j + bj(x))2 Ψ(t, x) − V (x)Ψ(t, x) with the initial condition Ψ(t, x) → ϕ(x) in L2(Rn, dx, dV ) as t → 0. We proved in [8] the Feynman-Kac Itô formula of the electromagnetic Schrödinger operator Ψ(t, x) which define as the equation (1) in [8] Ψ(t, x) = ∫ dµtx(ω)exp ( −i ∫ t 0 b(ω(s))dω − i 2 ∫ t 0 divbω(s)ds− ∫ t 0 V (ω(s)ds ) ϕ(ω(t)) converges and is an analytic function of the variable t. Keywords: i∂j; j=1; n∑ j=1; ψ(t
Rank-k perturbation of Hamiltonian Systems with Periodic Coefficients and Applications by Mouhamadou, Dosso; Arouna, Traore G. Y.; Brou, Jean-Claude Koua (2019) - Jordan canonical form of rank-k perturbation of a symplectic matrix Let W,J ∈ R2N×2N be two matrices and λ ∈ C such that J is skew-symmetric, W is J-symplectic and λ an eigenvalue of W . Suppose that W has the following Jordan canonical form : l1⊕ j=1 Jn1(λ) ⊕  l2⊕ j=1 Jn2(λ) ⊕ · · · ⊕  lm⊕ j=1 Jnm(λ) ⊕ J , where n1 > · · · > nm, m ∈ N∗ such that the algebraic multiplicity a of λ is of the form a = m∑ j=1 ljnj and J contains all the forms in Jordan blocks associated with eigenvalues of W that are different from λ. Keywords: eigenvalues; j=1; jordan; t k; ⊕
A Mathematical Framework for Modeling the Spread of HIV-disease within two Different Age Classes by Alassane, Mahamadou; Samake, Abdoulaye ; Mahamane, Amadou ; Diallo, Ouateni (2023) - Math, 16 (1) (2023), 207-232 224 −bκ6κ5κ1β1κ4κ3 + 2bκ2β2κ3κ4γa3 − bκ6κ5κ1β1a1κ4 − bκ6κ5κ1β1a1a2 − bκ2κ6κ5κ1κ3κ4 +2bκ5β2a1a4c2κ4 − bκ5κ1β2a1c2κ4 + 2bκ2κ6β2κ3κ4γ − κ6κ5κ1β2a1a2c3 + 2κ2β2κ3κ4γa3a4 +κ2κ6κ5κ 2 1κ3κ4 − c1β2κ3κ4κ1a3a4 − κ5κ1β2a1a4c2κ4 ) f44 = κ22 ( − κ2β2κ3κ4γa3a4 − bκ2κ6β2κ3κ4γ − bκ2β2κ3κ4γa3 + bκ6c1β2κ3κ4κ1 + bc1β2κ3κ4κ1a3 +c1β2κ3κ4κ1a3a4 − b2κ6κ5β1κ4κ3 − b2κ6κ5β1a1a2 + bκ6κ5κ1β1a1κ4 + κ6κ5κ1β2a1a2c3 −b2κ6κ5β1a1κ4 + bκ6κ5κ1β1a1a2 + κ5κ1β2a1a4c2κ4 − b2β2κ3κ4c1a3 + bκ6κ5κ1β1κ4κ3 −bβ2κ3κ4c1a3a4 − b2κ6β2κ3κ4c1 − b2κ5β2a1c2κ4 − bκ6κ5β2a1a2c3 − bκ5β2a1a4c2κ4 +bκ5κ1β2a1c2κ4 ) . κ1bκ3κ2 − κ6bκ3β1 − a1c2β2b− a1κ6β1b + κ1κ6κ3κ2 f29 = −κ6bκ4β1 + κ1κ6κ4κ2 − β2b 2c1 − κ5b 2β1 − γβ2bκ2 + κ1κ5bκ2 f30 = −β2bκ6c1 − a3β2bc1 − κ5κ6bβ1 − a3γβ2κ2 − γβ2κ6κ2 + κ1κ5κ6κ2 f31 = −a3γβ2κ3 − γβ2κ6κ3 + κ1κ5κ6κ3 − a3γβ2b− γβ2κ6b− a3γa4β2 + κ1κ5κ6b f32 = −γβ2κ4κ3 + κ1κ5κ4κ3 − β2bκ4c1 − κ5bκ4β1 − γβ2κ4κ2 + κ1κ5κ4κ2 f33 = −β2bκ3c1 − κ5bκ3β1 − γβ2κ3κ2 − a1κ5β1b + κ1κ5κ3κ2 Keywords: ij1; ij2; individuals; j=1; stage
Some Applications of Fuzzy Differential Subordination on Analytic Functions Connected with Lommel Function by Ali, Ekram E.; El-Ashwah, Rabha M. ; Alshuhail, Altaf ; Alshammari, Maryam F. (2025) - (µ (ξ)) , ξ ∈ U, where f(U) = sup(f(U), Ff(U)) = 1 and Re[βµ(ξ)+ y] > 0 (ξ ∈ U), and q(ξ) ∈ Keywords: j(ξ; j=1; lmn

Sequence

On Statistical and Ideal Convergence of Sequences of Bounded Linear Operators by Kolk, Enno (2015) - Suppose that the ideal I has property (AP) and let zk j ∈ X (k, j ∈ N). Assume that I -limk zk j = z j ( j ∈ N). Keywords: sequence; set
Simultaneous Approximation of New Sequence of Integral Type Operators with Parameter Î´_0 by Mohammad, Ali Jassim; Muslim, Hadeel Omar (2019) - xk(1− x)n−k and f ∈ C[0, 1]. − ...− r n xr−1 dr dxr ( cosh(nx) (δ0 + sinh(nx)) ) } − f r(x) + f (r+1)(x) (r + 1)! Keywords: sequence; sinh(nx
The Self-Shrinking Conflation Generator: A Proposed Improvement to the Self-Shrinking Generator by Kanth, Vikram; Martinsen, Thor; Stanica, Pantelimon (2022) - In fact, the proof shows that the period of SSCG is exactly per(0 − SSG) · per(1− SSG), where per(s) is the least period of the sequence s. 3.2. Conclusions We have presented a computationally inexpensive modification to the Self-Shrinking Generator that exhibits improved period, linear complexity, and added security against several known SSG attacks. Keywords: sequence; ssg; x10; x11
Exactness of the Functors $\text{Hom}_{\mathscr{A}}(X,-), \text{Hom}_{\mathscr{A}}(-,X)$, $\text{Hom}_{\text{Comp}(\mathscr{A})}(X,-), \text{Hom}_{\text{Comp}(\mathscr{A})}(-,X)$ and the Homological Functors $\tilde{H}_n(X,-) \text{ and } \tilde{H}_n(-,X)$ by Diallo, Ablaye; Ben Maaouia, Mohamed Ben Faraj; Sanghare, Mamadou (2025) - i⇒ f ◦ i+ f ◦ eK,X = f ◦ eK,X + f ◦ But eK,Y = f ◦ eK,X . Keywords: exact; homa; homcomp(a; sequence

Prime

Ï†-Prime and Ï†-Primary Elements in Lattice Modules by Bingi, Ashok V.; Manjarekar, C. S. (2021) - If a proper element N ∈ M is primary, then √ N : IM ∈ L is prime. Math, 14 (2) (2021), 551-577 553 every element N ∈ M there exists an element a ∈ L such that N = aIM . Keywords: element n; module m; primary; prime
On alpha-prime and Weakly alpha-prime Submodules by Khumprapussorn, Thawatchai (2018) - 2010 Mathematics Subject Classifications: 13C99 Key Words and Phrases: α-prime submodules, weakly α-prime submodules, α-prime ideals, weakly α-prime ideals 1. Weakly α-prime submodules In this section we begin with the definition of weakly α-prime submodules which is a generalization of α-prime submodules. Keywords: prime
Ï€-Modules by Jayaram, C. (2009) - In this paper we characterize π-modules. Math, 2 (2009), (508-519) 511 3. π-modules In this section, we characterize π-modules. Keywords: module; prime; submodule
On the Prime Radical of Nearrings which is Kurosh-Amitsur by Lakshminarayana, Kilaru J. ; Prasad, V.B.V.N. ; Ravi, Srinivasa Rao ; Ramakrishna, A.V. (2024) - Then H is a prime N -group of type 1 if: (i) every non-zero N -subgroup of H has a non-zero distributive element; (ii) hNx = {0}, 0 ̸= h ∈ H,x ∈ N implies Hx = {0}. For this, define (h0k)x := h0(kx) for all h0k ∈ K,x ∈ N , where k ∈ K. To show that this operation is well defined, suppose that h0y = h0z, y, z ∈ K. Let x ∈ N . Keywords: prime; type
Prime Labeling of Union of Some Graphs by AbuGhneim, Omar A.; Abughazaleh, Baha' (2024) - For more details about prime graphs see for example [2], [5], [6], [10]. On prime graphs. Keywords: c2n; prime
A Kurosh-Amitsur Completely Prime Radical for Near-rings by Kilaru J. Lakshminarayana; V.B.V.N. Prasad; Srinivasa Rao Ravi; Siva Prasad Korrapati; Amathi, V Ramakrishna (2025) - = {n + I ∈ N/I | g3(n + I) = 0} = {n + I ∈ N/I | g3n Keywords: prime; right; type

Values

Thermocapillary and Photocapillary Effects on a Spherical Droplet Embedded in a Brinkman Medium by Aamer, Ahmed; Adel, baraa; Mahrous, Samar (2025) - A consistent trend observed across all conditions is the decrease of U∗ T with increasing k, transitioning from an initial region where U∗ T exhibits near-constant values at low thermal conductivity ratio (k < 10−1) to near-zero values at high thermal conductivity ratio (k > 102). Math, 18 (3) (2025), 6505 of Figure 2: Normalized Thermocapillary velocity U∗ T versus permeability parameter α for different values of thermal conductivity ratio k at specific values of viscosity ratio(σ = 0 , σ = 3). Keywords: a. s.; droplet; medium; ratio; thermocapillary; values; viscosity

Edge

Infinitesimal Rigidity Analysis of a Bar-Joint Framework With Connected Braced Triangles by Badri, Ghada (2024) - − p8, u6⟩+ ⟨p8 − p6, u7⟩ = 0 (px6 − px8)u x 6 + (py6 − py8)u y 6 + (px8 − px6)u x 8 + (py8 − py6)u y 8 = 0 ux8 = ux6 The argument above, together with the appropriate substitutions we can identify the non trivial infinitesimal flex u = (u1, u2, . . . ⟨p6 − p8, u6⟩+ ⟨p8 − p6, u8⟩ = 0 (px6 − px8)u x 6 + (py6 − py8)u y 6 + (px8 − px6)u x 8 + (py8 − py6)u y 8 = 0 ux6 = ux8 Finally, applying the flex condition to the edge [p5, p6]: ⟨p5 − p6, u5⟩+ ⟨p6 − p5, u6⟩ Keywords: bar; edge; flex; framework; rigidity; velocity

Let

Locally Compact L-fuzzy Spaces by Breuckmann, T.K.; Kudri, S.R.T.; Aygun, Halis (2009) - Let x ∈ X , let p ∈ pr(L) and let f ∈ T such that f (x)� p. An L-topological space 〈X , T 〉 is locally compact if and only if for each x ∈ X , p ∈ pr(L) and f ∈ T with f (x) � p there exist g ∈ T and k ∈ LX , with χsupp(k) compact, such that f (x)� p and g ≤ k ≤ f . Keywords: let
Hyper Homomorphism and Hyper Product of Hyper UP-algebras by Amairanto, Rohaima M.; Isla, Rowena (2020) - Since f(a), f(x), f(y) ∈ H ′ and θ′ is a congruence relation on H ′, from R. Amairanto, R. Isla / Eur. Then there exist f(a) ∈ f(A) and f(b) ∈ f(B) such that y ∈ f(a) ~′ f(b). Keywords: congruence; hyper; let; relation
Single-valued Neutrosophic Soft Sets in Hyper UP-Algebra by Cano, Allan; Petalcorin, Gaudencio (2023) - y ◦ z ≪ (x ◦ y) ◦ (x ◦ z), A. Cano, G. Petalcorin / Eur. Thus, z ∈ G and so x ◦ y ⊆ G. By Proposition 2, G is a hyper UP -subalgebra of X. (⇐) Assume that G is a hyper UP -subalgebra of X and suppose x, y ∈ X. Consider the following cases: Keywords: hyper; let; set; svns
Further New Operators in Primal Spaces by Alghamdi, Ohud (2024) - Let r ∈ R and let O ∈ Γ0(r). Indeed, let r ∈ R and let O ∈ Γ0(r). Keywords: let

Energy

Mathematical Modeling of Condensing on Metric Spaces by Zahri, Mostafa (2013) - 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (a) Initial 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (b) Initial 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (a) Iteration 195 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (b) Iteration 175 Figure 5: Initial and final densities of condensing measures on the real line for simulations (a) and (b) 4.3. Furthermore, the convergence of the process of condensing sequences is not guaranteed. Keywords: condensing; energy; mass
Closeness Energy of Non-Commuting Graph for Dihedral Groups by Romdhini, Mamika Ujianita; Nawawi, Athirah ; Al-Sharqi, Faisal ; Al- Quran, Ashraf (2024) - n − 3 + n 2 , λ2 = −3 4 of multiplicity n 2 − 1 and λ3,4 = 1 8 ( 3n− 6± √ n(17n− 32) ) . 2020 Mathematics Subject Classifications: 05C25, 05C50, 15A18, 20D99 Key Words and Phrases: Closeness matrix, Energy of a graph, Non-commuting graph, Dihedral Groups 1. Keywords: energy

Integral

Backwards Ito-Henstock Integral for the Hilbert-Schmidt-Valued Stochastic Process by Rulete, Ricky; Labendia, Mhelmar Avila (2019) - Math, 12 (1) (2019), 58-78 66 Note that∑ i
Keywords: integral
Triple Integral involving the Product of the Logarithmic and Bessel Functions expressed in terms of the Lerch Function by Reynolds, Robert; Stauffer, Allan (2022) - Introduction In this paper we derive the triple definite integral given by (1) ∫ ∞ 0 ∫ ∞ 0 ∫ ∞ 0 tmxv−my 1 2 (−m−v−1)Jv(t)e −bx2−cy logk ( at x √ y ) dxdydt where the parameters k, a, b, c, v,m are general complex numbers and Re(b) > 0, Re(c) > 0, Re(v) > 0, Re(m) < −1. The Hurwitz-Lerch zeta Function The Hurwitz-Lerch zeta function (25.14) in [3] has a series representation given by Φ(z, s, v) = ∞∑ n=0 (v + n)−szn (4) where |z|< 1, v 6= 0,−1, .. and is continued analytically by its integral representation given by Φ(z, s, v) = 1 Γ(s) ∫ ∞ 0 ts−1e−vt 1− ze−t dt = 1 Γ(s) ∫ ∞ 0 ts−1e−(v−1)t et − z dt (5) where Re(v) > 0, and either |z|≤ 1, z 6= 1, Re(s) > 0, or z = 1, Re(s) > 1. R. Reynolds, A. Stauffer / Eur. Keywords: integral; ∫ ∞
A Quadruple Integral Involving the Hermite polynomial Hn(x): Derivation and Evaluation by Reynolds, Robert; Stauffer, Allan (2022) - A method for evaluating definite integrals in terms of special functions with examples. Introduction In this paper we derive the quadruple definite integral given by (1) ∫ ∞ 0 ∫ ∞ 0 ∫ ∞ 0 ∫ ∞ 0 t−mxm−1z1−mym−nHn(xα)e −α2x2−b ( t2+y2+z2 ) logk (axy tz ) dxdydzdt ∗Corresponding author. Keywords: integral; ∫ ∞
A Quadruple Integral Involving the Hermite Polynomial Hn(x): Derivation and Evaluation by Reynolds, Robert; Stauffer, Allan (2022) - A method for evaluating definite integrals in terms of special functions with examples. Introduction In this paper we derive the quadruple definite integral given by (1) ∫ ∞ 0 ∫ ∞ 0 ∫ ∞ 0 ∫ ∞ 0 t−mxm−1z1−mym−nHn(xα)e −α2x2−b ( t2+y2+z2 ) logk (axy tz ) dxdydzdt ∗Corresponding author. Keywords: integral; ∫ ∞
Triple Integral involving the Bessel-Integral Function Jiv(z): Derivation and Evaluation by Reynolds, Robert; Stauffer, Allan (2022) - On some expansions for bessel integral functions. Math, 15 (3) (2022), 916-923 918 = − 1 2πi ∫ ∞ 0 ∫ ∞ 0 ∫ ∞ 0 ∫ C 1 v2Γ(v) 2−vaww−k−1(m+ w)xm+w−1(αx)ve−by2−cz2 y−m+v−w+1z−m−v−w+1 1F2 ( v 2 ; v 2 + 1, v + 1;−1 4 x2α2 ) dwdxdydz = − 1 2πi ∫ C ∫ ∞ 0 ∫ ∞ 0 ∫ ∞ 0 1 v2Γ(v) 2−vaww−k−1(m+ w)xm+w−1(αx)ve−by2−cz2 y−m+v−w+1z−m−v−w+1 1F2 ( v 2 ; v 2 + 1, v + 1;−1 4 x2α2 ) dxdydzdw = 1 2πi ∫ C πaww−k−12m+w−3α−m−wb 1 2 (m−v+w−2)c 1 2 (m+v+w−2) csc ( 1 2 π(m+ v + w) ) dw (5) from equation (4) in [2], equation (3.37.4.1) in [1] and equation (3.326.2) in [4] where 0 < Re(w + m) < 2, Re(m) < Re(v) < 2, α ∈ R+ and using the reflection formula (8.334.3) in [4] for the Gamma function. Keywords: integral
On the Relationship between the Integral of Derivative and the Derivative of the Integral by Han, GilJun; Kim, Hwajoon (2022) - If a(x) and b(x) are constants, we can easily see that d dx ( ∫ b a f(x, t) dt) = ∫ b a ∂ ∂x f(x, t) dt. Keywords: integral

Finite

On Distinguishing Local Finite Rings from Finite Rings Only by Counting Elements and Zero Divisors by GonzÃ¡lez, Marcos JosÃ© (2014) - Then (i) Z(R) is the Jacobson radical of R; (ii) |R|= pnr, and |J|= p(n−1)r for some prime number p, and some positive integers n,r; (iii) Z(R)n New Proof of Theorem 2 In this section, we shall provide a new proof for Theorem 2 based on the fact that, for the case in which R is a finite commutative ring, the Jacobson radical J(R) coincides with the ideal of all the nilpotent elements of the ring R. Let R be finite commutative ring with identity of order |R|= pm and having |Z(R)| Keywords: finite; j(r
Numerical Methods for Advection Problem by Ngoma, Diogene Vianney Pongui; Nguimbi, Germain; Mabonzo, Vital Delmas; Batangouna, Narcisse (2020) - 2020 Mathematics Subject Classifications: 65M06, 65M12, 65K05, 65L12 Key Words and Phrases: Advection problem, truncation error, stability, convergence, Lax- Wendroff and finite difference methods 1. This paper aims is to solve an advection problem where u=u(x, t) is the solution by Lax-Wendrof and finite difference methods, to study the analytical stability in L2[0, 1], L∞[0, 1], then calculate the truncation error of these methods and finally study the analytical convergence of these methods. Keywords: difference; finite; lax; wendroff

Resolving

On 2-Resolving Sets in the Join and Corona of Graphs by Cabaro, Jean Mansanadez; Rara, Helen (2021) - Conversely, let S = V (Kn) and x ∈ V (K1). x, y ∈ S By Remark 3, rK1+G(x/S) and rK1+G(y/S) differ in at least 2 positions, the xth and yth positions. Keywords: resolving; set
On 2-Resolving Dominating Sets in the Join, Corona and Lexicographic Product of Two Graphs by Cabaro, Jean Mansanadez; Rara, Helen (2022) - Introduction The problem of uniquely determining the location of an intruder in a network was the principal motivation of introducing the concept of metric dimension in graphs by Slater [7], where the metric generators were called locating sets. A set S ⊆ V (G ◦H) is a 2-resolving set of G ◦H if and only if S = A∪B, where A ⊆ V (G) and B = ⋃ {Sv : Sv is a 2-resolving set of Hv, for all v ∈ V (G)}. Keywords: resolving; set
Restrained 2-Resolving Sets in the Join, Corona and Lexicographic Product of Two Graphs by Cabaro, Jean Mansanadez; Rara, Helen (2022) - Introduction The problem of uniquely determining the location of an intruder in a network was the principal motivation of introducing the concept of metric dimension in graphs by Slater [8], where the metric generators were called locating sets. The concept of metric dimension of a graph was also introduced independently by Harary and Melter in [4] where metric generators were called resolving sets. Keywords: resolving; set

Parameter

Smoothing Parameter Selection for Nonparametric Regression Using Smoothing Spline by Aydin, Dursun; Memmedli, Memmedaga; Omay, Rabia Ece (2013) - Aydin and Memmedli [3] recommended GCV and REML as being good smoothing parameter selection criteria for small and medium sized samples. 2010 Mathematics Subject Classifications: 62E17, 65C05, 65C20, 65C60 Key Words and Phrases: Nonparametric regression, Smoothing spline, Smoothing parameter, Selec- tion criteria, Generalized cross validation. Keywords: methods; parameter; selection; smoothing
One-Parameter Planar Motion in Affine Cayley-Klein Planes by Bayrak Gurses, Nurten; Yuce, Salim (2014) - If we use the equation (8) for a pole point P = (p1, p2) ∈ Pε of the motions Pε/P ′ ε, we have � −u̇2 + ϕ̇(−u1 + x1) Then, if we take the acceleration pole point Q = (q1,q2) ∈ Pε of the motions Pε/P ′ ε, we get the following equation system: ¨ ε � ϕ̇ �2 � x1 − p1 � + εϕ̈ � x2 − p2 � = εϕ̇ ṗ2 ϕ̈ � x1 − p1 � − ε � ϕ̇ �2 � x2 − p2 � = ṗ1ϕ̇ (15) If ε � ϕ̇ �4 + � ϕ̈ �2 6= 0, we obtain the pole point from the above system as follows:            � ε2 � ϕ̇(t) �4 + ε � ϕ̈(t) �2 � q1(t) Keywords: motions; parameter; plane

Value

Higher Order Nonlocal Boundary Value Problems at Resonance on the Half-line by Iyase, Samuel; Opanuga, Abiodun (2020) - ξn−1 u(ξ), u(n−1)(∞) = ∫ ξ 0 u(n−1)(s)dA(s), u(n) ∈ Z } and Lu(t) = u(n)(t), u ∈ domL, t ∈ = ∫ ξ 0 u (n−1)(s)dA(s), u(i)(0) = 0, i = 1, 2, . . . Keywords: value
Hybrid Cubic B-spline Method for Solving A Class of Singular Boundary Value Problems by Heilat, Ahmed Salem; Batiha, Belal; Qawasmeh, Tariq; Hatamleh, Raed (2023) - − 3(xi+3 − x)3, x ∈ Khuri and Sayfy suggested a new approach implementing a modified decomposition method in combination with the cubic B-spline collocation technique is introduced for the numerical solution of a class of singular boundary value problems arising in physiology Keywords: boundary; cubic; spline; value

Convex

Existence Results for Generalized Vector Equilibrium Problems on Unbounded Sets by Allevi, Elisabetta; Konnov, Igor; Rocco, Marco (2017) - Math, 6 (2013), 365-376 366 of the generalized vector equilibrium problem, namely the problems of finding x ∈ K such that (GVEP1) Φ(x , y) 6⊆ V (x), ∀y ∈ K; (GVEP2) Φ(x , y)∩ V (x) = ;, ∀y ∈ K . = {(x , y) ∈ K Keywords: convex; set; φ(x; ∈ k
On Convexity in Product of Riemannian Manifolds by Allehabi, Wedad Saleh; Kilicman, Adem (2016) - The intersection of any number of product convex subsets is convex subset. Convexity in Riemannian Manifolds Product In this section, we study some properties of convexity in Riemannian manifolds product. Keywords: convex; manifolds; riemannian
Convex Roman Dominating Function in Graphs by Fortosa, Rona Jane; Canoy, Sergio (2023) - = 1 if and only if G = K1 (ii) γCvR(G) Graphs G such that γCvR(G) = 2γcon(G) are called convex Roman graphs. Keywords: convex; γcvr(g
Modified Inertial Krasnosel'skii-Mann Type Method for Solving Fixed PointProblems in Real Uniformly Convex Banach Spaces by Akuchu, Besheng George ; Aphane, Maggie; Ugwunnadi, Godwin; Okereke, George Emeka (2024) - Using this in 7 and ∀n ≥ 0, we have ∥an+1 − a∗∥p ≤ ∥an − a∗∥p + δnD2 +Mν 1 2 n − wp(ξn)c||T nbn − bn||p From this, the fact that ∑ δn < +∞ and condition (iii), we have∑ n≥0 2[ξn(1− ξn)] pc||T nbn − bn||p ≤ ∑ n≥0 wp(ξn)c||T nbn − bn||p ≤ ∑ n≥0 [||an − a∗||p − ||an+1 − a∗||p] +D2 ∑ n≥0 δn +M ∑ n≥0 ν 1 2 n <∞. This implies from conditions (ii) that lim ||T nbn − bn||p = 0. [1 + ξn(κ 2 n − 1)]||(1 + νn)an − νnan−1 − z||2 − ξn(1− ξn)||T nbn − bn||2 Keywords: convex; nbn −; nonexpansive
Convex Roman Dominating Functions on Graphs under some Binary Operations by Fortosa, Rona Jane Gamayot; Jamil, Ferdinand; Canoy, Sergio (2024) - Then f = (V0, V1, V2) is a CvRDF on G ◦H if and only if each of the following conditions hold: (i) V0 ∩ V (G) = ∅ (ii) For each v ∈ V2 ∩ V (G), Sv 1 ∪ Sv 2 induces a complete subgraph of Hv or V (Hv) \ (Sv 1 ∪ Sv 2 ) is a non-connecting set in Hv. (iii) For each v ∈ V1∩V (G) such that Sv 1 ̸= V (Hv), Sv 2 ̸= ∅, Sv 0 ⊆ NHv(Sv 2 ), and Sv 1 ∪Sv 2 induces a complete subgraph of Hv or V (Hv) \ (Sv 1 ∪ Sv 2 ) is a non-connecting set in Hv and Proof. Let f = (V0, V1, V2) be a CvRDF of G ◦ H. Since V1 ∪ V2 is a dominating set of G ◦H, V (v +Hv) ∩ (V1 ∪ V2) ̸= ∅ (1) R. Fortosa, S. Canoy Jr. / Eur. Keywords: convex
Convex Accessibility Number of the Complements and Some Binary Operations of Graphs by Samson, Harold; Aniversario, Imelda S. ; Luga, Mary Joy F. (2024) - The distance between ver- tices (u, v) and (u′, v′) in the Strong product G ⊠ H is equal to dG⊠H((u, v), (u′, v′)) A set C ∈ V (G ⊠ H) is a convex set in G ⊠ H if and only if C = CG ⊠ CH , where CG and CH are convex sets in G and H respectively. Proof. Keywords: convex
Some New Fractional Hermite-Hadamard Type Inequalities for Generalized Class of Godunova-Levin Functions by Means of Interval Center-Radius Order Relation with Applications by Afzal , Waqar; Mehreen S. Khan; Mutum Zico Meetei; Abbas, Mujahid ; Jorge E. Mac´ıas-D´ıaz; Hector Varlas-Rodriguez (2024) - and ζ1 − ζ2 = [ε1 − ε2, ε1 − ε2], with the product ζ1 · +Φ ( (k−ȷ− 1)ε1 + (ȷ+ 1)ε2 k )] − 1 ε2 − ε1 ∫ ε2 ε1 Φ(ς)dς = k−1∑ ȷ=0 ε2 − ε1 2k2 Keywords: convex; h(1− ♭; inequalities; ε1)d ♭; ε2 ε1; ς +; ς−1; φ(ε1; φ(ε2; − ε1; ♭ +; ♭ h; ⪯cr
Convex Independent Neighborhood Polynomial of Some Special Graphs by Aguilon, Edison John; Artes, Rosalio; Dagondon, Susan (2025) - Preliminary Results This section illustrates the definition of convex independent neighborhood polynomial of a graph. This contributes to convex independent neighborhood polynomial of G as 3x4y. Keywords: convex; neighborhood; subsets; γin
Inertial Iterative Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem by Darvish, Vahid ; Ogwo, Grace Nnennaya; Oyewole, Oyewole Kazeem ; Abass, Hammed Anuoluwapo ; Ikramov, Amirbek Aminovich (2025) - − Df (p, xn)] = 0, which completes the proof. − f (xnk ) + ⟨∇f (znk ) , xnk − znk ⟩ − ⟨∇f (znk )−∇f (xnk ) , p∗ − xnk ⟩ , for p∗ ∈ F (T ). Keywords: convex; lim; ynk

Codes

Generalized Gaussian Numbers Related to Linear Codes over Galois Rings by Salturk, Esengul; Åžiap, Irfan (2012) - 2010 Mathematics Subject Classifications: 11T71, 94B05, 05A10 Key Words and Phrases: Gaussian binomial coefficients, linear codes over rings 1. Introduction Binomial coefficients and Gaussian binomial coefficients are two fundamental classes of numbers arising in enumerative combinatorics. In this paper, we define a family of Generalized Gaussian Numbers that gives the number of linear codes over Galois rings directly. Keywords: codes; number
Cyclic Isodual and Formally Self-dual Codes over F_q+vF_q by Batoul, Aicha; Guenda, Kenza; Kaya, Abidin; Yildiz, Bahattin (2015) - In addition to the theoretical work on the structure of these codes, we construct examples of good codes over different alphabets from cyclic self-dual and formally self-dual codes over R. 2010 Mathematics Subject Classifications: 94B15, 94B05 Key Words and Phrases: Isodual Codes, Duadic codes, formally self-dual codes, cyclic codes 1. Recently, Zhu et al. considered the structure of cyclic codes over F2 + vF2 in [17]. Keywords: codes; cyclic; dual; self
On (1+u)-cyclic and Cyclic Codes over F2+uF2+vF2 by Dertli, Abdullah; Cengellenmis, Yasemin (2016) - It is studied codes over the ring R= F2+uF2+vF2, u2 = 0, v2 = v,uv = vu= 0 which contains the two ring F2+uF2,u2 = 0 and F2+ vF2, v2 = v. It is introduced (1+u)-cyclic codes and cyclic codes over F2+uF2+ vF2. It is characterized codes over F2+ vF2 which are the images of (1+u)-cyclic codes and cyclic codes over F2 + uF2+ vF2. Keywords: codes; cyclic; length
(1 âˆ’ 2u_2)-Constacylic Codes over F_p + uF_p + u^2F_p by Mostafanasab, Hojjat; Karimi, Negin (2016) - Constacyclic codes over finite fields form a remarkable class of linear codes, as they include the important family of cyclic codes. Most coding theory concerns on linear codes since they have clear structure that makes them simpler to discover, to understand and to encode and decode. Keywords: codes
Optimal, Divisible binary Codes from Gray-Homogeneous Images of Codes over R_{k,m} by Yildiz, Bahattin; Tufekci, Nesibe (2017) - We then use the first order Reed-Muller codes to find a distance-preserving map that takes codes over Rk,m to binary codes. These will be binary codes of parameters [16n, 5, 8n] and [32n, 6, 16n], respectively. Keywords: binary; codes; rings; weight
Counting Z2 Z4 Z8-additive Codes by Caliskan, Basri; Balikci, Kemal (2019) - Since α − k0 = 2 − 1, β − k1 − k2 = 1 − 1 − 0 = 0, k2 = 0, θ − k3 − k4 − k5 = 1− 1− 0− 0 = 0 and k5 = k4 = 0; the type of the dual code is (2, 1, 1, 1, 0, 0, 0, 0, 0) and δ = (2− 1)(1 + 1) + 0 + 0 + 0 + 0 = 2. So, the dual code C⊥ is of type (α, β, θ;α− k0, β − k1 − k2, k2, θ − k3 − k4 − k5, k5, k4) . Keywords: codes
Mass Formula for Self-Dual Codes over Galois Rings GR(p3, r) by Vasquez, Trilbe Lizann Espina; Petalcorin, Gaudencio Jr. Cempron (2019) - This discovery led to much interest and attention given to codes over the ring Zm of integers modulo m and finite rings in general. The number of codes equivalent to a code C over GR(p3, r) of length n is |En| |Aut(C)| and hence the number Np3,r(n) of distinct self-dual codes over GR(p3, r) of length n is Np3,r(n) Keywords: codes; dual; mod; self
Self-orthogonal Codes over Fq + uFq and Fq + uFq + u 2Fq by Galvez, Lucky Erap; Betty, Rowena Alma; Nemenzo, Fidel (2020) - A key problem is to establish an explicit formula for the number of distinct self-dual codes of length n over a ring R, given by∑ C |En| |Aut(C)| where C runs through the set of all inequivalent self-dual codes of length n over R, En is the full group of transformations allowed in defining the equivalence for code C and Aut(C) is the automorphism group. Math, 13 (4) (2020), 873-892 878 � Define the sets X = { C | C ⊆ Rn1 , type {k0, 0}, C ⊆ C⊥, res(C) Keywords: codes; ik0; orthogonal; self
Peak-Shift Control Codes for the $L_1$ Metric by Alqwaifly, Nawaf A. (2025) - Zn q are important to describe l peak shift error correction codes in Section 3. On a new class of error control codes and symmetric functions. Keywords: codes; peak; shift
Construction and Classification of Generalized Hadamard Codes over Eisenstein Local Rings Z_(2^s )[ω] by Sajjad, Muhammad; Ali Khan, Muhammad Farhan; Alammari, Maha ; Julian Serna , Robinson (2025) - = Z2s Math, 18 (3) (2025), 6409 2 of 32 for several critical concepts in this area, including linear codes, cyclic codes, and BCH codes, which have seen practical applications in data storage, satellite communication, and cybersecurity [1–4]. Keywords: codes; hadamard; sajjad; z2s
Structural Insights and Decoding Strategies for BCH Codes over Quasi-Galois Rings by Sajjad, Muhammad; Abid, Muhammad Shoaib; Alammari, Maha ; Serna , Robinson Julian (2025) - Our findings demonstrate the ability of BCH codes under QGR to provide high reliability and performance for the communication systems, which will make them a candidate for future use in data transmission and storage. This section is devoted to the discussion of major achievements and the state of the progress as well as the results of recent decades in the study of BCH codes over different algebraic structures. Keywords: a(2; bch; bch codes; codes; cyclic; decoding; error; galois; polynomial; rings; sajjad

Module

On a Proper Subclass of Primeful Modules Which Contains the Class of Finitely Generated Modules Properly by Fazaeli Moghimi, Hosein; Rashedi, Fatemeh (2015) - A submodule Q of M is said to be primary- like if Q 6= M and whenever rm ∈ Q (where r ∈ R and m ∈ M) implies r ∈ (Q : M) or ∗Corresponding author. if P 6= M and for p = (P : M), whenever rm ∈ P (where r ∈ R and m ∈ M) then m ∈ P or r ∈ p Keywords: module
A Module Whose Second Spectrum Has the Surjective or Injective Natural Map by Ansari-Toroghy, Habibollah; Pourmortazavi, Seyed sajad (2017) - As a result of Theorem 2.7, the definition of the classical Krull dimension of modules, which is independent of Specs(M), becomes more significant for secondful modules M . A proper submodule N of M is said to be prime if for any r ∈ R and m ∈ M with rm ∈ N , we have m ∈ N or r ∈ (N :R M). Keywords: module; second; specs(m; submodule
On Slightly Compressible-Injective Modules by Hoa Nghiem, Nguyen Dang; Janmuang, Phatsarapa; Baupradist, Samruam; Chinram, Ronnason (2018) - M → s(M) such that s′(m) = s(m) for all m ∈ M , so is(M)s ′ = s where is(M) : s(M) → M and it(M) : t(M) → M are embedding. M → Im(s) by s′(m) = s(m) for all m ∈ M . Keywords: injective; module
On C-co-epi-retractable Modules by Diallo, Abdoul Djibril; Diop, Papa Cheikhou; Barry, Mamadou (2019) - As f 6= 0, M = N , and so M is simple. Thus I ⊕ R, being a submodule of R ⊕ R is a C3-module by (7). Keywords: epi; module; right
Some Results on C-retractable Modules by Diallo, Abdoul Djibril; Diop, Papa Cheikhou; Barry, Mamadou (2020) - 2020 Mathematics Subject Classifications: 13B10,13C05,13C13 Key Words and Phrases: Retractable modules, complement submodules, c-retractable modules, projective modules 1. In [19] again, the semisimplicity of retractable modules is studied. Keywords: module; submodule; uniform
Localization of Hopfian and Cohopfian Objects in the Categories of A âˆ’ Mod, AGr(A âˆ’ Mod) and COMP(AGr(A âˆ’ Mod)) by Balde, Seydina Ababacar; Ben Maaouia, Mohamed Ben Faraj; Chbih, Ahmed Ould (2021) - 2020 Mathematics Subject Classifications: Mathematics Subject classification codes Key Words and Phrases: graded ring, a saturated multiplicative part formed by the non-zero homogeneous elements of A,Ore conditions, hopfian, cohopfian, sequence complex, chain complex, quasi-injective and quasi-projective. [21] R. Abu-Dawwas More on crossed product over the support of graded rings, Interna- tional Mathematical Forum, 5 (63), 3121-3126. Keywords: cohopfian; hopfian; left; module; s−1(m
Direct Summand of Serial Modules by BA, Alhousseynou; Diompy, Mankagna A.; Diabang, Andre S. (2024) - Hence for every endomorphism g : R −→ R there exists always a endomorphism g : R −→ R such that g ◦ Theorem 1: Let M1, ...,Mn be uniserial local modules. Keywords: module; serial

N=0

Truncated Tangent Polynomials by Acala, Nestor Gonzales; Montero, Maribeth B. (2020) - Some of the recent works on truncated numbers polynomials include truncated Fubini polynomials − m−1∑ n=0 Tm,n(x) tn n! = ∞∑ n=0 ( 2 ( n+m n ) xn − Tm,n+m(x) ) tn+m (n+m)! Keywords: n=0
Analytical Solution of the Ginzburg-Landau Equation by Wellot, Yanick Alain Servais; Nkaya, Gires Dimitri (2022) - u(x, y, t) = u(x, y, 0)+ ∫ t 0 (1+2i)∆u(x, y, s)ds−(1+2i) ∫ t 0 |u(x, y, s)|2u(x, y, s)ds+γ ∫ t 0 u(x, y, s)ds) = 0 (47) Let’s put Nu = |u(x, y, t)|2u(x, y, t), we have u(x, y, t) = u(x, y, 0)+ ∫ t 0 (1+2i)∆u(x, y, s)ds−(1+2i) ∫ t 0 Nu(x, y, s)ds+γ ∫ t 0 u(x, y, s)ds) = 0 (48) Y. A. S. Wellot, G. D. Nkaya / Eur. (52) We obtain the following canonical form: ∞∑ n=0 un(x, y, t) = u(x, y, 0)+(1+2i) ∫ t 0 ∆un(x, y, s)ds−(1+2i) ∫ t 0 Ands+γ ∫ t 0 un(x, y, s)ds (53) From (53), for γ = 1 + 2π2 9 (because γ is a constant), we obtain the following Adomian algorithm: u0(x, y, t) Keywords: n=0
Some Explicit Formula of Hurwitz Lerch type Poly-Cauchy Polynomials and Poly-Bernoulli Polynomials by Lacpao, Noel (2023) - = ∞∑ n=m { n m } tn n! , (|t| < 1) such that [ n m ] = 0 and { n m } = 0 for n < m. Parallel to this, Kaneko [11] defined certain variation of Bernoulli numbers in terms of polylogarithm function Lik(z) EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 16, No. 3, 2023, 1747-1761 ISSN 1307-5543 – ejpam.com Published by New York Business Global Some Explicit Formulas of Hurwitz Lerch type Poly-Cauchy Polynomials and Poly-Bernoulli Polynomials Noel B. Lacpao Department of Mathematics, College of Arts and Sciences, Bukidnon State University, Malaybalay City, 8700, Philippines Abstract. Keywords: n=0
On Gould-Hopper-based Bivariate Fubini polynomials by Bago, Raimah; Abdulcarim, Normalah (2025) - = ye(x+1)t+ztj 1− y(et − 1) = ext+ztj − ext+ztj + yext+ztj − yext+ztj + ye(x+1)t+ztj 1− y(et − 1) = ext+ztj + yext+ztj − ext+ztj (1− yet + y) 1− y(et − 1) = ext+ztj 1− y(et − 1) + yext+ztj 1− y(et − 1) − ext+ztj . = ext+ztj 1− y(et − 1) , (23) where |t| < 2π, if y y+1 = 1, and |t| < ∣∣∣ln( y y+1 )∣∣∣, if y y+1 ̸= 1. Observe that when j = 2, ∞∑ n=0 HF (2) n (x, y; z) tn n! = ext+zt2 1− y(et − 1) = ∞∑ n=0 HFn(x, y; z) tn n! , (24) which are the 3-variable Hermite-Fubini polynomials. Keywords: n=0; tn n
An Analytical Study of Two-Dimensional Bell Polynomials and Their Properties by Wani, Shahid Ahmad ; Alqurashi, Taghreed ; Ramírez, William; Malge, Shilpa ; Berrio Valbuena, Jesus David (2025) - Math, 18 (3) (2025), 6054 5 of 16 Here, we have made a significant advancement in the field by developing a new formulation for the generating relation of 2D Bell polynomials given by the generating expression: ∞∑ n=0 B[j] n (q1, q2) ξn n! = eq1(e ξ−1)+q2(eξ−1)j . For n ≥ 0, let { B [j] n (q1, q2) } n≥0 be the sequences of 2D Bell polynomials in the variable q1, q2 and q3, they satisfy the following relation n∑ k=0 ( n k ) Keywords: n=0; ξn n

Mod

A Hybrid Inversive Congruential Pseudorandom Number Generator with High Period by Riera, Constanza; Roy, Tapabrata; Sarkar, Santanu; Stanica, Pantelimon (2021) - For a modulus M = 2ω and y0 ∈ GM , let yn+1 ≡ ay−1n + b+ cyn (mod M), n = 0, 1, . . . +m+ 2mV0 and y−1m+1 = y−11 +m+ 2mV1 (mod M), for some integers V0 and V1 (inverses are considered in ZM ). Keywords: mod; mod m; period
Cyclic Codes from a Sequence over Finite Fields by Nopendri, Nopendri; Muchtadi-Alamsyah, Intan; Suprijanto, Djoko; Barra, Aleams (2021) - The dimension of cyclic code C can be determined from degree of generator polynomial g. The error-correcting capability of cyclic codes may not be as good as some other linear codes in general. Optimal sets of frequency hopping sequences from linear cyclic codes. Keywords: cyclic; mod
Non-existence of Positive Integer Solutions of the Diophantine Equation $p^x+(p+2q)^y=z^2$, where $p$, $q$ and $p+2q$ are Prime Numbers by Tadee, Suton; Siraworakun, Apirat (2023) - If p is a prime number with 2q ̸≡ 1 (mod p) and satisfies any of the following conditions: (i) p ≡ q2 + 8n1r S2 (mod 8q), (ii) p ≡ − q2 + 8n1r S2 (mod 8q), (iii) p ≡ 3q2 + 8n1r S1 (mod 8q), or (iv) p ≡ − 3q2 + 8n1r S1 (mod 8q), where S1 ∈ {2, 4, 6, . . If p satisfies any of the following conditions: (i) p ≡ q2 + 32n0n1r S2 (mod 8q), (ii) p ≡ − q2 + 32n0n1r S1 (mod 8q), (iii) p ≡ 3q2 + 32n0n1r S2 (mod 8q), or (iv) p ≡ − 3q2 + 32n0n1r S1 (mod 8q), where S1 ∈ {2, 4, 6, . . . Keywords: mod
On the Diophantine equation $4(7^x)-p^y=z^2$ by Laipaporn, Kittipong; Jankaew, Ratcharut; Sae-Iu, Poomipat; Karnbanjong, Adisak (2025) - Motivated by previous studies on exponential Diophantine equations, we continue this line of inquiry by examining the equation 4(7x)− py = z2, where p is a prime and x, y, z ∈ Z0. − py = z2, where p is a prime. Keywords: mod; y ≡
On the Unsolvability of the Exponential Diophantine Equation $ 23^x + 22^y = z^2 $ in Nonnegative Integers by Assiry, Abdullah (2025) - This study contributes to the broader understanding of exponential Diophantine equations and their solutions. Discussion Our result adds to the growing body of work on exponential Diophantine equations, particularly those of the form px + (p − 1)y = z2. Keywords: integer; mod
On the Diophantine Equation $p^x + (p + 5k)^y = z^2$ by Bacani, Jerico Bravo; Avenilla, Merlyn (2025) - Finding for q we have, q = z2 − 22+4n = (z − 21+2n)(z + 21+2n). Math, 18 (3) (2025), 6593 23 of 24 There are finitely many solutions when y = 1 and x = 2 + 4n, n ∈ N0, where the value of k and z are given by k = (22+2n − 1)/5 and z = (5k + 3)/2. Keywords: mod
Edge Irregular Reflexive Labeling of Ladder Graph Corona Null Graph Families by Indriati, Diari; Sentosa, Muhammad Yogi ; Verdiana, Zhafirah Miranti ; Martini, Titin Sri ; Utomo, Putranto Hadi ; Kurdi, Nughthoh Arfawi ; Rosyida, Isnaini (2025) - − 3 6≡ 2, 3 (mod 6)” and “ ⌈ 2nm+3n−3 3 ⌉ + 1” for “2nm + 3n − 3 ≡ 2, 3 (mod 6)”. Moreover, res(DLn � Nm) for n ≥ 2 and m ≥ 1 are “ ⌈ 2nm+5n−4 3 ⌉ ” for “2nm+5n− 4 6≡ 2, 3 (mod 6)” and “ ⌈ 2nm+5n−4 3 ⌉ +1” for “2nm+ 5n− 4 ≡ 2, 3 (mod 6)”. Keywords: mod

