        item: #1 of 40
          id: m-1057
      author: Tom, Otobong Johnson; UDOAKA, OTOBONG G.
       title: SEMIGROUP APPROACH FOR THE SOLUTION OF BOUNDARY LAYER EQUATION WITH SINC FUNCTION TERM
        date: 2025
       words: 5355
      flesch: 74
     summary: A T t s f s S s ds f S dt       Using the properties of semigroups [3, 19],    AT t T t A , we write du Au f S dt    This implies that u is differentiable with the stated regularity[6]. 1 2 1 2 1 2 1 20 0 0 t u t u t T t u u T t s f s f s S s S s ds       
    keywords: t t;  ;  
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        item: #2 of 40
          id: m-1071
      author: Mj, Jyothi.; shivashankara, k.
       title: On SiO4 Molecular Topological Characterization of Chemical Structures
        date: 2025
       words: 8826
      flesch: 65
     summary: bond partition from Table 2, in the formula of forgotten topological �[�����] �� + � �[�����] ����~���� + � �[ ����~���� + (3�� + � + 2� − 5)��� + 2�3�� − 2(2� + By taking the first derivative of the polynomial in Theorem 2.25 at y forgotten topological index of chain of SiO4 SCqp as follows: Let p be odd and p < q. For p >1 and p = q, the symmetric division degree index of SC� � is2(3�� − 3� + 4) + ������������ � Theorem 2.15.
    keywords: + �; sc �; ~ �; ∈ �; − �; � +; � ∈; � −; � �
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        item: #3 of 40
          id: m-1112
      author: Georgallides, Markos
       title: THE POLYNOMIALS [ n.. Knots–FIGURES ] EDGE - POINTS VIBRATION & M-GEOMETRY
        date: 2025
       words: 60619
      flesch: 73
     summary: Cave–Spin-�̅� of PNS Space is �̅� = r m v and is the first Monad occupying 4-Spaces , i.e. From Number n , of the Equilibrium number of masses m 𝐧 in a System. From Momentum �̅� = r m v = m �̆� r² = ± [ 𝛑.𝐫𝟐 𝟐 ].
    keywords: anti; august; caves; charge �; circle; constant; e =; energy; energy e; energy 𝐄; force; g ≡; gravity; https://ijojournals.com/index.php/m/index; ijo; international; issn; issue; journal; material; mathematics; mechanism; mfmf; momentum �; motion; origination; p =; particles; pns; point; r =; space; spin �; system; unit; vector �; velocity �; volume; wave; | =; | �; ̅ �; ̆ �; ≡ |; ≡ ≡; ≡ �; ≡ 𝐀𝐁̅̅; � =; � |; � ̅; � ̆; � ←; � ≡; � �; � 𝐅; 𝐀 𝚽; 𝐄 𝐅; 𝐄 𝐊; 𝐄 𝐏; 𝐄 𝐑; 𝐄 𝐓; 𝐄 𝐔; 𝐅 𝐌; 𝐉𝟑.; 𝐋 𝐏
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        item: #4 of 40
          id: m-1141
      author: Tom, Otobong Johnson; Udoaka, Otobong G.; Udofia, E. S.
       title: ON STABILITY IN SEPARATIVE SEMIGROUP
        date: 2025
       words: 3166
      flesch: 68
     summary: A semigroup S is called separative if and only if the following two conditions hold for all a, b ∈ S: � a2 = ab and ba = b2 together imply a = b, and � a2 = ba and ab = b2 together imply a = b. The reader can also see [15] De�nition 3.2 (Qusi-separative). This result elevates stability from a supplementary condition to a built-in feature of separative semigroups, o�ering a uni�ed perspective that strengthens the foundations of semigroup theory and deepens its structural coherence.