Inverse

Natural Generalized Inverse and Core of an Element in Semigroups, Rings and Banach and Operator algebras by Mary, Xavier (2017) - = ae, f = f 2 = f a = a f and e f = e, f e = f . = e = (eae)b = eab and b is the inverse of a along e. Finally, note that Σ2(a) is a commutative band (commutative semigroup of idempotents, semilattice with e ∧ f = e f = f e). Keywords: drazin; element; inverse
Natural Generalized Inverse and Core of an Element in Semi- groups, Rings and Banach and Operator Algebras by Mary, Xavier (2012) - = e = (eae)b = eab and b is the inverse of a along e. Finally, note that Σ2(a) is a commutative band (commutative semigroup of idempotents, semilattice with e ∨ f = e f = f e). = ae, f = f 2 = f a = a f and e f = e, f e = f . Keywords: element; inverse
Inverse Limit of an Inverse System of BE-algebras by Albaracin, Jimboy Ruben; Vilela, Jocelyn P. (2021) - if: (F1) 1X ∈ F ; and (F2) x ∗ y ∈ F and x ∈ F imply y ∈ F . If I is the family of all normal filters of X such that X/F is finite for all F ∈ I, then we call the inverse limit of the inverse system {X/F,ϕFG, I} the normal completion of X. Example 1. Keywords: inverse

Subgroup

The Inï¬‚uence of C- Z-permutable Subgroups on the Structure of Finite Groups by Al-shomrani, Mohammed Mosa; Heliel, Abdlruhman A. (2018) - Let Z be a complete set of Sylow subgroups of a finite group G, that is, for each prime p dividing the order of G, Z contains exactly one and only one Sylow p-subgroup of G, say Gp. Recently, in 2003, Asaad and Heliel [1] introduced the concept of Z-permutability which generalizes S-permutability as follows: Let Z be a complete set of Sylow subgroups of a group G. A subgroup H of G is said to be Z-permutable in G if H permutes with every ∗Corresponding author. Keywords: subgroup
Finite Groups with Certain Permutability Criteria by Hijazi, Rola A.; Charaf, Fatme M. (2019) - Thus p is the largest prime dividing |G| and since K is cyclic, it follows, by Burnside′s p-Nilpotent Theorem ([10], Satz 2.8, p.420), that P C G. But G/P ∼= K, therefore G/P is cyclic and so abelian, then G′ ≤ P . Thus we may assume that there exists a subgroup H of P of order p such that H is not normal in G. By the hypothesis, H is S-permutable in G and hence by ([13], Lemma A), Op(G) ≤ NG(H) Keywords: nilpotent; subgroup
Subnormality and Theory of L-subgroups by Jahan, Iffat; Ajmal, Naseem; Davvaz, Bijan (2022) - [? ] Let η ∈ L µ . [15] Let η ∈ Lµ. Keywords: subgroup; subnormal
Finite Groups with Certain Weakly S-permutable Subgroups by Alsowait, Nawaf; Heliel, Abdelrahman A.; Al-Shomrani, Mohammed; A. S. Allehyani, Areej (2024) - A subgroup H of G is said to be weakly S-permutable in G if G has a subnormal subgroup T such that G = HT and T ∩H ≤ HsG, where HsG is the subgroup of H generated by all those subgroups of H which are S-permutable in G. (11) There exists a proper normal subgroup M of G such that |G/M | = p, G = LT , L ∩ T = (L)sG, where T is a subnormal subgroup of G and T ≤ M < G. By (10), L is not S-permutable in G. Then by the hypothesis, L is weakly S-permutable in G. Keywords: nilpotent; subgroup
Finite Groups with Certain $\mathcal{SSH}$-subgroups by Allehyani, A. S. (2025) - Clearly, P1 ⊴ G and (G/P1)/(H/P1) ∼=265 G/H ∈ F. By using similar arguments as in the second paragraph of (1) in Theorem 2,266 we can see that G/P1 ∈ F. But P1 ⩽ Φ(G), then G/Φ(G) ∈ F and, since F is saturated,267 we have G ∈ F, a contradiction. Let H and L be normal subgroups of G and let p ∈ π(G). Keywords: cyclic; lemma; ssh; subgroup; sylow
Notes on Finite Groups with Nearly S-permutable and Nearly S-permutable-Transitive Subgroups by Mutlaq Alotaibi, Abdulaziz ; Al-Tahat, Khalid ; Aljamal, Khaled Mustafa (2025) - One fundamental property of normal subgroups is that if N is a normal subgroup of G and H is any subgroup of G, then NH = HN . Let G be agroup and H is normal subgroup of G and let H ≤ K ≤ G for every prime number p ∈ P with (P, |H|), since H ⊴ G implies H ⊴ K. Then NK(H) Keywords: groups; subgroup

Linear

Weights of Codewords in Random Binary Linear Codes and Their Correlation Properties by Özen, İbrahim (2024) - Conclusion We obtained the expectations of single and pairwise products of weights of codewords in random binary linear codes. On the weight distribution of random binary linear codes. Keywords: binary; code; linear; nonzero

Operators

Stancu type generalization of modified Srivastava-Gupta operators by Mishra, Vishnu Narayan; Kumar, Alok; Tapiawala, Dipti (2017) - For x ∈ [0,∞), we consider the auxiliary operators G ∗(α,β) n,c defined by G ∗(α,β) n,c (f ;x) = G∗(α,β)n,c (f ;x)− f ( nx+ α n+ β ) + f(x). β we introduce the following Stancu type generalization of the operators (3): G∗(α,β)n,c (f ;x) = n ∞∑ k=1 pn,k(x, c) Keywords: g∗(α; operators; β)n
On a Modification of Dunkl Generalization of Szasz Operators via q-calculus by Mishra, Vishnu Narayan; Pandey, Shikha; Khan, Idrees A. (2017) - Since for fixed q with 0 < q ≤ 1, lim n→∞ [n]q = 1, to ensure the convergence properties we will assume q = qn as a sequence such that lim n→∞ qn = 1, and lim n→∞ qnn = c where c ∈ (0, 1). [8] presented the Dunkl generalization of Szász operators via q-calculus as Dn,q(f ;x) := 1 eµ,q([n]qx) ∞∑ k=0 ([n]qx)k γµ,q(k) f ( Keywords: eµ,q([n]qx; operators
Local Approximation Results for Stancu Variant of Modified Szasz-Mirakjan Operators by Devdhara, Ankita R.; Mishra, Vishnu Narayan (2018) - Indeed, the rapid development has led to the discovery of new generalizations of approximation operators (one may refer to [2],[7], Using above operators and (9), we get Ŝα,βn (t− x;x) Keywords: operators
Direct Estimates for Certain Integral Type Operators by Kumar, Alok; Tapiawala, Dipti; Mishra, Lakshmi Narayan (2018) - [0,∞)= sup x∈[0,∞) |f(x)|), ‖M (β,γ) n,α (f) ‖≤‖ f ‖ . A. Kumar, D. Tapiawala, L. N. Mishra / Eur. In view of (3) and Lemma 2, we get ‖M (β,γ) n,α (f)‖ ≤ ‖f‖M Keywords: operators
A General Family of the Srivastava-Gupta Operators Preserving Linear Functions by Gupta, Vijay; Srivastava, Hari M. (2018) - The general sequence of positive linear operators containing some well-known operators as special cases were introduced in the earlier work by Srivastava and Gupta [9], which reproduce only the constant functions. Here, in this paper, we have successfully provided a general sequence Gn,c(f, x) of positive linear operators which preserve not only the constant functions, but also linear functions. Keywords: operators
Invariant Subspace Problem for Norm Attaining Operators by Nasli Bakir, Aissa ; Fellag Ariouat , Ayyoub ; Benali, Abdelkader ; Alraddadi, Ibrahim ; Almuaddi, Saad M. (2025) - = inf{∥Tu∥ : u ∈ H and ∥u∥ = 1} is said to be the minimum modulus of T ∈ B(H), and the quantity me(T ) It is known that quasi-∗-paranormal operators are normaloid, that is, r(T ) Keywords: norm; operators; quasi-∗-paranormal

Systems

Monotone Flows with Dense Periodic Orbits by Hirsch, Morris W. (2019) - [15] P. Hess & P. Polacik, Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems, SIAM J. Mathematical Analysis 24 (1993), 1312-1330. [31, 32], and a sufficient condition for the nonstationary periodic points in a closed order interval to have rationally related periods (Theorem 2). 2010 Mathematics Subject Classifications: 37C65, 37C25, 57Sxx Key Words and Phrases: Monotone dynamical systems, Periodic points, Topological transformation groups 1. Keywords: monotone; periodic; systems
Sensitivity of Fuzzy Nonautonomous Dynamical Systems by Lan, Yaoyao (2019) - EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 12, No. 4, 2019, 1689-1700 ISSN 1307-5543 – www.ejpam.com Published by New York Business Global Sensitivity of fuzzy nonautonomous dynamical systems Yaoyao Lan Department of Mathematics, Chongqing University of Arts and Sciences, Yongchuan, China Abstract. Nonautonomous discrete dynamical systems For a compact metric space X, let {fn}∞n=1 be a sequence of continuous maps, where fn : X → X. An orbit {xn}∞n=1 of a point x1 ∈ X is defined as follows: xn+1 = fn(xn), n = 1, 2, · · · The set-valued extension of (X, {fn}∞n=1) is denoted by (K(X), {f̄n}∞n=1). Keywords: f(x; sensitivity; sup; systems

Population

Generalized Class of Estimators for Median Estimation Using Auxiliary Information by Ahmad, Sohaib; Masood, Saadia; Mustafa, Manahil SidAhmed ; Mohamed, Elsiddig Idriss ; Hussain, Elfarazdag M. M. (2025) - On four distinct datasets, the suggested generalized class of estimators is contrasted with existing estimators. 11389.3000 206.8794 12219.56 224.5767 12267.25 226.6069 12272.72 182.617 12154.72 101.3134 11996.84 Figure 1: MSE of median estimators using population 1 S. Ahmad et al. / Eur. Keywords: estimation; estimators; median; population
On Use of Predictive Technique for Estimation of Population Mean Using Auxiliary Information: Application on Real Data Sets by Khan, Sajid; Farooq, Muhammad; Ahmad, Sohaib; Mustafa, Manahil SidAhmed ; Mohamed, Elsiddig Idriss ; Hussain, Elfarazdag M. M.; Albadwi, Fatima Ibrahim Abdallah (2025) - − Z̄k2e2 − 1 2 Ȳ γe0e1 + Ȳ (γ2 + 2γ − 4γf)e21 8(1− f) + X̄k1γe 2 1 2(1− f) + Z̄k1γe1e2 2(1− f) (31) = NX̄ − nx̄ N − n Simplifying the right-hand side of Equation (29), multiplying and expressing the above equation in terms of e’s as follows: tp = Ȳ Keywords: estimation; estimators; mean; population; sampling

Performance

Towards Accurate Fake News Detection: Evaluating Machine Learning Approaches and Feature Selection Strategies by Al-Tarawneh, Mutaz; Al-Khresheh, Ashraf; Al-irr, Omar; Kulaglic, Ajla; Danach, Kassem ; Kanj, Hassan; AlMahadin, Ghayth (2025) - This detailed examination of feature selection techniques provides valuable insight into how different methods influence the effectiveness of fake news detection models. This holistic approach improves the accuracy and robustness of fake news detection models, which separates this study from others that focus primarily on advanced model architectures or specific feature sets. Keywords: accuracy; auc; components; detection; feature selection; features; knn; learning; methods; mlp; models; news; number; performance; precision; recall; roc; score; selection; svm

Gradient

A New Class of Optimization Methods Based on Coefficient Conjugate Gradient by Laylani, Yoksal; Hassan, Basim A. ; Khudhur, Hisham M. (2022) - Conjugate gradient methods using value of objective func- tion for unconstrained optimization optimization letters. Math, 15 (4) (2022), 1908-1916 1914 Table 1: The numerical results of the FR and New methods FR algorithm BN1 (16) BN2 (17) BN3 (18) P. No. n NI NF NI NF NI NF NI NF 1 100 19 35 18 33 18 33 18 34 1000 38 65 32 57 34 62 38 65 2 100 47 93 40 80 40 82 42 90 1000 78 131 37 78 34 74 39 85 3 100 61 1024 47 665 25 43 28 46 1000 Fail Fail Fail Fail Fail Fail Fail Fail 4 100 32 64 10 21 10 21 13 27 1000 77 129 16 31 16 31 15 31 5 100 37 67 40 63 40 63 44 70 1000 73 115 65 102 67 107 61 98 6 100 15 31 8 17 8 17 8 17 1000 8 17 7 15 7 15 7 15 7 100 40 65 35 56 37 58 36 56 1000 43 68 49 382 39 59 42 65 8 100 69 1202 45 637 38 364 26 48 1000 98 1967 65 1279 43 440 33 257 9 100 671 1066 441 689 480 763 612 982 1000 Fail Fail Fail Fail Fail Fail Fail Fail 10 100 20 33 10 19 10 19 10 19 1000 19 35 9 18 9 18 9 18 11 100 49 80 15 28 14 26 15 26 1000 129 166 13 26 13 26 13 26 12 100 43 88 38 86 33 75 37 79 1000 46 92 34 77 35 76 40 89 13 100 122 156 12 23 12 23 12 23 1000 130 166 12 23 12 23 12 23 14 100 112 147 34 57 37 61 34 58 1000 110 145 38 58 40 60 35 55 15 100 32 52 12 24 12 24 16 32 1000 22 42 12 24 12 24 19 38 Total 2240 7341 1194 4668 1175 2687 1314 2472 The novel procedure saves NI and NF over time when compared to the conventional Fletcher and Reeves (FR) methodology, notably for our set of test problems, as demon- strated in Table 2. Keywords: conjugate; fail; gradient; new
Image Impulse Noise Reduction Using a Conjugate Gradient of Alternative Parameter by Jabbar, Hawraz N.; Subhi, Yeldez J.; Hassan, Basim A. (2023) - [7] Basim A Hassan and Ali Ahmed A. Improvement of conjugate gradient methods for removing impulse noise images. Convergence properties of nonlinear conjugate gradient methods. Keywords: gk+1; gradient; new; stk

Type

Analysis of Hardy-type Inequalities Involving Green Functions and Taylor’s Polynomial Approximation by Abbasi, Anjum Mustafa Khan; Matloob Anwar (2025) - Math, 18 (1) (2025), 5694 3 of 18 + ∫ a2 a1 G1(ϖ, τ)F ′′′(τ)dτ, (1) F(ϖ) = F(a2) + (ϖ − a2)F ′(a1) + (ϖ − a1)(ϖ − a2)F ′′(a2)− (ϖ − a2) 2 2 F ′′(a1) − ∫ a2 a1 G2(ϖ, τ)F ′′′(τ)dτ, (2) F(ϖ) = F(a2) + (ϖ − a1)F ′(a1) + (a2 − a1)F ′(a2)− [ (ϖ − a1) 2 2 + (ϖ − a1)(a− b) ] F ′′(a1) + [ (a2 − a1) 2 2 + (ϖ − a1)(ϖ − a2) ] F ′′(a2)− ∫ a2 a1 G3(ϖ, τ)F ′′′(τ)dτ (3) and F(ϖ) = F(a2) + (a2 − a1)F ′(a1) + (b−ϖ)F ′(a2) + [ (a2 − a1) 2 2 + (ϖ − a2)(ϖ − a1) ] F ′′(a1) − [ (ϖ − a2) 2 2 + (ϖ − a2)(a2 − a1) ] F ′′(a2) = 1 (n− 4)! (∫ a2 a1 B1(τ)F (n)(τ)dτ − F (n−1)(a2)−F (n−1)(a1) (a2 − a1) ∫ a2 a1 B1(τ)dτ ) .(44) Keywords: a2 a1; inequalities; type
Multisorted Algebras of Trees of a Weakly Fixed Variable by Kumduang, Thodsaporn; Wattanatripop, Khwancheewa (2025) - Then we prove the following theorem which gives a necessary condition for any variety V to be weakly fixed variable. On a variety V of type τ , we let s ≈ t ∈ HIdwfv n (V ) and (σn)n∈N ∈ (Hypwfv n (τ))n∈N. Applying Theorem 2, we have σ̂n[s] ≈ σ̂n[t] ∈ Idn(V ) for all n ∈ N. Hence, s ≈ t is a weakly fixed variable hyperidentity in V , whence, a variety V is weakly fixed variable. Keywords: terms; type; variable; wwfv

Scheme

A New Approach to Construct Secret Sharing Schemes Based on Field Extensions by Molla, Fatih; Calkavur, Selda (2018) - In this paper, we propose a new approach to construct secret sharing schemes based on field extensions. Key Words and Phrases: Field extension, secret sharing, secret sharing scheme. Keywords: scheme; secret; sharing

Velocity

Unsteady Stokes Flow through Porous Channel with Periodic Suction and Injection with Slip Conditions by Bhatti, Kaleemullah; Bano, Zarqa; Siddiqui, Abdul Majeed (2018) - Results and Discussion The numerical values of axial and radial velocity components have been calculated for different values x, ωt and slip parameter λ. Figure 1: Axial velocity profile for λ=0.1, v1 = 1, v2 = 2 x = 0, H = 10, u0 = 0.5 and α=1 for different values of ωt Figures 1 to 7 are axial velocity profiles at different cross sections of the channel namely at x = 0, x = 2 and x = 4 and for different values of slip parameter namely for λ = 0, K.Bhatti, Z. Bano, A. M. Siddiqui / Eur. Math, 11 (4) (2018), 937-945 942 Figure 2: Axial velocity profile for λ=0.1, v1 = 1, v2 = 2 x = 2, H = 10, u0 = 0.5 and α=1 for different values of ωt Figure 3: Axial velocity profile for λ=0.1, v1 = 1, v2 = 2 x = 4, H = 10, u0 = 0.5 and α=1 for different values of ωt Figure 4: Axial velocity profile for λ=0.2, v1 = 1, v2 = 2 x = 0, H = 10, u0 = 0.5 and α=1 for different values of ωt K.Bhatti, Z. Bano, A. M. Siddiqui / Eur. Keywords: velocity

Cost

Cost Effective Domination in the Join, Corona and Composition of Graphs by Jamil, Ferdinand P.; Maglanque, Hearty Nuenay (2019) - As direct consequences, the bounds or the exact cost effective domination numbers, minimal cost effective domination numbers and upper cost effective domination numbers of these graphs were obtained. 2010 Mathematics Subject Classifications: 05C12 Key Words and Phrases: Cost effective dominating set, cost effective domination number, join, corona, composition 1. Therefore, S is a cost effective dominating set of G+H. In view of Theorem 1, all independent dominating sets of G and all independent dominating sets of H are cost effective dominating sets of G + H. Keywords: cost; dominating set; set
Distance k-Cost Effective Sets in the Corona and Lexicographic Product of Graphs by Caadan, Julius Guhiting; Paluga, Rolando N. ; Aniversario, Imelda S. (2023) - Hence, |Nk G[H](u, v) ∩ (V (G[H])\(A× V (H)))| − |Nk G[H](u, v) ∩ (A× V (H))| = |Nk G(u) ∩ (V (G) \A)||V (H)| − |Nk G(u) ∩A||V (H)| − |V (H)| = ( |Nk G(u) ∩ (V (G) The concept of cost effective set in graph was introduced by Haynes et al. in [7]. Keywords: cost; distance; effective

Curve

Elliptic curves and Pythagorean triples by Nabardi, Kamran; Izadi, Farzali; Khoshnam, Foad (2014) - With t := i/ j as a coordinate function on P1, this allows to write the family of cubics as y2 = x(x − (t2 − 1)2)(x − 4t2). So again, specialization yields infinitely many exam- ple of rank at least 2 over Q. By taking x = t2 − 1, one needs that 3t4 − 5t2 − 2 is a square, say = s2. Keywords: curve; points; rank
Frenet Apparatus of the Curves and Some Special Curves in the Euclidean 5-Space $E^5$ by Masal, Melek; Azak, Ayse Zeynep (2015) - (34) From the equations (28) and (30), we get Ẏ 2 Ÿ − Ẏ , Ÿ � Ẏ = −(c − s)3k4 1V1 + (c − s)3k3 1k2V3 (35) and Ẏ 2 Ÿ − Ẏ , Ÿ � Ẏ = (c − s)3k3 1 q k2 1 + k2 2. (36) If we use the equations (11) and (14), then we will obtain the second Frenet vector and the first curvature of curve Y as follows; V Y 2 = − k1 q k2 1 + k2 2 V1 + k2 q k2 1 + k2 2 V3 (37) and kY 1 = q k2 1 + k2 2 (c − s)k1 (38) respectively. (50) On the other hand, for the base � V1, V2, V3, V4, V5 and mi(s) ∈ R C − X (s) = m1(s)V1(s) +m2(s)V2(s) +m3(s)V3(s) +m4(s)V4(s) Keywords: curve
On the Involute of the Cubic Bezier Curve by Using Matrix Representation in E3 by Kilicoglu, Åžeyda; Åženyurt, Suleyman (2020) - − z0 − z2 + 6ητ mκ b13 2x0 − 2x1 + − z0 − z2 + 6ητ mκ b13 2x0 − 2x1 + Keywords: curve; ; 
Quasi Ruled Surfaces in Euclidean 3-space by Elsharkawy, Ayman; Elsayied, Hoda; Refaat, Aya (2025) - This paper introduces three distinct types of ruled surfaces, namely, the quasi- tangent surfaces , the quasi-normal surfaces, and the quasi-binormal surfaces. 2020 Mathematics Subject Classifications: 53A05 Key Words and Phrases: Ruled surface, Euclidean space, Quasi frame, developable surface, minimal surface 1. Keywords: curve; quasi; surface

Network

S-invariant Termwise Addition of Reactions Via Reaction Vector Multiples (STAR-RVM) Transformation by Magpantay , Daryl (2023) - Let N = (S ,C ,R) be a CRN and y → y′ ∈ R with y′ − y = (c1, . . . Deficiency of a CRN A central concept of the theory of chemical reaction networks is the deficiency of the CRN. Keywords: complexes; network; number; reactant; reaction; rvm; star
Computing and Simulating Fractal Dimensions to Advance Sustainable Cities: The Road Networks of Buraydah, Saudi Arabia by Sajid, Mohammad; Husain, Akhlaq (2025) - Urban road networks possess fractal characteristics due to ordered division and struc- tural layout of the road networks which contain inherent self-similarity and scale invariance. The planning and systematic structure of urban road networks have become an integral and im- portant part of urbanization which provides good connectivity, attracts industrialization, globalization and helps seamlessly in creating sustainable cities. Keywords: buraydah; city; dimension; fractal; geometry; network; number; road; urban

Submodule

Classical 2-absorbing Submodules of Modules Over Commutative Rings by Mostafanasab, Hojjat; Tekir, Unsal; Hakan Oral, Kursat (2015) - A proper submodule N of M is called a 2-absorbing submodule of M if whenever abm N for some a, b R and m M , then am N or bm N or ab ! N :R M . an (N :R M) or there are n& 1 of ai ’s whose product with m is in N , see [14]. Keywords: r m; submodule
A Note on Primary and Weakly Primary Submodules by Ulucak, Gulsen (2016) - Let 0M 6= r s m p ∈ NM for some r s ∈ RM and m p ∈ MM (for some r ∈ R, m ∈ M and s, p ∈ R\M). Let rm ∈ N for some r ∈ R, m ∈ M . Keywords: submodule
On Generalizations of phi-2-Absorbing Primary Submodules by Yiarayong, Pairote; Siripitukdet, Manoj (2018) - N is said to be a φ-2-absorbing primary submodule of M if whenever a1, a2 ∈ R and m ∈ M with a1a2m ∈ N − φ(N), then a1a2 ∈ √ (N : M) or a1m ∈ N or a2m ∈ N . Moreover, recall from [10] that a proper submodule N of M is said to be a φ-2-absorbing submodule of M if whenever a1, a2 ∈ R and m ∈ M with a1a2m ∈ N − φ(N) implies a1a2 ∈ (N : M) or a1m ∈ N or a2m ∈ N . Keywords: a1a2; primary; submodule; φ-2
e*-Essential Submodule by Baanoon, Hiba; Khalid, Wasan (2022) - We will introduce some examples and properties about this concept such that, what is the in- verse image of e∗-essential submodule, the intersection of e∗-essential submodules and direct sum of e∗-essential submodules. The purpose of this paper is to introduce a new concept in a module M over a ring R, this concept is called e∗-essential submodule, which is a generalization of an essential submodule. Keywords: submodule
On Ï†-Î²-Absorbing Submodules by Khumprapussorn, Thawatchai (2022) - In [2], a proper submodule P of a left R-module M is called β-absorbing if for any element r, s ∈ R and m ∈ M such that rsm ∈ P , we have rs + rs ∈ (P : M) or r(m + m) ∈ P or s(m + m) ∈ P . We recall that a proper submodule P of a left R-module M is called a prime submodule of M if for every r ∈ R and m ∈ M , rm ∈ P implies that m ∈ P or r ∈ (P : M). Keywords: submodule
e*-Essential Small Submodules and e*-Hollow Modules by Baanoon, Hiba; Khalid, Wasan (2022) - Since M N is e∗-hollow, then K+N N = M N , and M = K + N because N � M . A submodule N of M is called a small submodule of M denoted (N � M) if for any submodule A of M such that M = N + Keywords: submodule

Distance

Upper Distance k-Cost Effective Number in the Join of Graphs by Caadan, Julius Guhiting; Paluga, Rolando N.; Aniversario, Imelda S. (2020) - The concept of cost effective set in graph was introduced by Haynes, et.al. A set S ⊆ V (G) is a distance k- cost effective set of G if for every v ∈ S, |Nk G(v) ∩ Sc| − |Nk G(v) ∩ S| ≥ 0. Keywords: distance; set
2-distance Zero Forcing Sets in Graphs by Hassan, Javier; Udtohan, Lestlene T. ; Laja, Ladznar S. (2024) - We show that 2-distance zero forcing and hop domination(respectively, zero forcing parameter) are incomparable. Some properties of zero forcing hop dominating sets in a graph. Keywords: distance; forcing; set
Failed 2-Distance Zero Forcing in Graphs by Madjatul, Al-Fadzri; Hassan, Javier; Bonsocan, Maria Andrea O. ; Bilar, Vergel T. (2025) - Suppose that Q is a failed 2- distance zero forcing set of G+H. Then Q ̸= V (G + H). The join of G and H, denoted by G+H is the graph with vertex set V (G+H) Keywords: distance; forcing; graphs; set

Labeling

Graceful Labeling of Some Spider Graphs by Saengsura, Kittisak; Poomsa-ard, Tiang (2025) - A systematic presentation of diverse applications of graph labeling is presented in [2]. A graceful labeling of a tree is a special kind of labeling graph, i.e., a graceful label- ing f of a tree T is a bijective function from the set of vertices V (T ) of T to the set {0, 1, 2, . . . Keywords: labeling; spider
Cordial Labeling of Corona Product of Paths and Fourth Order of Lemniscate Graphs by Abd El-hay, Atef ; A. Alsatami, Khalid; ELrokh, Ashraf ; Rabie, Aya (2025) - 2020 Mathematics Subject Classifications: 05C78,05C15 Key Words and Phrases: Cordial labeling, corona, lemniscate, Social Networking, Network security, Edge Computing 1. Cordial labeling is a weaker version of graceful labeling and harmonious labeling introduced by Cahit in [3]. Keywords: labeling
A Novel Problem and Algorithm for Solving Cordial Labeling of Some Fifth Powers of Graphs by Abd El-hay, Atef; A. Alsatami, Khalid; Elrokh, Ashraf (2025) - The original concept of cordial graphs is due to Cahit[3]. One interesting application is to pro- duce new cordial families by using a technique called balanced cordial labeling, which can generate cordial graphs from two given graphs by taking one copy of one graph and j copies of another graph and joining them by an edge. Keywords: 10(r; labeling

Step

Convergence Analysis of Multi-Step Collocation Method to First-Order Volterra Integro-Differential Equation with Non-Vanishing Delay by Ali Eashel, Ahmet; Pishbin, Saeed; Darania, Parviz (2025) - , n− 1, (∫ si 0 K(t (µ) n,i , t (.) l + sh (.) l )β1(s)ds, ..., ∫ si 0 K(t (µ) n,i , t (.) l + sh (.) l )βm(s)ds ) , l = n. D̃DD (.),l n =  (∫ 1 0 K̂(t (µ) n,i , t (.) l + sh (.) l )β1(s)ds, ..., ∫ 1 0 K̂(t (µ) n,i , t (.) l + sh (.) l )βm(s)ds ) , l = r − 1, . . . , n− 1, (∫ si 0 K̂(t (µ) n,i , t (.) l + sh (.) l )β1(s)ds, ..., ∫ si 0 K̂(t (µ) n,i , t (.) l + sh (.) l )βm(s)ds ) , l = n. GGG (.),l n =  (∫ 1 0 K(t (µ) n,i , t (.) l + sh (.) l )α0(s)ds, ..., ∫ 1 0 K(t (µ) n,i , t (.) l + sh (.) l )αr−1(s)ds ) , l = r − 1, . . Keywords: k(t; step; µ−1

Manifold

On a Semi Symmetric Metric Connection With a Special Condition On a Riemannian Manifold by Yilmaz, Hulya; Ozen Zengin, Fusun; Uysal, S. Aynur (2011) - im , we get (2− n) � ak � w j − 1 n− 1 b j � − a j � wk − 1 n− 1 bk �� = 0 (23) Math, 4 (2011), 152-161 157 = gim � a j � wk − 1 n− 1 bk � − ak � w j − 1 n− 1 b j �� + gkm � ai � w j − 1 n− 1 b j � − a j � wi − 1 n− 1 bi �� + g jm � ak � wi − 1 n− 1 bi � − ai � wk − 1 n− 1 bk �� Conversely, let us assume that (24) is satisfied. Keywords: connection; manifold
A Note on Nearly Quasi-Einstein Manifolds by Hui, Shyamal Kumar (2012) - Also we have studied decomposable Riemannian manifold and it is shown that a decomposable Riemannian mani- fold is nearly quasi-Einstein if and only if both the decompositions are Einstein. 2010 Mathematics Subject Classifications: 53B30, 53B50, 53C15, 53C25 Key Words and Phrases: quasi-Einstein manifold, nearly quasi-Einstein manifold, Ricci-pseudosymmetric, scalar curvature, decomposable Riemannian manifold, Killing vector field, projective Killing vector field 1. The notion of quasi-Einstein manifolds arose during the study of exact solutions of the Einstein field equations as well as during considerations of quasi-umbilical hypersurfaces. Keywords: einstein; manifold
Pseudo Conharmonically Symmetric Manifolds by Ozen Zengin, Fusun; Yavuz Tasci, Ayse (2014) - [22], pseudo symmetric manifolds The notion of weakly symmetric manifolds was introduced by Tamassy and Binh Keywords: curvature; manifold; tensor
Locally Conformal Almost Cosymplectic Manifold of Î¦-holomorphic Sectional Conharmonic Curvature Tensor by Abood, Habeeb Mtashar; Al-Hussaini, Farah (2018) - Then the necessary and suffcient condition in which M is a manifold of point constant ΦHST-curvature C0 is Aadbc = 4BdahBchb +BadBbc − 4σ[aδh] c σ[hδ d b] + δac δ d bσ 2 0 − C0δ a b δ d c − 1 2n− 1 (rdb δ a c + rac δ d b ) Proof. i(ΦX)jXk(ΦX)l = C0gijgklX iXjXkX l According to the property (ΦX)a = √ −1Xa, (ΦX)â = − √ −1X â and (ΦX)0 = 0 and then using the properties of conharmonic tensor, we get −4Tâbcd̂ = 4C0δ a b δ d c Hence Aadbc = 4BdahBchb +BadBbc − 4σ[aδh] c σ[hδ d b] + δac δ d bσ 2 0 − C0δ a b δ d c − 1 2n− 1 (rdb δ a c + rac δ d b ) Keywords: curvature; manifold; tensor
Some Results on Projective Curvature Tensor of Nearly Cosymplectic Manifold by Mohammed, Nawaf Jaber; Abood, Habeeb Mtashar (2018) - In particular, the necessary and sufficient conditions that a projective tensor is vanishes are found. 2010 Mathematics Subject Classifications: 53C55, 53B35 Key Words and Phrases: Projective curvature tensor, almost contact manifold, nearly cosym- plectic manifold 1. [10] Jawarneh M., Samui S., Projective curvature tensor on (k, µ)-contact space forms, Journal of Pure and Applied Mathematics, V. 113, No.3, P. 425-439, 2017. Keywords: definition; manifold; tensor
Almost Hermitian Manifold with Flat Bochner Tensor by Abood, Habeeb Mtashar (2010) - The Kahler manifold with flat Bochner curvature tensor has been studied by many researchers. [9] proved that if M is a Kahler manifold with flat Bochner curvature tensor whose length of the Ricci tensor is constant, then M is a space of constant holomorphic sectional curvature Email address: iraqsafwan�yahoo. Keywords: bochner; manifold; tensor
On Conservative pseudo projective curvature tensor with respect to semi-symmetric metric connection on K-Contact and Trans-Sasakian Manifolds. by Channabasappa, Bagewadi (2008) - We obtain results on the vanishing of divergence of Pseudo projective curvature tensor P̃ with respect to semi-symmetric metric connection on k-contact and trans-Sasakian manifolds. A systematic study of semi-symmetric metric connection on a Riemannain manifold has been given by Yano Keywords: manifold
A Note on Kaehler Manifolds by De, Uday Chand (2010) - − S(∇Z JX , Y )− S(JX ,∇Z Y ) = −∇ZS(X , JY )− S(J∇Z X , Y )− S(X , J∇Z Y ), using (5) = −∇ZS(X , JY ) + S(∇Z X , JY ) + S(X ,∇Z JY ), by (5) = −(∇ZS)(X , JY ). (12) Taking X = Y = ei in (12) we get 1 2 dr(J Z) Keywords: manifold

Learning

Teaching, Learning and Retention of Statistical Ideas in Introductory Statistics Education by Qian, Guoqi (2011) - Introductory statistics courses are also called service statistics courses in Australian universities. Knowing the aforementioned factors that negatively affect students’ learning success in introductory statistics courses, there have been surged teaching and research activities in recent years aiming at improving the effectiveness and efficiency of learning introductory statistics. Keywords: course; education; introductory; learning; reasoning; statistics; students; studies; teaching; undergraduate

Regression

A Simulation Study of Some Logistic, Poisson, and Multiple Ridge Regression Estimators by Mohamad, Jerson; Delica, Angelyn; Esperat, Maydalyn; Labastilla, Aubrey; Ledesma, Shiela May; Misil, Doeyien (2025) - This study proposes new ridge regression estimators using linear combinations of known ridge parameters, developed through grid search and methods that leverage mean squared error (MSE) values from prior simulations. Proposed Estimators For logistic and Poisson regression, new ridge estimators k9l and k9p are introduced as weighted linear combinations of the above estimators. Keywords: coefficients; estimators; mse; regression; ridge; simulation

Methods

A New Technique to Speed Up Group Methods for Solving Hyperbolic Telegraph Equations by Saeed, AbdulkafiI Mohammed (2021) - Improved techniques using explicit group methods derived from the standard and skewed (rotated) finite difference operators have been developed over the last few years in solving the linear systems that arise from the discretization of the several types of partial differential equations. In the following sections of this research, we will study and discuss the formulation of two types of explicit group methods which are called Explicit group (EG) method and Explicit decoupled group(EDG) method for solving telegraph equations. Keywords: methods

Lim

Weak and Strong Convergence of a Two-Step Iterations for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Mappings by Dehghan, Hossein; Gharajelo, Amir (2012) - , m. Also, by taking lim supn in both sides of (5), we obtain that lim sup n ‖yn − p‖ ≤ lim sup n ‖xn− p‖ = a and so lim sup n ‖T n i yn − p‖ ≤ lim sup n ((1+ rin)‖yn − p‖+ sin) ≤ a (11) H. Dehghan, A. Gharajelo / Eur. Then, ‖xn+1 − xn‖ ≤ m ∑ i=1 � αin‖T n i yn − xn‖+ βin‖T n i xn− xn‖) � → 0. (12) Keywords: lim; limn
Common Fixed Points of Two Multivalued Asymptotically Nonexpansive Mappings by Khan, Safeer Hussain; Iqbal, Hira; Abbas, Mujahid (2019) - Since d(xnn, p) ≤ knd(xn, p), lim sup n→∞ d(xnn, p) ≤ c. (6) Also, lim sup n→∞ d(yn, p) ≤ c. (7) We know that if limn→∞ kn = 1 then limn→∞ k 2 n = 1, therefore, lim sup n→∞ d(ýnn, p) ≤ lim sup n→∞ knd(yn, p) ≤ lim sup n→∞ kn[βd(xn, p) + (1− β)d(xnn, p)] ≤ lim sup n→∞ kn[βd(xn, p) + (1− β)knd(xn, p)] = c, and c = lim n→∞ d(xn+1, p) = lim n→∞ d(αxn ⊕ (1− α)ýnn, p). Using (5) and (9), we get c ≤ lim inf n→∞ d(yn, p). Keywords: lim
Some Fixed Point Theorems for $\Theta-\phi$-Multivalued Contraction Mappings in Rectangular $b$-Metric Spaces by Massit, Hafida ; Rossafi, Mohamed ; Mitrovic, Zoran D.; Aloqaily, Ahmad ; Mlaiki, Nabil (2025) - If {xn} is not a Cauchy sequence then there exist ε > 0 and two sequences {mk} and {nk} of positive integers such that ε ≤ lim k→+∞ inf d(xmk , xnk ) ≤ lim k→+∞ sup d(xmk , xnk ) ≤ bε, ε ≤ lim k→+∞ inf d(xmk , xmk+1 ) ≤ lim k→+∞ sup d(xnk , xmk+1 ) ≤ bε, ε ≤ lim k→+∞ inf d(xmk , xnk+1 ) ≤ lim k→+∞ sup d(xmk , xnk+1 ) ≤ bε, ε b ≤ lim k→+∞ inf d(xmk+1 , xnk+1 ) ≤ lim k→+∞ sup d(xmk+1 , xnk+1 ) ≤ b2ε. Letting n→ +∞ we obtain lim n→+∞ supM(xn, z) = lim n→+∞ supmax{d(xn, z), d(xn, Txn), d(z, Tz), d(z, Txn)} ≤ lim n→+∞ supmax{d(xn, z), d(xn, xn+1), d(z, Tz), d(z, xn+1)} ≤ d(z, Tz) and lim n→+∞ supW (xn, z) = lim n→+∞ supmin{d(xn, Txn), d(z, Tz), d(Txn, z), d(xn, T z)} ≤ lim n→+∞ supmin{d(xn, xn+1), d(z, Tz), d(xn+1, z), d(xn, T z)} = 0. Keywords: lim
Uniqueness of Stationary Distribution in Markov Processes: A Quintuple Fixed Point and Coincidence Point Approach by Batul, Samina; Fida, Sidra; Sagheer, Dur-e-Shehwar; Aydi, Hassen; Mansour, Saber (2025) - − Γ̃)−1]n[I − (Γ̃ + Υ̃)(I − Γ̃)−1]−1µo. (κi2 − qi2)|+ |(ξi3 − κi3) +(κi3 − qi3)|+ |(ξi4 − κi4) + (κi4 − qi4)|+ |(ξi5 − κi5) + (κi5 − qi5)| )) ≤ ( n∑ i−1 ( |ξi1 − κi1|+ |κi1 − qi1|+ |ξi2 − κi2|+ |κi2 − qi2|+ |ξi3 − κi3| +|κi3 − qi3|+ |ξi4 − κi4|+ |κi4 − qi4|+ Keywords: lim; p(ξ

Semigroup

The relation B and Minimal Bi-ideals in Gamma-semigroups by Petro, Petraq; Braja, Islam (2014) - If aB–class B of a Γ–semigroup M contains an idempotent e = eγe,γ ∈ Γ, then B is a subgroup of semigroup Mγ. Consider the set of integers modulo 8, Z/8Z= {0, 1, 2, 3, 4, 5, 6, 7}, and Γ = {0,1, 2} ⊆ N∪ {0}. Keywords: semigroup
On the structure of regular H-cryptogroups by Shum, Kar Ping; Kong, Xiangzhi; Ding, Yue (2007) - [9]. Let S = (Y ;Sα) be a semilattice of the semigroups Sα, where each Sα is a subsemigroup of the semigroup S and Y is a semilattice. Definition 2.1 Let S = (Y ; Sα) be a semigroup. Keywords: semigroup; semilattice
On Gamma Acts over Gamma Semigroups by Rasouli, Hamid; Shabani, Ali Reza (2017) - Moreover, if A is a Γ-S-act over a Γ-semigroup S and γ is a fixed element of Γ, then S is a semigroup under the operation st := sγt for all s, t ∈ S, and A with the action sa := sγa, for every s ∈ S and a ∈ A, is an S-act. (ii) A Γ-S-act can have more than one zero, for instance, any non-empty set A becomes a Γ-S-act by definition sγa = a for every a ∈ A, s ∈ S and γ ∈ Γ, i.e. all elements of A are zero. Let s ∈ S, γ ∈ Γ, b ∈ B. Keywords: act; acts; semigroup
The Strong Semilattice of Pi-groups by Zhang, Jiangang; Yang, Yuhui; Shen, Ran (2018) - = (aϕα,β)(eβbθα,β) = aϕα,βbθα,β = aφα,βbφα,β. Case 4: if a ∈ Gα, b ∈ Qα, then ab ∈ Gα, similar to the above case, (ab)φα,β = (ab)θα,β = ((aeα)b)θα,β = (a(eαb))θα,β = aθα,β(eαb)θα,β = aθα,β(beα)θα,β (by Lemma 1) = aθα,βbϕα,βeβ = aθα,βbϕα,β (by Condition (iii)) = aφα,βbφα,β. Let S be a GV-inverse semigroup and RegS be an ideal of S. For any α ∈ Y , if a ∈ Gα, then Ha = La = Ra = Ja = Gα; if a ∈ Qα, then Ja = {a}. Keywords: semigroup
Implicative Negatively Partially Ordered Ternary Semigroups by Nakwan, Kansada; Luangchaisri, Panuwat; Changphas, Thawhat (2024) - Implicative ternary semigroups We start this section with the definition of n.p.o. ternary semigroups. In [14] D. A. Romano introduced the concept of an anti-filter within implicative semigroups and provided several equivalent conditions for when the special inhabited proper subset of an implicative semigroup qualifies as an ordered anti-filter. Keywords: implicative; semigroup; ternary
Generalization of Bi-antiideals in Semigroups by Al-Tahan, Madeleine; Hoskova-Mayerova, Sarka; Al-Kaseasbeh, Saba (2025) - More precisely and inspired by fuzzy interior antiideals introduced in [2] and fuzzy antiideals of a semiring The history of fuzzy sets can be traced back to the mid-20th century when Lotfi Zadeh Keywords: antiideal; n)-bi; semigroup

Quasi

Classical Quasi Primary Elements in Lattice Modules by Manjarekar, C. S.; Kandale, Ujwala Narahari (2015) - If N ¶ Q, (Q : N) = 1. This gives, abr IM ¶ Q. By classical quasi primality of Q, we have, either (ab)k IM ¶ Q or rk IM ¶ Q for some k ∈ Z+. Keywords: element; primary; quasi
Graphs and the Prime Spectrum of Unitary Commutative Rings by Alharbi, Badr (2023) - iv) X has a basis of quasi-compact open subsets. By the above item (1), (X,T ) has a base of quasi-compact open subsets if and only if (Y, T ′) has a base of quasi-compact open subsets. Keywords: quasi
A Note on Prufer Modules by Jayaram, C.; Raju, V.C.C. (2010) - Secondary 13C05, 13A15 Key Words and Phrases: multiplication module, Prüfer module, Dedekind module, quasi-principal ideal, quasi-cyclic module. Note that quasi-cyclic submodules have been studied in [1], [3] and Keywords: join; quasi

Variables

On the Limited Role of Conservation Laws in the Double Reduction Routine for Partial Differential Equations by Sinkala, Winter; Kakuli, Molahlehi Charles (2024) - (41) These symmetries have an associated nontrivial conservation law Dt(ϕ t) + Dx(ϕ x) = 0, where ϕt = u3 3 , ϕx = u2t − u2tx The PDE [7] uxxxx − utxx − nenuuxx + utt − n2enuu2x − 1 x4 = 0 (28) W. Sinkala, M.C. Kakuli / Eur. Keywords: canonical; conservation; variables

Supra

On New Classes of Soft Sets and Functions via Supra Preopen Sets by Gharib, Fatouh; Ezzat Mohamed, M.; El-Maghrabi, A. I. (2017) - Also, the supra soft closure of (F,E), denoted by cls(F,E) is the soft intersection of all supra closed super soft sets of (F,E) i.e cls(F,E) = ∩̃{(H,E) : (H,E) is supra closed soft set and (F,E)⊆̃(H,E)}. Let (X,µ,E) be a supra soft topological space over X, then the members of µ are said to be supra open soft sets in X. Keywords: set; supra
Supra b Limit Points and Supra b Separation Axioms by Al-shami, Tareq M.; Mhemdi, Abdelwaheb; Jameel, Mohammed; Abouhawwash, Mohamed (2022) - In [9–11, 20], Al-shami with his coauthors scrutinized the main properties of limit points using the famous generalizations of supra open sets. The members of Ω are said to be supra open sets and the complement of each member of Ω is said to be a supra closed set. Keywords: set; supra; supra b
On Supra bâˆ’open Sets and Supra b-continuity on Topological Spaces by Sayed, O. R.; Noiri, Takashi (2010) - The supra interior of a set A,denoted by Intµ(A), is the union of supra open sets included in A. [3] R. Devi, S. Sampathkumar and M. Caldas, On supra α-open sets and sα-continuous maps, General Mathematics, 16 (2) (2008), 77 - - 84. Keywords: set; supra

Forcing

Forcing Subsets of Connected Co-Independent Hop Domination in the Join and Corona of Graphs by Calanza, Yves Dave; Rara, Helen (2022) - In this study, the researchers define and establish the forcing subsets of minimum con- nected co-independent hop dominating sets in graphs and generate some characterizations of forcing subsets of minimum connected co-independent hop dominating sets of graphs resulting from the join and corona of two graphs and determine the values or bounds of their corresponding forcing connected co-independent hop domination numbers. 2020 Mathematics Subject Classifications: 05C69 Key Words and Phrases: Forcing subsets, connected co-independent hop domination, strictly co-independent set, co-independent set, join, corona 1. Keywords: coi; forcing; fγch; set
Forcing 2-Metric Dimension in the Join and Corona of Graphs by Managbanag, Dennis; Rara, Helen (2023) - Then S ⊆ V (G ◦ H) is a 2-metric basis for G ◦H if and only if S = ⋃ v∈V (G) Sv where Sv is an ln2-set of H v for all v ∈ V (G). A set S ⊆ V (G ◦H) is a 2-resolving set of G ◦H if and only if S = A ∪ B, where A ⊆ V (G) and B = ⋃ {Sv : Sv is a 2-resolving set of Hv, for all v ∈ V (G)}. Keywords: forcing; set

Graphs

New Improved Bounds for Signless Laplacian Spectral Radius and Nordhaus-Gaddum Type Inequalities for Agave Class of Graphs by V, Malathy; Desikan, Kalyani (2023) - 2020 Mathematics Subject Classifications: 05C50 Key Words and Phrases: Spectral radius, signless Laplacian spectral radius, Core-satellite graphs, Agave graphs, Complete split graph 1. Core–satellite graphs: Clustering, assortativity, and spectral properties . Keywords: bound; graphs
Signed Fuzzy Graphs Domination in Environmental Monitoring Wireless Sensor Networks by Chakaravarthy, Sankar; Saravanan, Mariappan; Sujatha, Ramalingam; Narayanan, Gangatharan Venkat (2025) - 2020 Mathematics Subject Classifications: 05C72, 05C22, 05C69, 05C12 Key Words and Phrases: Signed fuzzy graphs (Signed-FG), wireless sensor networks (WSN), environmental monitoring systems (EMS) 1. This section focuses on results related to domination in signed fuzzy graphs. Keywords: domination; graphs; nodes; set
The Total Choosability with Neighbor Sum Distinguishing Properties of Planar Graphs That Are Devoid of $C_5$ Adjacent to $C_3$ by Sittitrai, Pongpat; Nakprasit, Kittikorn; Jumnongnit, Patcharapan (2025) - [7] confirmed the conjecture by planar graphs without 3-cycles with maximum degree at least 7 and planar graphs without 5-cycles with maximum degree at least 7, respectively. Conjecture 1 has been verified for several classes of planar graphs as follows: planar graphs without adjacent 3-cycles with maximum degree at least 8 by [12], planar graphs without adjacent 6-cycles with maximum degree at least 7 [13], and planar graphs without 4-cycles adjacent to 3-cycles with maximum degree at least 7 by [14]. Keywords: face; graphs; total

Theory

Editor's Foreword by Huckleberry, Alan (2010) - Although I’ve spent most of my life studying higher-dimensional complex geometric set- tings, having grown up listening to Schiffer, Löwner, Royden and even experiencing Pólya in his 90’s, I have great appreciation for the powerful methods of the theory of functions on one complex variable or Funktionentheorie as it is still called in the land of Riemann and Weier- strass. It was therefore a great pleasure and honor for me to edit this volume which is devoted to Professor H. M. Srivastava. Keywords: theory

Product

The Proofs of Product Inequalities in Vector Spaces by Barnes, Benedict; Owusu-Ansah, E.D.J.; Amponsah, S.K.; Sebil, C. (2018) - Also, if f, g : Ω→ R, then ‖f‖p + ‖g‖p ≤ ‖f‖p‖g‖p. 2010 Mathematics Subject Classifications: 44B45, 44B46 Key Words and Phrases: Product inequality, first product nequality, second product inequality, generalized vector space, Cauchy-Schwarz inequality 1. EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 11, No. 2, 2018, 375-389 ISSN 1307-5543 – www.ejpam.com Published by New York Business Global The Proofs of product inequalities in a generalized vector space Benedict Barnes1,∗, E. D. J. Owusu-Ansah1, S. K. Amponsah1, C. Sebil1 1 Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana Abstract. Keywords: inequality; product
On Inner Products Derived from the Standard n-Inner Product on an Inner Product Space by Adam, Adam; Rante, Steven ; Gunawan, Hendra (2024) - In this paper, we study relations between inner products derived from the standard n-inner product defined on an inner product space. Inner product on n-inner product spaces. Keywords: product
Chen's Inequality for CR-warped Products in Locally Metallic Riemannian Manifolds by Alqahtani, Lamia; Al-Husainy, Ebtehal (2024) - Conclusion The exploration of warped product submanifolds in locally metallic Riemannian man- ifolds opens several intriguing avenues for future research. Additionally, establishing a comprehensive classification of warped product submanifolds, alongside concrete examples, will enhance the literature and provide benchmarks for further studies. Keywords: product; riemannian; submanifolds
Edge $k$-Product Cordial Labeling of Graphs by Jeyanthi, P.; Nawal M. , NourEldeen; J., Jenisha; K. , Jeya Daisy; M. E. , Abdel-Aal (2025) - Motivated by the concept of ‘edge product cordial labeling’, and the several results established on this concept, we take a step further and introduce a new labeling namely ‘Edge k-product cordial labeling’ as follows: For a graph G = (V (G), E(G)) having no isolated vertex, an edge labeling f : E(G) → {0, 1, ..., A graph that admits an edge k-product cordial labeling is called edge k-product cordial graph. Keywords: edge k; j ≤; product

Lie

A Note on Nonlinear Mixed (bi-Skew, skew Lie) Triple Derivations on $\ast$-Algebras by Raza, M. Arif ; Nisar, junaid; Rehman, Nadeem; Vahid Darvish (2025) - Introduction Let A be an ∗-algebra over the complex field C. For L,M ∈ A, we call [L,M]∗ = LM Inspired by the above results, in the present paper, we combined skew Lie product and bi-skew Lie product and defined nonlinear mixed bi-skew Lie triple derivations on ∗-algebras. Keywords: lie; skew
Tripolar Complex Fuzzy Lie Subalgebras of Lie Algebras by Balamurugan, M. ; Ellammal, G. ; Iampan, Aiyared (2025) - Then f ( ⟨⟨ξP̃ג , ξ P ̃ג ⟩⟩ ) (η̃) = sup { ⟨⟨ξP̃ג , ξ P ̃ג ⟩⟩(ϕ̃) | f(ϕ̃) = η̃ } = sup { sup { min { ξP̃ג (ε̃), ξ P ̃ג (ς̃) } | ε̃, ς̃ ∈ L̃1, [ε̃, ς̃] = ϕ̃, f(ϕ̃) = η̃ }} = sup { min { ξP̃ג (ε̃), ξ P ̃ג (ς̃) } | ε̃, ς̃ ∈ L̃, [ε̃, ς̃] = ϕ̃, f(ϕ̃) = η̃ } = sup { min { ξP̃ג (ε̃), ξ P ̃ג (ς̃) } | ε̃, ς̃ ∈ L̃1, [f(ε̃), f(ς̃)] = η̃ } = sup { min { ξP̃ג (ε̃), ξ P ̃ג (ς̃) } | ε̃, ς̃ ∈ L̃1, f(ε̃) = ϖ̃, f(ς̃) = ϑ̃, [ϖ̃, ϑ̃] = η̃ } ≥ sup { min { sup ε̃∈f−1(ϖ̃) ξP̃ג (ε̃), sup ς̃∈f−1(ϑ̃) ξP̃ג (ς̃) } = η̃ } = inf { inf { max { ξÑג (ε̃), ξÑג (ς̃) } | ε̃, ς̃ ∈ L̃1, [ε̃, ς̃] = ϕ̃, f(ϕ̃) = η̃ }} = inf { max { ξÑג (ε̃), ξÑג (ς̃) } | ε̃, ς̃ ∈ L̃1, [ε̃, ς̃] = ϕ̃, f(ϕ̃) = η̃ } = inf { max { ξÑג (ε̃), ξÑג (ς̃) } | ε̃, ς̃ ∈ L̃1, [f(ε̃), f(ς̃)] = η̃ } = inf { max { ξÑג (ε̃), ξÑג (ς̃) } | f(ε̃) = ϖ̃, f(ς̃) = ϑ̃, [ϖ̃, ϑ̃] = η̃ } ≤ inf { max { inf ε̃∈f−1(ϖ̃) ξÑג (ε̃), inf ς̃∈f−1(ϑ̃) ξÑג (ς̃) } | [ϖ̃, ϑ̃] = η̃ } = inf { max { f(ξÑג (ϖ̃)), f(ξÑג (ϑ̃)) } | [ϖ̃, ϑ̃] = η̃ } = ⟨⟨f(ξÑג ), f(ξÑג )⟩⟩(η̃). Keywords: inf; j∈n; lie; η̃j; ξñג; ξp̃ג

Ternary

A Note on Quotient Ternary Semirings and Isomorphism Theorems by Petapirak, Montakarn; Khan, Arbaz Jehan ; Chinram, Ronnason (2025) - In this paper, we present a variety of notions of quotient ternary semirings, along with examples and remarks. 2020 Mathematics Subject Classifications: 16Y60, 16Y99 Key Words and Phrases: Q-ideals, congruences, k-ideals, quotient ternary semirings, isomor- phism theorems 1. Keywords: ker(φ; semirings; ternary

Inequality

The Proofs of Triangle Inequality Using Binomial Inequalities by Barnes, Benedict; Wusu-Ansah, E.D J.O.; Amponsah, S. K.; Adjei, I.A. (2018) - 2010 Mathematics Subject Classifications: 44B43, 44B44 Key Words and Phrases: Triangle inequality, triangle through binomial inequality, triangle inequality through Euclidean norm, Hilbert space 1. Another version for obtaining this kind of triangle inequality in Banach space was obtained by authors in [6]. Keywords: inequality; v)2
The Proofs of the Arithmetic-Geometric Mean Inequality Through Both the Product and Binomial Inequalities by Barnes, Benedict; Harris, E.; Darquah, N. F.; Hughes, G. (2018) - These methods are alternative ways of proving AGM inequalities. Some researchers have applied AGM inequality to solve matrix algebra. Keywords: inequality
The Quotient Inequalities by Barnes, Benedict; Sebil, C.; Dontwi, I. K. (2019) - 2010 Mathematics Subject Classifications: 44B56, 44B57 Key Words and Phrases: Quotient inequalities, first quotient inequality, second quotient inequality, index power quotient inequalities 1. ‖u‖pn‖y‖pn ≤ ‖u‖pn + ‖v‖pn ∀u, v ∈ [0, 2] (first product inequality) P4(b).‖u‖+ ‖v‖ ≤ ‖u‖‖v‖, ∀u, v ∈ [2,∞) (second product inequality). Keywords: inequality; quotient
Some Refinements for Numerical Radius Inequalities of Operators by Al-Labadi , Manal; Audeh , Wasim; Al-Naimi , Raja'a ; Oudetallah, Jamal; Almuhur, Eman ; Khan, Nazneen (2025) - Math, 18 (3) (2025), 6461 12 of 13 References [1] M. Al-Labadi, R. Al-Naimi and W. Audeh, Singular value inequalities for generalized anticommutators, J Inequal Appl, 15(2025). [8] W. Audeh, Singular value inequalities for operators and matrices, Ann. Keywords: inequalities; inequality

Sup

Semidetached SUP-Subalgebras of Sheffer Stroke UP-Algebras by Oner, Tahsin ; Rajesh, Neelamegarajan ; Iampan, Aiyared; Senturk, Ibrahim (2025) - If (X, ℓµQk ) is a semidetached SUP-subalgebra over Ω = (1−k 2 , 1], then µ satisfies: (∀x, y ∈ X)(∀t, r ∈ Ω)(xt ∈ µ, yr ∈ µ ⇒ ((x|(y|y))|(x|(y|y)))max{t,r}qkµ). If (X, ℓµQk ) is a semidetached SUP-subalgebra over Ω = (0.5, 1], then µ satisfies: (∀x, y ∈ X)(∀t, r ∈ Ω)(xt ∈ µ, yr ∈ µ ⇒ ((x|(y|y))|(x|(y|y)))max{t,r}qµ). Keywords: subalgebra; sup
Generalized Ulam-Hyers Stability of a General Mixed AQCQ-functional Equation in Multi-Banach Spaces: a Fixed Point Approach by Xu, Tian Zhou; Rassias, John Michael; Xu, Wan Xin (2010) - . , yk ∈ E. Using the oddness of f and (6), we have sup k∈N ‖( f (x1 + ny1) + f (x1− ny1)− n2 f (x1+ y1)− n2 f (x1− y1) . , yk ∈ E. Using the evenness of f and from (26), we have sup k∈N ‖( f (x1+ ny1) + f (x1− ny1)− n2 f (x1+ y1)− n2 f (x1− y1)− 2(1− n2) Keywords: k∈n; n2 f; sup

Hyper

On a Graph Induced by a Hyper BCI-algebra by Panganduyon, Michelle Tandog; Canoy, Sergio Jr. Rosales (2019) - Since x /∈ I(Γ(H)), there exists y ∈ H \ {x} such that LH(x, y) = {0}. Then there exists y ∈ LH{x, 0}. Keywords: hyper
Some Results on Fuzzy Implicative Hyper GR-ideals by Macodi-Ringia, Amila Pagadilan; Petalcorin, Gaudencio (2019) - ∈ I; and ii) for all x, y ∈ H, x~ y ⊆ I and y ∈ I imply that x ∈ I. Definition 2.6. Clearly, x ∈ x ~ y for all x, y ∈ H. By routine calculations, we can show that any subset of I of H containing 0 is an implicative hyper GR-ideal of H. The next proposition will give a generalization when x ∈ x ~ y for all x and y in a hyper GR-algebra H. Proposition 3.7. Keywords: hyper; implicative
A Topology on a Hyper BCI-algebra Generated by a Hyper-order by Panganduyon, Michelle; Canoy Jr., Sergio Rosales; Davvaz, Bijan (2021) - = ⋂ a∈A LH({a}) (v) If x ∈ H, then x ∈ LH({x}). Then y � x and y ∈ K. Since H is ordered, y � a for all a ∈ A. Hence, y ∈ LH(A) ∩ K showing that LH(x) ∩ K ⊆ LH(A) ∩ K. Consequently,⋃ x∈LH(A)∩K (LH(x) ∩K) ⊆ LH(A) ∩K. Next, let z ∈ LH(A)∩K. By Proposition 1(v), z ∈ LH(z). Keywords: hyper; lh(a
Looking at Two Ways of Constructing Quotient Hyper $BN$-algebras and Some Notes on Hyper $BN$-ideals by Cabardo, Lyster Rey; Petalcorin Jr., Gaudencio (2024) - Assume x, y ∈ H such that x⊛ y ≪ ⋂ i∈I Ai and y ∈ ⋂ i∈I Ai. Let x, y ∈ H and suppose that (x⊛ y)∩ {0} ≠ ∅ and y ∈ {0}. Keywords: -algebra; hyper; hyper bn

Boundary

Existence and Uniqueness of Solutions for the System of First-order Nonlinear Differential Equations with Three-point and Integral Boundary Conditions by Mardanov, Misir; Sharifov, Yagub; Ismayilova, Kamala; Zamanova, Sevinc (2019) - Integral boundary value problems for first-order impulsive functional differential equations. Boundary value problems with nonlocal boundary conditions for the nonlinear differential equations arise in several branches of physics and applied mathematics. Keywords: boundary; n(ξ)dξ
Existence and Uniqueness of Solutions for the First Order Non-linear Differential Equations with Multi-point Boundary Conditions by Mardanov, M.J.; Sharifov, Y.A.; Aliyev, Humbet; Sardarova, R.A. (2020) - T. Finally we see that the solution of boundary value problem (1)-(2) may be presented in the form x(t) = N−1α+ T∫ 0 G(t, τ)y(τ)dτ. Let x(t) be a solution of boundary value problem (1)-(2). Keywords: boundary

Domination

Perfect Equitable Isolate Dominations in Graphs by Caay, Mark; Hernandez, Andrew (2024) - A subset S ⊆ V (G) is said to be a perfect equitable isolate dominating set of a graph G if it is both perfect equitable dominating set of G and isolate dominating set of G. The minimum cardinality of a perfect equitable isolate dominating set is called perfect equitable isolate domination number of G and is denoted by γpe0(G). A dominating set S ⊆ V (G) is said to be a perfect equitable isolate dominating set (PEID) of G if it is both perfect equitable isolate dominating set. Keywords: domination; perfect; set

Mathematics

Congratulation Messages to Professor Hari M. Srivastava on the Occasion of His 70th Birthday by Message Senders, . (2010) - THE OCCASION OF HIS 70th BIRTHDAY Congratulation Messages to Professor Hari M. Srivastava on the Occasion of His 70th Birthday European Journal of Pure and Applied Mathematics It is our great honor and pleasure that we publish a special issue, entitled Complex Analy- sis: Theory and Applications, dedicated to Prof. Hari M. Srivastava on the occasion of his 70th birthday. Professor Hang-Chin Lai Chung Yuan Christian University, Taiwan (Republic of China) National Tsing Hua University, Taiwan (Republic of China) *** I feel honored to give my warmest celebration on the occasion of the seventieth birth anniversary of Professor Hari M. Srivastava, an internationally renowned mathematician, in the Special Dedication Issue of the European Journal of Pure and Applied Mathematics. Keywords: mathematics; professor; srivastava

Quantum

A Note on Quantum Gates SWAP and iSWAP in Higher Dimensions by Pourkia, Arash (2023) - Preliminaries and Notations Let us recall that in quantum computing quantum logic gates can be represented by unitary matrices on a Hilbert space H with dimension d. Universal quantum gates. Keywords: gate; quantum; xswap
Classification and Taxonomy of Undeniable Signatures: From Early Designs to Post-Quantum Approaches by Almenderj, Hussah; Shahril Ismail, Eddie (2025) - 2020 Mathematics Subject Classifications: 94A60, 68P25, 68Q12 Key Words and Phrases: Undeniable signatures, Post-quantum cryptography, Zero-knowledge proofs, Signature scheme, The signer, The verifier, public key, message 1. In this article, focused on classification and taxonomy of undeniable signature schemes through evolution from early concepts to solutions that are resistant to quantum alterations. Keywords: key; knowledge; pages; post; protocol; quantum; rsa; schemes; security; signature; signature schemes; signer; undeniable; verification; verifier

Definition

A New Decision-Making Approach Using Bipolar Interval-Valued Fuzzy Soft Matrices by Hazaymeh, Ayman A. ; Al-Qudah, Yousef ; Al-Sharqi, Faisal; Romdhini, Mamika Ujianita ; Rodzi, Zahari Md (2025) - In this article, we introduce a new hypermodel called bipolar interval fuzzy soft sets (BIVFSSs) in matrix form when we extend the bipolar fuzzy soft matrix to effectively and flexibly represent and manipulate uncertain information with increased flexibility. [ā+,L (n×m), ā +,U (n×m)] and B−(τ̇n, σm) Keywords: biv; definition; n×m

Test

Equivalence of Pepin's and the Lucas-Lehmer tests by Jaroma, John H. (2009) - 2000 Mathematics Subject Classifications: 11A41, 11A51, 11B39 Key Words and Phrases: Primes, primality test, Lehmer sequence, Pepin’s test, Lucas-Lehmer test. †Although Lucas did not attempt to give necessary tests, one of them is in fact necessary. Keywords: lehmer; test
A Novel Normality Test Using an Identity Transformation of the Gaussian Function by Akbilgic, Oguz; Howe, J. Andrew (2011) - Tests are evaluated according to the Type I error and Power. 2000 Mathematics Subject Classifications: 62E15,62F03 Key Words and Phrases: normality test, Gaussian distribution,probability distributions 1. Although there are many normality tests in the literature, none dominate for all conditions. Keywords: test
Variance-ratio Tests Robust to a Break in Drift by Kim, Yunmi; Kim, Tae-Hwan (2010) - 2000 Mathematics Subject Classifications: 62 Key Words and Phrases: Random walk hypothesis; variance ratio tests; spurious rejection; exchange rates 1. References [1] Cavaliere, G. and Taylor, A.M.R. Testing the null of co-integration in the presence of variance breaks. Keywords: break; exchange; hypothesis; ratio; test; variance; walk

Cover

bT- compactness and bT - connectedness in Supra Topological Spaces by Kaliswami, Krishnaveni; Mandarasalam, Vigneshwaran (2017) - Math, 10 (2) (2017), 323-334 334 5 K.Krishnaveni and M.Vigneshwaran,Some Stronger forms of supra bTµ - continuous function, Int. Then X cannot be expressed as disjoint union of two non empty proper subset of X. Suppose X is not bTµ -connected space. Keywords: btµ; cover

Skew

Characterizations of Nonadditive Mappings in Prime $*$-Rings Involving Bi-Skew Products by Ansari, Moin A.; Abbas Hussain Shikeh; Nisar, Junaid; Shahid Tamboli (2025) - In view of [27, Theorem 3.5], it follows that there exists q ∈ Qml(ℜ) such that Ω(u) = uq for all u ∈ ℜ and Ω−1(v)∗ = qv∗ for all v ∈ ℜ. Note that qv∗ = Ω−1(v)∗ ∈ ℜ for all v ∈ ℜ. = {u α | u ∈ ℜ and 0 ̸= α ∈ Z(ℜ)}. Keywords: ring ℜ; skew; ω(u; ∈ ℜ

Inequalities

Twice Differentiable Ostrowski Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces by Stojiljkovic, Vuk (2023) - Since our paper is about tensorial Ostrowski type inequalities, we give the brief introduc- tion to the topic. −A⊗ 1∥2 16 (∫ 1 0 l2 (( 1− l 2 )∥∥f ′′(A)∥∥+ l 2 ∥∥f ′′(B) ∥∥) dl + ∫ 1 0 (l − 1)2 ( 1− l 2 ∥∥f ′′(A)∥∥+ 1 + l 2 ∥∥f ′′(B) ∥∥) dl). Keywords: inequalities
Gradient Descent and Twice Differentiable Simpson-Type Inequalities via K-Riemann-Liouville Fractional Operators in Function Spaces by Afzal, Waqar; Mujahid Abbas; Jorge E. Mac´ıas-D´ıaz; Mutum Zico Meetei; Mehreen S. Khan; Armando Gallegos (2025) - Math, 18 (1) (2025), 5790 6 of 30 U ⊗ D and a mapping (ν1, ν2) 7→ ν1 ⊗ ν2 of U × D into U ⊗ D, holds (ν1 + ν2)⊗ ν2 = ν1 ⊗ ν2 + ν2 ⊗ ν2 (λν1)⊗ ν2 = λ(ν1 ⊗ ν2) ν1 ⊗ (ν3 + ν4) Consider the eventually similar to the tensorial product : (Uβ)⊗ (DS) = (U ⊗ D)(U ⊗ S), that holds ∀U ,D, β,S ∈ B(ν2). Keywords: + w; 1⊗d; inequalities; k w; s+k k; u ⊗; σ 2; ∆ ∫; ∫ ∆
Hermite-Hadamard Inequalities via Riemann-Liouville Fractional Integrals with Generalized Convex Functions by Samraiz, Muhammad; Atta, Tahira ; Naheed, Saima; Rahman, Gauhar; Vivas-Cortez, Miguel (2025) - It has been demonstrated that fractional integral inequalities are one of the best tools for the growth of many fields of pure and applied mathematics. Applications to special means, fractional integral inequalities for differentiable convex maps and midpoint formulas were explored in [17], while the in- tegral inequality of the Ostrowski’s type and Hermite-Hadamard integral inequality were investigated in [18, 19]. Keywords: ā)2; inequalities; θ +

Concentration

Nonlinear Reaction-Diffusion and Mediated Electron Transfer Process at Conducting Polymer Modified Ultramicroelectrodes by Yokeswari, G. ; Jayasimman, I. Paulraj ; Lyons, M. E. G. ; Abukhaled, Marwan; Rajendran, L. (2024) - Figure 3: Normalized substrate concentration u at a polymer microelectrode. [41] employed analytical and numerical solutions of nonlinear diffusion equations to investigate the chronoamperometric limiting current generated by an electrochemical reaction in rotating disc electrodes. Keywords: concentration; reaction

K=1

On Integrability of Trigonometric Series with Special Type of Coefficients by Krasniqi, Xhevat Z. (2017) - Note that for r = 1 we obtain ordinary differences 4ak = ak − ak+1 and 42ak =4 � 4ak � = ak − 2ak+1+ ak+2. Math, 6 (2013), 451-459 453 B0 n+1,r,k(x) = cos(k+ nr)x , BC1 n,r,0(x) = sin � (2n+ 1)r x 2 � 2sin � r x 2 � B1 n,r,k(x) Keywords: k=1
Two-dimensional Inverse Boundary Value Problem for a Third-order Pseudo-hyperbolic Equation with an Additional Integral Condition by Mehraliyev, Yashar; Sadikhzade, Rena ; Ramazanova, Aysel (2023) - (x, y, t) ∈ DT , (1) in the domain DT = Qxy × {0 < t ≤ T}, where Qxy = {(x, y) : 0 < x < 1, 0 < y < 1} an inverse boundary problem with initial conditions u(x, y, 0) = ϕ(x, y), ut(x, y, 0) = ψ(x, y), 0 ≤ x, y ≤ 1, (2) with boundary conditions ux(0, y, t) = u(1, y, t) ψ(x, y), ψx(x, y), ψy(x, y), ψxx(x, y), ψxy(x, y), ψyy(x, y) ∈ C(Q̄xy), ψxxy(x, y), ψxyy(x, y), ψxxx(x, y), ψyyy(x, y) ∈ L2(Qxy), ψx(0, y) = ψ(1, y) = ψxx(1, y) = 0, 0 ≤ y ≤ 1, ψ(x, 0) = ψy(x, 1) = ψyy(x, 1) Keywords: k=1; n=1
New Improvements to Heron and Heinz Inequality Using Matrix Techniques by Rashid, Mohammad H.M.; Mohammad Salameh, Wael Mahmoud (2025) - = ∣∣∣∣∣∣∣∣∣∣∣∣(1− ϑ)T 1/2XS1/2 + ϑ ( TX +XS 2 )∣∣∣∣∣∣∣∣∣∣∣∣, (13) This definition involves matrices T , S, and X, subject to the conditions that T and S belong to the set of positive definite matrices in C, denoted as M++ n (C), and X is a member of the set of n× n matrices over C, denoted as Mn(C). Utilizations of the improved Young-type inequalities for traces, determinants, and norms of positive definite matrices In this section, we introduce a collection of improved Young-type inequalities designed specifically for traces, determinants, and norms of positive semi-definite matrices. Keywords: k=1

N=1

On the Number of Representation of Integers by the Direct Sum of BQFs with Discriminant -191 by Kokluce, Bulent (2012) - Math, 5 (2012), 451-468 457 6 For 2Ω2 = 12x2 1 + 2x1 x2+ 16x2 2 + 12x2 3 + 2x3 x4+ 16x2 4, by taking A12 = −191, A22 = 12.191 we get; ϕ12 = x1 x2+ 1 2.191 Ω2,ϕ22 = x2 2 − 6 191 Ω2, which will be spherical functions of second order with respect to Ω2. 7 For 2Π2 = 12x2 1 + 10x1x2 + 18x2 2 + 12x2 3 + 10x3x4 + 18x2 4, by taking A11 = 18.191, A22 = 12.191 we get, ϕ11 = x2 1 − 9 191 Π2,ϕ22 = x2 2 − 6 191 Π2, which will be spherical functions of second order with respect to Π2. 8 For 2(F1⊕Φ1) = 2x2 1 +2x1x2+96x2 2+4x2 3+2x3 x4+48x2 4 the determinant D = 1912, A12 = −191, A33 = 48.191, the spherical functions of second order with respect to F1 ⊕Φ1 are; ϕ12 = x1 x2+ 1 2.191 (F1 ⊕Φ1),ϕ33 = x2 3 − 24 191 (F1 ⊕Φ1), 9 For 2(F1⊕Ψ1) = 2x2 1 +2x1x2+96x2 2+8x2 3+2x3 x4+24x2 4 the determinant D = 1912, A12 =−191, A44 = 8.191, the spherical functions of second order with respect to F1⊕Λ1 are; ϕ12 = x1 x2+ 1 2.191 (F1 ⊕Λ1),ϕ44 = x2 4 − 4 191 (F1 ⊕Λ1), 11 For 2(F1⊕Υ1) Keywords: n=1; quadratic
A Specific Category of Meromorphic Functions with Positive Coefficients by Alnajar, Omar; K. Alshammari, K. Alshammari; Darus, M. Darus; Amourah, Ala (2025) - Coefficient estimation utilizing the faber polynomial for a subfamily of bi-univalent functions. Applications of q-ultraspherical polynomials to bi-univalent functions defined by q-saigo’s fractional integral operators. Keywords: f(z; n=1; µ+ξ)(1+n
Partial Sums for Normalized Mittag-Leffler-Prabhakar Function and Barnes-Mittag-Leffler Function by Khan, Shahid ; Shah, Niaz Ali ; Ahmad, Hijaz; Kamel , Alwaleed; Abdelfattah, Waleed Mohammed ; Oqilat, Osama (2025) - Introduction Let A be the set of analytic functions (AFs) in the disc U = {ξ ∈ C : |ξ| < 1}. Partial sums of analytic functions play a significant role in Geometric Function Theory, particularly in finding the largest disk Ur = {ξ ∈ C : |ξ| < Keywords: n=1; |bn|; σ d

Self

Self-Dual Codes over R_k and Binary Self-Dual Codes by Dougherty, Steven T.; Yildiz, Bahattin; Karadeniz, Suat (2013) - By the observation about the lengths of binary Type II codes, we know that we should only look for Type II codes of even lengths over R2. Hence we need not consider that special case for binary codes. Keywords: binary; code; dual; length; self; u1u2

Vector

Vector Space-Groupoids by Ivan, Mihai (2017) - If (G,α,β , m,ε, i,⊕, G0) is a G−groupoid, then: x · y = x ⊕ y and x−1 = x̄ , (∀)x , y ∈ G(e0). = e, x ⊕ e = x and e⊕ y = y . Keywords: groupoid; vector
Ricci Solitons and Their Associated Vector Fields in Locally Rotationally Symmetric Bianchi Type I Spacetime by Nasib, Uzma ; Khan, Jamshed ; Saleem Akhtar, Sumaira ; Haque, Salma; Mlaiki, Nabil (2025) - Implications for Spacetime Evolution and Stability The discovery of Ricci soliton solutions within the LRS Bianchi-I framework has pro- found implications for understanding the possible evolution and stability of such space- times. The LRS Bianchi-I spacetime admits a rich variety of Ricci soliton solutions, in- cluding shrinking (δ > 0), steady (δ = 0), and expanding (δ < 0) types. Keywords: ricci; solitons; spacetime; vector

Left

On Po-injective and Po-surjective Wreath Product of Pomonoids by Al Subaiei, Bana; Almulhim, Ahlam ; Shah, Aftab; Ul Haq, Syed (2025) - If r ∈ R is not left po-cancellable then (r, c1) ∈ T is not left po-cancellable. Now suppose that ra ≤ ra′ and a ≰ a′, where r ∈ R and a, a′ ∈ A. Also let f(a)b ≤ f(a′)b′ for some b, b′ ∈ B. Then, B. Al Subaiei et al. / Eur. Keywords: acts; left

Cyclic

Z_2-Triple Cyclic Codes and Their Duals by B, Srinivasulu; Bhaintwal, Maheshanand (2017) - (3) It easy to see that Q3h3(g1 | g2 | 0) This implies that, Q3h3(g1 | g2 | 0) ∈ span(S1 ∪ S2). Keywords: b |; cyclic

Family

Proximity Between Selfadjoint Operators and Between Their Associated Random Measures by Boudou, Alain; Viguier-Pla, Sylvie (2018) - If A and A′ are two bounded selfadjoint operators which com- mute, of respective associated s.m.’s E and E ′, then E ∗ E ′ is the s.m. associated with the operator A+A′. A. Boudou, S. Viguier-Pla / Eur. As E ′ commute with E ∗ wE ′, Lemma 3.1 allows us to affirm that E ′ ∗ (E ∗ wE ′) ‖A−A ′‖∼ E ′, so that E ‖A−A ′‖∼ E ′, and the property is proved. Keywords: associated; family; s.m
General Results for General Transmuted-G Distributions by Shahbaz, Saman Hanif; Rahman, Md. Mahabubur; Shahbaz, Muhammad Qaiser (2021) - 2020 Mathematics Subject Classifications: 62E10, 62E15, 62G30 Key Words and Phrases: Transmuted Distributions, Order Statistics, TX Family, Distribution Function 1. Section 4 contains some examples of general transmuted distributions. Keywords: distributions; family

Process

Double Lusin Condition for the Ito-Henstock Integrable Operator-Valued Stochastic Process by Labendia, Mhelmar Avila; Arcede, Jayrold (2018) - A Q-Wiener process Wt, t ∈ Given η > 0, a given δ-fine belated partial division D = {((ξ, v], ξ)} is said to be a (δ, η)-fine belated partial division of [0, T ] if it fails to cover [0, T ] by at most length η, that is, ∣∣∣T − (D) ∑ (v − ξ) Keywords: process
A Version of Fundamental Theorem for the Ito-McShane Integral of an Operator-Valued Stochastic Process by Cagubcob, Jeffer Dave; Labendia, Mhelmar Avila (2019) - A Q-Wiener process Wt, t ∈ × Ω → L(U, V ) be an adapted process on a filtered probability space (Ω,F , {Ft},P) such that for t ∈ Keywords: process

Estimator

Bootstrapping the Shrinkage Least Absolute Deviations Estimator by Kim, Tae-Hwan; White, Halbert (2010) - The estimators we study are shrinkage estimators that have themselves been taken in a novel direction. Using the bootstrap to obtain the sampling distribution of shrinkage estimators is a famil- iar approach in the literature. Keywords: bootstrap; confidence; estimator; shrinkage; � �

Pre

Pre-irresolute Functions in Closure Spaces by Darwesh, Halgwrd M.; Namiq, Sarhad F. (2019) - The preopen sets are used to define pre-open functions, pre-closed functions, pre- continuous functions, contra-pre-continuous functions and pre-irresolute functions which are inves- tigated. They are also used to introduce a new type of connectedness and compactness in closure spaces, they called p-connectedness and p-compactness respectively 2010 Mathematics Subject Classifications: 54A05 Key Words and Phrases: Closure operator, closure space, pre-open functions, pre-closed func- tions, contra-pre-continuous functions, pre-irresolute functions, p-connectedness, p-compactness, Tp-spaces 1. Keywords: closure; pre
On Some Closed Sets and Low Separation Axioms via Topological Ideals by Boonpok, Chawalit (2022) - (1) ⇒ (2): Let y ∈ X and x ∈ X −{y}. ̸∈ V and y ∈ V . Keywords: p(⋆; pre; set

Sin

Comparison of SBA Numerical Method and Method of Separation of Variables (Fourier) on Wawe Equations by Yaro, Rasmane; Pare, Youssouf; Abbo, Bakari (2019) - = 0 (30) Solving yhe wave equation involves identifyinf the functions u(x, y, t) that solve the partial differential equation that represent the amplitude of the wave at any position x and y at any time t. • Solving by SBA method By Integrating (29) we get the Adomian canonical form The method of separation of variables relies upon the assumption that a function of the form: u(x, t) = X(x)T (t) (8) if we are in the case of one -dimension x of space(1−D) and u(x, y, t) = U(x, y)T (t) = X(x)Y (y)T (t) (9) if we are in the case of two dimension x and y of space (2 −D) will be a solution to linear homogeneous partial differential equation in x and t when when we are in (1−D) and x, y and t when when we are in (2.−D). Keywords: sin
Atomic Solution of Fractional Abstract Cauchy Problem of High Order in Banach Spaces by Bekraoui, Fatema; Al Horani, Mohammad; Khalil, Roshdi Rashid (2022) - − c2 cos 1 α tα − c3 sin 1 α tα +exp ( − 1 α tα ) − c2 cos 1 α tα − c3 sin 1 α tα +exp ( − 1 α tα ) Keywords: cos; exp; sin; t α; α tα

Fractal

Mathematical Visualization of Fractal-Based Batik Designs by Ahmad, Khaleel; Ishtiaq, Umar; Akram, Mohammad ; Popa, Ioan-Lucian (2025) - With a total of 50 iterations (K = 100), the Julia set is computed allowing for a finer approxi- mation of the complex boundary structures and subtle details unique of Julia fractals. Figure 1 shows the Julia set fractal structure produced by a generalized viscosity approximation process under various parameter settings, primarily due to changes in the parameter β. Keywords: 0.001i; 0.2i; 0.3i; et al; figure; fractal; julia; set

Cos

Free Vibration Frequency of Thick FGM Spherical Shells Based on a Third-order Shear Deformation Theory by Zannon, Mohammad; Abu-Rqayiq, Abdullah; Al-bdour, Ammar (2020) - Numerical results which include spherical shell panels with all edges simply supported or clamped are presented to validate the accuracy of the present approach. Examples below show spherical shell panels with all edges clamped or simply supported. Keywords: cos; shells; vibration
Some Properties for Certain Subclasses of Spiral-Like and Robertson Analytic Functions by Seoudy, Tamer (2024) - = ξ + ∞∑ j=2 ρjξ j (1) in U = {ξ ∈ C : |ξ| < 1}. Let ψ (ξ) ∈ SKγ [α, β;C,D] satisfy the coefficient inequality (21) and suppose that ϕ (ξ) = ξ + ∞∑ j=2 σjξ j ∈ K. Then, by Definition 2, the condition (28) will hold true if ( α+2β α+β ) Keywords: c −d; cos

Structure

Note on (i, j) âˆ’ mX âˆ’ Î²âˆ’Exterior Sets in Biminimal 3 Structure Spaces by Prasertsang, Torsak; Prasertsang, Patarawadee (2021) - 2020 Mathematics Subject Classifications: 22A05, 22A15 Key Words and Phrases: Exterior sets, Biminimal structure spaces, (i, j) −mX − β−exterior sets,(i, j)−mX − β−closed sets,(i, j)−mX − β−open sets 1. Biminimal structure space has been of wide interest in studying in Topology. Keywords: biminimal; mij; structure

Neighborhood

On the Independent Neighborhood Polynomial of the Rooted Product of Two Trees by Abdulcarim, Normalah Sharief; Dagondon, Susan C. (2022) - Then n ∈ N∗ and d(ω, y) = 2n which implies y ∈ Ω, a contradiction since y /∈ For any tree T with independent neighborhood sets Ω and ∆, if uv ∈ E(T ), then u ∈ Ω and v ∈ ∆. Proof. Keywords: neighborhood
Advancements in Topological Approaches via Core Minimal Neighborhoods and Their Applications by Shbair , Ismail; Salama, Amgad; Embaby, Osama; El-Atik, Abdelfattah (2024) - Then, the families τj = {B ⊆ X : CMj(ξ) ⊆ B, ξ ∈ B} are topologies on X, for all j ∈ J. Proof. = {ξ ∈ X : [ξ] ⊆ B}, and upper approximation is defined by ℵ(B) Keywords: core; neighborhood

Sp)-open

(Λ, sp)-open Sets in Topological Spaces by Boonpok, Chawalit; Khampakdee, Jeeranunt (2022) - The set of all (Λ, sp)-cluster points of A is called the (Λ, sp)-closure of A and is denoted by A(Λ,sp). For the (Λ, sp)-closure, the following properties hold: (1) A ⊆ A(Λ,sp) and [A(Λ,sp)](Λ,sp) = A(Λ,sp). Keywords: a(λ; sp)-open
Contra-(Λ, sp)-continuity and δ(Λ, sp)-closed sets by Boonpok, Chawalit; Viriyapong, Chokchai (2022) - Then, Y − V is a δ(Λ, sp)-closed set of Y . In particular, F−(y) = {x ∈ X | y ∈ F (x)} for each point y ∈ Y . Keywords: sp)-open
Weak α(Λ, sp)-continuity for multifunctions by Boonpok, Chawalit; Thongmoon, Montri (2023) - Math, 16 (1) (2023), 465-478 471 (1) F is upper weakly α(Λ, sp)-continuous; (2) for each x ∈ X and each (Λ, sp)-open set V of Y containing F (x), there exists an α(Λ, sp)-open set U of X containing x such that F (U) ⊆ V (Λ,sp); (3) F+(V ) ⊆ Then, there exists a (Λ, sp)-open set U of X such that U ⊆ G ⊆ U (Λ,sp). Keywords: sp)-open
Upper and lower weakly (Λ, sp)-continuous multifunctions by Boonpok, Chawalit; Pue-on, Prapart (2023) - (2) For every pair of (Λ, sp)-open sets U and V whose union is X, there exist (Λ, sp)- closed sets F and H such that F ⊆ U , H ⊆ V and F ∪H = X. (3) For every (Λ, sp)-closed set F and every (Λ, sp)-open set G containing F , there exists a (Λ, sp)-open set U such that F ⊆ U ⊆ U (Λ,sp) ⊆ G. (4) For every pair of disjoint (Λ, sp)-closed sets F and H, there exist disjoint (Λ, sp)- open sets U and V A multifunction F : (X, τ) → (Y, σ) is said to be: (i) upper weakly (Λ, sp)-continuous if, for each x ∈ X and each (Λ, sp)-open set V of Y containing F (x), there exists a (Λ, sp)-open set U of X containing x such that F (U) ⊆ V (Λ,sp); (ii) lower weakly (Λ, sp)-continuous if, for each x ∈ X and each (Λ, sp)-open set V of Y such that F (x) ∩ V ̸= ∅, there exists a (Λ, sp)-open set U of X containing x Keywords: sp)-open
Upper and Lower Almost Contra-(Λ, sp)-continuity by Boonpok, Chawalit; Khampakdee, Jeeranunt (2023) - A topological space (X, τ) is called strongly s(Λ, sp)-regular if, for each s(Λ, sp)-closed set K and each x ∈ X −K, there exists a r(Λ, sp)-closed set F containing x such that F ∩K = ∅. Lemma 6. For a multifunction F : (X, τ) → (Y, σ), the following properties are equiv- alent: (1) F is upper almost contra-(Λ, sp)-continuous; (2) F+(K) is (Λ, sp)-open in X for every r(Λ, sp)-closed set K of Y ; (3) F−(V ) is (Λ, sp)-closed in X for every r(Λ, sp)-open set V of Y ; (4) F−([V (Λ,sp)](Λ,sp)) is (Λ, sp)-closed in X for every (Λ, sp)-open set V of Y ; (5) F+([K(Λ,sp)] (Λ,sp)) is (Λ, sp)-open in X for every (Λ, sp)-closed set K of Y ; (6) for each x ∈ X and for each s(Λ, sp)-open set V of Y with F (x) ⊆ V , there exists a (Λ, sp)-open set U of X containing x such that F (U) ⊆ V (Λ,sp); (7) F+(V ) ⊆ Keywords: set; sp)-open