    keywords: semigroup; separative; stability
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        item: #5 of 40
          id: m-1151
      author: Obi, Boniface Inalu; Esekhaigbe, Edwin; Uka, Uchenna Awucha
       title: Numerical Computation of Reactive Flow of Third Grade Fluid With Heat Generation
        date: 2025
       words: 2661
      flesch: 57
     summary: Issue 09 || September, 2025 || “Numerical Computation of Reactive Flow of Third Grade Fluid With Heat Generation Numerical Computation of Reactive Flow of Third Grade Fluid With Heat Generation *1 Boniface Inalu Obi,2 Edwin Esekhaigbe, 3Uchenna Awucha Uka 1Department of Mathematics, Imo State University, Owerri, Nigeria 2Mathematics and Computer Science Department, University of Africa, Bayelsa State, Nigeria 3Basic Science Department, School of Science and Technology, Babcock University, Ogun State, Nigeria Corresponding author *1 Boniface Inalu Obi, Abstract Computation of reactive flow of third grade fluid in cylindrical pipe with heat generation is considered. [10] examined the stability properties of third grade fluids.
    keywords: flow; fluid; grade; issue
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        item: #6 of 40
          id: m-1152
      author: Tom, Otobong Johnson; Udoaka, Otobong G.
       title: Stability in Semigroups of Bounded Linear Operators: Bridging Algebraic and Analytic Notions
        date: 2025
       words: 5026
      flesch: 70
     summary: We further provide precise spectral conditions under which KW-stability aligns with analytic stability notions�strong, asymptotic, exponential, and uniform�thereby unifying algebraic semigroup stability with spectral/operator-theoretic stability. This condition enforces the collapse of Green's relations�fundamental equivalence rela- tions describing semigroup structure�so that D = J = L = R. Stability in this sense IJO - INTERNATIONAL JOURNAL OF MATHEMATICS (ISSN: 2992-4421 )
    keywords: operator; semigroup; stability
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        item: #7 of 40
          id: m-1153
      author: Olokuntoye, Bolanle Adeola
       title: A Mathematical Model on Cholera Outbreak with Vaccination
        date: 2025
       words: 3516
      flesch: 49
     summary: Vaccination has increasingly been incorporated into cholera models. This innovation highlighted the role of aquatic environments in sustaining cholera transmission and explained the persistence of outbreaks beyond simple person-to-person dynamics.
    keywords: cholera; vaccination
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        item: #8 of 40
          id: m-1155
      author: Sylvester, Thomas, Henry; Sunday, Udofia, Ekere; Dominic, Akpan, Ubong; Joy Ijeoma, Uwakwe,
       title: CAPUTO-FABRIZIO FRACTIONAL DRIVATIVES OF AGE-STRUCTURED DIPPTHERIA INFECTION MODEL WITH LAPLACE ADOMIAN DECOMPOSITION ANALYSIS
        date: 2025
       words: 13700
      flesch: 45
     summary: Issue 09 || September, 2025 || “CAPUTO-FABRIZIO FRACTIONAL DRIVATIVES OF AGE-STRUCTURED DIPPTHERIA INFECTION MODEL WITH LAPLACE ADOMIAN DECOMPOSITION ANALYSIS �� − ��������� ������������ ���� ���� �� �� − ��������� ������������ ���� ���� �� �� − ����������� �������� ��� �� �� − ����������� �������� ��� �� � − ������� �������� � − �������� ���� ���� �� �� �� � − ��� ������ ����ℎ ���� �� ℎ����� ��� − ������������ ���� �� �� ��� − ������������ ���� �� �� � − ���� �� ����������� �� − ��������� ���� (��� ������� ������� ) ��� �� �� − ��������� ���� (��� ������� ������� ) ��� �� � − ����ℎ ��� �� ��������� � − ������� ����ℎ ���� ��(�) = ��(���� + ����) �� − �� ��(�) = ��(���� + ����) �� − �� 2.4 MODEL EQUATIONS IJO JOURNALS Volume 08 − Detected infectious humansat time �(Asymptomatic and symptomatic) population through testing, 2.3 PARAMETERS �� − �������� ���� ���� ������� �� ��, Asymptomatic infection population �� − �������� ���� ����� ������� �� ��, symptomatic infection population � − �������� �� ��� ��������� �ℎ�� ��� ��, Asymptomatic 1 − � − �������� �� ��� ��������� �ℎ�� ��� ��, symptomatic IJO JOURNALS Volume 08
    keywords: time �; | �; ℒ �; ℝ �; − �; � =; � ℎ; � ℑ; � ∈; � −; � �
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        item: #9 of 40
          id: m-191
      author: Nurhayati, Lina; Gunawan, Hendra; Gunawan, Iwan; Hermawan, Haryono Edi
       title: BOUNDEDNESS OF GENERALLY FRACTIONAL INTEGRAL OPERATOR ON GENERAL MORREY SPACE
        date: 2019
       words: 3407
      flesch: 66
     summary: In this study I will discuss the limits of fractional integral operators in the homogeneous and nonhomogeneous Lebesgue space, the Morrey space and the general Morrey space. Volume 02 |Issue 07 | July 2019 www.ijojournals.com 3 Next, for Based on (5) obtained, Z |Mµf(x)|pdµ(x)B(a,r So, got it ||f|| Lp,φ(µ)Maximum operator limitation Mµ above is needed in proving the fractional integral operators and fractional integral operators commonly from the Morrey space are generally Lp, φ to the Morrey space is generally for 1 <p <q <∞ with 5].