K=0

Boundedness of Nonregular Pseudo-differential Operators and Their Adjoints on Variable Exponent Besov-Morrey Spaces by Congo, Mohamed; Ouedraogo, Marie Francoise (2022) - The expression f ≲ g means that f ≤ cg for some independent constant c, and f ≈ g means f ≲ g ≲ f . Estimation of the term ∥∥∥∥∥ N1∑ k=0 φ̌0 ∗ fk ∥∥∥∥∥ Mp(·),u(·) One has suppF (φ̌0 ∗ fk) ⊂ {ξ ∈ Rn : |ξ| ≤ 2} . Keywords: k=0; p(·),u(·),q; ℓq(·)(mp(·),u; ∥∥∥∥∥∥
A Chaundy-Bullard Type Identity and its $q$-analogue by Chammam, Wathek; Khliﬁ, Mongia ; Gulistan, Muhammad (2025) - For n and m nonnegative integers and X = Y = p ∈ N∗ in (12), we have m∑ k=0 n+ 1 (n+ k + 2)(n+ k + 1) + n∑ k=0 m+ 1 (m+ k + 2)(m+ k + 1) the Chaundy–Bullard identity [7–9] defined by (1−X)n+1 m∑ k=0 ( n+ k k ) Xk +Xm+1 n∑ k=0 ( m+ k k ) (1−X)k = 1. (10) The q-analogue of Chaundy–Bullard identity (10) defined in [10] by the equality: m∑ k=0 Keywords: k=0

Problems

A New Approach in Solving a Class of Control Problems with Fractional Objectives by Saeed, Tareq; Treanta, Savin (2025) - Math, 18 (4) (2025), 6921 5 of 14 ψτ,γ(x, λ(x), π(x))− λτγ(x) = 0, x ∈ K } . − Eδ(λ, ω) ( Υδ ω − d dxξ Υδ ωξ )} ≦ 0, x ∈ K, q∑ δ=1 Ωδ { Iδ(λ, ω) ( χδ ζ − 0 ) − Eδ(λ, ω) ( Υδ ζ − 0 )} ≦ 0, x ∈ K, ωT q∑ δ=1 Ωδ { Iδ(λ, ω) ( χδ ω − d dxξ χδ ωξ ) Keywords: duality; problems

Indices

M-Polynomial and Degree-Based Topological Indices forIterative Graphs by Sarhan, Nihad Titan ; Abdulkhaleq Ali, Didar; Mohiaddin, Gohdar H. (2025) - Plotting Representation Our figures 2D and 3D of M-polynomials and topological indices are obtained by Wolfram Mathematica. Math, 18 (1) (2025), 5711 14 of 15 References [1] A. Ali, W. Nazeer, M. Munir, and S. M. Kan. M-polynomials and topological indices of zigzag and rhombic benzenoid systems. Keywords: benzene; indices; polynomial; topological

Matrices

Determinants of Arrowhead Matrices over Finite Commutative Chain Rings by Jitman, Somphong ; Modjam, Pornrudee (2024) - Arrowhead matrices have attracted attention due to their rich algebraic structures and numerous applications. 2020 Mathematics Subject Classifications: 11C20, 15B33 Key Words and Phrases: Arrowhead matrices, Determinants, Finite fields, Finite commutative chain rings, Enumeration 1. Keywords: arrowhead; matrices; |an(r
Eigenvalue Analysis and Simultaneous Nilpotence in Intuitionistic Fuzzy Matrices by Sarah Aljohani; Padder, Riyaz Ahmad; Pratiksha Devshali (2025) - 〈β, β′〉 ≤ 〈1, 0〉 since, (〈aij , a′ij〉)(〈β, β′〉〈x, x′〉) a′1j〉 ∧ 〈xj , x′j〉 ... n∨ j=1 (〈anj , a′nj〉 ∧ 〈xj , x′j〉  = O Thus, 〈aki, a′ki〉 ∧ 〈xi, x′i〉 = 〈0, 1〉 for all k. Since 〈xi, x′i〉 6= Keywords: aij; a′ij; matrices

Interval

Binomials Arising from Buchberger Algorithm on Polyomino Ideals by Hamonangan, Yoshua; Muchtadi-Alamsyah, Intan (2024) - Case p = c and e
Keywords: interval; polyomino; s(f

Weight

MacWilliams Identity for m-spotty Hamming Weight Enumerator Over the Ring $\mathbb{F}_2+v\mathbb{F}_2$ by ?iap, Vedat; Ozen, Mehmet (2012) - b∏ j=0 �� V (t) j (z) ��α j , V. Şiap, M. Özen / Eur. n∏ i=1 z⌈w(vi)/t⌉ = ∑ v∈Rnb 2 χ � c1, v1 � + c2, v2 � + .. cn, vn �� n∏ i=1 z⌈w(vi)/t⌉ Keywords: weight
Gelfand-Tsetlin Modules for Lie Algebras of Rank 2 by Andelic, Milica; M. da Fonseca, Carlos; Futorny, Vyacheslav; Tsylke, Andrew (2025) - , c5 via c4, c3, c2, c1, h1, h3, z1 in U ′ 0: c12 =− c10 − c2 − 2c8 + Math, 18 (3) (2025), 6458 10 of 21 z2 = c5 + c4 + 1 3 (h1 − h2)c3 − 1 3 (6 + 2h1 + h2)c2 + 1 3 (h1 + 2h2)c1 + 1 27 (−h2 − 3 + h1)(6 + 2h1 + h2)(h1 + 2h2) (4.14) Using the relations (4.1)-(4.14), we can reduce the number of generators of U0(g): applying (4.2), (4.13), and (4.14) we can exclude c3, c4, c5 from all other relations. Keywords: elements; modules; monomials; set; weight

Element

Baer Elements in Lattice Modules by Manjarekar, C. S.; Kandale, Ujwala Narahari (2015) - For F1, F2 ∈ F(L∗) (i) F1 ⊆ F2 implies 0F1M ¶ 0F2M . (ii) 0F1M ∧ 0F2 We have y ∈ F and xn IM ¶ 0F M . Keywords: element

Lemma

Common Terms of k-Pell and Tribonacci Numbers by Taher, Hunar; Dash, Saroj Kumar (2024) - = − log(1− 0.1) 0.1 · 7.6 ϕk/2 < 8.1 ϕk/2 . If (m,n, k) is a positive integers solution of equation (22) with k ≥ 2 and n ≥ k + 2, then the inequalities 0.63m < n < 7.6 · 1016k5(log(k))3 hold. Keywords: lemma

Act

Gamma-semigroups with Unities and Morita Equivalence for Monoids by Sardar, Sujit Kumar; Gupta, Sugata; Shum, Kar Ping (2013) - In this paper we show that the left operator and right operator semigroups of a Γ-semigroup with unities are Morita equivalent monoids. Let L and R be Morita equivalent monoids. Keywords: act; monoids; morita
On M-Principally Injective and Projective S-acts by Hussain, Javed; Shabir, Muhammad (2018) - = γα(m) for all m ∈ M, hence β = γα ∈ HomS (M,N )α. For m ∈ M we have βu(m) = ψ(m) ∈ β(M) Keywords: act; projective

Representation

K-theory, Chamber Homology and Base Change for GL(2) by Aeal, Wemedh (2017) - We are concerned with the effect of base change E/F on each of these compact spaces. Math, 6 (2013), 282-298 291 classes of irreducible cuspidal representations of GL(2, F). Keywords: change; gl(2; map; representation
On the Irreducibility of Perron Representations of Degrees 4 and 5 by Dally, Malak M.; Abdulrahim, Mohammad N. (2018) - = b1 0 0 b2 0 0 b3 0 0  , C =  λ1d1 λ2d1 λ3d1 λ1d2 λ2d2 λ3d2 −t(1+t+t2) 1+t λ1 −t(1+t+t2) 1+t λ2 −t(1+t+t2) 1+t λ3  , and D =  d1 0 0 d2 0 0 −t(1+t+t2) 1+t 0 0  . Thus, b3 b1 = (−d1(1+t)+d2+b1t)((λ1b1+λ2b2+λ3b3)(1+t)+b1t) b1t . Keywords: representation

Prey

Dynamical Analysis of a Three Species Food-WebModel With Extended Holling Type II Functional Response by Kamal, Bakhan Bahman ; Mustafa, Arkan (2025) - − [ r2 X − α2 2T2Z ∗ G2(X,Y ) ] (Y − Y ∗)2 − r3 (X + Y ) (Z − Z∗)2 − [ 2 ( α2 + α1α2T1X ∗ + α2 2T2Y ∗) G2(X,Y ) − [ r2 K − α2 2T2Z ∗ G2 (K1,K2) ] (Y − Y ∗)2 − r3 2K (Z − Z∗)2 − [ 2 ( α2 + α1α2T1X ∗ + α2 2T2Y ∗) G2(X,Y ) Keywords: prey; species

Banach

Module Extension Banach Algebras and (sigma,tau)-amenability by Eshaghi-Gordji, Madjid; Niyazi-Motlagh, Abolfazl (2009) - = d(a) = (σ(a), 0)( f , g)− ( f , g)(τ(a), 0) = (σ(a) f − f τ(a),σ(a)g (2)⇒ (3): Let D :A −→ X be a σ-derivation from A into A -bimodule X and let JX : X −→ X ∗∗ be the canonical embedding, then for each a, b ∈A we have eD(ab) Keywords: banach
Automatic Continuity of Higher Derivations on Banach-Jordan Pairs by Marhnine, Hassan; Zarhouti, Chafika (2017) - Let V = (V +, V −) be a normed Jordan pair and let b be a nonzero element in V −σ. Let V = (V +, V −) be a nondegenerate Banach-Jordan pair with nonzero socle. Keywords: banach; jordan; pair
Some Aspects of b(Î±n, Î²n)-hypermetric Spaces over Banach Algebras by Dehghan Nezhad, Akbar; Radenovic, Stojan (2021) - Quotient b(αn,βn)-hypermetric space over Banach algebra A Let (X,Γ(αn,βn)) be a b(αn,βn)-hypermetric space over Banach algebra A and X̃ be a partition of X. For each point p ∈ X, we denote p̃ a point in X̃ containing p, and we denote the equivalent relation induced by the relation by ∼. Definition 7. The pair (X,Γn) is called an b(αn,βn)-hypermetric space over Banach algebra A. For example, we can place A+ = Z0 + or R0 +, where Z0 + := N ∪ {0} = {0, 1, 2, . . . } and R0 + := [0,+∞). Keywords: b(αn; banach; γ(αn

Example

Regularization of heptahedra using geometric element transformation method by Pal, Buddhadev; Dey, Santu; Bhattacharyya, Arindam (2018) - Now, we give an example of a heptahedron which is regular base heptahedron but q(H) 6= By Geometric element transformation method (GETMe) always we get a new element. Keywords: example; heptahedron; transformation;  ;  

Projective

General Deformations of Sprays on Finsler Manifolds by Elgendi, Salah Gomaa; Soleiman, Amr (2025) - Math, 18 (3) (2025), 6204 15 of 18 In the following two examples, for simplicity, we consider S̃ = S − 2Pξ = S − 2ζ, where we set ζ = Pξ. − 2Pξ = S − 2ζ, then the coefficients G̃i as follows: G̃1 = G1 + ζ1, G̃2 = G2 + ζ2. Keywords: deformation; finsler; projective; spray

Block

On the Symmetric Block Design with Parameters (306,61,12) Admitting a Group of Order 61 by Gashi, Menderes (2018) - 2010 Mathematics Subject Classifications: 05B05 Key Words and Phrases: Symmetric block design, Orbit structure, Automorphism group 1. Among symmetric block designs of square order, a study of symmetric block designs of order 49 is of a particular interest. Keywords: block; design; orbit
On the Symmetric Block Design with Parameters (210,77,28) Admitting a Frobenius Group of Order 57 by Gashi, Menderes (2020) - 2020 Mathematics Subject Classifications: 05B05 Key Words and Phrases: Symmetric block design, Orbit structure, Automorphism group 1. Among symmetric block designs of square order, a study of symmetric block designs of order 49 is of a particular interest. Keywords: block; design; orbit
On the Symmetric Block design with Parameters (220,73,24) Admitting a Group of Order 73 by Gashi, Menderes (2024) - The full automorphism group for this orbit structure is provided. 2020 Mathematics Subject Classifications: 05B05 Key Words and Phrases: Symmetric block design, Orbit structure, Automorphism group 1. The determination of the spectrum for symmetric block designs is a widely open problem. Keywords: block; design; orbit

Mapping

Some New Characterizations of Open and Closed Fuzzy Mappings Inspired by Induced Mappings by Kaur, Sandeep; Birkea, Fathea M.; Özkan, Alkan; AL-shami, Tareq; Omran, M. (2025) - In this paper, we use the induced mappings to obtain some new characterizations of open fuzzy mappings in connection with closures and closed fuzzy mappings in connection with interiors of fuzzy sets. 2020 Mathematics Subject Classifications: 54A40, 03E72, 54C05, 94D05 Key Words and Phrases: Fuzzy set, Fuzzy topological space, Open fuzzy mapping, Closed fuzzy mapping, Induced mapping 1. Keywords: mapping; subset
Random Stability of a Functional Equation Related to An Inner Product Space by Shin, Dong Yun; Lee, Jung Rye; Park, Choonkil (2012) - ρ� x 2 , x 2 ,−x ,0,...,0 �(t) which is equivalent to µ f (x)−2 f � x 2 �(t) ≥ ρ� x 2 , x 2 ,−x ,0,...,0 �(2nt) for all x ∈ X and all t > 0. ρ� x 2 ,− x 2 ,0,...,0 � (2t) for all x ∈ X and all t > 0. Keywords: mapping; � �

Blow

Blow-up for nonlinear heat equations with absorptions by Zhang, Hailiang; Guo, Xiulan (2008) - Moreover, there exits a constant C > 0 such that sup x∈Ω u(x , t)≤ C (T − t) 1 r−p ε0 < t < T, ε0 > 0. [7] A. W. Leung, Q.Zhang, Finite extinction time for nonlinear parabolic equations with nonlinear mixed boundary data, Nonlinear Analysis 31(1998) 1-13. Keywords: blow; u(x

Algebras

Properties of Nilpotent Evolution Algebras with no Maximal Nilindex by Alarfeen, Ahmad; Qaralleh, Izzat; Ahmad, Azhana (2021) - = ϕnk = 0, k ≤ n− 2. (44) (65) Finally, taking v′ = e2 + en, we obtain γe1 = γv, βe1 = βv, sen = sv, and ten = tv, for any v ∈ E. REFERENCES 298 Thus, we conclude that local automorphism ψ = (ϕij) has the following form: ϕij =  α2i−1 e1 , i = j > n− 1 γe1 , i = 1, j = n− 1 βe1 , i = 1, j = n ϕ (e1) Keywords: algebras; derivation; evolution; n−1
Exploring Categorical Perspectives on Soft BCK/BCI-algebras by Muhiuddin, G.; Mohamed E. Elnair; Ahmed A. Khidir; Mohammed Hassan (2025) - [8] explored new operations on soft sets, while ongoing research continues to advance soft set theory. In recent years, researchers have merged category theory with soft set theory to estab- lish the category of soft sets across various domains. Keywords: algebras; bci; bck; sbcki

Locating

2-Locating Sets in a Graph by Canete, Gymaima; Rara, Helen; Mahistrado, Angelica Mae (2023) - Resolving sets and locating sets, however, are defined differently in more recent studies. On the other hand, Canoy and Malacas [8] defined a locating set as a set S ⊆ V (G) of G such that for every two distinct vertices u and v of V (G) \ S, NG(u)∩S ̸= NG(v)∩S. Other variations of locating sets are studied in [16], [6], [11], [13], Keywords: locating; set

Subalgebra

Investigating Length and Mean-Fuzzy Subalgebras in Sheffer Stroke Hilbert Algebras by Rajesh, Neelamegarajan ; Oner, Tahsin ; Iampan, Aiyared; Rezaei, Akbar (2025) - Math, 18 (2) (2025), 5914 20 of 21 but also underscores the practical relevance of fuzzy subalgebras in fields such as logic, computer science, and uncertainty modeling. [15], multi fuzzy sets [16], bipolar- valued fuzzy sets Keywords: inf; subalgebra
Generalized Fuzzy Subalgebras of Sheffer Stroke Hilbert Algebras by Rajesh, Neelamegarajan ; Iampan, Aiyared; Oner, Tahsin ; Saeid, Arsham Borumand (2025) - New fuzzy subalgebras of Sheffer stroke Hilbert algebras In this section, let H = ⟨H, |, 0⟩ denote the Sheffer stroke Hilbert algebra unless oth- erwise specified. 2020 Mathematics Subject Classifications: 03G25, 03E72 Key Words and Phrases: Sheffer stroke Hilbert algebra, subalgebra, fuzzy set, fuzzy subalgebra 1. Keywords: sheffer; subalgebra
On Interval-Valued Intuitionistic Fuzzy Subalgebras of Sheffer Stroke Hilbert Algebras by Iampan, Aiyared; Rajesh, Neelamegarajan ; Oner, Tahsin ; Ates, Firat ; Geetha, Kannan ; Saeid, Arsham Borumand (2025) - Intuitionistic fuzzy sets. Additionally, the role of fuzzy sets in Sheffer stroke BE-algebras [5] has been investigated, underscoring the far-reaching effects of the Sheffer stroke operation across diverse algebraic systems. Keywords: sheffer; subalgebra; γa(d

Pythagorean

Structure of Primitive Pythagorean Triples in Generating Trees by Koszegyova, Lucia; Csókási, Evelin; Hirjak, Juraj (2024) - 2020 Mathematics Subject Classifications: 11D09, 11A41, 11C99 Key Words and Phrases: Primitive Pythagorean triples, Berggren’s tree, Price’s tree, Euclid’s formula 1. To use primitive pythagorean triples, we need to understand them and their generating better. Keywords: pythagorean; triple

Entropy

A Comparative Analysis of Entropy Measures for Exponentiated Exponential and Truncated Exponentiated Exponential Distributions by Dar, Javid; Sajjad, Irsa; Tamboli, Shahid (2025) - Many authors contributed to overcoming this problem and proposed different entropy measures. In this section, by following section 2.1, different entropies measures of EED and TEED are derived. Keywords: entropy; teed
Mathai-Haubold Interval Entropy and Related Inequalities by Dar, Javid; Alsheikh, Sara Mohamed Ahmed; Jadhav, Prakash (2025) - Using (2.2), we get Kα (X; t1, t2) = 1 α− 1 [ t2 − t1 (t2 − t1) 2−α Math, 18 (4) (2025), 6480 4 of 14 Given that a system has survived up to time t1 and has been found to be down at time t2, then K (X; t1, t2) measures the uncertainty about its lifetimes between t1 and t2. Keywords: entropy; t2 t1

Γ(β

Multi-step Residual Power Series Method for Solving Stiff Systems by Al Zurayqat, Mohammad ; Hasan, Shatha (2024) - [0.7, 0.8], 9G(t) for t ∈ [0.8, 0.9], 10G(t) for t ∈ [0.9, 1], W (t) =  1W (t) for t ∈ [0.2, 0.3], 4W (t) for t ∈ Keywords: frpsm; γ(3β; γ(β

Contraction

Fixed Point Theorems for Mappings Contracting Perimeter of Triangles Embedded with F-Contractions in b-Metric Spaces by Batul, Samina; Qawaqneh, Haitham; Ulfat, Hira; Sagheer, Dur-e-Shehwar; Aydi, Hassen (2025) - Additionally, we construct examples of mappings contracting perimeters of triangles embedded with F-contractions which are not contraction mappings in the framework of b-metric spaces. Fur- thermore, we provide examples of mappings that contract the perimeters of triangles embedded with F-contractions in b-MSs, but do not qualify as contraction mappings in the traditional sense. Keywords: contraction; σb(η
Applications and Theoretical Foundations of Best Proximity Points in Generalized Interpolative Proximal Contractions by Javed, Khalil; Nazam, Muhammad; Arshad, Muhammad; De la Sen, Manuel (2025) - In the absence of a precise solution, best proximity point theorems investigate the existence of such best proximity points for approximate solutions to the fixed point problem. In fact, best proxim- ity point theorems look into the possibility of such best proximity point for approximate solutions to the fixed point equation P(b) = b in the absence of a precise solution. Keywords: contraction

J)−

Some Fundamental Properties of Beta-open Sets in Ideal Bitopological Spaces by Caldas, Michel; Jafari, Saied; Rajesh, Neelamegarajan (2013) - Arbitrary intersection of (i, j)− β −I -closed sets is always (i, j)− β −I -closed. for (i, j)− βI Cl(A) is the smallest (i, j)− β −I -closed set containing A. Then f ((i, j)− βI Cl(A))⊂ σi −Cl( f (A)). Keywords: -open; j)−

J(r

Generalized Thermoelasticity Problem of a Hollow Sphere Under Thermal Shock by Kar, Avijit (2009) - − γ(T + δ1kαṪ )δi j (1) and generalized heat conduction equation is � δ1k + δ2k ∂ ∂ t � K∇2T + δ2kK∗∇2T = ρCe � δ1k Ṫ + � δ1kα ∗ + δ2k � T̈ � + γT0 � ζδ1k + δ2k ∂ ∂ t � ∆̇, (2) where τi j(i = r,θ) is the stress tensor, ∆ is the dilatation, T is the temperature increase over the absolute reference temperature T0, γ = (3λ+ 2µ)αt , λ and µ are the Lame’s constants, αt is the coefficient of linear thermal expansion of the material, α and α∗ are the relaxation times, K is the coefficient of thermal conductivity, K∗ is the additional material constant, ρ is the mass density, Ce is the specific heat of the solid at constant strain, δi j is the Kronecker delta. Consider the following partial cases of equations (1) and (2): (i) if α = 0, α∗ = 0, k = 1, and ζ = 0, then the equations (1) and (2) are reduced to the equations of classical theory of thermo-elasticity (CTE). (ii) if α = 0, α∗ = 0, k = 1, and ζ = 1, then the equations (1) and (2) are reduced to the equations of classical coupled theory of thermo-elasticity (CCTE). (iii) if k = 1, and ζ = 1, then the equations (1) and (2) are reduced to the equations of temperature rate dependent thermo-elasticity theory (TRDTE(GL). Keywords: j(r; stress; thermo

Semi

On some mappings in topological spaces by Hussain, Sabir; Ahmad, Bashir; Noiri, Takashi (2009) - γ-pre-semi-open functions Definition 4.1. The class of γ-pre-semi-open functions is a subclass of class of γ-semi-open functions defined in [5]. Keywords: semi; γ∗-semi
Semi-mathscr{I}-submaximality by Boonpok, Chawalit (2022) - Semi-I -submaximal ideal topological spaces In this section, we introduce the notion of semi-I -submaximal ideal topological spaces. This paper presents the concept of semi-I -submaximal ideal topological spaces. Keywords: scli; semi

Semigroups

An Application of Generalized Fuzzy Ideals in Ordered Semigroups by Lekkoksung, Somsak; Davvaz, Bijan; Lekkoksung, Nareupanat (2024) - On fuzzy ordered semigroups. Ordered semigroups are algebraic systems consisting of a nonempty set, an associative binary operation, and a partial order compatible with this binary operation. Keywords: ideals; interior; semigroups; χa)i

Likelihood

Likelihood Ratio Tests on Cointegrating Vectors, Disequilibrium Adjustment Vectors, and Their Orthogonal Complements by Morin, Norman (2010) - A A S H H S H H S A φ φ φ φ φ ⊥ ⊥ ⊥ ⊥ − ⊥ ⊥ ⊥ ⊥ − ⊥ ⊥ ⊥ ⊥ = ′ × ′ ′ ′ ′ ′ ′ ′ ′− . A A S A A S Keywords: h h; h r; likelihood; r s; s h; s s; φ ⊥; − −; − ⊥; ⊥ ω; ⊥ −; ⊥ ⊥

Binary

Binary Soft Set Theory by Acikgoz, Ahu; Tas, Nihal (2016) - Also some properties of binary soft sets are investigated. In Section 3 we introduce the concept of a binary soft set and the operations on binary soft sets such as binary subset, binary equality, union of two binary soft sets, intersection of two binary soft sets, difference of two binary soft sets, symmetric difference of two binary soft sets etc. Keywords: binary; set

Points

On the Existence of Roots of Some p-adic Exponential-Polynomials by Dalloul, Amran (2018) - Now apply the previous steps to obtain The Newton polygon of exp(X) as follows: Rotate the vertical half-line of the negative part of the y-axis until it reaches to a position parallel to the line Y = − 1 p−1(X − 1). The line hits a finite number of points. Keywords: line; newton; points; polygon

Monoid

On Gamma-Ideals, Gamma-Submonoids and Isomorphism Theorems of Gamma-Monoids via Gamma-Submonoids by Sarapuddin, Hulsen; Vilela, Jocelyn (2023) - [2] A monoid is a semigroupM which contains an identity element 1M ∈ M such that 1M ∗m = m ∗ 1M = m for all m ∈ M . A left Γ-ideal (respectively, right Γ-ideal) of M is a subset I of M such that for any α, β ∈ Γ, for all a ∈ I and m ∈ M , αm ∗ βa ∈ I (respectively, αa ∗ βm ∈ I). Keywords: monoid

Hausdorff

On Hausdorff Spaces via Ideals and Semi-I-irresolute Functions by Hatir, Esref; Noiri, Takashi (2009) - Math, 2 (2009), (172-181) 173 present authors defined the notion of semi-open sets via ideals to obtain decomposi- tion of continuity. [10] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Keywords: hausdorff

Water

Solution of Burger's Equation in a One-Dimensional Groundwater Recharge by Spreading Using q-Homotopy Analysis Method by Shah, Kunjan (2016) - If the porous medium is soil, water content is same as the soil moisture. The motion of water flow through unsaturated porous media is governed by continuity equation ∂ (ρSθ ) ∂ t = −∇M , (2) where ρS is the bulk density of medium on dry weight basis, θ is the moisture content at any depth Z on a dry weight basis and M is a mass of flux of moisture at any time t ≥ 0. Keywords: content; moisture; water

Complex

Narrowing Cohomology for Complex S^6 by McHugh, Andrew Patrick (2017) - Namely, h2,0 = a = c = d = 0. Some results on the Dolbeault cohomology of compact complex manifolds and of complex S6. Keywords: complex; q bc
An Innovative Method for Employing Complex Intuitionistic Fuzzy Ideals in $\mathcal{B}\mathcal{C}\mathds{K}/ \mathcal{B}\mathcal{C}\mathcal{I}$-Algebras by Jawad, Muhammad; Hoskova-Mayerova, Sarka; Nigar, Niat; Mateen, Muhamad Haris (2025) - [35] An IFS L of M is known as an IFSA of M if it meets (i) µL(0) ≥ µL(s), (ii) νL(0) ≤ νL(s), (iii) µL(s ⋆ l) ≥ µL(s) ∧ µL(l), ∀s, l ∈ M , (iv) νL(s ⋆ l) ≤ νL(s) ∨ νL(l), ∀s, l ∈ M . A CIFS L = (s, µL(s), νL(s)) is considered a CIFSA of M if s, l ∈ M , and it satisfies following: (i) Keywords: bck; cifi; cifs; complex; l l

G(t

Generalized Monotone Iterative Method for Caputo Fractional Integro-differential Equation by Devi, J. Vasundhara; Sreedhar, Chaduvula Venkata (2016) - Next we proceed to show that v0 ≤ w1 ≤ v2 ≤ w3 ≤ u≤ v3 ≤ w2 ≤ v1 ≤ w0. Then for any solution u(t) of (10), (11) with v0 ≤ u ≤ w0. Keywords: g(t
Approximating Riemann-Stieltjes Integral Using New Time and Cost Efficient Trapezoid-type Quadrature by Memon, Kashif ; Shaikh, Muhammad Mujtaba ; Mahesar, Sara ; Malik, Kamran ; Ahmad, Hijaz; Uzun, Berna ; Özsahin, İlker; Abdelfattah , Waleed Mohammed (2025) - − β ∫ β α ∫ t α ∫ y α g(x) dx dt+ ∫ Obviously, the RS-integral can be regarded as an enhancement of the usual integration by Riemann, in a way that besides the integrand f , the integrator also depends on x. While a considerable effort in literature has been done on enhancing quadrature rules for the classical Riemann integrals as compared to the RS-integrals, only some investigations have been attempted to approximate the RS-integral. Keywords: g(t; quadrature; t α; xk−1 ∫; α ∫; β α; ∫ t; ∫ xk; ∫ y; ∫ β

Pseudo

The Structure of Pseudo-BF /BF*-algebra by M. Al-Malki, Hessah; S. Al-Kadi, Deena (2020) - We study some elementary properties related to pseudo-BF -algebra and pseudo-BF ∗-algebra. 2020 Mathematics Subject Classifications: 06F35, 03G25 Key Words and Phrases: pseudo-BF -algebra, pseudo-BF ∗-algebra, pseudo-ideal, pseudo- atoms. Keywords: pseudo
Quotient Pseudo Hyper GR-algebras by Manzano, Jr., Ramises; Petalcorin, Jr., Gaudencio C. (2022) - Thus, there exists an element Iz ∈ H/I such that φ(Iz) So, there exists v ∈ y ⊛ x such that f(v) = 0H′ . Keywords: pseudo

Property

Modules that Have a Î´-Supplement in Every Extension by Ozturk Sozen, Esra; Eren, Åženol (2017) - A submodule N of M is said to be δ-small in M (denoted by N �δ M) N �δ M Keywords: property

Cone

Common Fixed Point Theorems for Three Mapsin Cone Pentagonal Metric Spaces by Auwalu, Abba; Hincal, Evren (2017) - if and only if x = y; (ii) ρ(x, y) = ρ(y, x) for all x, y ∈ X; (iii) ρ(x, y) ≤ ρ(x,w) + ρ(w, z) + ρ(z, y) for all x, y, z ∈ X and for all distinct points w, z ∈ X − {x, y} [Rectangular property]. The study of existence and uniqueness of fixed points of a mapping and common fixed points of two or more mappings has become a subject of great interest. Keywords: cone; d(gx0

Option

British Call Option on Stocks under Stochastic Interest Rate by Falcasantos, Kreanne ; Sumalpong, Felipe Jr. (2022) - [0, T − t] with t ∈ + | Xt = x2 ] = Eµc [ ( λx1Z µc t,T + (1− λ)x3Z µc t,T − λK − (1− λ)K )+ | Xt = x2 ] = Eµc [ ( λx1Z µc t,T − λK + (1− λ)x3Z µc t,T − (1− λ)K )+ | Xt = x2 ] = Eµc [( (λx1Z µc t,T − λK) + ((1− λ)x3Z µc t,T − (1− λ)K) )+ |Xt = x2 ] ≤ λEµc [( x1Z µc t,TK )+ |Xt = x1 ] + (1− λ)Eµc [( x3Z µc t,T −K )+ |Xt = x3 ] = λGµc(t, x1) + (1− λ)Gµc(t, x3). Keywords: option; price; t t; ∂2v

Density

Selberg-Type Generalized Quadratic Forms Gamma and Beta Integrals by Gupta, Arjun K.; Kabe, D. G. (2017) - = x1 − ix2 − jx3 − kx4 − lx5 −mx6 − nx7 − rx8. = (α1 − θ)−g1 ...(αn − θ)−gn = (α1 − θ)−g1((α1 − θ)− (α1 − α2))−g2 ...((α1 − θ)− (α1 − αn))−gn = (α1 − θ)−(g1+...+gn+r2+...rn) ∑∞ r2=0 ... ∑∞ rn=0 ( g2+r2−1 r2 ) ... ( gn+rn−1 rn ) (α1 − α2)r2 ... (α1 − αn)rn , (17) where α1 = max{α1, ..., αn}. Keywords: density; kabe

Exp

Application of the SBA Method to Solve the Nonlinear Biological Population Models by Mayembo, Stevy Mikamona; Bonazebi-Yindoula, Joseph; Pare, Youssouf; Bissanga, Gabriel (2019) - Math, 12 (3) (2019), 1096-1105 1099 u(x, y, t) = exp ( 1 2 √ hr 2 (x+ y) ) + ∫ t 0 R(u(x, y, s))ds+ ∫ t 0 N(u(x, y, s)ds (14) If now we Apply the Adomian algorithm to equation (15), we obtain: uk0(x, y, t) = exp ( 1 2 √ hr 2 (x+ y) ) + ∫ t 0 N(uk−1(x, y, s)ds ukn(x, y, t) Keywords: exp

Resp

A Generalization of Some Forms of g-Irresolute Functions by Noiri, Takashi; Popa, Valeriu (2009) - ∈mInt( f −1(V )) for every V ∈ mY containing f(x); (3) x ∈ f −1(mCl( f (A))) for every subset A of X with x ∈mCl(A); (4) x ∈ f −1(mCl(B)) for every subset B of Y with x ∈mCl( f −1(B)); (5) x ∈mInt( f −1(B)) for every subset B of Y with x ∈ f −1(mInt(B)); (6) x ∈ f −1(K) for every mY -closed set K of Y such that x ∈mCl( f −1(K)). There exists an mY -open set V of Y containing f (x) such that U ∩ (X − f −1(V )) Keywords: closed; resp

Poisson

Characterization of Three-dimensional Jacobi-Poisson Manifolds by Ali, Mahamane Saminou ; Hamidine, Ibrahima; Tankary Banaou, Tankary Banaou; Hassirou, Mouhamadou (2025) - A straightforward computation show that [E ∧ Z,E ∧ Z] = ( −A ∂B ∂x − C ∂A ∂y −A ∂C ∂y − C ∂B ∂z −B ∂C ∂z ) ∂x ∧ ∂y ∧ ∂z. + 2π13 ∂A ∂x ) ∂x ∧ ∂y ∧ ∂z. Keywords: jacobi; poisson

Filter

Normal Paradistributive Latticoids by Bandaru, Ravikumar ; Patel, Prashant ; Rafi, Noorbhasha ; Shukla, Rahul; Ajjarapu, Suryavardhani (2024) - Normal PDL In this section, we introduce the notion of a normal paradistributive latticoid and characterize interms of prime filters and minimal prime filters. It is also proved that each minimal prime filter belonging to O(P) is contained in P, and O(P) is the intersection of all the minimal prime filters contained in P. The concept of a normal paradistributive latticoid is introduced and characterized in terms of the prime filters and minimal prime filters. Keywords: filter
Weak Filters of Sheffer Stroke Hilbert Algebras Based on Intuitionistic Fuzzy Set by Ahn, Sun Shin; Seo, Young Joo; Jun, Young Bae (2025) - The notion of intuitionistic fuzzy weak filters in Sheffer stroke Hilbert alge- bras is introduced, and their properties are investigated. Conditions for an intuitionistic level set and an intuitionistic q-set to be weak filters are provided. 2020 Mathematics Subject Classifications: 03B05, 03G25, 06F35, 08A72 Key Words and Phrases: Weak filter, intuitionistic fuzzy point, intuitionistic level set, intu- itionistic q-set, (0, 1)-set, intuitionistic fuzzy weak filter 1. Keywords: filter

Max

On a System of Linear Singular Partial Differential Equations with Weight Functions by Guerrero, Euler Yoland Bancayrin (2019) - j and k are integers, 1 ≤ j ≤ N, 0 < k ≤ n(i, j)}, (2) n(i, j) = n(i)− n(j) + 1, where n(i), i = 1, 2, ..., N , are nonnegative integers. Hence, by Remark 3 (5), for t ∈ I1(s), we have ‖(µ0D)ηv0,i(t)‖s = ‖(µ0D)ηu1,i(t)‖ ≤ Rr22ηKη(s0 − s)−ηµ(t)ηση0,sµ(t)α ≤ Rr22ηKη aη0ω(t)cη ω(t)ηµ(t)κη µ(t)ηση0,sµ(t)α ≤ Rr22ηKηa0µ(t)(1−κ)ηω(t)(c−1)ηση0,sµ(t)α ≤ Rµ(t)α, provided a0 is small enough. Keywords: max
Fermatean Neutrosophic INK-algebras by Al-Masarwah, Anas ; Kaviyarasu, M.; Alnefaie, Kholood ; Rajeshwari, M. (2024) - M. Kaviyarasu et al. / Eur. For more results on algebraic structures with uncertainty (see works M. Kaviyarasu et al. / Eur. Keywords: max; m×n

Triangle

Generalizing the Equal Incircles Theorem: Insights from Sangaku Problems by Boonsomchua, Perawit (2024) - Corollary 3 (Area minimum on bisecting triangle angle scenario) Consider a triangle △AB1C1 with vertices A, B1, and C1. Sangaku problems are traditional Japanese geometrical puzzles, often displayed in reli- gious temples, that have intrigued mathematicians for centuries. Keywords: circles; sangaku; tan; triangle

Wall

Squeeze Flow of Ethylene Glycol-based Carbon Nanotube with the Influence of Joule Heating, Viscous Dissipation and Chemical Reactions by Khan, Naseer; Farooq, Muhammad; Ullah Jan, Wajid; Uzun, Berna; Pamucar, Dragan; Ozsahin, Ilker; Ahmad, Hijaz (2025) - Math, 18 (4) (2025), 6395 5 of 34 otube, single wall carbon nanotube (SWCNT), multi wall carbon nanotube (MWCNT), Homotopy analysis method(HAM)). Error analyses are displayed in Figures 2-3 for single wall carbon nanotubes and multi wall carbon nanotubes and Tables (1-19) to examine the two approaches’ dependability for different levels of physical parameters. Keywords: -0.6832; carbon; carbon nanotubes; e1 =; h =; lines; multi; mwcnt; nanotubes; sr =; wall; wall carbon; γ1 =; φ(υ; ϕ1 =; −ϑ′(0

Approximation

Best Approximation of Unbounded Functions by Modulus of Smoothness by Auad, Alaa Adnan; Hilal, Mohammed A. ; Khalaf, Nihad Shareef (2023) - Math, 16 (2) (2023), 944-952 945 Let Lp,λ[−π, π] = {f : f is unbounded function on [−π, π], 1 ≤ p <∞}, with the norm ∥f∥Lp,λ[−π,π] = (∫ π −π |f(x)λ(x)|pdx ) 1 p <∞. Also, let N be the set of all natural numbers and for every k ∈ N ∪ {0}, we denote by Tk the set of all trigonometric polynomials of degree less than or equal to k. For a given function f ∈ Lp,λ[−π, π], we define Ek(f)Lp,λ[−π,π] = inf{∥f − g∥Lp,λ[−π,π] ; g ∈ Tk}, (1) which is called the kth degree best approximation of f with respect to Tk. Let k ∈ N and f ∈ Lp,λ[−π, π]. Keywords: approximation; λ[−π

Symmetry

Real Spectra in Logarithmic Model PT-symmetry Operators: Iso-spectra in Logarithmic PT-symmetry by Rath, Biswanath; Jarrar, Rabab; Shanak, Hussein; Wannan, Rania; Asad, Jihad (2023) - Hence these two potentials can be considered as iso-spectral models in PT-symmetry. This motivates the present author to calculate spectra of H1,2 and suggest new models on logarithmic potentials. Keywords: symmetry

I=0

A Numerical Method for Investigating Fractionali Volterra-Fredholm Integro-Differential Model by Syam, Muhammed I. ; sharadga, Mwaffag; Hashim, Ishak (2024) - tr = jr, j ∈ 0, 1, 2, ...,M − 1, r = 1 M . i < l ≤ M − 1 0, 0 ≤ l < i ≤ M − 1 . Keywords: i=0; m−1∑
Behavior and Solution Representations of Fourth-Order Rational Systems of Difference Equations by S. Gafel, Hanan; Altamimi, Haya (2025) - Math, 18 (3) (2025), 6218 20 of 28 =  (−1)n−1ηnλn−1σn−1µn−1τn−1κn−1[ ∏n−2 i=0 ((2i + 2)η − τ)(λ + (2i + 1)µ)((2i + 1)λ − κ)(σ + (2i + 2)τ) ((2i + 2)σ − δ)(ζ + (2i + 1)κ) ]  (−1)nηn−1λn−1σnµnτnκn−1[ (σ + τ)(σ − δ) ∏n−2 i=0 ((2i + 1)η − τ)(λ + (2i + 2)µ)((2i + 2)λ − κ) (σ + (2i + 3)τ)((2i + 3)σ − δ)(ζ + (2i + 2)κ) ]  −  (−1)n−1ηnλn−1σn−1µn−1τn−1κn−1[ ∏n−2 i=0 ((2i + 2)η − τ)(λ + (2i + 1)µ)((2i + 1)λ − κ)(σ + (2i + 2)τ) ((2i + 2)σ − δ)(ζ + (2i + 1)κ) ]  +  (−1)n−1ηn−1λn−1σn−1µn−1τnκn−1[ ∏n−2 i=0 ((2i)η − τ)(λ + (2i + 1)µ)((2i + 1)λ − κ)(σ + (2i + 2)τ) ((2i + 2)σ − δ)(ζ + (2i + 1)κ) ]  =  (−1)n−1ηnλn−1σnµnτnκn−1[ (σ + τ)(σ − δ) ∏n−2 i=0 ((2i + 2)η − τ) ∏n−2 i=0 ((2i + 1)η − τ)(λ + (2i + 2)µ) ((2i + 2)λ − κ)(σ + (2i + 3)τ)((2i + 3)σ − δ)(ζ + (2i + 2)κ) ]  [ η∏n−2 i=0 ((2i+2)η−τ) ] − [ τ∏n−2 i=0 ((2i)η−τ) ] =  (−1)n−1ηnλn−1σnµnτnκn−1[ (σ + τ)(σ − δ) ∏n−2 i=0 ((2i + 1)η − τ)(λ + (2i + 2)µ)((2i + 2)λ − κ) (σ + (2i + 3)τ)((2i + 3)σ − δ)(ζ + (2i + 2)κ) ]  η − [ τ ∏n−2 i=0 ((2i+2)η−τ)∏n−2 i=0 ((2i)η−τ) ] =  (−1)n−1ηnλn−1σnµnτnκn−1[ (σ + τ)(σ − δ) ∏n−2 i=0 ((2i + 1)η − τ)(λ + (2i + 2)µ)((2i + 2)λ − κ) (σ + (2i + 3)τ)((2i + 3)σ − δ)(ζ + (2i + 2)κ) ]  η + ((2n − 2)η − τ) H. S. Gafel, H. A. Altamimi / Eur. = (−1)nηn+1λnσnµnτnκn[ ∏n−1 i=0 ((2i + 2)η − τ)(λ + (2i + 1)µ)((2i + 1)λ − κ)(σ + (2i + 2)τ) ((2i + 2)σ − δ)(ζ + (2i + 1)κ) ] , Θ6n+1 = (−1)n+1ηnλnσn+1µn+1τnκn[ (σ − δ) ∏n−1 i=0 ((2i + 1)η − τ)(λ + (2i + 2)µ)((2i + 2)λ − κ) (σ + (2i + 1)τ)((2i + 3)σ − δ)(ζ + (2i + 2)κ) ] , Θ6n+2 = (−1)n+1ηn+1λn+1σnµnτnκn+1[ (λ − κ)(ζ + κ) ∏n−1 i=0 ((2i + 2)η − τ)(λ + (2i + 1)µ)((2i + 3)λ − κ) (σ + (2i + 2)τ)((2i + 2)σ − δ)(ζ + (2i + 3)κ) ] , Ω6n−3 = (−1)nηnλnσnµnτnκnδ[ ∏n−1 i=0 ((2i)η − τ)(λ + (2i + 1)µ)((2i + 1)λ − κ)(σ + (2i)τ) ((2i)σ − δ)(ζ + (2i + 1)κ) ] , Ω6n−2 = (−1)nηnλnσnµnτnκn+1[ ∏n−1 i=0 ((2i + 1)η − τ)(λ + (2i)µ)((2i)λ − κ)(σ + (2i + 1)τ) ((2i + 1)σ − δ)(ζ + (2i + 2)κ) ] , Ω6n−1 = (−1)nηnλnσnµnτn+1κn[ ∏n−1 i=0 ((2i)η − τ)(λ + (2i + 1)µ)((2i + 1)λ − κ)(σ + (2i + 2)τ) ((2i + 2)σ − δ)(ζ + (2i + 1)κ) ] , Ω6n = (−1)nηnλnσnµn+1τnκn[ ∏n−1 i=0 ((2i + 1)η − τ)(λ + (2i + 2)µ)((2i + 2)λ − κ)(σ + (2i + 1)τ) ((2i + 1)σ − δ)(ζ + (2i + 2)κ) ] , Ω6n+1 = (−1)nηn+1λnσnµnτnκn+1[ (ζ + κ) ∏n−1 i=0 ((2i + 2)η − τ)(λ + (2i + 1)µ)((2i + 1)λ − κ) (σ + (2i + 2)τ)((2i + 2)σ − δ)(ζ + (2i + 3)κ) ] , Ω6n+2 = (−1)n+1ηnλnσn+1µn+1τn+1κn[ (σ + τ)(σ − δ) ∏n−1 i=0 ((2i + 1)η − τ)(λ + (2i + 2)µ)((2i + 2)λ − κ) (σ + (2i + 3)τ)((2i + 3)σ − δ)(ζ + (2i + 2)κ) ] , where Θ−3 = ζ, Θ−2 = σ, Θ−1 = λ, Θ0 = η, Ω−3 = δ, Ω−2 = κ, Ω−1 = τ and Ω0 = µ. Proof. Keywords: i=0; σ +; ∏n−2; ∏n−2 i=0
On the Solution of Some Difference Equations by Elsayed, Elsayed M. (2011) - 2000 Mathematics Subject Classifications: 39A10 Key Words and Phrases: difference equations, recursive sequences, periodic solution. This is largely due to the fact that difference equations manifest themselves as mathematical mod- els describing real life situations in probability theory, queuing theory, statistical problems, stochastic time series, combinatorial analysis, number theory, geometry, electrical network, quanta in radiation, genetics in biology, economics, psychology, sociology, etc. Keywords: difference; i=0; xn+1

Sultan

Boundedness of the Sublinear Operators on Anisotropic Herz-slice Spaces by Sultan, Babar; Hussain, Amjad ; Sultan, Mehvish; Popa, Ioan-Lucian (2025) - [27] Let u ∈ (0,∞), p, r ∈ (1,∞), if x0 ∈ Rn, and 1 < r0 < ∞, then the characteristic function on B (x0, r0) fulfills∥∥χB(x0,r0) Sobolev-type Theorem for commutators of Hardy operators in grand Herz spaces. Keywords: sultan

Eisenstein

Classification and Enumeration of Primitive Eisenstein Triples using Prime Factorization Techniques by Jitman, Somphong; Mohammad, Mohd Sham; Sangwisut, Ekkasit (2025) - Eisenstein Triples In this section, some properties and geometric interpretation of Eisenstein triples are recalled in terms of triangles with a 60◦ angle. From Eisenstein Triples to the ω-Rational Unit Circle This section presents a connection between Eisenstein triples and points on the ω- rational unit circle (see (3) for the definition). Keywords: eisenstein; g(q; triples

Contra

Some Properties of Contra-b-Continuous and Almost Contra-b-Continuous by Al-omari, Ahmad Abdullah; Noorani, Mohd. Salmi Md. (2009) - Recall that a function f : X → Y is almost-continuous if f −1(V ) is open in X for each regular open set V of Y . Since f is almost contra-b-continuous and contra continuous f −1(V ) is b-closed and open, Thus bCl( f −1(V )) Keywords: contra

-open

On Decompositions of Continuity and Complete Continuity in Ideal Topological Spaces by Hatir, Esref (2017) - A subset A in X is said to be δβ − B − I -set (resp. but it is not δβ − B − Keywords: -open
Idealization of Some Topological Concepts by Mareay, Roshdey; Nasef, Arafa; Michael, F.I. (2015) - Since A⊆ B, we have that G \ B ⊆ G \ A∈ I ; moreover, B \ cl(G) Indeed, if A is I − β -open, then there is a preopen set G such that G \ A,and A\ cl(G) Keywords: -open

P(x

On the asymptotics and zeros of a class of Fourier integrals by Paris, Richard Bruce (2012) - The zeros labelled A, B, C , D indicate the zeros when ν = 1; the next real zero in the sequence when ν = 1 (which results from the coalesence of x2 and its conjugate) is labelled E. A similar behaviour is exhibited by the other zeros with the result that when ν = 3, all the zeros are again real. Keywords: asymptotic; p(x; zeros

Code

Quantum Codes Obtained through Constacyclic Codes over Z3 + Î½Z3 + Ï‰Z3 + Î½Ï‰Z3 by Singh, Jagbir; Mor, Prateek; ., Shikha; ., Meena (2021) - Some authors constructed quantum codes using the Gray image of cyclic codes on some finite rings. For example, a new technique of constructing quantum codes from cyclic codes over finite ring F2 + vF2 where v2 = v given by Qian Keywords: code

Map

Functions on $n$-generalized Topological Spaces by Balingit, Cherry Mae Rivas; Benitez, Julius (2019) - 2010 Mathematics Subject Classifications: 54A05, 54C05, 54C08, 54C10, 54H99 Key Words and Phrases: G -continuous map, G -open map, G -homeomorphism 1. f is called G -open map Keywords: map; set

Multi

Compact Soft Multi Spaces by Osmanoglu, Ismail; Tokat, Deniz (2014) - .∪ f −1 ��Fn, A �� . .∪ f −1 ��Fn, A �� = f � f −1 ��F1, A �� ∪ . . Keywords: multi; � �

Base

Orthogonal Decompositions of Regular Graphs and Designing Tree-Hamming Codes by Shabana, Hanan; El-Shanawany, Ramadan ; Halawa, Sahar (2024) - Math, 17 (4) (2024), 3492-3516 3493 V (X), E(X) for the vertex set and edge set of the graph X respectively, Pk for a path of k vertices, mG for m disjoint copies of G, and G∪H for disjoint union of graphs G and H. Let G1 = {G1, G2, · · · , Gk} and G2 = {F1, F2, · · · , Fk} be two distinct edge decompositions of H by G such that for each i ∈ {1, 2, · · · k} , Gi ≊ G ≊ Fi. The incidence matrix L = L (s, t) for such ODC G ={Gi a; a ∈ Zn, i ∈ {1, 2}} is a 2n× n2 binary matrix showing the relation between the edges of Kn,n and the the members of G such that every row in L corresponds to a unique graph in G and every column in L corresponds to a unique edge in Kn,n. Let the edge (α0, β1) ∈ E (Kn,n) . Keywords: base; odc; v(g

Finsler

Left Invariant Finsler Manifolds are Generalized Berwald by Aradi, Bernadett (2015) - 2010 Mathematics Subject Classifications: 53C60, 58B20, 22E99 Key Words and Phrases: Generalized Berwald manifold, Lie group, left invariant Finsler function, averaging process, geodesics 1. We also have a look at the more specific bi-invariant case, and review some essential results concerning bi-invariant Finsler functions with (at least partly) new and conceptual proofs. Keywords: berwald; finsler
On Finsler s-manifolds by Bahmandoust, Parisa; Latifi, Dariush (2017) - If we drop the involution property in the definition of symmetric Finsler space keeping the property sx ◦ sy = sz ◦ sx, z = sx(y), we get a bigger class of Finsler manifolds as symmetric Finsler spaces. The definition of symmetric Finsler space is a naturall generalization of E. Cartan’s definition of Riemannian symmetric spaces [8]. Keywords: finsler

∥∥∥∥

Inverse Problem for a Parabolic Equation with Integral Condition by Azizbayov, Elvin Ibrahim; Mehraliyev, Yashar (2017) - Problem Statement Denote by QT the domain {(x, t) : 0 ≤ x ≤ 1, 0 ≤ t ≤ T} and consider the equation c(t)ut(x, t) = uxx(x, t) + a(t)u(x, t) + b(t)g(x, t) + f(x, t), (x, t) ∈ QT (1) with nonlocal initial condition u(x, 0) + δu(x, T ) = ϕ(x) (0 ≤ x ≤ 1), (2) Neumann boundary condition ux(0, t) = 0 (0 ≤ t ≤ T ), (3) nonlocal integral condition 1∫ 0 u(x, t)dx = 0 (0 ≤ t ≤ T ), (4) and the additional conditions u(0, t) = h1(t) (0 ≤ t ≤ T ), (5) u(1, t) = h2(t) (0 ≤ t ≤ T ), (6) where δ ≥ 0 is a fixed number, 0 < c(t), g(x, t), f(x, t), 0 ≤ p(t), hi(t) (i = 1, 2) are given functions, u(x, t), a(t) and b(t) are unknown functions. [13] T.E. Oussaeif and A. Bouziani, Inverse problem of a hyperbolic equation with an integral overdetermination condition, Electronic Journal of Differential Equations, 2016(138):1-7, 2016. Keywords: c(t; c[0,t; ∥∥∥∥
The Saks-Henstock Lemma and the Change of Variable Formula of the PU integral by Flores, Greig Bates; Flores, Ann Leslie (2025) - ψ ) − (P) ∫ [a,b] f + (P) ∫ [a,b] f − ∑ D2 f(η) ∫ J ψ ∥∥∥∥ ≤ ∥∥∥∥(∑ D1 f(ξ) ∫ I ϕ · φ+ ∑ D2 f(η) ∫ J (1− ϕ) · ψ ) − (P) ∫ [a,b] f ∥∥∥∥ + ∥∥∥∥(P) ∫ [a,b] f − ∑ D2 f(ξ) = ∑ D1 φ(x), and Df = {(η,J , ψ)} be δ-fine division of [a, b]. Keywords: ∥∥∥∥
Fixed Point Theorems for a Subfamily of Non-expansive Evolution Operators by Sarwar, Muhammad; Rahmat, Gul; Hussain, Sadam; Bani Mufarrej, Mohammad Yousef ; Abodayeh, Kamaleldin (2025) - − ς∗∥2 − 2ηn(1− λn)⟨ς∗, ςn − ς∗⟩ ) [1− ηnµn + ηnµnλn + ηnµn − ηnµnλn]max{∥ςn − p∥, ∥p∥}. Keywords: 0 e(s; e(s; γt 0; ∥∥∥∥

N→∞

Mixed Type Algorithms for Asymptotically Nonexpansive Mappings in Hyperbolic Spaces by Thianwan, Tanakit (2021) - Fixed point iterations of nonexpansive mappings. Iteration processes for nonexpansive mappings. Keywords: nonexpansive; n→∞
On Inductive Limit of Commutative Triples by Timite, Lamine; Toure, Ibrahima (2022) - By the equation (3.1), we have χδn(k)(Φ(ykx)v, v) = χδn(k)(Φ U l (ykx)ξl, ξl),∀x, y ∈ G∞, k ∈ Kn. (3.2) Let us put En i = 〈πn(k)ξni , k ∈ Kn〉, i = 1, 2, the Hilbert completion of the vector subspace generated by the family {πn(k)ξni , k ∈ Kn} . Keywords: n→∞

Secret

Secret Sharing Schemes Based on Extension Fields by Calkavur, Selda (2018) - There is numerous research about secret sharing schemes. However there is little research on secret sharing schemes based on extension fields. Keywords: schemes; secret; sharing

Form

A Note on One-dimensional Varieties Over the Complex p-adic Field by Dalloul, Amran (2018) - If P has a root of the form (exp(x1), exp(x2)) for some elements x1, x2 ∈ E, then P (exp(x1), exp(x2)) ∈ V , then x1, x2 are Q-linearly dependent. Keywords: form
Cartan's Approach to Second Order Ordinary Differential Equations by Bracken, Paul (2020) - Given a trace-free matrix valued one-form $ with $2 = −ϑ $2 1 = dx and $ a multiple of ϕ, the remaining elements of $ are uniquely determined by the following conditions on its curvature form Π: it must be strictly upper-triangular and Π1 2 is a multiple of dx ∧ ϑ. γ̄ ∧ φ ᾱ ∧ γ̄ + β̄ ∧ β̄′ + γ̄′ ∧ ᾱ′ φ̄ ∧ ᾱ− (ᾱ+ ᾱ′) ∧ φ+ β̄′ ∧ θ φ̄ ∧ β̄ + β̄′ ∧ φ φ̄ ∧ γ̄ − (ᾱ+ ᾱ′) ∧ β + β̄′ ∧ ᾱ′ θ ∧ ᾱ+ φ ∧ φ̄+ ᾱ′ ∧ θ θ ∧ β̄ − φ ∧ (ᾱ+ ᾱ′) + ᾱ′ ∧ φ θ ∧ γ̄ + φ ∧ β̄′  (100) Keywords: form

Hierarchy

Hierarchy Sets in Almost Distributive Lattices and Their Structural Properties by Chinnayya, G. ; Ramesh, S. ; Jogarao, G. ; Bandaru, Ravikumar ; Iampan, Aiyared (2025) - {h ∈ L | a ∧ h = h} (iii) a ≤ b and b ∈ HS imply a ∈ HS (iv) h ∈ HS implies (h] ⊆ HS, where (h] = {h ∧ a | a ∈ L} (v) Ha is an ideal of L. Theorem 1. A proper hierarchy set HS of L is said to be prime, if given a, b ∈ L, a ∧ b ∈ HS implies a ∈ HS or b ∈ HS. Keywords: hierarchy

S−1

Convergence of β-Modified Jacobi-Perron algorithm over the field of formal power series by Chandoul, Amara; Aljuaydi, Fahad (2019) - A (s−1) ik + asn+1B s−1 i for 0 ≤ i ≤ n. (8) From (5), we find that B (s) i increases as s increases and degB (s) i1 > degA (s) i1,κ(s) > degA (s) i1,i2 A. Chandoul, F. Aljuaydi / Eur. i ≤ n (10) From (9) and (10), the assertion of theorem holds for s = 1. Keywords: s−1

L−1

Resolution of Nonlinear Convection - Diffusion - Reaction Equations of Cauchy Kind by the Laplace SBA Method by Pare, Youssouf; Youssouf, Minoungou; Nebie, Abdoul Wassiha (2019) - For k = 2, we get :  u20 = L−1t  1 sm m−1∑ j=0 sjum−j−1(0, x) + L−1t + 1 2 (cosx) t3λγ2 + 1 3! (sinx) t3γ3 u14(t, x) = L−1t [ 1 s Lt ( R(u13) )] ⇒ u14(t, x) = L−1t ( (sinx)λ4 − 4 (cosx)λ3γ − 6 (sinx)λ2γ2 + 4 (cosx)λγ3 + (sinx) γ4 s5 ) ⇒ u14(t, x) = 1 4! (sinx) t4λ4− 1 3! (cosx) t4λ3γ−1 4 (sinx) t4λ2γ2+ 1 3! (cosx) t4λγ3+ 1 4! (sinx) t4γ4 u15(t, x) = L−1t Keywords: cosx; l−1; l−1 t; sinx

Proposition

Semi-primitive Roots and Irreducible Quadratic Forms by Wolf, Marc; Wolf, François (2024) - × N∗ we let Px,y := {p ∈ P | p ≡ x Moreover if p ∈ P1,4: g ∈ GS ⇔ g ∈ GQR and ∀q ∈ P ( αq ≥ 1 ⇒ g p−1 2q ̸≡ 1 ) ⇔ ∅ ⊊ Rp (g) ⊂ GZ . Keywords: proposition; p−1

Respect

Generalized Linear Differential Equation using Hyers - Ulam Stability Approach by Bowmiya, S. ; Balasubramanian, G.; Govindan, Vediyappan; Donganont, Mana ; Byeon, Haewon (2024) - if ρ ̸= η ̸= 0, γ = σ = 0 (1−e−γ(β−α))(1−e−η(β−α)) γη (β − α)2 ∈; if γ ̸= η ̸= 0, ρ = σ = 0 (1−e−ρ(β−α)) ρ (β − α)3 ∈; if ρ ̸= 0, σ = γ = η = 0 (1−e−γ(β−α)) γ (β − α)3 ∈; if γ ̸= 0, σ = ρ = η = 0 (1−e−σ(β−α)) σ (β − α)3 ∈; if σ ̸= 0, ρ = γ = η = 0 (1−e−η(β−α)) η (β − α)3 ∈; if η ̸= 0, σ = γ = ρ = 0 (β − α)4 ∈; if ρ = σ = γ = η = 0 with respect to ω ∈ [α, β]. Proof. if ρ ̸= η ̸= 0, γ = σ = 0 (1−e−γ(β−α))(1−e−η(β−α)) γη (β − α)2 ∈; if γ ̸= η ̸= 0, ρ = σ = 0 (1−e−ρ(β−α)) ρ (β − α)3 ∈; if ρ ̸= 0, σ = γ = η = 0 (1−e−γ(β−α)) γ (β − α)3 ∈; if γ ̸= 0, σ = ρ = η = 0 (1−e−σ(β−α)) σ (β − α)3 ∈; if σ ̸= 0, ρ = γ = η = 0 (1−e−η(β−α)) η (β − α)3 ∈; if η ̸= 0, σ = γ = ρ = 0 (β − α)4 ∈; if ρ = σ = γ = η = 0 (63) with respect to ω ∈ [α, β], and α ̸= 0, β ̸= 0. 3. Keywords: respect; β ω; ω ∈

Waste

The Mathematical Modelling of Refuse Build-up on the University Campus: A Case Study of KNUST Campus by Barnes, Benedict; Adjei, I. A.; Sebil, C. (2019) - Math, 12 (4) (2019), 1426-1440 1433  1 ψ κ γ−(ν−ψ) κ −φ κ 0 1 γ−(ν−ψ) ψ − φ ψ 0 0 0 φ− (ν − ψ) 0 0 0 0   m1 m2 m3 m4  =  0 0 0 0  , where, v2 =  m1 m2 m3 m4  is the eigenvector which corresponds to λ2 = ν − ψ. λ2 − ( − ανγ + αψγ − κνγ − κψγ − βνγ + βψγ + αφν − αψφ− κφν + κφψ − βφν + βψφ+ αγφ− κγφ− βγν − γψφ ) λ = 0. (3) The following parameter values in table 1 were estimated based on the data collected on the KNUST campus from June, 2017 to April, 2018. Keywords: waste; ; 

Conjecture

Proof of Golombâ€™s conjecture in Fq with Î“$-pseudorandom sequences by Liu, Yonghong (2020) - In this paper we prove that the Golombs conjecture in Fq, and we show that a new pseudorandom sequence (denote Γ$) in F2 is existent by Golomb conjecture and additive groups. [2] proved that Golombs conjecture is true for all q < 260. Keywords: conjecture

U(x

Laplace-SBA Method for Solving Nonlinear Coupled Burger's Equations by Bonazebi-Yindoula, Joseph (2021) - = sinx+ L−1t ( 1 sLt ( ∂2v(x, t) ∂x2 )) + L−1t ( 1 sLt (N2 (u(x, t)v(x, t))) ) (23) J. B. Yindoula / Eur. = sinx+ L−1t ( 1 sLt ( ∂2uk(x, t) ∂x2 )) + L−1t ( 1 sLt ( N1 ( uk−1(x, t)vk−1(x, t) ))) vk(x, t) Keywords: l−1 t; u(x

Triangular

Characterizations and Identities for Isosceles Triangular Numbers by Punpim, Jiramate; Jitman, Somphong (2021) - − 2l2 − 2nl + 2l − 2l − 2 2 ) = l ( n2 + n2(n2 − 1)l 2 ) − (2n2 − 2n + 1) ( 2(l + l(l − 1)(n− 1) 2 )− l − 1 ) = lT (n2, l)− (2n2 − 2n + 1)(2T (l, n− 1)− (l + 1)). Then N = n + n(n− 1)l 2 for some positive integer n. It follows that rN + s = (2l + 1)2 ( n + n(n− 1)l 2 ) + l3 − 3l2 + 4 2 = n2l(2l + 1)2 + (2− l)n(2l + 1)2 + l3 − 3l2 + 4 2 = 4l3n2 + 4l2n2 + ln2 + 8l2n + 8ln + 2n− 4l3n− 4l2n− ln + l3 − 3l2 + 4 2 = (4l3 + 4l2 + l)n2 − (4l3 − 4l2 − 7l − 2)n + (l3 − 3l2 + 4) 2 = l ( (4l2 + 4l + 1)n2 − (4l2 − 6l − 4)n + (l2 − 4l + 4) ) − (l − 2) ((2l + 1)n− (l − 2)) 2 = l ((2l + 1)n− (l − 2))2 − (l − 2) ((2l + 1)n− (l − 2)) 2 = 2 ((2l + 1)n− (l − 2)) + l ((2l + 1)n− (l − 2))2 − l ((2l + 1)n− (l − 2)) 2 = ((2l + 1)n− (l − 2)) Keywords: triangular

Key

Group and Cipher in Wormhole and Quantum Entanglement by Liu, Yonghong (2021) - = (1 • y) • x = y • x for all x, y ∈ G. Definition 3. [7] A BCL+ algebra is a triple (X; •, 1), where X is a nonempty set, • is a binary operation on X, and 1 ∈ X is an element such that the following three axioms hold for any x, y, z ∈ X. (BCL+1) x • x = 1. (BCL+2) x • y = 1 and y • x = 1 imply x = y. (BCL+3) ((x • y) • z) • ((x • z) • y) Keywords: key; wcs

Spline

New Spline Method for Solving Linear Two-Point Boundary Value Problems by Heilat, Ahmed Salem; Zureigat, Hamzeh; Hatamleh, Raâ€™ed; Batiha, Belal (2021) - − 3(xi+3 − x)3, x ∈ [23], and HCBSM for Example 3 with n = 10 x CBSM TCBSM ECBSM HCBSM (λ = −1.6500E − 02) (γ = −3.0919) 0.1 1.270E − 03 9.568E − 04 2.769E − 07 5.184E − 09 0.2 2.415E − 03 1.820E − 03 5.267E − 07 9.861E − 09 0.3 3.324E − 03 2.505E − 03 7.249E − 07 1.357E − 08 0.4 3.908E − 03 2.945E − 03 8.522E − 07 1.596E − 08 0.5 4.109E − 03 3.096E − 03 8.960E − 07 1.678E − 08 0.6 3.908E − 03 2.945E − 03 8.522E − 07 1.596E − 08 0.7 3.324E − 03 2.505E − 03 7.249E − 07 1.357E − 08 0.8 2.415E − 03 1.820E − 03 5.267E − 07 9.862E − 09 0.9 1.270E − 03 9.568E − 04 2.769E − 07 5.182E − 09 L∞ 4.109E − 03 3.096E − 03 8.960E − 07 1.678E − 08 L2 9.188E − 03 6.923E − 03 2.004E − 06 3.751E − 08 Figure 3: Numerical solution S(x) and exact solution u(x) for Example 3 using HCBSM with n = 10 and γ = −3.0919 Example 4. Keywords: spline

Lattice

Closed Ideals and Annihilators of Distributive Dual Weakly Complemented Lattice by Rezk, Eman (2022) - then I = IO∗ = I∗∗ and I∗ = IO ∈ IO∗. Then x ≤ bH for all b ∈ K. So x ≤ bH for all b ∈ I. It implies x ∈ IO. Keywords: lattice
Crystal Reduced Motif via the Vectors Exchange Theorem I: Impact of Swapping on two Orthogonalization Processes and the AE Algorithm by Abdelalim, Seddik; Elmouki, Ilias (2023) - i , e ∗∗(k) j ⟩ = 0 for 1 ≤ i ≤ k k ⟩ = ⟨e∗∗k , e∗∗k ⟩ and also, ⟨e∗∗(k−1) j , e∗∗k ⟩ = ⟨e∗∗(k−1) j , e∗∗i ⟩ = ⟨e∗∗(k−1) j , e ∗∗(k−1) Keywords: basis; crystal; e∗∗1; e∗∗k; lattice; reduction; vectors

I∈i

Direct Product of Infinite Family of B-Algebras by Chanmanee, Chatsuda; Chinram, Ronnason; Prasertpong, Rukchart; Julatha, Pongpun; Iampan, Aiyared (2022) - Since ∗i is a binary operation on Pi for all i ∈ I, we have pi ∗i qi ∈ Pi for all i ∈ I. ∈ Pi ∀i ∈ I}. Keywords: i∈i
A Fuzzy Semibipolar Soft Filter and its Association with Green's Relation $\mathcal{N}$ by Prasertpong, Rukchart ; Julatha, Pongpun ; Iampan, Aiyared (2024) - An application of fuzzy soft sets to a real-life problem: Classification of wood materials to prevent fire-related injuries and deaths. Fuzzy soft sets. Keywords: i∈i; set
Direct Product of Q-algebras by Anantayasethi, Ananya; Sangsura, Kittisak ; Sarasit, Napaporn (2025) - Since 0i ∈ Xi for all i ∈ I, then (0i)i∈I ∈ ∏ i∈I Xi. Properties (Q1) and (Q2) imply that (0i)i∈I ⊛ (0i)i∈I = (0i)i∈I ∈ S, (ai)i∈I ⊛ (ai)i∈I = (0i)i∈I ∈ S) and (ai)i∈I ⊛ (0i)i∈I = (ai)i∈I ∈ S. Since (ai)i∈I ∈ G( ∏ i∈I Xi), then (0i)i∈I ⊛ (ai)i∈I = (ai)i∈I . Keywords: ai)i∈i; i∈i

Cauchy

Global Well Posedness for Damped Wave Models with Damping in the Memory by Tayeb, Hadj Kaddour; Hakem, Ali; Benali, Abdelkader ; Alraddadi, Ibrahim; Ahmad, Hijaz; Radwane, Taha; Pamucar, Dragan (2025) - Math, 18 (4) (2025), 6266 17 of 24 Now, we turn to estimate the norm ∥∥|D|σ−1 ( (ut − w(ut − vt))|ut − w(ut − vt)|p−2 ) In this way we get∥∥|D|σ−1 ( (ut − w(ut − vt))|ut − w(ut − vt)|p−2 )∥∥ Lr4 . ∥∥ut Keywords: cauchy; estimate; x(t

Coloring

Acyclic and Star Coloring of Powers of Paths and Cycles by Etawi, Ali; Ghanem, Manal; Al-Ezeh, Hasan (2022) - − k − 1 and let w1 ∈ {1, 2, ..., j − 1}, w2 ∈ {1, 2, ..., h − 1}. Let n = (k + 1)2 + k, and c′4(vi) =  ck+2 if i = j(k + 3) for j ∈ {0, 1, ..., k − 1} ck+1 if i = k(k + 3) c′2(vi) otherwise. Keywords: acyclic; coloring; k n

Δp(λ

$\delta p(\Lambda,p)$-open Sets in Topological Spaces by Boonpok, Chawalit; Thongmoon, Montri (2023) - Then, the following properties hold: (1) y ∈ δp(Λ, p)Ker({x}) Since x ∈ {x}δp(Λ,p), we have x ∈ {y}δp(Λ,p) and by (1), y ∈ δp(Λ, p)Ker({x}). Keywords: x}δp(λ; δp(λ
Characterizations of $\delta p(\Lambda,s)$-$R_0$ Spaces by Boonpok, Chawalit; Pue-on, Prapart (2024) - Then, x ∈ U ∈ δp(Λ, s)O(X, τ) and y ∈ V ∈ δp(Λ, s)O(X, τ). Since x ∈ {x}δp(Λ,s), x ∈ {y}δp(Λ,s) and by (1), y ∈ δp(Λ, s)Ker({x}). Keywords: x}δp(λ; δp(λ
Properties of Generalized $\delta p(\Lambda,s)$-closed Sets by Boonpok, Chawalit; Srisarakham, Napassanan (2023) - Then, X − A ⊆ X − F ∈ δp(Λ, s)O(X, τ) and X − A is g-δp(Λ, s)-closed. For each g-δp(Λ, s)-closed set F and each δp(Λ, s)-open set G containing F , there exists a δp(Λ, s)-open set U such that F δp(Λ,s) ⊆ U ⊆ U δp(Λ,s) Keywords: δp(λ

G(x

The Generalization of Integral Transforms Combined with He's Polynomial by Mustafa, Junaid Idrees (2023) - GN2{P (t)} =h2(ϑ) ∫ ∞ 0 S(Ψ(ϑ)ν)ν ∫ ∞ 0 e−σ(ϑ)t P (Ψ(ϑ)(t− ν))t =h2(ϑ) ∫ ∞ 0 e−σ(ϑ)tt ∫ t 0 S(Ψ(ϑ)ν) P (Ψ(ϑ)(t− ν))ν =h(ϑ) ∫ ∞ 0 e−σ(ϑ)t ( h(ϑ) ∫ t 0 S(Ψ(ϑ)ν)P (Ψ(ϑ)(t− ν))ν ) t. So, GN1{S(t)} GN2{P (t)} =GN{S(t) ∗ P (t)}. t =− σ′(ϑ) h(ϑ) h(ϑ) ∫ ∞ 0 t F ′(Ψ(ϑ) t) e−σ(ϑ) tt+ ∫ ∞ 0 F ′(Ψ(ϑ) t) ϑ e−σ(ϑ) tt =− σ′(ϑ) h(ϑ) GN [t F ′(t)] + ∫ ∞ 0 F ′(Ψ(ϑ) t) Keywords: g(x; h(ϑ; σ′(ϑ; ψ(ϑ
Relations between G-part and Atoms in Q-algebras by Anantayasethi, Ananya; Kunawat, Tanabat ; Moonnipa, Panuwat (2024) - Let b ∈ X such that b /∈ G(X). In this work the concepts of G-part G(X), atoms and strong atoms in Q-algebras are discussed. Keywords: a(x; g(x

Basis

On the Basis Property in Lp( 0,1) of the Root Functions of Non-self Adjoint Sturm-Lioville Operators by Mamedov, Khanlar R. (2010) - Similarly, is proved the basisness in L2(0,1) of root functions of boundary problem (1),(3). All the eigenvalues of this problem starting with the second one are double, the general number of associated that the chosen specially system of root functions form an unconditional basis in L2 (0,1). Keywords: basis

P)-open

Properties of Weakly $\beta(\Lambda,p)$-open Functions and Weakly $\beta(\Lambda,p)$-closed Functions by Boonpok, Chawalit; Thongmoon, Montri (2024) - Moreover, Caldas and Navalagi [8] introduced and investigated the concepts of weakly semi-open functions and weakly semi-closed functions as a new generalization of weakly open functions and weakly closed functions, respectively. The concept of weakly open functions was first introduced by Rose Keywords: p)-open
Almost strong $\theta(\Lambda,p)$-continuity for Functions by Boonpok, Chawalit; Khampakdee, Jeeranunt (2024) - Introduction The notion of θ-continuous functions was introduced by Fomin [10]. [20] studied some properties of θ-continuous functions. Keywords: p)-open
Weakly $\theta b(\Lambda,p)$-open Functions and Weakly $\theta b(\Lambda,p)$-closed Functions by Boonpok, Chawalit; Khampakdee, Jeeranunt (2024) - This article is concerned with the concepts of weakly θb(Λ, p)-open functions and weakly θb(Λ, p)-closed functions. Moreover, some characterizations of weakly θb(Λ, p)-open func- tions and weakly θb(Λ, p)-closed functions are established. Keywords: p)-open; θb(λ

Min

Matrix Mixed Inequalities by Zhang, Feng; Zhang, Chunwen (2024) - We now focus on the location of the eigenvalues of complex matrices. For complex matrix with order n(n > 2), then the computation of Theorem 2.4 requires approximately n3 2 additional calculations compared to the computation of inequality(3). Keywords: min

Der

Two-dimensional Coupled Asymmetric van der Pol Oscillator by Erturk, V. S. ; Rath, B. ; Al-Khader, Taqwa M. ; Alshaikh, Noorhan ; Mallick, P. ; Asad, Jihad (2024) - It can be said that the considered approach can be easily extended to other nonlinear van der Pol oscillator systems and therefore is widely applicable in engineering and other sciences. Since most real-world systems are described by nonlinear differential equations, mechanical systems, ∗Corresponding author. Keywords: der; pol; van

Sum

On a b-chromatic Sum of a Myceilskian of Paths by Tangjai, Wipawee; Vichitkunakorn, Panuponng; Chaiyakhot, Sittichai; Sinthuket, Rawit (2025) - In comparison to the well-known chromatic number, the idea of chromatic sum was originated in 1989 by Kubicka and Schwenk An introduction to chromatic sums. Keywords: sum

Sheffer

Sheffer Stroke BN-algebras and Connected Topics by Gemawati, Sri ; Mashadi; Kartini; Musraini; Fitria, Elsi (2025) - In Sheffer stroke BN algebras, homomorphisms are mappings that keep algebraic op- erations consistent. Furthermore, the notions of Sheffer stroke BN-subalgebras, BN-ideals, and BN-homomorphisms are defined, along with normal subsets of Sheffer stroke BN-algebras, and the relationships between these concepts are explored. Keywords: psbn; sheffer; stroke; stroke bn

A(x

Entropy solutions for nonlinear elliptic equations with measure data and without strict monotonocity condition by Rhoudaf, Mohamed; Akdim, Y; Azroul, E. (2009) - Then ∫ Ω 〈a(x , u,∇ϕ),∇Tk[u−ϕ]〉 d x ≤ ∫ Ω f Tk[u−ϕ] d x + ∫ Ω 〈F,∇Tk[u−ϕ]〉 d x . x ! 1 p , (2.4) is equivalent to the usual norm (2.3), and there exists a weight function σ(x) on Ω and a parameter q, 1< q <∞ such that the Hardy inequality, � ∫ Ω |u(x)|qσ(x) d Keywords: a(x; d x

Quaternions

On Properties of the Dual Quaternions by Ercan, Zeynep; Yuce, Salim (2011) - Also, the matrix representation of dual quaternions is expressed. 2000 Mathematics Subject Classifications: 11R52 Key Words and Phrases: Dual number, Dual quaternion, Euler’s formula, De Moivre’s Formula 1. The set of dual quaternions denoted by HD = {Q = a+ bi + c j + dk| a, b, c, d ∈ R, i2 = j2 = k2 Keywords: quaternions

Φ(x

On $L^{\infty }$ and $L^{2}$ Bounds for Weak Solutions of Time Flowsfor Certain Functionals of Linear Growth by Wunderli, Thomas (2024) - × Ω ∂u ∂n = 0 on [0, T ]× ∂Ω u(0, x) = uδ0(x) for x ∈ Ω, uδ0 ∈ BV (Ω) ∩ C∞ ( Ω ) . (2) In fact, we show the weak solution to (2) satisfies u ∈ L∞ ([0,∞);BV (Ω) ∩ L∞ (Ω)), ut ∈ L2 ((0,∞)× Ω). Keywords: φ(x

U(t

Stability Results in Terms of Two Measures for Set Differential Equations Involving Causal Operators by Chadaram, Appala Naidu; Dhaigude, D.B.; Jonnalagadda, Vasundhara Devi (2017) - Let K(Ko) be the subfamily of Kc(Rn) consisting of set U ∈ Kc(Rn) such that any u ∈ U is a non-negative (positive) vector of n components satisfying ui ≥ 0 (ui > 0) for i=1... To define this set, we consider V ∈ C[R+ ×Bb,R+], where Bb = B(θ, b) = {U ∈ Kc(Rn) : Keywords: u(t

Lines

The Linear Span of Four Points in the Pl\"ucker's Quadric in ${\mathbb P}^5$ by Rojas, Jacqueline; Mendoza, RamÃ³n (2014) - In fact, let p ∈ P3 and Π ⊂ P3 be a plane through p. Set Ωp(Π) In fact, let p ∈ P3 and Π ⊂ P3 be a plane. Keywords: lines; quadric;  

Monomorphisms

Categorical properties of regular monomorphisms of $S$-posets by Rasouli, Hamid (2014) - , tm ∈ S such that a ≤ s1c1, s1d1 ≤ s2c2, s2d2 ≤ s3c3, . . . The notion of regular monomorphism, solves this problem in these two categories. Keywords: monomorphisms; poset

Equivalent

Affine Subspaces of the Lie Algebra se(1,1) by Barrett, Dennis I.; Biggs, Rory; Remsing, Claudiu C. (2014) - REFERENCES 154 Appendix Table 1: Classification of affine subspaces and parametrized affine subspaces Type Affine subspaces Parametrized affine subspaces (1, 1) E1 + 〈E3〉   1 0 0 0 γ1 α   αE3 + 〈E1〉   0 1 0 0 α 0   (2, 0) 〈E1, E3〉   γ1 1 0 0 0 0 γ2 γ3 α     γ1 0 1 0 0 0 γ2 α 0   (2, 1) E2 + 〈E1, E3〉   γ1 1 0 β1 0 0 γ2 γ3 α     γ1 0 1 β1 0 0 γ2 α 0   E1 + 〈E1 + E2, E3〉   β1 1 0 0 1 0 γ1 γ2 β2     1 1 0 −1 1 0 γ1 γ2 β1     β1 0 1 0 0 1 γ1 β2 0     1 0 1 −1 0 1 γ1 β1 0   αE3 + 〈E1, E2〉   0 γ1 1 0 α 0 β1 0 0     0 β2 1 0 0 1 β1 0 0     0 1 1 0 −1 1 β1 0 0   α > 0, βi 6= 0, γi ∈ R REFERENCES 155 Table 2: Classification of parametrized (3,0)-affine subspaces Π : A+ u1B + u2C + u3D Classifying conditions Parametrized affine subspaces E∗3(〈C , D〉) 6= {0} E1 + E2, E1 − E2 /∈ We classify the full-rank affine subspaces (resp. Keywords: equivalent

Addition

Unitary Addition Cayley Signed Graphs by Sinha, Deepa; Dhama, Ayushi; Acharya, B.D. (2013) - The structure and various properties of unitary Cayley graphs have been studied in literature (see [7, 9, 13, 15, 20–23, 34, 37, 39]). [13] P. Berrizbeitia and R.E. Giudici, On cycles in the sequence of unitary Cayley graphs, Dis- crete Mathematics, 282(1-3)(2004), 239-243. Keywords: addition; cayley; sigraph

Expansion

The Asymptotic Expansion of a Generalisation of the Euler-Jacobi Series by Paris, Richard Bruce (2016) - When p = 6, we have κ= 5, q = 6 5 , N = 1, K = ⌊13 m⌋ and X = 5( 1 3 π)6/5 a−1/5, λ j (11) ∗The nearest integer part corresponds to [x] = N when x is in the interval (N − 1 2 , N + 1 2 ]. Keywords: expansion

Hyperring

Regular Multiplicative Hyperrings by Ameri, Reza; Kordi, Ali (2016) - Since, for all a ∈ R, there exists r ∈ R such that a = ara. Also, for all a ∈ R, there exists r ∈ R such that a = ara. Keywords: hyperring; m(r; multiplicative
Zariski Topology of (Krasner) Hyperrings by Afshar, Behnam ; Ameri, Reza ; Al-Tahan, Madeleine (2025) - and I be an ideal of R. (1) Consider R̄ = R/G = {rG; r ∈ R} and rG⊕sG = {tG; t ∈ rG+sG}, rG⊙sG = rsG. Then (R̄,⊕,⊙) is hyperring and 0R̄ = {0}, 1R̄ = G. (3) If R̄ = {r+I; r ∈ R}, r+I⊕s+I = {t+I; t ∈ r+s+I} and r+I⊙s+I = {t+I; t ∈ rs+ I}, then (R̄,⊕,⊙) is general hyperring and Spec(R̄) = {P/I;P ∈ Spec(R)} Keywords: hyperideal; hyperring; spec(r

Ρ(x

Best Approximation in Uniformity Type Spaces by Tallafha, A.; Khalil, Roshdi Rashid (2009) - Then we study best approximation in semi-linear uniform spaces. One can generate semi-linear uniform spaces as follows. Keywords: ρ(x

F(z

Sufficient conditions for starlikeness of reciprocal order by Frasin, Basem; Sabri, Mustafa Abd (2017) - 2010 Mathematics Subject Classifications: 30C45 Key Words and Phrases: Analytic functions, starlike and convex functions, starlike function of reciprocal order, sufficient conditions 1. The object of the present paper is to derive certain sufficient conditions for starlikeness of reciprocal order of analytic functions in the open unit disk. Keywords: f(z

D(xn

n-tupled Fixed Point Results with Rational Type Contraction in b-metric Spaces by Sarwar, Muhammad; Hussain, Saddam; Li, Yongjin (2018) - Suppose X = R and S, T : Xn → X be defined by S(x1, x2, x3, · · · , xn) Coupled fixed point theorems for ϕ-contractive mixed monotone map- pings in partially ordered metric spaces. Keywords: 2k+1; d(x1; d(xn
Some Fixed Point Results for Hybrid Contraction in Metric Spaces and Ulam-Hyers Stability by Ramaswamy, Rajagopalan ; Kumar, Manoj; Sharma, Prem Lata; Alkhowaiter, Rayan Abdulrahman; Nabway, Hossam A; Abdelnaby, Ola Ashour A; Mani, Gunaseelan (2025) - In the present manuscript, we introduce a new notion of (β, ϕ)− admissible hybrid contractions in metric spaces and establish fixed point results in the setting of these spaces. In the recent past, interpolative contractive conditions were reported by some re- searchers and fixed point results please see [4–12]. Keywords: d(xn

State

Stochastic Approach in Epidemic Modeling Using the SEIRS by Talkibing, Hay Yoba; Diakarya, Barro; Fabrice, Ouoba (2019) - A model of the dynamics of infectious disease transition can be formulated using a stochastic process {Xn, n = 1, 2, 3, ...} as a Markov string with continuous time T and discrete state space X0, X1, ..., Xn satisfying the following Markov property : P (Xn+1 = jn+1/X0 = j0, X1 = j1, ..., Xn = jn) The study of infectious diseases represents one of the oldest and richest sectors of biomathematics. Keywords: state

Bounds

Numerical Computation of Lower Bounds of Structured Singular Values by Anwar, M. Fazeel; Rehman, Mutti-Ur (2018) - Real perturbation values and real quadratic forms in a complex vector space. In Section 3 it is explain that how the inner algorithm works for the case of pure complex structured perturbations. Keywords: bounds; comparison; mussv; ssv

Case

On the Irreducibility of Fourth Dimensional Tuba's Representation of the Pure Braid Group on Three Strands by Haidar, Hasan A.; Abdulrahim, Mohammad N. (2018) - Math, 11 (3) (2018), 682-701 694 In the case λ2 − λ3 = 0, we get Iλ3 = 0, a contradiction (Lemma 10). Substituting, β = Iλ3 λ3−λ2 in the equation (λ3 − λ2)N1 = 0, we get α ( λ21 − λ23 ) (λ3 − λ2) + IJλ3λ2 (λ1 + λ2) + Jλ3[λ1 + λ3 + Iλ2](λ3 − λ2) = 0. Keywords: case

Hypervector

On Dimension of Hypervector Spaces by Ameri, Reza; Dehghan, O.R. (2008) - Note that (Kn,+, ◦K ,K) is a strongly distributive hypervector space with trivial ex- ternal operation ◦K , that is:{ ◦K : K ×Kn −→ P∗ (Kn) a ◦K (a1, . . , cn ∈ K, 0 ∈ c1 ◦ v1 + · · · + cn ◦ vn, implies that c1 = c2 = · · · = cn = 0. Keywords: hypervector