    keywords: space
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        item: #10 of 40
          id: m-274
      author: Linus, Okafor Uchenwa; Oladejo, M.O.; Uwa, C.O.; A.T, Jighjigh,; Chineyob, D.T.
       title: DISTINCTION BETWEEN SPEPECTRAL ANALYSIS AND HARMONIC ANALYSIS IN TIME SERIES ANALYSIS: EXPERIENCE FROM THE NUMBER CRUNCHER STATISTICAL SYSTEM (NCSS) SOFTWARE.
        date: 2020
       words: 3097
      flesch: 66
     summary: In Harmonic analysis, one uses the frequencies identified from spectral analysis to form a model and harmonic analysis gives about eight different specific results as shown through Table 3 to Table 10.Fourier analysis is part of harmonic analysis, but in literature, most authors’ mistake spectral analysis for harmonic analysis and most statistical software’s also fall into the same misconception, but the use of the Number Cruncher Statistical System(NCSS), illustrates the role of either spectral analysis or harmonic analysis. Keywords: Harmonic analysis, spectral analysis, period, wavelength, model, forecasting.
    keywords: analysis; harmonic; ─ lag; ─ ─; � �
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        item: #11 of 40
          id: m-293
      author: Kazmierczak, A
       title: The Great Gun Grab
        date: 2020
       words: 3059
      flesch: 42
     summary: Chapman et al. 2006. Irvin et al. 2014.
    keywords: et al; g =; guns; https://en.wikipedia.org/wiki/gun_control https://en.wikipedia.org/wiki/gun_control
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        item: #12 of 40
          id: m-339
      author: Kazmierczak, A
       title: Modeling and Analysis of the Interaction of Neutral and Drug Populations: A Competing Species Model
        date: 2020
       words: 5665
      flesch: 62
     summary: A hierarchy of drug use in adolescence: behavioral and attitudinal correlates of substantial drug use. The involvement of tobacco in alcoholism and illicit drug use.
    keywords: abuse; drug; drug abuse; drug use; editor; equilibrium; health; institute; journal; national; new; population; research
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        item: #13 of 40
          id: m-347
      author: Kazmierczak, A
       title: Modeling and Analysis of the Interaction of Neutral Populations and Violent Cop Populations: A Competing Species Model
        date: 2020
       words: 6276
      flesch: 61
     summary: Abstract The rise of police violence in the United States has brought concern, debate, and contention to the modern world. Police violence is national and is no longer concentrated in a particular location.