R(s

Existence of Nonoscillatory Solutions of Higher Order Nonlinear Neutral Differential Equations by Cina, Bengu; Candan, Tuncay; Senel, M. Tamer (2023) - ∫∞ t (s−t)n−2 r(s) ∫ s t1 [f1(u, x(σ1(u))) −f2(u, x(σ2(u)))− g(u)]duds, t ≥ t1 (Sx)(t1), t0 ≤ t ≤ t1. ∫∞ t (s−t)n−2 r(s) ∫ s t1 [f1(u, x(σ1(u))) −f2(u, x(σ2(u)))− g(u)]duds, t ≥ t1 (Sx)(t1), t0 ≤ t ≤ t1. Keywords: r(s; ∫ ∞

Q(x

Hankel Transform of the First Form (q,r)-Dowling Numbers by Corcino, Roberto Bagsarsa (2021) - Then Vr,q (xn) = n∑ k=0 W ∗m,r[n, k]qVr,q (〈x〉r,m,k) = n∑ k=0 W ∗m,r[n, k]qq rk+m(k2)Vr,q (〈〈x〉〉r,m,k) = n∑ k=0 W ∗m,r[n, k]qq rk+m(k2)xk = Φn[x, r,m]q Consider the polynomial gn,q(x, a, r,m) = n∑ k=0 (−a)kq( k 2) Wm,r(n, k), where n is a nonnegative integer and the parameters m and r may be real or complex numbers. Keywords: q(x

Micro

On Micro-generalized Closed Sets and Micro-generalized Continuity in Micro Topological Spaces by Jasim, Taha H.; Mohsen, Saja S.; Eke, Kanayo Stella (2021) - then f−1(B) is Micro-closed set in (X, τR(A), µR(A)) and by remark 3.5 (Every Micro closed set is Micro-generalized closed set) Then f−1(B) is Micro-closed set in (X, τR(A), µR(A)). Keywords: micro; set
On Micro Pre Operators in Micro Topological Spaces by Sathishmohan, P. ; Stanley Roshan, S.; Rajalakshmi, K. ; Brindha, S. ; Poongothai, G. (2024) - } Since every micro open is micro pre-open, x ∈ Mic-ker(A). Therefore, x ∈ Mic-Pker(A ∪ B). (iii) Let x ∈ Mic-Pker(A ∩ B) ⇒ x ∈ Mic-Pker(A) and x ∈ Mic-Pker(B) Therefore, x ∈ Mic-Pker(A) ∪ Mic-Pker(B). (iv) Let x ∈ Mic-Pcl(A) ∩ Mic-Pker(A) By Lemma 3.7(1) Keywords: mic; micro

Deg

Note on Irreducible Polynomials over Finite Field by Chandoul, Amara; M. Sibih, Alanod (2021) - The situation over Q is much different from the situation over R or C. Over Q, there are many irreducible polynomials of every degree, and determining which polynomials are irreducible is difficult, compared to the real or complex case. This criterion is very nice when it works, but there are many irreducible polynomials to which it does not apply. Keywords: deg

Γ∗tpw

Forcing Subsets for Î³âˆ— tpw -sets in Graphs by Armada, Cris Laquibla (2021) - Thus, it is not possible to start with vertex u2 to form Tk for all k ≥ 2, that is, u2 /∈ Clearly, k is a positive integer, k > 1, and k is not constant for any pair of vertices x and y. Keywords: γ∗tpw
Forcing Total dr-Power Domination Number of Graphs Under Some Binary Operations by Armada, Cris Laquibla (2021) - Total dr-power dominating sets in graphs. The following concepts: total dr-power domination [6], forcing domination number of graphs under some binary operations [7], forcing total domination number and forcing connected domination number under the lexicographic product of graphs [8], forcing independent domination number of a graph [4], and A-differential of graphs [3] was studied by Canoy, et al. Keywords: γ∗tpw

∥∥∥∥∥∥

Boundedness of Nonregular Pseudo-differential Operators on Variable Exponent Triebel-Lizorkin-Morrey Spaces by Congo, Mohamed; Ouedraogo, Marie Francoise (2022) - =  tp(x) if p(x) ∈ (0,+∞), 0 if p(x) = +∞ and t ∈ With t ∈ (0,min {1, p−, q−}), lemma 4 yields∥∥∥∥∥∥ 2js(·) Keywords: ∥∥∥∥∥∥

Regular

Regularity on Variants of Transformation Semigroups that Preserve an Equivalence Relation by Tantong, Piyaporn; Sawatraksa, Nares (2022) - For each A ∈ X/E, we choose A′ ∈ X/E such that A ∩Xαθ ⊆ A′θαθ. ∈ A′ such that x′θαθ ∈ P and A′ ∈ X/E. We also have that Keywords: regular; te(x

Paper

Origami Wrapping with an Equilateral Triangular Prism by Khachorncharoenkul, Prathomjit; Wongpradit, Attawut (2022) - From the tall wrapping described in Section 2, the tall, encased wrapping by rectan- gular paper in tall wrapping is achieved by increasing the paper size from the projection of an equilateral cross-section prism shape, as shown in Figure 13. L be the length of paper edge A1A2, s be the distance between the paper edge A1A2 and the point B′ 6, and t be the distance between the paper edge A1A4 and the lateral edge B1B4. Keywords: figure; paper; prism; wrapping

Law

Extensions of Two Classical Poisson Limit Laws to Non-stationary Independent Sequences by Niang, Aladji Babacar; Sangar´e, Harouna ; Kpanzou, Tchilabalo Abozou; Lo, Gane Samb; Ngom, Nafy (2022) - Under the conditions ( ∀n ≥ 1, ∀1 ≤ k ≤ k(n), ak,n = 0 ) and k(n)∑ k=1 σ2k,n = 1, the summands Sn[X] of the arrayX converges to standard Gaussian law and max1≤k≤k(n) σ 2 k,n → 0 if and only if the following Lynderberg-Gaussian condition holds: ∀ε > 0, Ln,G(ε) Math, 15 (2) (2022), 511-527 526 (GP4) for 0 < ε < 1, n ≥ 1, 1 ≤ k ≤ k(n), and for B(ε, k, n) = 1∑ j=0 1(∣∣∣∣j−qk,n−1 ∣∣∣∣≥ε )( j − pk,n )2 pjk,nq 1−j k,n , we have B(ε, n) = k(n)∑ k=1 B(ε, k, n) → 0. Keywords: law

Dokdo

Dokdo BE-subalgebras and BE-filters of BE-algebras by Jun, Young Bae; Ahn, Sun Shin; Roh, Eun Hwan (2022) - ∈ φ̊(max,min), φs((z ∗ y) ∗ (z ∗ x)) ⊇ φs(z ∗ (y ∗ x)), φ̃((z ∗ y) ∗ (z ∗ x)) Using (BE4), (26) and (29), we have φ−((z ∗ y) ∗ (z ∗ x)) Keywords: dokdo; z ∗; ∗ x; ∗ y
Dokdo Filters and Deductive Systems of Sheffer Stroke Hilbert Algebras by Ahn, Sun Shin; Kim, Hee Sik; Song, Seok-Zun; Jun, Young Bae (2023) - A Dokdo structure Dokf := (f̊ , fs, f̃) is called a Dokdo filter of (U,X ) if it satisfies: (∀x ∈ X) ( 1 (x,x) ∈ f̊(M,m) fs(1) ⊇ fs(x), f̃(1) ⊵ f̃(x) ) , (19) (∀x, y ∈ X)  x|(y|y) (y,y) ∈ f̊(M,m) fs(x|(y|y)) Every Dokdo filter Dokf := (f̊ , f s, f̃) of (U,X ) satisfies: (∀x, y ∈ X)  (x|(y|y))|(y|y) (x,x) ∈ f̊(M,m) fs((x|(y|y))|(y|y)) ⊇ f s(x) f̃((x|(y|y))|(y|y)) Keywords: dokdo

Rainbow

Weakly Connected $k$-Rainbow Domination in Graphs by Hamja, Jamil; Sheikholeslami, Seyed Mahmoud ; Aniversario, Imelda S.; Cabardo, Lyster Rey B. (2025) - Weakly connected domination critical graphs. Further insights into weakly connected domination can be found in [13–19]. Keywords: rainbow; γwc

Mosquitoes

Discrete Wolbachia Diffusion in Mosquito Populations with Allee Effects by Ufuktepe, Unal (2022) - = ( B11 B12 B21 B22 ) . where B12 = b(b1 − d1) 2 − αd1 ( (b1(αcd1 − d1 − 1) + b12 + d1 ) α(b21 , B11 = b21(α+ β) + d21(α(−αb1c+ b1 − 1) + β) + b1d1(α− b1) + α− 2β) αb21 , B21 = − b2(αd1 + 2β(b1 − d1)) ( β(b1 − d1) 2 − αd1(b1(αcd1 − 1) + d1) )2 αb21d1(b1 − d1)2(αd1 + β(b1 − d1))2 , and B22 = ( αd1(b1(αcd1 − b2β(b1 − d1) 2 ) G αb21d1(b1 − d1)2(αd1 + β(b1 − d1))2 where G = (α2d21 ( b31(d2 − 1)(αcd1 + 1) + b1b2(d1(2− αc) + 1) + b21(−2b2 − d1d2 + d1)− b2d1 ) + αβd1(b1−d1) ( b1b2(d1(2− 2αc) + 3) + b31(d2 − 1) + b21(−2b2 − d1d2 + d1)− 3b2d1 ) +2β2b2(b1−d1) 3) By the trace-determinant (Jury Condition), if |trJ | − 1 < We study stability analysis of a discrete-time dynamical system of Wolbachia diffusion in mosquito populations with Allee effects on the wild mosquito population. Keywords: mosquitoes; wolbachia

Independent

$J^2$-Independence Parameters of Some Graphs by Hassan, Javier; Tapeing, Aziz; Copel, Hounam B. ; Bakkang, Alcyn ; Aming, Sharifa Dianne A. (2024) - Math, 17 (1) (2024), 124-134 125 called maximum if it is of largest cardinality, that is, if V ′ ∪{v} is not an independent set for any v ∈ V (G)\V ′, and it is denoted by i(G) to be the number of maximal independent sets of G. In 1992, Jiuqiang Liu[8] developed new properties for the number of maximal indepen- dent sets i(G) and the number of maximum independent sets im(G), as well as determine the largest number of maximal and maximum independent sets possible in a k-connected graph of order n(with n large) and characterize the respective extremal graphs. The structure and maximum number of maximum independent sets in trees. Keywords: independent; set

Stk

A New Scalar of Conjugate Gradient Methods for Solving Unconstrained Minimization by Mohammad T., Saja O. ; Saeed Chilmeran, Hamsa Th. ; Al-Kawaz, Rana Z. (2023) - Ak ωT k Akωk + sks T k sTk ωk )) µk+1 (13) Then we make the search direction memoryless, i.e. by replacing each Ak = I, we get: pk+1 = − ωT k sk ∥µk∥2 ( µk+1 − ωT k µk+1 ∥ωk∥2 ωk + sTk µk+1 sTk ωk sk ) (14) To increase the efficiency of the search direction for CG methods, we equate it with the new search direction for QN methods, and we deduce from the equation a new γk parameter as in the following steps: −µk+1 + γksk = − ωT k sk ∥µk∥2 ( µk+1 − ωT k µk+1 ∥ωk∥2 ωk + sTk µk+1 sTk ωk sk ) (15) A modified bat algorithm with conjugate gradient method for global optimization. Keywords: stk; µk+1

Clique

Cliques and Supercliques in Graphs by Canoy , Jr., Sergio; Dela Cerna, Ramil; Abragan, Armalene (2023) - Next, let x ∈ S and suppose that |Tx| ≥ 2. Let p, q ∈ Tx such that p ̸= q. Let x ∈ S and let p, q ∈ Tx such that p ̸= q. Keywords: clique
Forcing Clique Domination in Graphs by Armada, Cris L.; M. Kiunisala, Edward; Rosero, Cristopher John S.; Malusay, Jeneveb T. (2025) - Connected graphs with forcing clique domination number equal to 0, 1, or a, where a is greater than 1 but less than the clique domination number, are characterized. A subset S of V (G+H) is a clique dominating set of G+H if and only if one of the following statements holds: (i) S is clique dominating set of G (ii) S is a clique dominating set of H. (iii) S = S1 ∪ S2, where ⟨S1⟩ and ⟨S2⟩ are cliques in G and H, respectively. Keywords: clique; set; γcl

Generator

Some Generator Subgraphs of the Square of a Cycle by Mame, Realiza (2024) - Generator graphs. This paper provides characterization for the star graph, path graph, (3, r)− tadpole graph, and kite graph Ktr,s so that these classes of graphs are generator subgraphs of the square of a cycle. Keywords: generator; subgraph

Degenerate

On Degenerate Laplace-type Integral Transform by Campos, Harren; Fernandez, Jezer; Natuil, Jade Bong (2023) - − Gα,λ{e−ia λ (t)} ] H. J. Campos, J. C. Fernandez, J. B. M. Natuil / Eur. Now, using Theorem 2 and Theorem 6, we obtain Gα,λ{sinh (a) λ (t)} = 1 2 [ Gα,λ{eaλ(t)} − Gα,λ{e−a λ (t)} ] Keywords: degenerate

Y;u

Some Properties of the Bell-Based Apostol-Frobenius-Type Tangent Polynomials by Ontolan, Jay; Malusay, Jeneveb; Kiunisala, Edward; Buloron, Joris (2025) - 2020 Mathematics Subject Classifications: 05A15, 11B68, 11B73, 26C05, 33B10 Key Words and Phrases: Tangent polynomials, Bell polynomials, Apostol-Frobenius- Type poly-Tangent polynomials, Bell-based Apostol-Frobenius-Type poly-Tangent polynomials, Stirling numbers, Appell polynomials 1. Bell polynomials, denoted as Bn(x), are another important class, defined by the gen- erating function: ∞∑ n=0 Bn(x) Keywords: y;u

Primal

On a New Operator Based on a Primal and its Associated Topology by Özkoç, Murad; Şaşmaz, Pınar (2024) - Let x ∈ A⋄ ω(X,σ,P) and τ ⊆ σ. x ∈ A⋄ ω(X,σ,P) ⇒ (∀U ∈ ωOσ(X,x))(U c ∪Ac ∈ P) τ ⊆ σ } ⇒ ⇒ (∀U ∈ ωOτ (X,x))(U c ∪Ac ∈ P) ⇒ x ∈ A⋄ ω(X, τ,P). P is a primal on X } ⇒ Ac ∈ P Keywords: primal
Primal Approximation Spaces by $\kappa $-neighborhoods with Applications by Hosny, Rodyna A.; El-Bably, Mostafa K. ; El-Gayar, Mostafa A. (2025) - Primal is defined as novel structures designed to generalize rough set approximations beyond the traditional methods. Comparison between rough set approximations based on different topologies. Keywords: primal; τpκ

N+1

On Generalized Mersenne Numbers and Extended Fermat Numbers by Bani Melhem, Shefa A.; Al-Kateeb, Ala'a; Dagher, Afnan (2025) - − 2 = (k − 1)nMk,ℓ−n • Fk,ℓFk,n+1 − Fk,ℓ+1Fk,n = (k − 1)ℓ + 2k − 5 (k − 2) (k − 1)n+1 + 2k − 5 (k − 2) − (k − 1)ℓ+1 + 2k − 5 (k − 2) (k − 1)n + 2k − 5 (k − 2) = (2k − 5) −(k − 1)ℓ+1 + (k − 1)ℓ + (k − 1)n+1 − (k − 1)n (k − 2)2 = (2k − 5) (k − 1)ℓ(2 − k) + (k − 1)n(k − 2) (k − 2)2 = (2k − 5) (k − 1)n − (k − 1)ℓ (k − 2) = (2k − 5)(k − 1)n 1 − (k − 1)ℓ−n (k − 2) = −(5 − 2k)(k − 1)nMk,ℓ−n. = (k − 1)n − (k − 1)n+i − (k − 1)n+j + (k − 1)n+i+j (k − 2)2 = (k − 1)n 1 − (k − 1)i − (k − 1)j + (k − 1)i+j (k − 2)2 = (k − 1)n 1 − (k − 1)i − (k − 1)j(1 − (k − 1)i) (k − 2)2 Sh. A. Bani Melhem, Al-Kateeb, A. Dagher / Eur. Keywords: k −; n+1; − k)mk

D(x

Upper Bound of Radio Span for Shadow-path Network and Its Mathematical Modeling by NourEldeen, Nawal M.; Badr, Elsayed; Shabana, Hanan; Abdel-Aal, M. E. (2025) - [(n+ 2) + (2n+ 7)(k − 2) + 2(k − 2)(k − 3)+ + (2n+ 1) + (n+ 1)(k − 1) + 2(k − 1)(k − 2)]| = |(2n+ 7)(k − 1) + 2(k − 2)(k − 3) + (2n+ 1) + (n+ 1)(k − 1)+ + 2(k − 1)(k − 2)| ≥ n, where n = 4k, d(x, y) ≥ 1 ≥ diam(D2(Pn)) + 1− d(x, y) case 9If {x, y} = {v1, v3k−1} then |f(x)− f(y)| = |f(v1)− Keywords: d(x; j ≤; radio; ≤ k

Liquid

Electrohydrodynamic Stability of Walters B′ Viscoelastic Dielectric Liquid Jet Streaming with Variable Velocity into Another Viscoelastic Fluid via Porous Medium by El-Sayed, Mohamed F. ; Mostafa, Doaa M.; Alrashdi, Ashwaq M. F. (2025) - It is also demonstrated that the Walters B′ viscoelastic liquid jet is more stable than an inviscid liquid jet, and the breakup process in the atomization mode of instability occurs faster than in Rayleigh mode since liquid jet instability is closely related to drop formation and breakup. Introduction The problems of liquid jet instability have attracted the interest of researchers for a long time since they have applications in numerous industrial processes and machines. Keywords: atomization; instability; jet; liquid; m. f.; mode; rayleigh; sayed; viscoelastic

Z=0

On a New Stochastic Space with Applications to Nonlinear Economic Models by Alsolmi, Meshayil M.; Alshabhi, Salah H. ; Mohammed, Mustafa; Khalid, Thwiba A.; Magzoub, Mona ; Taha, Nidal E. ; Taha, Khdija O. ; Bakery, Awad A. (2025) - The conditions (1c) and (a2): ∥δd̂∥p−qN = ∑ l∈N  ℏ̂ (∑l z=0 f 2 zqzδd̂z, 0̂ ) flfl+1 tl ≤ sup l |δ|tl ∑ l∈N  ℏ̂ (∑l z=0 f 2 zqzd̂z, 0̂ ) flfl+1 tl = C1∥d̂∥p−qN < ∞. Hence, δd̂ ∈ γSf (q, t). The conditions (2c) and (a4): Assume |d̂b| ≤ |k̂b|, for b ∈ N and |k̂| ∈ γSf (q, t). Keywords: flfl+1; z=0; γsf; ∥.∥p−qn

Iup

Structural Insights into IUP-Algebras via Intuitionistic Neutrosophic Set Theory by Suayngam, Kannirun ; Julatha, Pongpun ; Nakkhasen, Warud ; Iampan, Aiyared (2025) - x = y · 0), (2.7) (∀x, y, z ∈ X)(x · y = x · z ⇔ y = z), (2.8) (∀x, y ∈ X)(x · y = 0 ⇔ x = y), (2.9) (∀x ∈ X)(x · 0 = 0 ⇔ x = 0), (2.10) (∀x, y, z ∈ X)(y · x = z · x⇔ y = z), (2.11) (∀x, y ∈ X)(x · y = y ⇒ x = 0), (2.12) (∀x, y, z ∈ X)((x · y) · 0 2020 Mathematics Subject Classifications: 03G25, 03E72, 03B60 Key Words and Phrases: IUP-algebra, intuitionistic neutrosophic set, intuitionistic neutro- sophic IUP-subalgebra, intuitionistic neutrosophic IUP-ideal, intuitionistic neutrosophic IUP-filter, intuitionistic neutrosophic strong IUP-ideal 1. Keywords: iup
Pythagorean Neutrosophic IUP-Algebras: Theoretical Foundations and Extensions by Suayngam, Kannirun ; Julatha, Pongpun ; Nakkhasen, Warud ; Prasertpong, Rukchart ; Iampan, Aiyared (2025) - Let x, y ∈ X. Then PT (y) = PT (0 ? Let x, y ∈ X. Then PT (y) = PT (0 ? Keywords: iup

R+1

Computational Illustration of Fractional Inequalities via 2D Graphs with Application by Mehmood, Ahsan; Younis, Muhammad ; Aloqaily, Ahmad ; Santina, Dania ; Samraiz, Muhammad ; Rahman, Gauhar ; Mlaiki, Nabil (2025) - In control systems and automation, fractional inequalities help establish stability criteria for fractional-order con- trollers, improving system robustness in robotics, aerospace and process control industries. In materials science and mechanical engineering, fractional inequalities contribute to mod- eling stress-strain relationships in viscoelastic and complex materials, optimizing designs in structural engineering and manufacturing. Keywords: k kγk(β; kz β; r+1; s+1; β k

⟨0.5

T-Ordering on Generalized Regular Intuitionistic Fuzzy Matrices by Jenita, P. ; Princy Flora, M. ; Jana, Chiranjibe; Popovic, E.; Ivkovic, N. (2025) - uP1u = ⟨0.5, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩  ̸= u, uP2u = ⟨0.5, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩ ⟨0.2, 0⟩  ̸= u. uP3u = ⟨0.2, 0⟩ ⟨0.5, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩  ̸= u, uP4u = ⟨0.2, 0⟩ ⟨0.5, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩ ⟨0.5, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩  ̸= u, uP5u = ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩ ⟨0.5, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩ ⟨0.2, 0⟩  ̸= u and uP6u = ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩  ̸= u. Therefore, u is not regular. = [⟨0.5, 0⟩ ⟨0.2, 0⟩ ⟨0, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩ ] [ ⟨0.5, 0⟩ ⟨0.2, 0.5⟩ ⟨0, 0⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩ ⟨0.2, 0.5⟩ ⟨0.2, 0.5⟩ ⟨0.2, 0⟩ ⟨0.5, 0⟩ ] Keywords: 0⟩ ⟨0.2; ⟨0.5

Q(ξ

Picture Fuzzy Modal Ideal Multifunctions by Shi, Dali; Abu_Shugair, M.N.; Abbas, S.E.; Ibedou, Ismail (2025) - Axiom 7*: K ↠ Q = ♯ implies that K ⊆ Q, and K ⊆ Q implies that K ↠ Q is a PFTaut set. Math, 18 (2) (2025), 5956 24 of 30 τ(K) =  ⟨1, 0, 0⟩ if K ∈ {♭, ♯} , ⟨0.6, 0.2, 0.2⟩ if K = K1, ⟨0, 1, 0⟩ otherwise, , σ( Q ) =  ⟨1, 0, 0⟩ if Q ∈ {♭, ♯} , ⟨0.5, 0.3, 0.1⟩ if Q = Q 1, ⟨0, 1, 0⟩ otherwise, ℓP ( Q ) =  ⟨1, 0, 0⟩ if Q = ♭, ⟨0.7, 0.15, 0.15⟩ if {⟨ζ, 0.4, 0.5, 0.1⟩ |ζ ∈ Υ} ⊆ Q ⊆ ♯, ⟨0, 1, 0⟩ otherwise. Keywords: q(ξ; ∈ ξ

Observations

A Self-Organizing Model for Logic Regression by Farlow, Stanley Jerry (2010) - m mg E Y b b L b L b L= + + + where both the coefficients 0 1, ,..., mb b b and the logical expressions , 1,...,jL j m= are determined, whereby a logical expression one means logical relationships among the predictor variables, such as 1 2 ,X X are true but not 5 X , or 3 5 7 , ,X X X are true but not 1X or 2 X In paper By logical expressions jL , we mean Boolean expressions such as 1 2 ,X X are true but not 5 X , or 3 5 7 , ,X X X are true but not 1X or 2 X or if 1X and 2X are true then 5X is true. Keywords: observations

Crossing

Sheffer Stroke Hilbert Algebras in Connection with Crossing Cubic Structures by Al-Masarwah, Anas; Bani Abd Al-Rahman, Noor ; Alqahtani, Mohammed; Abuqamar, Majdoleen (2025) - = ((n | v) | (n | v)) Then, Π = (Υ̃Π, ϖΠ) is a crossing cubic filter of ϑ if and only if it satisfies (ii) of Proposition 2 and condition (B), where (B) (∀n, v ∈ ϑ) ( Υ̃Π((n | v) | (n | v)) Keywords: crossing; v |

Quaternion

Codes over Quaternion Integers by Ozen, Mehmet; Guzeltepe, Murat (2010) - = − ji = k, ik = −ki = j, jk = −k j If r is an element of Zp, then r = kπ+ z and r = r = kπ+ z, hence, z(vπ) + z(uπ) Keywords: quaternion

Secη+

Subordination Results for Spirallike Functions by Murugusundaramoorthy, Gangadharan; Magesh, Nanjundan (2009) - Let f ∈ Rl m (η,γ,λ) and g(z) be any function in the usual class of convex functions C , then ((1−λ) secη+ Let f ∈ Rl m (η,γ,λ) and suppose that g(z) Keywords: secη+

|z|

Some Characterizations of Weighted Bloch Space by Rashwan, Rashwan Ahmed; Ahmed, Ahmed El-Sayed; Mohamed, All Kamal (2009) - If f ∈ QK,ω, then by the above estimate we have that sup a∈∆ (1− |a|)p+2| f ′(z)|p ωp(1− |a|) <∞. R. Rashwan, A. Ahmed and A. Kamal / Eur. The last inequality shows that f ∈ B p+2 p ω The proof of (ii) is similar to proof (i) by taking the limit when |a| −→ 1− in (i), hence it can be omitted. Keywords: |z|; � �

J(m

On the Vanishing Properties of Local Cohomology Modules Defined by a Pair of Ideals by Parsa, M. Lotfi; Payrovi, Sh. (2012) - Suppose that M is finitely generated with dimR M Let R be local and M finitely generated with dimR M = n> 0. Keywords: j(m

Randić

Randi Ìc Energy and Randi Ìc Estrada Index of a Graph by Bozkurt, Åž. Burcu; Bozkurt, Durmus (2012) - In this paper, we introduce a new index of the graph G which is called Randić Estrada index. Now we give a result which states a lower bound for the Randić Estrada index involving Randić index. Keywords: randić

G(r

Coordinated Search for a Randomly Located Target on the Plane by El hadidy, Mohamed Abdallah; Mohamed, Abd el moniem Anwar; Abou Gabal, Hamdy Mohamed (2009) - Key words: coordinated search, optimal search plan, symmetric distribution. = � 4a1+ 2π ω1 �     n ∑ k=1 a1 ∫ 0 θ k ∫ θ k−1 g(r cosθ , r sinθ)rd rdθ     A. El-Moneim, H. Gabal, and M. El-Hadidy / Eur. Keywords: g(r;  ;  ;  

-closed

Locally Beta-closed Spaces by Basu, Chanchal Kumar (2009) - (e) Every cover of S by β -regular sets of X has a finite subcover. For every family {Uα : α ∈ I} of β -regular sets of X with [∩α∈I Uα] ∩ S = ;, there is a finite subset I0 of I such that [∩α∈I0 Uα]∩ S = ;. (g) Every filter base on S, β -θ -adheres to some point of S. (h) Keywords: -closed

Wijsman

Statistically Almost Î»-convergence of Sequences of Sets by Hazarika, Bipan; Esi, Ayhan (2013) - − L � �≥ ε © � � �= 0. The generalized de la Vallée-Poussin mean is defined by tn (x) = 1 λn ∑ k∈In xk where In = � n−λn+ 1, n � . Keywords: wijsman; � d(x; � �

O32

Low Dimensional Homology Groups of the Orthosymplectic Lie Superalgebra $\osp(1,2)$ by Biyogmam, Guy Roger (2014) - From the formulas (24)–(32), (34), (35) above, it is clear that all the cycles but E23 ∧ e23 ∧ o23 ∧ o32 − e23 ∧ e32 ∧ o32 ∧ o32, E23 ∧ e32 ∧ o23 ∧ o32 − e23 ∧ e32 ∧ o23 ∧ o23 are boundaries, so are zero in homology. = 0 d(e32 ∧ o23 ∧ o23 ∧ o23) Keywords: d(e23 ∧; e23 ∧; o32; ∧ e32; ∧ o23; ∧ o∧2

Q)s

Nil(n)-Modules Bifibred over Groups by Atik, Hasan (2017) - 〈(1, 〈〈m1, m2〉, m3〉), (p4, m4)〉 . . . 〈〈(〈m, m′〉, q)S, (m′′, q)S〉 . . Keywords: q)s

Εn10

Osculating Spheres of a Semi Real Quaternionic Curve in E_2^4 by Bektas, O.; Bayrak Gurses, N.; Yuce, S. (2014) - Then there exists a sphere which contacts at the fourth order to the curve β at β (0) and the equation of the semi quaternionic osculating sphere according to the Frenet frame ¦ T0,N10 ,N20 ,N30 © such that εT0 X 2 1 + εN10 X2− εT0 εN10 ς0 !2 + εN20 X3− εT0 εN10 εn10 ς′0ρ0 !2 + εN30 � X4−Ω0 � εT0 εN10 � � ς′0ρ0 �′ + εt0 � εn10 � ς0 ρ0 � − εN10 ρ0 − 4 � ρ0 ς0 � � + 3 εT0 εN10 � ρ0 ς0 ��2 Ö. Bektaş, N. Gürses, S. Yüce / Eur. = 2 � β ′′ (0) ,β (0)−M � + β ′ (0) ,β ′ (0) �� = 0 and g ′′ (0) . Keywords: εn10; εt0; � �

Hurewicz

On Locally Hurewicz Spaces by Kudri, Soraya Rosana Torres; Roika, Clarice Aparecida; Breuckmann, Tomaz. K. (2015) - Consider ∀n ∈ N, Hn = {Un j} j∈Jn ∪ Y c , then Hn is a covering of H by open sets in X , because Y is a closed set we have that Y c is an open set in X and for each x ∈ H if x ∈ Y then x ∈ H ∩ Y , then there exists j ∈ Jn such that x ∈ Un j , if x /∈ Jn, such that Hn = {Vn j} j∈In . (ii) ∀y ∈ Y,∃n0 ∈ N such that ∀n ∈ N if n≥ n0 then there exists V ∈ Keywords: hurewicz

Simplicial

Some Relations Between Crossed Modules and Simplicial Objects in Categories of Interest by Boyaci, Yasar; Avcioglu, Osman (2014) - = x ∗ y + x ∗ z; (d) for each ω ∈ Ω′1 and ∗ ∈ Ω′2, E includes the identities ω(x + y) = ω(x) + ω(y) and ω(x ∗ y) =ω(x) ∗ y . c′1 = c1 + c′1 − c1, ∂ (c1) ∗ c′1 = c1 ∗ c′1, for all c1, c′1 ∈ C1, and ∗ ∈ Ω′2, then the triple (C1, C0,∂ ) is called a crossed module in C. Definition 7. Keywords: simplicial

Mpq

On the Exponential Diophantine Equation $ (M_{pq} )^x+(M_{pq}+1)^y=z^2$ by Hoque, Azizul (2016) - This gives pq y = z2 − (Mpq k)2 and thus pq y = (z + Mpq k)(z − Mpq k). Thus we have Mpq = 3, x = 2k = 2, y = 2 and z = p j + (Mpq) k = 5. Keywords: mpq

R(x

Generalized Hyers-Ulam Stability of a System of Bi-Reciprocal Functional Equations by Ravi, K.; Kumar, Senthil (2015) - i=0 4iH(2i+1 x , 2i y, 2i y)<& % & & & ' & & & ( (6) for all x , y % X . i=0 4iH(2i+1 x , 2i y, 2i y) (9) for all x , y % X . Keywords: r(x

Extension

Essentiality in the Category of S-acts by Barzegar, Hasan (2016) - = p2s2 = q2s2 = p3s3 = . . For b ∈ A, Ib = S and the result is obvious. Keywords: extension; monomorphism

S(s

C-cycle Compatible Splitting Signed Graphs S(S) and Î“(S) by Jain, Rashmi; Kansal, Sangita; Acharya, Mukti (2015) - In this paper, we establish a structural characterization of signed graph S for which S(S) and !(S) are isomorphic and ! 2010 Mathematics Subject Classifications: 05C22; 05C75 Key Words and Phrases: canonical marking, splitting signed graph, ! Keywords: s(s

∆2,8

Fourier Coefficients of some Eta Quotients of Weight 8 by Kendirli, Baris (2015) - = ( 1 2 p+ 15 4 p2 + 91 8 p3 + 273 16 p4 + 41 4 p5 − 99 16 p6 − 65 4 p7 − 213 16 p8 − 23 4 p9 − 21 16 p10 − 1 8 p11)k8, f2 := ∞ ∑ n=0 f2 (n) = η5 (4z)η33 (6z) η7 (2z)η15 (12z) = ( 1 2 p+ 15 4 p2 + 45 4 p3 + 65 4 p4 + 33 4 p5 − 33 4 p6 − 65 4 p7 − 45 4 p8 − 15 4 p9 − 1 2 p10)k8, f3 := ∞ ∑ n=0 f3 (n) = η9 (2z)η17 (6z) η3 (4z)η7 (12z) = ( 1 2 p+ 15 4 p2 + 37 4 p3 + 13 4 p4 − 87 4 p5 − 121 4 p6 + 19 4 p7 + 135 4 p8 + 65 4 p9 − 17 2 p10 − 9p11 − 2p12)k8, f4 := ∞ ∑ n=0 f4 (n) = η17 (2z)η9 (6z) η7 (4z)η3 (12z) = ( 1 2 p+ 15 4 p2 + 33 4 p3 − 13 4 p4 − 135 4 p 5 − 99 4 p6 + 171 4 p7 + 225 4 p8 − 63 4 p9 − 44p10 − 6p11 + 12p12 + 4p13)k8, f5 := ∞ ∑ n=0 f5 (n) = η25 (2z)η (6z)η (12z) η11 (4z) = ( 1 2 p+ 15 4 p2 + 29 4 p3 − 39 4 p4 − 175 4 p 5 − 33 4 p6 + 375 4 p7 + 219 4 p8 − 399 4 p9 − 145 2 p10 + 54p11 + 40p12 − 12p13 − 8p14)k8, f6 := ∞ ∑ n=0 f6 (n) = η33 (2z)η5 (12z) η15 (4z)η7 (6z) − 172211/62730k10 + 85609/62730k11 − 21547/31365k12 + 6041/31365k13 − 2038/31365k14 − 5968/31365k15 + 11936/31365k16, r8 =8170304/31365k0 − 553454/1845k1 + 8087054/31365k2 − 6100906/31365k3 + 4250186/31365k4 − 2796223/31365k5 + 1754294/31365k6 − 1053046/31365k7 + 597956/31365k8 − 18419/1845k9 + 139724/31365k10 − 32926/31365k11 − 24124/31365k12 + 65132/31365k13 − 74056/31365k14 + 91904/31365k15 − 183808/31365k16, r9 =− 1116896/6273k0 + 1011709/6273k1 − 836363/6273k2 + 649939/6273k3 − 479906/6273k4 + 336985/6273k5 − 223349/6273k6 + 137143/6273k7 − 74396/6273k8 + 30469/6273k9 − 575/6273k10 − 19181/6273k11 + 30910/6273k12 − 38834/6273k13 + 39148/6273k14 − 39776/6273k15 + 79552/6273k16, r10 =1067584/31365k0 − 933638/31365k1 + 784454/31365k2 − 635366/31365k3 + 494146/31365k4 − 364693/31365k5 + 14642/1845k6 − 147746/31365k7 + 61556/31365k8 + 9607/31365k9 − 66056/31365k10 + 108554/31365k11 − 138764/31365k12 + 160012/31365k13 − 9608/1845k14 + 169984/31365k15 − 339968/31365k16, r11 =− 185456/94095k0 + 326609/188190k1 − 280927/188190k2 + 234563/188190k3 − 93929/94095k4 + 70492/94095k5 − 5531/11070k6 + 47033/188190k7 − 14/94095k8 − 23483/94095k9 + 93923/188190k10 − 140797/188190k11 + 93751/94095k12 − 116933/94095k13 + 8222/535k14 − 185456/94095k15 + 370912/94095k16. Keywords: ∆2,8; � �

Cl∗e

Weak Separation Axioms via $e$-I- sets in Ideal Topological Spaces by Al-Omeri, Wadei Faris; Noorani, M. S. Md.; Al-omeri, Ahmad; Noiri, T. (2015) - = ;. (iii) ⇒ (iv): Suppose that Cl∗e ({x}) 6= Cl∗e ({y}) for distinct points x , y ∈ X . if and only if for x , y ∈ X , IeKer({x}) 6= IeKer({y}), there exist disjoint e-I -open sets U and V such that Cl∗e ({x}) ⊂ Keywords: cl∗e

Αgrw

A Note on alpha grw-closed Sets by Rosas, Ennis; Nataraj, selvanayaki; Ilango, Gnanambal (2016) - Semi-open sets and semi-continuity in topological spaces. A topological space (X ,τ) is said to be s-normal if for each pair of disjoint closed sets A and B, there exists disjoint semi-open sets U, V such that A⊆ U and B ⊆ V . Keywords: αgrw

Semimodule

On "Essential" Subsemimodules and Weakly Co-Hopfian Semimodules by Diop, Elhadji Demba Wade (2016) - A monomorphism f : M −→ M ′ is said to be essential if f (M)Ã M ′. It is known that an R-monomorphism f : M −→ M ′ of left R-modules is essential iff for any R-homomorphism g : M ′ −→ M”, g ◦ f is a monomorphism implies that g is a monomorphism. An R-monomorphism f : M −→ M ′ of left R-semimodules is essential if for any R-homomorphism g : M ′ −→ M ′′, g ◦ f is a monomorphism implies that g is a monomorphism. Keywords: semimodule

Encoding

On Indifferentiable Deterministic Hashing into Elliptic Curves by Diarra, Nafissatou; Sow, Djiby; Ould Cheikh Khlil, Ahmed Youssef (2017) - = (x, y) if u 6= −1, where x = −u ( d3u3+ u3 + 1 )1/3 , v = − ( d3u3+ u3 + 1 )1/3 + du; • and hd(u) Math, 10 (2) (2017), 363-391 386 • if y = − √ x3 + ax2 + c, let r = √ s(s+ x)/u 6= 0; then define v, ε, x, y from r as in theorem 6. Keywords: encoding; square; α2(1 +

Nzi

Global Existence of Solutions for a System Modelling Electromigration of Ions Through Biological Cell Membranes with L1 Data by Alaa, Noureddine; Aqel, Fatima (2017) - Math, 10 (2) (2017), 272-294 279 which means that by passing to the limit, we obtain∫ T 0 ∫ Ω ∂(qi,nZi,n) ∂t sign−(Zi,n) ≤ 0 therefore ∫ T 0 ∫ Ω ∂(qi,nZi,n)− ∂t ≤ 0 this implies the following inequality∫ Ω (qi,nZi,n)−(t, x) ≤ ∫ Ω (qi,nZi,n)−(0, x) as (qi,nZi,n)(0, x) ≥ 0 for almost everywhere then we deduce∫ Ω (qi,nZi,n)−(t, x) ≤ 0. Using now the boundary conditions to obtain∫ QT ∂t(jk(qi,nZi,n)) + di ∫ QT ∇Tk(qi,nZi,n)(qi,n∇Zi,n) = ∫ QT Tk(qi,nZi,n)Sni (Zn, φn) which implies that∫ QT ∂t(jk(qi,nZi,n)) + di ∫ QT T ′ k(qi,nZi,n)|qi,n∇Zi,n|2 = ∫ QT Tk(qi,nZi,n)Sni (Zn, φn) +mi ∫ QT T ′ k(qi,nZi,n)(qi,n∇Zi,n)(qi,nZi,n)∇φn the integration over (0, T ) yields to the equality above∫ Ω jk(qi,nZi,n)(t) + di ∫ QT T ′ k(qi,nZi,n)|qi,n∇Zi,n|2 = ∫ Ω jk(q n i,0Z n i,0) + ∫ QT Tk(qi,nZi,n)Sni (Zn, φn) + mi ∫ QT T ′ k(qi,nZi,n)(qi,n∇Zi,n)(qi,nZi,n)∇φn. Keywords: nzi; ∫ qt

1)b

Existence, Nonexistence and Decay Estimate of Global Solutions for a Viscoelastic Wave Equation with Nonlinear Boundary Damping and Internal Source Terms by Di, Huafei; Shang, Yadong (2017) - If u ∈ L∞(0, T ;H1 Γ0 (Ω)) with ut ∈ L∞(0, T ;Lρ+1(Ω))∩Lq+1(0, T ;Lq+1(Γ1)) satisfy the following conditions (i) For any v ∈ H1 Γ0 (Ω) ∩ Lq+1(Γ1) ∩ Lρ+1(Ω) and a.e 0 ≤ t ≤ T , such that 1 ρ (|ut|ρ−1ut, v) + ∫ t 0 b1(u, v)ds+ ∫ t 0 b2(u, v)ds − ∫ t 0 (|u|p−1u, v)ds+ ∫ t 0 (|ut|q−1ut, v)Γ1ds = 1 ρ (|u1|ρ−1u1, v), (2.12) where b1(u, v) = (∇u,∇v), b2(u, v) = −( ∫ s 0 g(s− τ)∇u(τ)dτ,∇v); (ii) u(x, 0) = u0(x) in H1 Γ0 (Ω), ut(x, 0) = u1(x) in Lρ+1(Ω) ∩ Lq+1(Γ1). Math, 10 (4) (2017), 668-701 683 = ∣∣ ∫ t 0 g(t− s) ∫ Ω |∇u(s)−∇u(t)|2dxds− ∫ t 0 g(t− s) ∫ Ω |∇um(s)−∇um(t)|2dxds ∣∣ ≤ ∫ t 0 g(t− s)‖∇u(s)−∇um(s)‖2‖∇u(s) +∇um(s)‖2ds + ∫ t 0 g(t− s)‖∇u(s)−∇um(s)‖2ds‖∇u(t) +∇um(t)‖2 + ∫ t 0 g(t− s)‖∇u(s) +∇um(s)‖2ds‖∇u(t)−∇um(t)‖2 + ∫ t 0 g(s)ds‖∇u(t) +∇um(t)‖2‖∇u(t)−∇um(t)‖2 ≤ C ∫ t 0 g(t− s)‖∇u(s)−∇um(s)‖2ds+ C ∫ t 0 g(s)ds‖∇u(t)−∇um(t)‖2 → 0, (3.46) as m→∞. Taking into account the nonlinear term of the functional J(u), we deduce ‖um‖p+1 p+1 − ‖u‖ p+1 p+1 ≤ (p+ 1)| ∫ Ω |u+ θmum|p−1(u+ θmum)(um − u)dx| ≤ (p+ 1)‖u+ θmum‖pp+1‖um − u‖p+1 ≤ C‖um − u‖p+1 → 0, (3.47) as m→∞, where 0 < θm < 1. Keywords: 1)b; 1)e(0; g(t−; p+1; ρ+1

B]t

On McShane-Stieltjes Integrals of Interval-valued Functions and Fuzzy-number-valued Functions on Time Scales by Elsheikh Hamid, Muawya (2018) - b∫ a F (t)dα = I0 and F ∈ IMSα∆[a, b]T. Remark 1. b∫ a F (t)∆t = I0 and F ∈ IM∆[a, b]T. Definition 5. Keywords: b]t; ms∆; t)dα

A]p

On Approximation Properties of (p,q)-Bernstein Operators by Karahan, Done; Izgi, Aydin (2018) - For f ∈ C [ 0, [n+a]p,q [n+b]p,q ] , F p,q n,a,b(f ;x) = 1 p n(n−1) 2 n∑ k=0 f ( [k]p,q[n+ a]p,q pk−n[n]p,q[n+ b]p,q ) qp,qn,k,a,b(x), 0 ≤ x ≤ For ∀x ∈ [ 0, [n+a]p,q [n+b]p,q ] and ∀n ∈ N, (p, q)-Bernstein operators (9) are satisfied the following equalities: i. F p,q n,a,b(1;x) Keywords: a]p; b]p

Chaudhary

Some Theta-Function Identities Related to Jacobi’s Triple-Product Identity by Srivastava, Hari M.; Chaudhary, M. P.; Chaudhary, Sangeeta (2018) - − 6q37 − 2q40 − 4q45 − 4q46 − 2q49 − 2q50 − 2q52 − 2q53 − 4q54 − 2q55 − 2q56 − 2q59 − 2q61 − 6q64 − · · · . − 2q22 − 4q24 − 2q25 − 2q26 − 2q28 − 2q29 − 4q30 − 2q31 − 2q35 Keywords: chaudhary

Diframe

Separation Axioms in Diframes by Korkmaz, Esra; Erturk, Riza (2018) - = ⋂ {c(k) : k ∈ Lcf and k ≤ a} for all a ∈ Lfr. (d) ∀a ∈ Lfr, ∀x, y ∈ Le, a � y → x⇒ k ∈ Lcf ; k ≤ a, y � k → x. (ii) Now, by regularity of L, ai = ∨ j∈J {bij ∈ Lfr : ∃fij ∈ Lcf ; bij ≤ fij ≤ ai} for all i ∈ I. Keywords: diframe; lcf; lfr

D(a

A Common Best Proximity Point Theorem for Ï•-dominated Pair by Iranmanesh, Mahdi; Ganjbakhsh Sanatee, Ali (2018) - 2010 Mathematics Subject Classifications: 47H09, 47H10 Key Words and Phrases: Common best proximity point, φ-dominated pair, φ-contraction, fixed point 1. An element x ∈ X is said to be common best proximity point of the non- self-mappings S : A −→ B and T : A −→ B if it satisfies the condition that d(x, Sx) = d(x, Tx) = d(A,B). Keywords: d(a

Σ(z

Fixed Point Results for Geraghty Type Generalized F-contraction for Weak alpha-admissible Mapping in Metric-like Spaces by Qawaqneh, Haitham Ali; Noorani, Mohd Salmi; Shatanawi, Wasfi (2018) - if there exist F ∈ F and τ > 0 such that d(Tx, Ty) > 0⇒ (τ + F (d(Tx, Ty)) ≤ F (d(x, y)), for all x, y ∈ X. 2. Suppose there exist f ∈ F and τ > 0 such that, for all x, y ∈ X with σ(fx, fy) > 0 and α(x, y) ≥ 1, 0 < α(x, y)(τ + F (σ(fx, fy)) ≤ Keywords: σ(z

Eif

Analyzing the Locus of Soft Spheres: Illustrative Cases and Drawings by Åženel, Guzide (2018) - In the studies that have been carried out so far, the definition of soft sphere has been made, although it has been accepted very hard to revive it mathematically. For each of the cases the simplest and most fruitful method which the soft metric proposed was the introduction of the notion of soft distance and soft spheres. Keywords: eif; exf; set

Hh(x

Anti-type of Hesitant Fuzzy Sets on UP-algebras by Mosrijai, Phakawat; Iampan, Aiyared (2018) - This paper aims to introduce the notions of anti-hesitant fuzzy UP-subalgebras of UP-algebras, anti-hesitant fuzzy UP-filters, anti-hesitant fuzzy UP-ideals, and anti-hesitant fuzzy strongly UP-ideals, and prove some results. Furthermore, we discuss the relationships between anti-hesitant fuzzy UP-subalgebras (resp., anti-hesitant fuzzy UP-filters, anti-hesitant fuzzy UP- ideals, anti-hesitant fuzzy strongly UP-ideals) and some level subsets of hesitant fuzzy sets on UP-algebras. Keywords: hh(x

Aru

Value-at-Risk Modeling with Conditional Copulas in Euclidean Space Framework by Loyara, Vini Yves Bernadin; Barro, Diakarya (2019) - − pt‖ so C (u1, ..., un/wt) = ∣∣f−1 w (wt) ∣∣ ∥∥∥∥ ∂ ∂wt (V aRu (X/wt)) ∥∥∥∥ ‖Pt − pt‖ and if we take it the relation (11) 〈V aRu (X/wt) , Pt − pt〉 = 1 4 (∥∥∥ ∂ ∂wt (V aRu (X/wt)) + Then C (u1, ..., un/wt) = f−1 w (wt) 〈 ∂ ∂wt (V aRu (X/wt)) , (Pt − pt) 〉 (16) and where Pt = (p1,te zt,1 , ..., pn,te zn,1) , V aRu (X/wt) is a Value at risk of the X such that wt and ‖‖ euclidean norm and noted. Keywords: aru

2,2,t

On the Existence of Solution to Multidimensional Third Order Nonlinear Equations by Aliyev, Samed Jahangir; Aliyeva, Arzu Q.; Abdullayeva, Goncha Z. (2019) - It is easy to obtain that, for any u, v ∈ B3,2 2,2,T ‖Q1(u)−Q1(v)‖ B3,2 2,2,T ≤ (√ T + 1√ 2 ) T∫ 0 ∫ Ω  n∑ i,j=1 aij(ξ) ∂ ∂ξi (F1(u(τ, ξ)) [0, 1], (24) that is, all the possible solutions uµ of equations (22) are a priori bounded in B3,2 2,2,T and belong to the ball K0(‖u‖ B3,2 2,2,T ≤ a0). Keywords: 2,2,t; b3,2

I(x

On Interval-Valued Fuzzy on Ideal Sets by Togonon, Mary Joy S.; Caga-anan, Randy L. (2019) - An ideal here is a nonempty collection of subsets of a set X, denoted by I(X), that satisfies: i. A ∈ I(X) and B ⊆ A implies B ∈ I(X); and ii. A ∈ I(X) and B ∈ I(X) implies A ∪B ∈ I(X). Keywords: i(x; ivfi; set

Covering

Rough Spaces on Covering Based Rough Sets by Alharbi, Nof; Aydi, Hassen; Ozel, Cenap (2019) - Subspaces The inclusion operation on covering based rough sets X and Y is defined by Y ⊆C X ⇐⇒ Y ⊆ X, and Y ⊆ X. Let (U,C) be a covering approximation space. EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 12, No. 2, 2019, 533-543 ISSN 1307-5543 – www.ejpam.com Published by New York Business Global Rough spaces on covering based rough sets N. Alharbi1, H. Aydi2,∗, C. Özel1 1 Department of Mathematics, King Abdulaziz University, P.O. Box: 80203 Jeddah 21589, Saudi Arabia 2 Université de Sousse, Institut Supérieur d’Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia Abstract. Keywords: covering

Divergence

Divergence Measures Estimation and its Asymptotic Normality Theory in the Discrete Case by Ba, Amadou Diadie; Lo, Gane Samb (2019) - 2010 Mathematics Subject Classifications: 62G05, 62G07, 62F05 Key Words and Phrases: φ-divergence measure estimation, Rényi, Tsallis, Kullback-Leibler divergence measures, symmetrized divergence measures 1. We are interested in divergence measures in the discrete case. Keywords: divergence; j∈d; measures; α(p

E)∗s

Soft Semi Local Functions in Soft Ideal Topological Spaces by Gharib, Fatouh; Abd El-latif, Alaa Mohamed (2019) - Recently, in 2011, Shabir and Naz [28] initiated the study of soft topological spaces. [4] B. Chen, Soft semi open sets and related properties in soft topological spaces, Appl. Keywords: e)∗s

Tubings

Labelled Maximal Tubings on Paths and Graph Associahedra by Gurbuzer, Sabri Kaan; Akyar, Bedia (2019) - The sum of T1 and T2 is splitted into two parts as T1 + T2 = (T1 + T l 2) ∨ T r 2 ∪ T l 1 ∨ (T r 1 + T2), for T1 = T l 1 ∨ T r 1 and T2 = T l 2 ∨ T r 2 , where T l i and T r i are left and right parts of the tubing respectively. a1 = T̄2 \ T̄1, T1 \ T2 = a1 . . . Keywords: tubings

Tmax

Global Dynamics of an Hepatitis C Virus Mathematical Cellular Model with a Logistic Term by Nangue, Alexis; Donfack, Thiery; Ndode Yafago, David Avava (2019) - [ − r Tmax (T − T 0)− r Tmax I ] − δI + (1− η)(1− ε)pβT 0I c −α(1− η)2β2V TT 0 c = − r Tmax [(T − T 0)2 − (T − T 0)I] + ( (1− η)(1− ε)pβT 0I c − δ ) I −α(1− η)2β2V TT 0 c This leads to : dL1 dt = − r Tmax = T − T 0 Keywords: tmax

Controllability

Simultaneous Null Controllability for Two Stroke Nonlinear Systems: Application to the Sentinel of Detection in Population Dynamics Model with Incomplete Data by Some, CÃ©dric KpÃ¨bbÃ¨wÃ¨wÃ¨rÃ¨; Sawadogo, Somdouda (2019) - Assume that (H1) holds and set p1 = q1 + q2 ; p2 = q1 − q2. × (0, A), Q = U × Ω, Qω = U × ω, QT = (0,T) × Ω, QA = (0,A) Keywords: controllability

L2(u

Boundary Sentinel with Given Sensitivity in Population Dynamics Problem and Parameters Identification by Soma, Mifiamba; Sawadogo, Somdouda (2019) - A 0 β(t, a, x)ρ̃(t, a, x)da in QT , ρ̃ = 0 on Σ From (64) ∂ρε ∂ν ⇀ ∂ρ̃ ∂ν weakly in L2(U × γ) (72) We know on the one hand that (ṽ, q̃) is solution to null controllability (14)− (16) , and on the other other hand that, there exists a unique v̂ ∈ ε such that (w0 − v̂) is of minimal norm in L2(U ×γ). The control w is of minimal norm in L2(U × γ) among ” the admissible controls”, i.e. ‖w‖2L2(U×γ) Keywords: l2(u

D2(x

A Characterization of Derivations in Prime Rings with Involution by Ali, Shakir; Mozumder, M. Rahman; Abbasi, Adnan; Khan, M. Salahuddin (2019) - [d1(y), d2(x ∗)] = 0 (5) for all x, y ∈ R. Replacing y by hy in (5), where y ∈ R and h ∈ H(R) ∩ Z(R), we get h([d1(x), d2(y ∗)] + Replacing y by x in (25), we get [x, x∗]d1(h)d2(h) + h[d1(x), x]d2(h) + hd1(h)[x, d2(x)] = 0 (28) for x ∈ R and h ∈ H(R) ∩ Z(R). Keywords: d2(x

F1(t

Generalized Quasilinearization Using Coupled Lower and Upper Solutions for Periodic Boundary Value Problem of an Integro Differential Equation by Sreedhar, Chaduvula Venkata; Devi, J. Vasundhara (2019) - Now we claim that α0 ≤ α1 ≤ α2 ≤ ... ≤ αn−1 ≤ αn ≤ ... Now we claim that α0 ≤ α1 ≤ α2 ≤ ... ≤ αn−1 ≤ αn ≤ ... Keywords: f1(t

Page

Corrigendum [On Î²-Open Sets and Ideals in Topological Spaces, European Journal of Pure and Applied Mathematics, Vol. 12, No. 3, 2019, 893-905] by Baldado, Michael Jr. Patula; Padua, Roberto N.; Catalan, Glaisa T. (2019) - In Lemma 2 (page 895), Lemma 3 (page 895), Lemma 4 (page 896), Lemma 7 (page 901), Theorem 1 (page 896), Theorem 7 (page 899), Theorem 8 (page 899), and Theorem 9 (page 900) in [1], the topological space in the assumption should be a τω-space, where τω-space is a topological space X that satisfies the condition: int(cl(A)) = int(cl(intA)) for every A ⊆ X. In Theorem 11 (page 901), Theorem 12 (page 901), Theorem 13 (page 901), Theorem 14 (page 902), and Theorem 16 (page 902) in [1], the topological space in the assumption should be a τζ-space, where τζ-space is a topological space X that satisfies the conditions: (1) cl(A ∩B) Keywords: page

Grand

On Embedding Theorems in Grand Grand Nikolskii-Morrey Spaces by Najafov, Alik Malik; Gasimova, Azizgul M. (2019) - ‖f‖p),κ),a,α;G · T µ̄0 , (24) by (11) for U = G, Mi = Ψi , η = T we get∥∥EiT∥∥q−ε,G ≤ C2(ε) ∥∥∥t−λili∆mi A note on boundednes of operators in grand grand Morrey spaces. Keywords: grand; tλi

Hks

Simple Properties and Existence Theorem for the Henstock-Kurzweil-Stieltjes Integral of Functions Taking Values on C[a,b] Space-valued Functions by Cunanan, Andrew Felix IV Suarez; Benitez, Julius (2020) - If F ∈ HKS([f, r], H) and F ∈ HKS([r, g], H), then F ∈ HKS([f, g], H) and (HKS) ∫ g f FdH = (HKS) ∫ r f FdH + (HKS) ∫ If F ∈ HKS([f, g], H) and [r, s] ⊆ [f, g], then F ∈ HKS([r, s], H). Keywords: g f; hks

R−,k

Bipolar Soft Topological Spaces by Fadel, Asmaa; Dzul-Kiï¬‚i, Syahida Che (2020) - Shabir and Naz [20], investigated the concept of bipolar soft sets depending on the role of bipolarity which was introduced by Dubois and Prade [6]. To define bipolar soft set on a universal set S we need a set of parameters W , then we get a set called the not set of parameters ¬W . Keywords: r−,k; set

Τ−1

Some New Oscillation Results for Fourth-Order Neutral Differential Equations by Moaaz, Osama; Cesarano, Clemente; Muhib, Ali (2020) - We see by induction that un (t) ≤ un+1 (t) and vn (t) ≤ vn+1 (t) for t ≥ t0, n > 1. ∣∣∣ for t ≥ tµ. Lemma 3. Keywords: τ−1

Mcshane

McShane Integrability Using Variational Measure by Sumalpong Jr, Felipe Raypan; Benitez, Julius V. (2020) - [1, 5] Let {fn}∞n=1 be an increasing se- quence of McShane integrable functions on [a, b] such that lim n→∞ fn(x) REFERENCES 312 Consider the sequence {fn}∞n=1, defined by fn = |f · χXn | for all n ∈ N. Since Xn ⊆ Xn+1 for each n, {fn}∞n=1 is an increasing sequence of McShane integrable functions on [a, b] and fn → |f · χX | pointwisely on [a, b]. Keywords: mcshane

K(x

Asymptotic Solutions of Scalar Integro-Diï¬€erential Equations with Partial Derivatives and with Fast Oscillating Coeï¬ƒcients by Kalimbetov, Burkhan; Temirbekov, Akisher; Tolep, Abdimuhan (2020) - Math, 13 (2) (2020), 287-302 299 ⇒ Ŝ(x, t, τ) = g(x) 2 [ ∑ 2 ≤ |m| ≤ Ny, m2 + 1 = m3 ym(x, t)σ1 + ∑ 2 ≤ |m| ≤ Ny, m3 + 1 = m2 ym(x, t)σ2+ + ∗∑ 2 ≤ |m| ≤ Ny, m2 + 1 6= m3,m3 + 1 6= m2 ym(x, t)e(m,τ)+ +  ∑ 1 ≤ |m| ≤ Ny, m2 + 1 = m3 ye1+m(x, t)σ1 + ∑ 1 ≤ |m| ≤ Ny, m3 + 1 = m2 ye1+m(x, t)σ2  e τ1+ + ∗∑ 1 ≤ |m| ≤ Ny, m2 + 1 6= m3,m3 + 1 6= m2 ye1+m(x, t)e(e1+m,τ), After embedding, the right-hand side of system (15) will look like Ĝ(x, t, τ) [0, T ]) are arbitrary function, y0(x, t) is the solution of an integral equation (130), m ≡ (0,m2,m3) ,m2 6= m3, |m| = m2 +m3 ≥ 1. 4. Keywords: k(x

L+1

Approximation of Function in generalized Holder Class by Rani, Supriya; Nigam, H. K. (2020) - Math, 13 (2) (2020), 351-368 354 (a) (C,α)(C,α) or CαCα means if ξ(z) = ∏α j=1 z j , α ≥ 1. (b) (C,α)(E, ql) or CαEq means if hl,j = ( l j ) ql−j (1+q)l , 0 ≤ j ≤ l. (c) (C, 1)∆H or C1∆H means if α = 1. (ii) ( H, 1 l+1 ) ∆H or H1/l+1∆H means further reduces to (a) ( H, 1 l+1 ) (C,α) or H1/l+1Cα means if ξ(z) = ∏α j=1 z j , α ≥ 1. (b) ( H, 1 l+1 ) (E, ql) or H1/l+1Eq if hl,j = ( l j ) ql−j (1+q)l , 0 ≤ j ≤ l. (iii) (N, pl, ql)∆H or Np,q∆H means further reduces to (a) (N, pl, ql)(C,α) or Np,qCα means if ξ(z) = ∏α j=1 z j , α ≥ 1. (b) (N, pl, ql)(E, ql) or Np,qEq means if hl,j = ( l j ) ql−j (1+q)l , 0 ≤ j ≤ l. (iv) (N, pl)∆H or Np∆H means further reduces to (a) (N, pl)(C,α) or NpCα means if ξ(z) = ∏α j=1 z j , α ≥ 1. (b) (N, pl)(E, ql) or NpEq means if hl,j = ( l j ) ql−j (1+q)l , 0 ≤ j ≤ l. (v) (Ñ , pl)∆H or Ñp∆H means further reduces to (a) (Ñ , pl)(C,α) or ÑpCα means if ξ(z) = ∏α j=1 z j , α ≥ 1. (b) (Ñ , pl)(E, ql) or ÑpEq means if hl,j = ( l j ) ql−j (1+q)l , 0 ≤ j ≤ l. (vi) (E, ql)∆H or Eq∆H means further reduces to (a) (E, ql)(C,α) or EqCα means if ξ(z) = ∏α j=1 z j , α ≥ 1. (b) (E, ql)(E, ql) or EqEq means if hl,j = ( l j ) ql−j (1+q)l , 0 ≤ j ≤ l. (vii) T (C,α) or TCα means further reduces to (a) T (C, 1) or TC1 means if α = 1. (viii) T (E, ql) or TEq means further reduces to (a) T (E, 1) or TE1 means if ql = 1 ∀ l. Remark 3. We write φ(x, s) = g(x+ s) + g(x− s)− 2g(x); ∆bl,j = bl,j − bl,j+1; KT∆H l (s) = 1 2π l∑ j=0 bl,j j∑ a=0 ∫ 1 0 ( j a ) za(1− z)j−a dξ(z) sin ( a+ 1 2 ) Keywords: l+1; means

Ẋ1

Mixed Type Symmetric and Self Duality for Multiobjective Variational Problems by Husain, Iqbal; Mattoo, Rumana G (2009) - = 0 (41) (τ− (τT e)λ)T ( f y1 − D f ẏ1) + (θ 1(t)− (τT e) ȳ1(t))T ×(λT f y1 y1 − DλT f ẏ1 y1) Particularly, the equations (29)-(32) are the famous Euler-Lagrange differential equation when second order derivatives appear in H. Using the analogies of the observation of Dφ ÿ from the notational section, the equations (29)-(32) become, τ( fx1 − D f ẋ1)− (θ 1(t)− (τT e) ȳ1(t))T (λT f y1 x1 − DλT f ẏ1 x1) Keywords: ẋ1; ẏ1

U,∆m

Applications of Lacunary Sequences to Develop Fuzzy Sequence Spaces for Ideal Convergence and Orlicz Function by Raj, Kuldip; Mohiuddine, S. A. (2020) - [17] used the idea of Orlicz function to define the following sequence space `M = { x ∈ w : ∞∑ k=1 M ( |xk| ρ ) <∞, for some ρ > 0 } which is called as an Orlicz sequence space. A = (ank) an infinite matrix and M = (Mk) be a sequence of Orlicz functions. Keywords: m v; u,∆m; u,∆m v

Êxt

Adjunction and Localization in the Category A-Alg of A-Algebras by Thiaw, Moussa; Ben Maaouia, Mohamed Ben Faraj (2020) - We say that S satisfies the left Ore conditions if: (i) ∀a ∈ A, ∀s ∈ S ∃t ∈ S and b ∈ A such that ta = bs (ii) ∀a ∈ A, ∀ s ∈ S such that as = 0, then it exist t ∈ S such that ta = 0. So the elements of S−1(A)⊗A are written in the form 1 s ⊗ Y , where Y ∈ A and s ∈ S. Let 1 s ⊗ Y ∈ KerθA ⇔ θA ( 1 s ⊗ Y ) Keywords: êxt

Φ(t)dt

Common Fixed Point Results for Set-valued Integral Type Contractions on Metric Spaces with Directed Graph by Benchabane, Saadia; Djebali, Smail; Nazir, Talat (2020) - If F (T ) is complete, then the Pompeiu-Hausdorff weight assigned to the U, V ∈ F (T ) is 0. (ii) XT 6= ∅ provided F (T ) 6= = V , that is V ∈ F (S). Keywords: ϕ(t)dt

Kfd

On Semitotal k-Fair and Independent k-Fair Domination in Graphs by Ortega, Marivir; Isla, Rowena (2020) - Math, 13 (4) (2020), 779-793 781 G and H, denoted by G�H, is the graph with vertex-set V (G�H) [{x} × Tx] ⊆ V (G�H) is a kfd-set in G�H if and only if (i) V (H)\Tx ⊆ NH(Tx) ∪ ( ⋃ z∈NG(x) Keywords: kfd; set

P10

Use of Some Topological Concepts in the Study of Some COVID-19 Symptoms by ALZahrani, Samirah (2020) - From the table 1 appears the class RXY of symptom temperature X and breathing diffi- culty Y , it shows equivalence class RXY of patients : RXY = {{p1, p4}, {p2}, {p3}, {p5}, {p6, p7, p8}, {p9, p10}}. When we looked at table 1 from through symptom temperature X, it showed us the classes RX contain three sets of patients according to their pain: XV Keywords: p10

X3k+2

Solving a Class of Integral Equations via Contractive Mapping with Rational Type by Abdullah, Abdullah; Sarwar, Muhammad; Mustafa, Zead; Jaradat, Mohammed M.M. (2020) - if Gb(x, y, z) = 0 then x = y = z. (2) G(x, y, z) ≤ s(Gb(x, x, y) +Gb(x, x, z)). (3) Gb(x, y, y) ≤ 2sGb(y, x, x). The mappings F,H, T : X ×X → X are said to satisfy the generalized contraction if for a, b, u, v, x, y ∈ X Gb ( F (a, b), H(u, v), T (x, y) ) ≤ N (a, b, u, v, x, y), where N (a, b, u, v, x, y) = α1(a, u) · Keywords: x3k+2; y3k+1

X(n

Asymptotic Laws for Upper and Strong Record Values in the Extreme Domain of Attraction and Beyond by Lo, Gane Samb; Ahsanullah, Mohammad; Diallo, Moumouni; Ngom, Modou (2021) - 2. Results Before stating our results, we recall that any F ∈ D is associated to a pair of functions (a(u), b(u)) of u ∈ [0, 1] as defined in the representations of Proposition 2 for F ∈ D(Gγ), γ 6= 0. That approach is based on representations of F ∈ D due to Karamata and to de Haan for example. Keywords: x(n

A+1

Translated Logarithmic Lambert Function and its Applications to Three-Parameter Entropy by Corcino, Cristina Bordaje; Corcino, Roberto Bagsarsa (2021) - Then y = W ( xe C A+1 A+ 1 ) − C A+ 1 + u(x) (20) = W ( xe C A+1 A+ 1 )1− C A+1 W ( xe C A+1 A+1 ) + u(x) W ( xe C A+1 A+1 )  , (21) C. Corcino, R. Corcino / Eur. In this paper another variation of Lambert W function called the translated logarithmic Lambert function will be introduced. Keywords: a+1

Brk

Fuzzy Translation and Fuzzy multiplication in BRK-algebras by Alshehri, Halimah Abdulrahman (2021) - In [2,3], Elgendy introduced fuzzy BRK-ideal of BRK-algebra and cubic BRK-ideal of BRK- algebra. [0, 1] is said to be a fuzzy magnified-αβ-translation of µ. Assume µ is fuzzy BRK-ideal of X. Then µ(0 ∗ x) ≥ min{µ(0 ∗ (x ∗ y)), µ(0 ∗ y)} Keywords: brk

N≥0

Comparison of the Adomian Decomposition Method and Regular Perturbation Method on Nonlinear Equations Second Kind of Volterra by Yaro, Rasmane; Abbo, Bakari; Francis, Bassono; Pare, Youssouf (2021) - = √ x ϕ1(x) = −16 15εx 2√x+ ε ∫ x 0 A0(t)√ x− t dt ... ϕn(x) = √ x ϕ1(x) = −16 15 εx2 √ x+ ε ∫ x 0 A0(t)√ x− t dt = −16 15 εx2 √ x+ 16 15 εx2 √ x = 0 ϕ2(x) = ε ∫ x 0 A1(t)√ x− t dt = ε ∫ x 0 4ϕ3 0 (t)ϕ1(t)√ x− t dt = 0 ϕ3(x) Keywords: n≥0

T)bp]1−

New Generalized Hermiteâˆ’Hadamard Type Inequalities for pâˆ’convex Functions in the Mixed Kind by Bilal, Muhammad; Khan, Asif R. (2021) - Here, we are going to introduce some new types of p−convex function, which we call as quasi p−convex function and P − p−convex function respectively. (v) If we choose r = 1 and s = 0 in (2), we get P − p−convex function. Keywords: t)bp]1−; tap

2imπ

Definite Integral of Logarithmic Trigonometric Functions Expressed in terms of the Incomplete Gamma Function by Reynolds, Robert; Stauffer, Allan (2021) - Then we replace k with k − 1 to get 2k−1πk ( i a )k−1 csc(t)e im(π−t) a ( Φ ( e 2imπ a , 1− k, −t−ia log(α)+π 2π ) − Φ ( e− 2imπ a ,−k, t+ π 2π )) + e 2iπm a ( akΦ ( e 2imπ a , 1− k, π − t 2π ) + 2iπmΦ ( e 2imπ a ,−k, π − t 2π )) Keywords: 2imπ

L(e

Chatterjee and Extension of Chatterjee Fixed Point Theorems on Operators on Hilbert C*-Modules by Rashwan, Rashwan A; AlFran, Howida Adel; Fangary, Asmaa; Omran, Saleh (2021) - Since M ∈ (l(E))̀+ with ∥M 2 ∥l(E) ⪯ 1 2 , one have (Il(E) − M 2 ) −1 ∈ (l(E))̀+, and furthermore M 2 (Il(E) − M 2 ) −1 ∈ (l(E))̀+ with ∥M 2 (Il(E) − M 2 ) −1∥l(E) ≤ 1 . Math, 14 (4) (2021), 1237-1248 1246 ∥xn+1 − xm∥l(E) ⪯ ∥xn+1 − xn∥l(E) + Keywords: l(e

D(q

Quadruple g-best Proximity Point for New Contraction in Complete Metric Space by Rathee, Savita; Swami, Monika (2022) - = inf{d(x, y) : x ∈ Q, y ∈ R}, Q0 = {x ∈ Q : there exists some y ∈ R such that d(x, y) = d(Q,R)}, R0 = {y ∈ R : there exists some x ∈ Q such that d(x, y) = d(Q,R)}. 2020 Mathematics Subject Classifications: 47H10, 54H25 Key Words and Phrases: Best proximity point, quadruple best proximity point, metric space, contraction 1. Keywords: d(q

Levels

Investigation of the Infinite Discrete Levels from Finite Discrete Levels in Position Dependent Mass Quantum Systems by Rath, Biswanath; Asad, Jihad; Shanak, Hussein; Jarrar, Rabab; Kaabar, Mohammed K. A. (2022) - Energy levels of this oscillator has been reflected in Fig. M=1/(1 + 2x 2 ) Im a x is Figure 1: Energy levels of H = [p2 +Mx2]; withM = 1 (1+2x2) J. Asad et al. / Eur. Keywords: levels

S(λ

On Almost α(Λ, sp)-continuous Multifunctions by Boonpok, Chawalit; Khampakdee, Jeeranunt (2022) - [[[F+(G s(Λ,sp) 1 ) ∩ F−(G s(Λ,sp) 2 )](Λ,sp)] (Λ,sp)](Λ,sp) for any (Λ, sp)-open sets G1, G2 of Y such that F (x) ∈ G+ 1 ∩G− 2 . Proof. [[U(Λ,sp)] (Λ,sp)](Λ,sp) ⊆ Keywords: s(λ

˜̃g

Bipolar Soft Generalized Topological Structures and Their Application in Decision Making by Saleh, Hind; Asaad, Baravan; Mohammed, Ramadhan (2022) - This paper mainly aims at defining a new bipolar soft generalized topological space; setting out of the point that the collection of bipolar soft sets forms the basis for the definition of the new concept is defined. A number of definitions, operations, and applications on bipolar soft sets have been investigated in ([4], Keywords: ˜̃g; θ1,λ1; θ2,λ2

X}(λ

Some Applications of (Λ, sp)-open Sets in Topological Spaces by Boonpok, Chawalit; Viriyapong, Chokchai (2022) - The set of all (Λ, sp)-cluster points of A is called the (Λ, sp)-closure [2] of A and is denoted by A(Λ,sp). The union of all (Λ, sp)-open sets contained in A is called the (Λ, sp)-interior [2] of A and is denoted by A(Λ,sp). Keywords: x}(λ

Meet

Annihilator Hyperideals in Strong Bounded Dual Distributive Meet-hyperlattice by Rezk, Eman; Abughazalah, Nabilah (2022) - In this paper, we study the properties of annihilator hyperideals in the class of strong bounded dual distributive meet-hyperlattice. Representation and characterization theorems of annihilator hyperideals in sub-meet-hyperlattice and product meet-hyperlattice are proved. 2020 Mathematics Subject Classifications: 06B75, 06F99, 08A05 Key Words and Phrases: Annihilator,Boolean algebra, Homomorphism, Hyperideal, Hyperlat- tice 1. Keywords: meet

Γkgr(g

On the Global Distance Roman Domination of Some Graphs by Entero, Giovannie; Espinola, Stephanie (2023) - Since G ∈ G, with n = |V (G)| ≥ 4, the distances and eccentricities in graph G are finite. Let G ∈ G be any graph of order n ≥ 4 and let its vertex set be V (G) = {u1, u2, u3, . . . Keywords: graph g; v f; γkgr(g

Integrable

Pettis Integrability in L1E′ [E] Related to the Truncation by Sabiri, Noureddine; Guessous, Mohamed (2022) - [16] if the set {∥f(.)∥ : f ∈ K} is UI in L1 R(µ), and we say that a set H of E-valued scalarly integrable functions is scalarly uniformly integrable briefly SUI (resp w-scalarly uniformly integrable briefly WSUI), if the set {⟨x′, f⟩ : ∥x′∥ ≤ 1, f ∈ H} (resp for each x′ ∈ E′, the set {⟨x′, f⟩ : f ∈ H}) is UI in L1 R(µ). Let E be a separable Banach space and f ∈ L1 E′ [E]. Keywords: integrable; pettis

J(t)g

On Mixed Type Duality for Nondifferentiable Multiobjective Variational Problems by Husain, Iqbal; Mattoo, Rumana G. (2009) - I , i ∈ P and g(t, x , ẋ , ẋ)≦ 0, t ∈ I , these inequalities yield, ∫ I � f i(t, x , ẋ , ẍ)d t + (x(t)T Bi(t)z i(t)) t with η implies ∑ j∈Jα ∫ I {ηT (y j(t)g j x) + (Dη) T y j(t)g j ẋ + (D2η)T y j(t)g j ẍ}d t ≦ 0 As earlier, integrating by parts and using the boundary conditions, we have ∑ j∈Jα ∫ I ηT {(y j(t)g j x ) + Keywords: j(t)g; � �

B)-open

Weak forms of (Λ, b)-open sets and weak (Λ, b)-continuity by Boonpok, Chawalit; Srisarakham, Napassanan (2023) - EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 16, No. 1, 2023, 29-43 ISSN 1307-5543 – ejpam.com Published by New York Business Global Weak forms of (Λ, b)-open sets and weak (Λ, b)-continuity Chawalit Boonpok1, Napassanan Srisarakham1,∗ 1 Mathematics and Applied Mathematics Research Unit, Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham, 44150, Thailand Abstract. 2020 Mathematics Subject Classifications: 54A05, 54C08, 54G05 Key Words and Phrases: (Λ, b)-open set, (Λ, b)-submaximal space, (Λ, b)-extremally discon- nected space, weakly (Λ, b)-continuous function 1. Keywords: b)-open

Intf

$F-$open and $F-$closed sets in Topological Spaces by Alqahtani, Mesfer Hayyan (2023) - In general, countable union of F -open sets may not be F -open set. In general countable intersection of F -open sets may not be F -open set. Keywords: intf; set

Ee1

Classification of Four Dimensional Train Algebras of Degree 2 and Exponent 4 by Zangré, W. Achile; Conseibo, André (2022) - Case: α0 ̸= 0 and α1 ̸= 0, then 0 = γ = ρ = µ = β1γ1. = γ1µ1 = 0. i) µ1 ̸= 0, then γ0 = γ1 = 0 and e2 = e, ee0 = 1 2e0, ee1 = 0, ee2 = λe2, e20 = e1, e21 = 0, e22 = 0, e0e1 = e2, e0e2 = 0, e1e2 = µe0. Keywords: = 0; = e0; = e2; e0e1 =; ee1; ee2; λe2

Hyperplanes

On the Partition of Space by Hyperplanes by Bagdasaryan, Armen (2023) - Direct problem: find the minimum number of hyperplanes (1) that divide Rd into s regions according to the rule (2); Inverse problem: determine the maximum number of regions into which Rd can be divided by means of n hyperplanes (1) according to the rule (2). The question of how many such partitions are possible arises in various applications, for example, in the theory of pattern classification and machine learning [3, 5, 10] which employs partitions using some number k of parallel hyperplanes; in cluster analysis [6] dealing with the methods of partitioning of a set of objects on the basis of their characteristics or properties into clusters or groups so that the objects of a cluster are closely related according to certain criteria; data analysis and classification in which space partitioning by hyperplanes may be used together with linear regression techniques based on least absolute value estimates approach and its generalizations; in the theory of hybrid systems and control [9]. Keywords: hyperplanes

Sβcli

Upper and Lower weak $s\beta(\star)$-continuity by Boonpok, Chawalit; Khampakdee, Jeeranunt (2023) - Then F is said to be surjection if F (X) = Y , or equivalent, if for each y ∈ Y there exists x ∈ X such that y ∈ F (x) and F is called injection if x ̸= y implies F (x) ∩ F (y) = ∅. 3. In particular, F−(y) = {x ∈ X | y ∈ F (x)} for each point y ∈ Y . Keywords: set; sβcli

Δs(λ

Characterizations of Some Topological Spaces by Boonpok, Chawalit; Thongmoon, Montri (2023) - Then, for each pair of distinct points x, y of X, there exist U, V ∈ s(Λ, p)O(X, τ) such that x ∈ U, y ∈ V and U (Λ,p) ∩ V (Λ,p) = ∅. Since U ∈ s(Λ, p)O(X, τ), U (Λ,p) = [U(Λ,p)] (Λ,p) and U (Λ,p) is r(Λ, p)-closed. For a topological space (X, τ), the following properties are equivalent: (1) (X, τ) is s(Λ, p)-connected; (2) U ∩ V ̸= ∅ for every nonempty sets U ∈ β(Λ, p)O(X, τ) and V ∈ δs(Λ, p)O(X, τ); (3) U ∩ V ̸= ∅ for every nonempty sets U ∈ p(Λ, p)O(X, τ) and V ∈ δs(Λ, p)O(X, τ); (4) U ∩ V ̸= ∅ for every nonempty sets U ∈ s(Λ, p)O(X, τ) and V ∈ δs(Λ, p)O(X, τ); (5) U ∩ V ̸= ∅ for every nonempty sets U ∈ α(Λ, p)O(X, τ) and V ∈ δs(Λ, p)O(X, τ); (6) U ∩ V ̸= ∅ for every nonempty sets U ∈ ΛpO(X, τ) and V ∈ δs(Λ, p)O(X, τ); (7) U ∩ V ̸= ∅ for every nonempty sets U ∈ δs(Λ, p)O(X, τ) and V ∈ δs(Λ, p)O(X, τ). Keywords: δs(λ

N∈z

Localization in the Category $COMP(G_{r}(A-Mod))$ of Complex associated to the Category $G_{r}(A-Mod)$ of Graded left $A-$modules over a Graded Ring by Ould Chbih, Ahmed; Ben Maaouia, Mohamed Ben Faraj; Sanghare, Mamadou (2023) - The relation S −1 H (−) : Gr(A−Mod) −→ Gr(S −1 H A−Mod) which that for any graded left A−module M we made to correspond S −1 H (M) and for all graded morphism of degree k ∈ Z of graded left A−modules f : M −→ N we correspond S −1 H (f) of degree k ∈ Z is a exact additively covariant functor; (iii) Furthermore let P a prime ideal of A and SH is a part formed of regular homogeneous elements of A\P and SPH is the homogeneous multiplicatively closed subset of A generated by SH , then the relation S −1 PH (−) : Gr(A−Mod) −→ S −1 PH A−Mod which that for any graded left A−module M −→ N is a morphism of left A−modules, then we say that f is a graded morphism of degree k ∈ Z if for any m ∈ Ms then f(m) ∈ Ns+k. Keywords: n∈z; −1 h

Ν+1

Degree of Convergence of a Function in Generalized Zygmund Norm Using Karamata-Matrix (KλA) Product operator by H. K. Nigam; Manoj Kumar Sah (2023) - From (22) and (26), we get ∥ρv(·)∥(η2)r = O DOI: https://doi.org/10.29020/nybg.ejpam.v16i2.4756 Email addresses: hknigam@cusb.ac.in (H. K. Nigam), manojsah@cusb.ac.in (M. K. Sah) https://www.ejpam.com 1302 Keywords: ν+1

Gbasp

Approximation of Generalized Biaxisymmetric Potentials in $L^{\beta}$-norm by Kumar, Devendra Kumar (2023) - Introduction Let F = F (x, y) be a real-valued regular solution of the generalized biaxisymmetric potential (GBASP) equation ∂2F ∂x2 + 2µ y ∂F ∂y + ∂2F ∂y2 + 2ν x ∂F ∂x = 0, µ, ν > 0, (1.1) which are even in x and y. A polynomial of degree n which is even in x and y is said to be a GBASP polynomial of degree n if it satisfies (1.1). The series (1.2) can be represented in (r, θ) by F ≡ F (r, θ) Keywords: gbasp

Γ(1+(s+1)γ

Exploring the Companion of Ostrowski's Inequalities via Local Fractional Integrals by Saleh, Wedad; Meftah, Badreddine; Lakhdari, Abdelghani; Kiliçman, Adem (2023) - Some local fractional maclaurin type inequalities for generalized convex functions and their applications. 2020 Mathematics Subject Classifications: 26D10, 26D15, 26A51 Key Words and Phrases: Tow-point Newton-Cotes, generalized s-convex functions, local frac- tional integral, fractal set 1. Keywords: γ b; γ(1+(s+1)γ; ∣∣∣j

Aλ2

Derivations and Representations of Commutative Algebras Verifying a Polynomial Identity of Degree Five by Ouédraogo, Hamed; Dembega, Abdoulaye; Conseibo, André (2023) - = −t(t − 1)(t − λ1)(t − λ2), in which case A = A0 ⊕ A1 ⊕ Aλ1 ⊕ Aλ2 , where Aµ = {x ∈ A|ex = µx}, λ1 = 3+i √ 3 6 and λ2 = 3−i √ 3 6 . Sup- pose that the polynomial 3t2 − 3t + 1 = 3(t − λ1)(t − λ2) in K[t]. Keywords: aλ2

Yj(ε

Ideals of BCK-algebras and BCI-algebras Based on a New Form of Fuzzy Set by Roh, Eun Hwan; Yang, Eunsuk; Jun, Young Bae (2023) - Hence 0 ∗ (y ∗ z) = (0 ∗ y) ∗ (0 ∗ z) = 0 by (III) and (6), and so 0 ≤X y ∗ z, E. H. Roh, E. Yang, Y. B. Jun / Eur. ∗ x (4) = ((x ∗ y) ∗ x) ∗ (0 ∗ y) (4) = ((x ∗ x) ∗ y) ∗ (0 ∗ y) (III) = (0 ∗ y) ∗ (0 ∗ y) (III) = 0, that is, (x ∗ y) ∗ (0 ∗ y) ≤X x. Keywords: yj(ε

Primes

On Prime Counting Functions Using Odd $K$-Almost Primes by Rashid, T.; Jaradat, M. M. M.; Yolacan, E.; Ahmad, H. (2024) - Then u = pq, where p, q are odd prime numbers. Introduction Greek mathematicians were the first to study prime numbers and their characteristics in depth. Keywords: number; primes

2n−1

Spectral Properties of Power Graph of Dihedral Groups by Romdhini, Mamika Ujianita; Nawawi, Athirah ; Al-Sharqi, Faisal ; Al-Quran, Ashraf (2024) - 2020 Mathematics Subject Classifications: 05C25, 05C50, 15A18, 20D99 Key Words and Phrases: Characteristic polynomial, Power graph, Dihedral Groups 1. The characteristic polynomial of NA(ΓD2n) is PNA(ΓD2n )(λ) = ∣∣∣∣∣∣∣∣ λ − 1√ (2n−1)(n−1) J1×(n−1) Keywords: 2n−1; 2n−1)(n−1

Qge

On Quasi Generalized Exchange Algebras by Jun, Young Bae ; Bandaru, Ravikumar ; Shukla, Rahul (2024) - Using (GE2), we have 1 ∗ (κ ∗ δ) = κ ∗ δ ∈ F , and so δ = 1 ∗ δ ∈ F by (GE2) and (27). If we take ς := 1 in (25) and use (GE2), then 1 ∗ (δ ∗ κ) = δ ∗ κ ∈ F and 1 ∗ δ = δ ∈ F . Keywords: qge

Division

Real Division Algebras with Left Unit Satisfying Some Identities. by Diabang, André Souleye; Mballo, Ama Sékou ; Diop, Pape Cheikhou (2024) - Introduction The discovery of the real algebra of Quaternions H by Hamilton in 1843, caused: On the one hand to the study of real division algebras by great researchers mathematians and physicists. [1] have studied Real division algebras satisfying some identities. Keywords: division; satisfies; unit

Mds

On the McShane-Dunford-Stieltjes Integral and McShane-Pettis-Stieltjes Integral by Omayan, Develin; Flores, Greig Bates (2024) - (Additivity of the MDS-integral) Let f : [a, b] → X, g : [a, b] → R and I,J ∈ A function f is said to be McShane-Stieltjes integrable, or simply MS-integrable, with respect to g on [a, b] if there exists J ∈ X with the following property: for each ε > 0 there is a gauge δ such that for every δ-fine M-partition P = {(t, [u,v])} of [a, b] the inequality∥∥∥∥∥∥ ∑ (t,[u,v])∈P f(t)∆g([u,v])− J ∥∥∥∥∥∥ X < ε D. Omayan, G.B. Flores / Eur. Keywords: mds

Hs1

Hierarchy Elements in an Almost Distributive Lattice by Ramesh, S. ; Chinnayya, G. ; Jogarao, G. ; Bandaru, Ravikumar ; Iampan, Aiyared (2024) - Therefore, h ∧ ŝ1 ∈ Ŝ. (iii) Let ŝ1 ∈ Ŝ. Then ŝ1 ∧ s1 = s1 ∧ ŝ1 = ŝ1. Now, s1 ∧ h = s1 ∧ (s1 ∧ s′1 ∧ h) Keywords: hs1; s1 ∧

Dpd

Distance Neighbourhood Pattern Matrices in a Graph by Augustine, Germina Kizhekekunnel; Joseph, Alphy; Jose, Sona (2010) - Any dpd-graph G, with dpd-set M and the M-dnp matrix DM G as an identity matrix of order n is isomorphic to a path Pn on n vertices with dpd-set M as any of its pendent vertices. Let G be a graph with dpd-set M such that DM G ∼= In, the identity matrix of order n. From Corollary 4, sum of the entries in each row of DM G = |M |. Keywords: dpd; set;  ;  

Rh(k

Theoretical Foundations of h-Rough Sets by Al-Rehili, Amjad (2024) - Since we have K ⊆ K ∪ Q and Q ⊆ K ∪ Q. Then Rh(K) ⊆ Rh(K ∪ Q) and Rh(Q) ⊆ Rh(K ∪Q) by (iii) in Proposition 7, then Rh(K ∪Q) ⊇ Rh(K) ∪Rh(Q). Additionally, K is open iff K = K◦. Keywords: rh(k

Kim

Probabilistic Type 2 poly-Bernoulli Polynomials by Lee, Si Hyeon; Chen, Li ; Kim, Wonjoo (2024) - Based on these new definition, we derive some meaningful formulae of probabilistic type 2 poly-Bernoulli polynomials and prob- abilistic unipoly-Bernoulli polynomials and numbers attached to p. 2020 Mathematics Subject Classifications: 11B68 Key Words and Phrases: Bernoulli polynomials, Stirling numbers, Probabilistic type 2 poly- Bernoulli polynomials, Probabilistic unipoly-Bernoulli polynomials. Probabilistic degenerate bell polynomials associated with random variables. Keywords: kim

Α(τ1

Upper and Lower Slight $\alpha(\tau_1,\tau_2)$-continuity by Viriyapong, Chokchai ; Sompong, Supannee ; Boonpok, Chawalit (2024) - In particular, F−(y) = {x ∈ X | y ∈ F (x)} for each point y ∈ Y . European Journal of Pure and Applied Mathematics, 15(3):300–309, 2022. Keywords: set; α(τ1

Dense

On the Category of (i,j)-Baire Bilocales by Nxumalo, Mbekezeli (2025) - n ∈ N} be a collection of i-dense j-open sublocales. (⇐=): Let {Un : n ∈ N} be a collection of τi-dense τj-open subsets of X. Then {o(Un) : n ∈ N} is a collection of i-dense j-open sublocales of τ1 ∨ τ2. Keywords: dense; n∈n

U12

Nonlinear Mixed $\lambda$-Jordan Triple Derivation on $\ast$-algebras by Alali, Amal S. ; Nisar, junaid; Rehman, Nadeem; Alnoghashi, Hafedh M. (2024) - For any U, V ∈ A, we write U = U11 + U12 + U21 + U22 and V = V11 + V12 + V21 + V22. Since [U12, P1]∗♢λP2 = 0 and by using Lemma 2.1, we have Π([U12 + V21, P1]∗♢λP2) = Π([U12, P1]∗♢λP2) + Π([V21, P1]∗♢λP2) Keywords: u12; ∗ ♢; ♢ λp1; ♢ λp2; ♢ λx12

Pchs

Plithogenic Crisp Hypersoft Topology by Ahmed, Nehmat; Pirbal, Osama (2024) - Let (Γ,C, Vψ)PC , (Γ1, C1, Fψ)PC and (Γ2, C2, Hψ)PC be PCHS sets over UP . The intersection of any two PCHS sets in τPC belongs to τPC , (iii) The union of any number of PCHS sets in τPC belongs to τPC . Keywords: pchs; v ψ

|ℶ2|+

Some Inclusion Properties for Hohlov Operator to be in Comprehensive Subfamilies of Analytic functions by Al-Hawary, Tariq ; Massa’deh, Mourad Oqla ; Fallatah, Ahlam omar (2024) - ∞∑ τ=2 (τ − 1) (|ℶ1|)τ−1 (|ℶ2|)τ−1 (ℶ3)τ−1 (1)τ−1 (Υ1)τ−1 (1)τ−1 +(κ2 − κ3(κ1 + κ2) + 1) ∞∑ τ=2 (|ℶ1|)τ−1 (|ℶ2|)τ−1 (ℶ3)τ−1 (1)τ−1 (Υ1)τ−1 (1)τ−1 ≤ (κ2 + 1) |ℶ1ℶ2| (|ℶ1|+ 1) (|ℶ2|+ 1) (Υ1 + 1)Υ1 ℶ3(ℶ3+1)(2)1 ∞∑ τ=3 (|ℶ1|+ 2)τ−3 (|ℶ2|+ 2)τ−3 (Υ1 + 2)τ−3 (ℶ3 + 2)τ−3 (1)τ−3(3)τ−3 (3(κ2 + 1)− κ3(κ1 + κ2)) |ℶ1ℶ2|Υ1 ℶ3(1)1 ∞∑ τ=2 (|ℶ1|+ 1)τ−2 (|ℶ2|+ 1)τ−2 (Υ1 + 1)τ−2 (ℶ3 + 1)τ−2 (1)τ−2(2)τ−2 +(κ2 − κ3(κ1 + κ2) + 1) ∞∑ τ=2 (|ℶ1|)τ−1 (|ℶ2|)τ−1 (Υ1)τ−1 (ℶ3)τ−1 (1)τ−1(1)τ−1 . Main Results This section will provide sufficient conditions for Hohlov operator function to be in the subfamilies Cκ3(κ1, κ2) and S∗κ3(κ1, κ2). Keywords: |ℶ2|+

Ωswd(z

A Generalization for Somewhere Dense Sets with Some Applications by Rawshdeh, Amani; Al-jarrah, Heyam; Al-zoubi, Khalid (2024) - Then H ∈ ωSWD(Z, τ) iff for each x ∈ H there is S ∈ SWD(Z, τ) with x ∈ S and S −H is countable. Then H ∈ ωSWD(Z, τ) iff for each x ∈ H there is S ∈ SWD(Z, τ) and a countable set G with x ∈ S −G ⊆ H. Theorem 8. Keywords: ωswd(z

Id−r

Additional Studies on Displacement Mapping with Restrictions by Alwadani, Salihah (2024) - and we learn from Example 4 that D = Fix R = U⊥. (ii): PD⊥ − 1 2 PD⊥ (from (16)) = PD⊥ T◦ PD⊥ = T◦ (from (17)), as claimed. Keywords: id−r; m−1; pd⊥

Ρ̌0

An Innovative Perspective on Bipolar Fuzzy Fantastic Ideals in BCK/BCI-Algebras by Balamurugan, M.; Hakami, Khalil H.; Ansari, Moin A.; Loganathan, K. (2024) - ≤ ζ̄−((ϱ̌0 ≬ ϱ̌1) ≬ ϱ̌2) ∨ ζ̄−(ϱ̌2), and ζ̄+(ϱ̌0 ≬ (ϱ̌1 ≬ (ϱ̌1 ≬ ϱ̌0))) ≥ ζ̄+((ϱ̌0 ≬ ϱ̌1) ≬ ϱ̌2) ∧ ζ̄+(ϱ̌2). ≤ ζ̄−((ϱ̌0 ≬ ϱ̌1) ≬ ϱ̌2) ∨ ζ̄−(ϱ̌2) ∨ (φ2 − φ⋇ 2 ), (iii) ζ̄+(ϱ̌0 ≬ (ϱ̌1 ≬ (ϱ̌1 ≬ ϱ̌0))) ≥ ζ̄+((ϱ̌0 ≬ ϱ̌1) ≬ ϱ̌2) ∧ ζ̄+(ϱ̌2) ∧ (−φ 2 + φ⋇ 2 ) for all ϱ̌0, ϱ̌1, ϱ̌2 ∈ ℵ̌. Proof. Keywords: ζ̄+((ϱ̌0 ≬; ϱ̌0; ≬ ϱ̌1; ≬ ϱ̌2

G(k

A Certain Class of Filters in Generalized Complemented Distributive Lattices by Sirisetti, Ramesh ; Gunda, Jogarao ; Bandaru, Ravikumar ; Shukla, Rahul (2025) - Given u ∈ A, we have v, u ≤ v ∨ u, which implies (v ∨ u)g ≤ vg, ug (By Proposition 2.1(iii)) and then (v ∨ u)g ≤ vg ∧ ug ∈ K (since vg ∈ K, ug ∈ A, and K is an ideal). vg ∈ G(K) or wg ∈ G(K) if G(K) is prime. Keywords: g(k

Irregularity

Data Analysis and Irregularity Measurements in the Identical Structures of Carbon nanocones $\boldsymbol{C N C}_{\boldsymbol{t}}(\mathrm{m})$ by Jebreen, Kamel; Kanj, Hassan ; Nawajah, Inad ; Chendeb, Nancy ; Amro, Rami M. (2025) - Irregularity indices are topological indices by nature. 5.58 11.12 16.68 22.24 Al (ξt) 8 16 24 32 Irl (ξt) 3.24 6.49 9.73 12.97 Irlu (ξt) 4 8 12 16 Irlf (ξt) 3.27 6.53 9.80 13.06 Irf (ξt) 8 16 24 32 Irla (ξt) 3.20 6.40 9.60 12.8 Ird 1 (ξt) 5.55 11.10 16.65 22.2 Ira (ξt) 0.13 0.27 0.40 0.54 Irga (ξt) 0.16 0.33 0.49 0.65 Irb (ξt) 0.81 1.62 2.42 3.23 Irr (ξt) 4 8 12 16 Table 3: Depiction of irregularity indices with some test values for ξ4 = CNC4( m). Keywords: irregularity; jebreen; ρµ∈e(ξt

1+ε

Local and Global Weak Solutions for Elliptic Nonlinear Equations by Habeeb Ibrahim; Dafaalla, Mohammed; Osman Abdalla Adam Osman; Ashraf. S. ELshreif (2025) - The following are recollections of estimates for um to [5, 12]:∫ Bs |∇um|pdx ≤ C ∫ Bs |∇vm|pdx, (10) and sup Bp |∇um| ≤ C (∫ Bs |∇um|pdx) ) 1 p (11) in the range p ∈ (0, s/2], with C = C(n, p, α). i | N1+ε 0 , consequently, as shown in Lemma 3 that 1/ ( ≤ {2x ∈ B1 i : s∑ m=1 |∇vm| > 2N0(λ∗ + ϵ) )1/2 ≤ C̄ε1+ε 1 λ1+ε ∫ {x∈B0 i : ∑s m=1 |∇vm|>(λ∗+ε)/4} s∑ m=1 |∇vm|1+δdx in that where C̄ = C̄(n, 1 + ϵ, (1+ϵ ϵ )1, α). Keywords: 1+ε; m=1

B1−ξ

Existence of Solutions to a New Class of Fractional Differential Equations With Antiperiodic Boundary Conditions by Aljurbua, Saleh Fahad; Hammad, Hasanen A.; Almutairi, Najat Bandar (2025) - This study introduces a novel class of fractional differential equations characterized by antiperiodic parametric boundary conditions of order µ ∈ (2, 3]. Fractional differential equations can provide a comprehen- sive scheme to examine complex and regular systems in numerous fields, such as physics, biology, economics, engineering, social sciences, and material science Keywords: b1−ξ; γ(µ−; ξ)(θ1−ξ

|n2

k-Hop Domination Defect in a Graph by Anoche, Jesica; Canoy, Sergio (2025) - If v ∈ V (G), then (G +H) − v = (G − v) +H. Otherwise, (G +H) − v = G + (H − v). To see this, consider G = C4. Keywords: |n2; γh(g

Functional

Ulam Stability of a Pexiderized Additive-quadratic Equation by Dehghanian, Mehdi; Sayyari, Yamin; Donganont, Siriluk; Park, Choonkil (2025) - ∥y∥p ) for all x, y ∈ E. Interchanging x with y in (14), we get ∥h(x+ y)− h(y − x)− 2h(x) + 2h(0)∥ ≤ ϵ ( 2∥y∥p + ( 6 + 24−p ) ∥x∥p ) (15) for all x, y ∈ E. By (12), (14) and (15), we have ∥2h(x+ y)− 2h(x)− 2h(y) + 2h(0)∥ ≤ ∥h(x+ y)− h(x− y)− 2h(y) + 2h(0)∥+ ∥h(x+ y)− h(y − x)− 2h(x) + 2h(0)∥ +∥h(x− y) + h(y − x)− 2h(0)∥ ≤ ( 8 + 24−p ) ϵ (∥x∥p + ∥y∥p) + 24−pϵ∥x− y∥p, M. Dehghanian et al. / Eur. [η (∥x∥p + ∥y∥p) + θ∥x− y∥p] for all x, y ∈ E and n ∈ N0. Keywords: functional

Eccentricity

Eccentricity-Based Energies of Non-Commuting Graph for Dihedral Groups by Romdhini, Mamika Ujianita; Nawawi, Athirah; Al-Sharqi, Faisal; Abdurahim; Hakim Maharani, Andika Ellena Saufika; Dani, Ifan Hasnan (2025) - By Lemma 1, with a = 2, b = c = d = 1, n1 = n− 1 and n2 = n, we obtain PE(ΩD2n )(µ) = (µ+ 2)n−2(µ+ 1)n−1 ( µ2 − (3n− 5)µ+ (n− 1)(n− 4) ) . Math, 18 (2) (2025), 5776 11 of 13 (d) for n − 1 ≤ i, j ≤ n + n 2 − 2, n + n 2 − 2 ≤ i, j ≤ 2n − 2, and i ̸= j, aij = 1 4 (2(n− 2) + 2(n− 2) + 2 + 2) = n− 1; (e) for i = j, j = n− 2 + n 2 + i, i = n− 2 + n 2 + j, aij = 0. Keywords: eccentricity; ωd2n

|b|

Dual Approach to the Generalization of Extended Bessel Function by Shah, Syed Ali Haider ; Hafsa; Aloqaily, Ahmad ; Rahman, Gauhar; Elmasry, Yasser ; Haque, Salma ; Mlaiki, Nabil (2025) - Researchers are currently working in area of generalized Bessel functions including k, (s, k) , (p, k), q-Bessel functions and also properties of Bessel, modified Bessel functions and generalized Bessel functions. Teodor and Hanaa [1] gave the graphical representations of generalized Bessel function, defined by: Wξ,a = x+ ∞∑ m=1 (−a)m 4m(1)m(ξ)m xm+1, x ∈ U where ( ξ = c+ d+2 2 ) /∈ {0,−1,−2, ...} and Pochhammer’s symbol defined by: (a)p = (a)(a+ 1)(a+ 2)...(a+ p− 1). Keywords: |b|

Cohomology

Cocycles in Lie Groups, Cochains and Regularity Problem by Laureano, Rosário D. (2025) - Veech obtained an important result in this direction in [10], where he establishes the C∞ Livschitz property for partially hyperbolic endomorphisms of the torus (i.e. showing that C∞ cocycles satisfying conditions relative to periodic orbits possess C∞ trivializations). From Livschitz’s foundational results to generalizations for C∞ cocycles and actions on mani- folds, this area continues to reveal profound connections between dynamical properties and cohomological invariants. Keywords: cohomology

Gµ-paracompact

On $g \mu$-Paracompact Sets by AL-Jarrah, Heyam H.; Rawshdeh, Amani; Y. Al-Zoubi, Khalid; Bani Melhem , Shefa A. (2025) - For a GTS (S, µ) the elements of µ are called µ-open sets and the collection of all µ-open sets containing s ∈ S will be denoted by µ(s). If s ∈ S, then either s ∈ E or s /∈ E. Keywords: gµ-paracompact

Ζhgk

$k$-Geodetic Hop Domination Defect in a Graph by Anoche, Jesica; Canoy, Sergio (2025) - = ⋃ v∈A NG(v) is called the open neighborhood of A and NG[A] = NG(A) ∪ A is called the closed neighborhood of A. A vertex v of G is isolated if |NG(v)| = 0. The geodetic closure of a set S ⊆ V (G), denoted by IG[S], is the union of the intervals IG[u, v], where u, v ∈ S. The set S is a geodetic set in G if IG[S] = V (G). Keywords: ζhgk

F(ζ

Second Order Differential Subordination with the Mittag-Leffler Operator by Amini, Ebrahim; Al-Omari, Shrideh; Khandaqji, Mona (2025) - Conclusion In this paper, new linear operator of analytic univalent functions was defined by the linear Mittag-Leffler and the Komatu integral operators. Let Ω be a subset of C, γ ∈ H ∩ A and µ ∈ C, (µ ̸= 0, 1). Keywords: f(ζ; βf(ζ

C[a

Stieltjes Limits in Continuous Function Spaces by Alifuddin, Moch. ; Yunus, Mahmud; Ilham Dwi Firmansyah, Mohamad; Cahya Ramdani, Indra (2025) - Given f ∈ C[a, b] and a positive real number ε, the ε-neighborhood of the function f is defined as the set: Vε(f) Math, 18 (2) (2025), 5909 10 of 17 (ii) For an operator F : A → C[a, b], the function L is called the left limit of the operator F at f0 if, for every real number ε > 0, there exists a real number δ > 0 such that for every f ∈ A ∩ {f ∈ C[a, b] : f ≺ f0} and 0 ≺ |f − f0| ≺ δe, the following holds: |F (f)− F (f0)| ≺ εe. Keywords: c[a; number; real

S)-f

Some Characterizations of $(r,s)$-Fuzzy $b$-Open Sets with Applications in Double Fuzzy Topological Spaces by Taha, Islam; Al-Mufarrij, Jawaher ; Taha, Osama (2025) - Therefore, M ∈ IG is (r, s)-F-b-open containing gθ with P(M) ≤ I𭟋∗(C𭟋∗(N , r, s), r, s). According to the assumption there is M ∈ IG that is (r, s)-F-b-open containing gθ with P(M) ≤ I𭟋∗(C𭟋∗(N , r, s), r, s). Keywords: s)-f

˜̃m

Bipolar Soft Minimal Structures by Mohammed, Ramadhan (2025) - = ϕ for each ϑ ∈ µ and ¬ϑ ∈ ¬µ. That means, a form of a bs set (λ̈, ζ̈, µ) is: (λ̈, ζ̈, µ) = {(ϑ, λ̈(ϑ), ζ̈(¬ϑ)) : ϑ ∈ µ, λ̈(ϑ) ∩ ζ̈(¬ϑ) = ϕ}. The bs set (ζ̈, λ̈, µ) is named a bs point (bsp) if there is α, β ∈ Π, ϑ ∈ µ and ¬ϑ ∈ ¬µ s. t. ζ̈(δ) = { {α}, δ = ϑ, ϕ, δ ∈ µ \ {ϑ}. Keywords: ˜̃m; ζ̈1; λ̈1; λ̈2

Θ(i

A Theoretical Exploration of Rough Approximations in Hilbert Algebras by Iampan, Aiyared; Vennila, R. ; Rajesh, Neelamegarajan ; Subasini, Ramasamy (2025) - b ∈ I ⊆ S. Since a, b ∈ S and S is an ideal of A, we have y1 ∈ S and y2 ∈ S and (y1 · (y2 · x)) · x ∈ S. Note that (y1 · (y2 · x)) · x ∈ I(y1·(y2·x))·x, thus (y1 · (y2 · x)) · x ∈ I(y1·(y2·x))·x ∩ S, that is, I(y1·(y2·x))·x ∩ S ̸= ∅. Hence, (y1 · (y2 · x)) · x ∈ Θ(I, S) and therefore, Θ(I, S) is an ideal of A. (2) Let S be an ideal of A containing I. Let x ∈ I1. Ip, y ∈ Iq, x ∈ S, and y ∈ T . Keywords: θ(i

0.6

The Effect of the Weighted Expert Factor on Time Fuzzy Soft Expert Sets by Bataihah, Anwar (2025) - The complement of time fuzzy soft expert set (F,A)wt , denoted by (F,A)w c t , is defined by (F,A)w c t = (F c, ⌉A)wt where Fwc t :⌉A → P (U) is a mapping given by Fwc t (α) = c(Fw t (⌉α)), ∀α ⊂⌉A, where c is a time fuzzy soft expert set complement. In [13], the authors discussed fuzzy parameterized fuzzy soft expert sets, which offer a membership value for each parameter in a collection of parameters and are an extension of fuzzy soft expert sets. Keywords: 0.6; u1 t3; u2 t2; u3 t1

Exp−1

Hierarchical Fixed Point Results for a Countable Family of Strict Pseudo-contractive Mappings in Hadamard Manifolds by Patel, Prashant ; Shukla, Rahul (2025) - Next we prove that the {ζn} is a Cauchy sequence in Γ and {ζn} converges to ζ ∈ Π. GζΓ → Γ is said to be a diffeomorphism for all ζ ∈ Γ, any pair of points ζ, η ∈ Γ, there exists a unique normalized geodesic Υ : Keywords: exp−1; gλi; hλi

Ω(γ

The Conformable DoubleLaplace-Sawi Transform by Abu Awwad, Raed; Al-Momani, Monther; Abughazaleh, Baha'; Jaradat, Ali; Farah, Abdulkarim (2025) - Math, 18 (2) (2025), 6034 8 of 17 The following two figures illustrate the 2D graph of the solution with respect to γ and η at α1 = α2 = 0.7, 0.9, 1. Math, 18 (2) (2025), 6034 11 of 17 The following two figures illustrate the 2D graph of the solution with respect to γ and η at α1 = α2 = 0.5, 0.8, 1. Keywords: ω(γ

Möbius

The Complete List of Solutions to M\"{o}bius's Exponential Equation by Maungchang, Rasimate ; Atiponrat, Watchareepan ; Suwansri, Tarid ; Wattanapan, Jaturon ; Suksumran, Teerapong (2025) - Möbius addition is a non-associative binary operation defined on the complex open unit disk D = {z ∈ C : |z| < 1} by a ⊕M b = a+ b 1 + ab , and Möbius’s Exponential Equation is a non-linear functional equation of the form L(a ⊕M b) = L(a)L(b), where L is a complex-valued function defined on D. In [Aequat. 2020 Mathematics Subject Classifications: 39B32, 30D05, 20N05 Key Words and Phrases: Möbius addition, Möbius’s Exponential Equation, associator function, gyrogroup, non-linear equation 1. Keywords: möbius

ℵa(s)e

Exponential Fuzzy Sets and Applications of AI-Powered Investment Decision-Making Using the Weighted Mean Method by Kaviyarasu, M.; Alqahtani, Mohammed ; Rajeshwari, M. (2025) - 0.1487 s10 0.1726 0.1353 0.1737 Table 2: exponential fuzzy membership values for each stock Weighted Mean Aggregation Using the formula: ℵEG(s) Senior Analyst (Weight = w2 = 0.3) • E3: AI Model (Weight = w3 = 0.5) where ∑3 j=1wj = 1 and ⊺ = 2. Experts assign fuzzy membership values ℵAj (s) to each stock: Investments ℵA1(s) ℵA2(s) ℵA3(s) s1 0.3 0.4 0.5 s2 0.6 0.7 0.8 s3 0.8 0.9 1.0 s4 0.5 0.6 0.7 s5 0.9 1.0 0.9 s6 0.7 0.4 0.8 s7 0.5 1.0 0.3 s8 1.0 0.3 0.2 s9 0.1 0.5 0.9 s10 0.7 1.0 0.4 Table 1: Fuzzy Membership Values for Each Stock The exponential fuzzy membership formula is ℵEAj (s) = ℵAj (s)e −2ℵAj (s) (5.1) M. Kaviyarasu, M. Rajeshwari, M. Alqahtani / Eur. Keywords: ea ∪; eac ∩; ℵa(s)e; ℵc a(s)e; −⊺ℵa(s; ∩ eb; ∩ ebc

Ð=0

Generalized Fractional Integral Extensions of Hermite-Hadamard Inequalities via Extended Mittag-Leffler Kernel by Naheed, Saima ; Rafi, Adeeba ; Rehman, Gauhar ; Ayoob, Irshad ; Mlaiki, Nabil (2025) - In this article, we look into fractional integral inequalities to Atangana-Baleanu and Prabhakar fractional calculus op- erators. Fractional integral inequalities for differential convex mappings and applications to special means and a midpoint formula. Keywords: c ℑ1; ð=0; υ(ℑ1; υ(ℑ2; ℑ2 c; ℑ2 −ℑ1; ℵð+℘; ∫ ℑ2; ♭ ℑ1

S(ξ

Solving Partial Differential Equations via the Conformable Double ARA-Sawi Transform by Al-Momani, Monther; Jaradat, Ali; Abughazaleh, Baha'; Farah, Abdulkarim (2025) - The CA-SW systematically reduces complex conformable fractional equations into solvable algebraic forms while preserving key properties like linearity and scaling. To solve conformable fractional partial differential equations, researchers have explored several techniques. Keywords: s(ξ

Αw(g

Weakly Connected Independence Number of a Graph by Merontos, Reignver; Aniversario, Imelda; Frondoza, Michael; Canoy, Sergio (2025) - Conclusion The concept of weakly connected independent set as well as the parameter weakly connected independence number were introduced and initially investigated in this study. Since C ∩NG(C) = ∅ and C and Sv and are independent sets, S is an independent set in G◦ Keywords: set; αw(g

S̃ℓ

A Fixed Point Result in a Double Control Metric Space Setting and a Fredholm Integral Equation by Aydi, Hassen; Hammouda, Hamdi; Mansour, Saber (2025) - At this moment, for t, r ∈ [0, 1], x, y ∈ ℧ = C([0, 1]) with x(r) ≤ y(r) for all r ∈ [0, 1], we estimate the difference |K (t, r, x(r), x(g(r)), x(τ1), x(τ2))−K (t, r, y(r), y(g(r)), y(τ1), y(τ2))| ≤ 1 256 ∣∣∣ |x(r)|(1+|x(r)|) 2+|x(r)| − |y(r)|(1+|y(r)|) 2+|y(r)| ∣∣∣+ 1 256 ∣∣∣∣ |x( r2 )|(1+|x( r2 )|)2+|x( r2 )| − |y( r2 )|(1+|y( r2 )|) 2+|y( r2 )| ∣∣∣∣ + 1 256 ∣∣∣ tr|x(0)|(1+|x(0)|) 2+|x(0)| − tr|y(0)|(1+|y(0)|) 2+|y(0)| ∣∣∣+ 1 256 ∣∣∣ tr|x(1)|(1+|x(1)|) Assume there are two distinct FPs, say x ̸= y ∈ ℧. Keywords: s̃ℓ

Tpf

Multifunctions between Temporal Picture Fuzzy Ideal Structures by Shi, D.L.; Abu_Shugair, M.N.; Abbas, S.E.; Ibedou, Ismail (2025) - Fuzzy sets described the positivism of an element ϱ of a universal set ℵ to a subset G ⊆ ℵ by the membership value ωG(ϱ), and posited that the negativism of that element ϱ ∈ ℵ to the set G is 1− ωG(ϱ). The values ωG(ϱ) and ϖG(ϱ) represent the positivism and negativism of each ϱ ∈ ℵ to G, respectively, with the condition that 0 ≤ ωG(ϱ) + ϖG(ϱ) ≤ 1. Keywords: tpf

I→1

Algebraic Operations on Complex Trigonometric Fuzzy Sets with Reciprocal Fractional Floor Functions by M, Palanikumar; Kausar, Nasreen; Brikena Vrioni; Hoxha, Ervin (2025) - Then the AO is determined as CTNWA⌊Υ1,Υ2, ...,Υz⌋ =  ∝ √ p −△z i→1 ⌊ p −⌊⌊λRi⌋⌋∝ ⌋ζi · e ∝ √ p−△z i→1 ⌊ p−⌊⌊λIi⌋⌋∝ ⌋ζi , △z i→1⌊⌊⌊λ℧i⌋⌋∝⌋ζi · e△ z i→1⌊⌊⌊λΛi⌋⌋∝⌋ζi  . It valid for z ≥ 3, Thus, CTNWA⌊Υ1,Υ2, ...,Υz⌋ =  ∝ √ p −△z i→1 ⌊ p −⌊⌊λRi⌋⌋∝ ⌋ζi · e ∝ √ p−△z i→1 ⌊ p−⌊⌊λIi⌋⌋∝ ⌋ζi , △z i→1⌊⌊⌊λ℧i⌋⌋∝⌋ζi · e△ z i→1⌊⌊⌊λΛi⌋⌋∝⌋ζi  . Keywords: i→1; p −; − △; ∝ √; ⌋ζi; △ z

Srl

Roughness of Bipolar Soft Sets via Ideals and its Applications by Shi, Dali; Khiamy, H.M.; Abbas, S.E.; Ibedou, Ismail (2025) - The two cases lead to SRL β+(=) ∩ =c ∈ L . Then, for all ¬ς ∈ ℵ, we have g(¬ς) ∩ =c ∈ L . Keywords: = l; = ∗; l β−(=; sr l; srl; srl β−(=; β+(=; − psr; − sr; ∗ −

Ρ̃γ

Hybrid Ideals of a Near algebra by Narasimha Swamy, P. ; Harika, Bhurgula ; Bandaru, Ravikumar ; Iampan, Aiyared (2025) - Thus, i, q, ς ∈ Y, ς(q + i) Since q, ς ∈ Y , we have qς ∈ Y . Keywords: ϱ̃γ

F2℘

Common Fixed Points of Triplet Mappings in GM-Spaces with Applications to AI Convergence and Cryptographic Consensus by Noorwali, Maha ; Hatamleh, Raed ; Khattak, Arif Mehmood; Al-Husban, Abdallah ; Khaled A. Aldwoah, Khaled ; L. Armada, Cris L; J. Hamja, Jamil ; M. Abd El-latif, Alaa (2025) - By G-completeness of X, there exists ℘ ∈ X such that {xk} converges to ℘ as k →∞. By G-completeness of X, there exists ℘ ∈ X such that {xk} converges to ℘ as k →∞. Keywords: + g(℘; f2℘; g(x(3k+1; x(3k+2; x3k

Sla

A Unified Operational and Algebraic Approach of $\Delta_h$-Hybrid Polynomials Associated with Appell Sequences by Wani, Shahid Ahmad; Alqurashi, Taghreed; Khan, Waseem Ahmad; Kus, Semra; Malge, Shilpa; Jadhav, Prakash (2025) - Laguerre polynomials, introduced by Edmond Laguerre in the 19th century, are a prominent class of orthogonal polynomials defined on [0,+∞). These include bivariate forms of “Chebyshev, Hermite, and Laguerre polynomials, frequently used in approximation theory, numerical computation, and signal analysis [1– 10]’. Keywords: sla; u h; w h; ϕ=0

Γ(κ

Abundant Solitary Solutions for the Fractional Unidirectional Wave Model Using in Oceanography, Coastal engineering, and Meteorology by Mohammed, Wael; Alshammary, M. W. ; Matouk, Ahmed E. ; Iqbal, Naveed (2025) - Exact periodic wave solutions to the coupled schrödinger-kdv equation and ds equations. Exp-function method for nonlinear wave equations. Keywords: γ(κ; ρ3z

Diag

A Natural Extension of the Banach Fixed Point Theorem in a b-Metric Space with an Orthogonal Direct Sum Structure by Albeladi, Ghadah; Omran, Saleh (2025) - Let Rd denotes the orthogonal direct sum R ⊕ R ⊕ · · · ⊕ R of d-copies of R. Let R⊕d be the direct sum set, and x, y ∈ R⊕d , x = (x1, x2, · · · , xd), y = (y1, y2, · · · , yd) by x ≾ y (respectively, xi < yi) for all i = 1, 2, · · · d. In addition, R⊕d + = {x ∈ R⊕d : xi ≥ 0, ∀i = 1, 2, · · · , d} is the set of positive elements in R⊕d , and we denote x ≿ 0̃ if xi ≥ 0 for all i = 1, 2, · · · , d, where 0̃ is the d× d zero matrix in R⊕d . Keywords: diag; δb r⊕d

A1+κ̄

A Fractional Calculus Approach to Interval-Valued Variational Programming Problems by Vivekananda Rayanki; Krishna Kummari; Ahmad, Izhar ; Gaketem, Thiti (2025) - ϕU ε (ς, ε, CFDθ• a1+ε) + (Θ̄)T (ς)hε(ς, ε, CFDθ• a1+ε(ς)) = −CFDθ• a2− { ϕL CFDθ• a1+ ε(ς) (ς, ε,CFDθ• a1+ε) + ϕU CFDθ• a1+ ε(ς) (ς, ε,CFDθ• a1+ε) +(Θ̄)T (ς)hCFDθ• a1+ ε(ς)(ς, ε, CFDθ• a1+ε(ς)) } , a2∫ a1 (Θ̄)T (ς)h(ς, ε(ς),CFDθ• a1+ε(ς))dς ≤ 0, Θ̄(ξ) ≥ 0, ς ∈ ℑ,where a1 = 0, a2 = 1. V. Rayanki et al. / Eur. [a1, a2] → R of order θ• ∈ (0, 1) is stated to be cDθ• a1+κ(ς) Keywords: + cfdθ•; a1+κ̄; a2∫ a1; cfdθ• a1; κ̄,cfdθ•; κ̄,cfdθ• a1+κ̄; ς a1; ϕu cfdθ•

Ti−1

A Boundary Value Problem with Caputo–Hadamard Fractional Derivative: Analysis and Numerical Solution by Hasan, Afrah; Murad, Shayma (2025) - Fractional differential equations: an introduction to fractional deriva- tives, fractional differential equations, to methods of their solution and some of their applications. Introduction It is an indisputable fact that fractional differential equations (FDEs) are crucial for modeling complex systems where traditional integer-order equations fall short, see [1, 2]. Keywords: t τ; ti−1; η(t

Alt(n

Menger Algebras of Alternating Terms by Changphas, Thawhat (2025) - For any i ∈ I and σ ∈ Alt(n), (1) fi(ωσ(1), ωσ(2), . . . , ωσ(n)) is an n-ary alt-term; (2) . , ϑn)) for any fi, σ ∈ Alt(n), θ1, . . Keywords: alt(n

L(sdg

Topological Approaches of Graphs using $j$-neighbourhoods and Their Applications by Abushaaban, Amal; El-Atik, Abdelfattah; Embaby, Osama (2025) - The foundation of topological graph theory, which seeks to apply topological concepts to graph structures, dates back to the foundational work of Kuratowski and others in the early twentieth century. Fifthly, comparison with existing topological graph theories: Conduct a comparative analysis of this new topological approach with existing methods in topological graph theory to identify its strengths, limitations, and potential A. Abushaaban, A. El-Atik, O. Embaby / Eur. Keywords: l(sdg; l)(k; l3 l4; ϕ,l(sdg

Aczel

Type-2 Neutrosophic Aczel-Alsina Hamy Mean Aggregation Operators for Multiple-Attribute Decision-Making Problems by Kara, Karahan; Yalçın, Galip Cihan; Simic, Vladimir; Pamucar, Dragan (2025) - [0, 1]. =⇒ 0 ≤ T̃Ñ (z) ≤ 1. ĨÑ (z) = ⟨ e − ( 1 Cτ n ∑ 1≤i1<···Keywords: aczel; alsina; e −; ñµ; z)))ξ; z)))ξ)1; ξ e; τ ∑τ; ∑τ µ=1(−; − ln(1−e

S(α1

Applications Of Differential Subordination To Certain Subclasses Of Meromorphically Multivalent Functions Associated With Generalized Hypergeometric Function by Aouf, Mohamed Kamal (2012) - If each of the functions f j ∈ Σp satisfies the following subordination condition: (1−λ)zpHp,q,s(α1) f j(z) +λzpHp,q,s(α1 + 1) f j(z) ≺ 1+A jz 1+ B jz ( j = 1,2; z ∈ U), (38) then (1−λ)zpHp,q,s(α1)G(z) +λzpHp,q,s(α1 + 1)G(z)≺ 1+ (1− 2ζ)z 1− z (z ∈ U), (39) where G(z) = If the functions f j ∈ Σp ( j = 1,2) satisfy the following inequality: Re � (1+λ)zp f j(z) + λ p zp+1 f ′ j (z) � > φ j (0≤ φ j < 1; j = 1,2; z ∈ U), (45) then Re � (1+λ)zp( f1 ∗ f2)(z) + λ p zp+1( f1 ∗ f2)(z)) ′ � > Keywords: s(α1

-regular

Simultaneous Generalizations of Regularity and Normality by Das, Ananga Kumar (2011) - Every Lindelöf θ -regular space is normal. Throughout the present paper, the closure of a set A will be denoted by A or clA and the interior by intA. A set U ⊂ X is said to be regularly open if U = intU . Keywords: -regular; set

Fix

Further Study on R-Sets Operator in Acyclic Fashion by Alwadani, Salihah (2025) - − ∥xn − x∥2 + 2 ⟨x, x − y⟩ − ∥x − y∥2 = ∥xn − y∥2 − ∥xn − x∥2 + 2 ⟨x, x − y⟩ − ⟨x − y, x − y⟩ = ∥xn − y∥2 − ∥xn − x∥2 + ∥x∥2 − ∥y∥2 (∀n ∈ N) 2 ⟨xn, x − y⟩ = ∥xn − y∥2 − ∥xn − x∥2 + ∥x∥2 − ∥y∥2 (21) (⟨xn, x − y⟩)n∈N converges as well. − T[C1 ...CN ]xnk , T[C1...CN ]xnk − T[C1 ...CN ]x 〉 + ∥xnk − x∥2 − ∥xnk − x∥2 − 2 〈 xnk − x, Keywords: fix; t[c1

Γs(g

Strong and Weak Dominating Sets of Graphs Under Some Binary Operations by Molles, Jerra Mae ; Jamil, Ferdinand; Canoy Jr, Sergio (2025) - Since S ∈ Γs(G), there exists u ∈ S for which v ≼ u. Necessarily, degG(u) To prove (i), let v ∈ V (G) \A. There exists u ∈ S for which v ≼G◦H u. Since degG◦H(v) > degG◦H(w) for all w ∈ V (Hv), u /∈ Keywords: set; γs(g

Qω1

Development of Quantum Hermite-Hadamard Type Inequalities Using Green’s Function Techniques by Khan, Muhammad Adil; Saeed, Tareq; Ali, Sajjad; Yildiz, Cetin; Kbiri Alaoui, Mohammed (2025) - − 1 2 ω2 1(ω2 − ω1) 1 + q + 1 3 ω3 1 + − qω3 1 3 + ω3 2 6 − ω1ω2 2 2 1 + q } + φ′′(ω1) { − ω2 2 ( (ω2 − ω1) 2 1 + q + q2 ) − ω1ω2(ω2 − ω1) 1 + q − ω1 2ω2 2 + 1 6 (ω2 − ω1) 3 (1 + q)(1 + q2) + 1 2 ω1(ω2 − ω1) 2 1 + q + q2 + 1 2 ω2 1(ω2 − ω1) 1 + q + 1 6 ω3 1 + qω2 1ω2 2 − qω3 1 6 + ω3 2 3 1 + q }] . − ω1ω2(ω2 − ω1) 1 + q − ω1 2ω2 2 + 1 6 (ω2 − ω1) 3 (1 + q)(1 + q2) + 1 2 ω1(ω2 − ω1) 2 1 + q + q2 + 1 2 ω2 1(ω2 − ω1) 1 + q + 1 6 ω3 1 + qω2 1ω2 2 − qω3 1 6 + ω3 2 3 1 + q . Keywords: qω1; ω2 q; ω2 ω1; ω2 −; − ω1

Gmcϱ

Improving Cardinality Rough Neighborhoods via Grills and Their Applications by Azzam, A. A. ; Aldawood, M.; Alreshidi, B. (2025) - ⊒ MCϱ(∆) for ϱ ∈ {u, ⟨u⟩, ⟨r⟩}. (11) GMCϱ (D) ⊓ GMCϱ (∆) = GMCϱ (D ⊓ ∆) for ϱ. (12) GMCϱ (D) ⊔ GMCϱ (∆) = GMCϱ (D ⊔ ∆) for ϱ. Proof. For a ϱ-NS (ℵ,Γ, ξϱ) and ∆ ⊑ ℵ, let G be a grill, then (1) GMCu (∆) ⊑ GMCr (∆) ⊓ GMCl (∆) ⊑ GMCr (∆) ⊔ GMCl (∆) ⊑ GMCi (∆). Keywords: gmcϱ; gm̃cϱ

Λ,ℓ

Differential Subordination and Superordination on p-Valent Meromorphic Functions Defined by an Extended Multiplier Transformations by El-Ashwah, Rabha; Aouf, M.K. (2010) - C3× U → C such that ϕ   1+Meiθ , 1+ k+ � ℓ λ � � ℓ λ � Meiθ , 1+ L + h � 1+ 2 � ℓ λ �� k+ � ℓ λ �2 i Meiθ � ℓ λ �2 ; z    /∈ Ω (18) whenever z ∈ U, θ ∈ R, Re � Le−iθ � ≥ (k− 1)kM for all real θ and k ≥ 1. Email addresses: r_elashwah�yahoo. Keywords: λ �; λ,ℓ; � ℓ; � �

Ln+1

Fixed Point Results in b-Fuzzy Metric Spaces with Applications to Nonlinear Fuzzy Integral Equations by Dinesh K; Dritan Gerbeti; Kastriot Zoto; B. Shoba; B. Shoba; Hawa Ibnouf Osman Ibnouf (2025) - Since Ln+1 ∈ T (Ln) and Ln+1 → K, we obtain K ∈ T (K). Hence sn → 0 as n → ∞. In particular Ln is a Cauchy sequence with respect to d. To check this directly, for m < n, d(Lm,Ln) ≤ s n−1∑ k=m d(Lk,Lk+1) = s n−1∑ k=m sk, and since sk → 0 at a geometric rate the series ∑ sk converges, showing d(Lm,Ln) → 0 as m,n → ∞. Completeness of (X, d) yields a limit K ∈ X with Ln → K. It remains to show K ∈ T (K). Keywords: ln+1

Grill

Exploring the Applications of Grill Rough Topological Structures Generated by Different Minimal Neighborhood Types by Azzam, A.A.; Alreshidi, B.; Aldawood, M. (2025) - L. Consequently, C ∈ MN r for all π1 ∈ C, and C ∈ MN l for all π1 ∈ C. I such that π1 ∈ Ci0 , i.e., MN ι ⊓ (Ci0) c /∈ L. ⇒ MN ι ⊓ (⊔i∈ICi) /∈ Keywords: grill; mn r; mn ι; ×l mn; τlmn

Extropy

Concomitant Extropy of Lai and Xie’s Extensions under Generalized Order Statistics: Properties, Estimation, and Application to Saudi Arabia Industrial Data by Mohamed S. Mohamed; S.M. EL-Arishy; A. Gamal; Faqih, Saqer A. ; Aldallal, R.A. (2025) - = ξ(Y )− δη∗[r,n,w,l]E((1− u)α+1uλ 1 g(G−1 Y (u)) )− (δη∗[r,n,w,l]) 2 2 × E((1− u)2αu2λ 1 g(G−1 Y (u)) ). 2ḠY (y) 2αG2λ Y (y) ] dy. = ξ(Y )− δη∗[r,n,w,l] ∫ ∞ 0 (1− u)α+1uλ 1 g(G−1 Y (u)) du− (δη∗[r,n,w,l]) 2 2 × ∫ ∞ 0 (1− u)2αu2λ 1 g(G−1 Y (u)) Keywords: extropy

Δ(p

Growth and Chebyshev Approximation of Entire Function Solution of Helmholtz Equation in R2 by Kumar, Devendra (2010) - = L(p,q), if p > 2; 1+ L(p,q), if p = q = 2; max(1, L(p,q)), if 3≤ p = q <∞; ∞, if p = q =∞. where 0≤ Ω(p,q)≤∞. 3. (p, q)-Growth of Solutions and Chebyshev Polynomial Approximation In this section we shall prove our main results. 1, if 3≤ p = q <∞. M(f) and M(E) are defined similarly. Keywords: δ(p

Is⋆g

On I (s*g)-Continuous Functions in Ideal Topological Spaces by Khan, Moiz ud Din; Noiri, Takashi (2011) - So x ∈ U ⊂ f −1(V ). By putting U = f −1(V ), we have x ∈ U and f (U)⊂ V . (2) ⇒ (3) Let V be an open set in Y and let f (x) ∈ V . Keywords: is⋆g

Λ,µ

Inclusion Properties for Certain Subclasses of Analytic Functions Defined by a Multiplier Transformation by Kwon, Oh Sang; Cho, Nak Eun (2010) - Let N be the class of all analytic functions h which are univalent in U and for which h(U) is convex with h(0) = 1 and and Re{h(z)} > 0 in U. For any real number s, we define the multiplier transformations I s λ of functions f ∈ A by I s λ f (z) = z + ∞∑ k=2 � k+λ 1+λ �s akzk (λ > −1). = I s λ,µ f (z) z ( f ∈ T s λ,µ(γ2; h) : z ∈ U). Keywords: λ,µ

Integrals

Selberg-type squared matrices gamma and beta integrals by Gupta, A. K.; Kabe, D. G. (2007) - = X1 − iX2 − jX3 − kX4 − `X5 −mX6 − nX7 − rX8, (13) is the HC conjugate of Y , and dY = dX1dX2 . . . Math, 1 (2008), (197-201) 199 where Σ0, p× p, is [Σ1 − Σ2 − Σ3 − Σ4 − Σ5 − Σ6 − Σ7 − Σ8Σ2Σ1 − Σ4Σ3 − Σ6Σ5Σ8 − Σ7Σ3Σ4Σ1 -Σ2 −Σ7Σ8Σ5Σ4Σ4 −Σ3Σ2Σ1 −Σ8Σ7 −Σ4Σ3Σ5Σ6Σ7Σ8Σ1 −Σ2 −Σ3 −Σ4Σ6 −Σ5 − Σ8 − Σ7Σ2Σ1Σ4Σ3Σ7 − Σ8 − Σ5Σ6Σ3 − Σ4Σ1Σ2 − Σ8Σ7Σ6 − Σ5Σ4Σ3 − Σ2Σ1], (10) where now t = 2, and we use Hamilton’s octonions, Halberstam and Ingram (1967, p. 654, equation (1)). Keywords: integrals; selberg

Epilogue

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Created: 2025-12-29