    keywords: amnesty; brutality; equilibrium; international; journal; july; june; news; october; police; police violence; policing; rights; violence
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        item: #14 of 40
          id: m-348
      author: Kazmierczak, A
       title: Modeling and Analysis of the Interaction of Neutral and Protester Populations: A Competing Species Model
        date: 2020
       words: 2080
      flesch: 47
     summary: │2/(1+2P)-2P/(1+2N)^2-N -2/(1+2P)^2-2N/(1+2N) │ J = │ │ │ -6P/(1+3N)^2-2P/(1+2N)^2 2/(1+3N)-2N/(1+2N)-P │ 2.2 Equilibrium Points Using Maple CAS, on (3) and (4) weobtained the following real valued equilibrium points: {N = 0., P = 0.}, {N = 0., P = 4.}, {N = 4., P = 0.}, {N = .4301871556, P = .8213492010}, {N = -.4311081397, P = -1.121275136}, {N = -.4346164212, P = .1299378971}, {N = -3.952306486, P = -2.658090053} 2.3Analyzing equilibrium points for stability In our framework, we let N represent the neutral population.
    keywords: equilibrium; population
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        item: #15 of 40
          id: m-362
      author: Siregar N, Hasratuddin; Fauzi, KMS. M. Amin; Siregar, Nurhasanah
       title: GEOMETRY LEARNING BASED ON COGNITIVE CONFLICT IN THE DEPARTMENT OF MATHEMATICS
        date: 2020
       words: 3886
      flesch: 56
     summary: Geometry is one of the compulsory courses for students majoring in mathematics at the State University of Medan. Cognitive conflict occurs when students become aware of a mismatch between what is on their mind and information from outside.
    keywords: cognitive; conflict; geometry; intelligence; learning; mathematics; people; students
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        item: #16 of 40
          id: m-386
      author: Makky, Mosaed Magmoud
       title: Effectiveness similar transposed set of polynomials of two complex variables in different regions.
        date: 2020
       words: 8834
      flesch: 89
     summary: k k M p r               from which, we obtain 11 (1) (1) , 1 2 , 7 7 4 4 1 1 1 1 sup [ ; ] sup , m nm n m n m n m n m n Lim M u Lim k k M P r r r r          k s t p z w p z w p p z w        .
    keywords: h k; k k; m p; n m
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        item: #17 of 40
          id: m-392
      author: ALsawi, Khalil Mostafa; El-Saeiti, Intesar N.; Shamia, Gebriel M.
       title: Adequacy of H-Likelihood Estimation Method for Unbalanced Clustered Counting Data Models.
        date: 2021
       words: 3314
      flesch: 50
     summary: Next table is Table(2); for the simulated sample of size (5,10,50) observations and 3, 10, and 50 clusters; where the actual value is equal to 0.2 for the parameter �� , and the value for the �� parameter is equal to zero because there is no X2 value, it is used only to calculate the power and the probability of type-I error rate” Table (2): the estimate parameters Cluster Observations Unbalanc ed Balanced ��� ��� ��� ��� K=3 n=5 n=10 n=50 0.2033534 0.1947158 0.2008493 0.003756905 -0.00445098 0.004040149 0.2041509 0.2028573 0.2045826 -0.00518115 0.01137586 0.00065012 K=10 n=5 n=10 n=50 0.1994582 0.1980559 0.2008564 -0.00049512 estimate values (���) 0.188 0.19 0.192 0.194 0.196 0.198 0.2 0.202 0.204 0.206 n=5 n=10n=50 n=5 n=10n=50 n=5 n=10n=50 Balanced unbalanced -0.01 -0.005 0 0.005 0.01 0.015 n=5 n=10 n=50 n=5 n=10 n=50 n=5 n=10 n=50 Balancd Unbalanced IJO - INTERNATIONAL JOURNAL OF MATHEMATICS Volume 3| Issue 12|
    keywords: data; linear; models; n=5; � �
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        item: #18 of 40
          id: m-411
      author: Hamaden, Ghazala Ahmad
       title: Physiological responses of Solanum nigrum L. Species to the heavy crude oil
        date: 2021
       words: 5823
      flesch: 62
     summary: Although exactly how crude oil originated is not established, it is generally agreed that crude oil is derived from the remains of animals and plants that lived in marine water millions of years ago, types of crude oil: Based on the density crude oil is divided in to the following groups: Light crude oil and heavy crude oil 1.1. Key words: Solanum nigrum L. black nightshade, heavy crude oil, phytoremediation.
    keywords: black; dilutions; germination; growth; journal; nightshade; nigrum; oil; plant; seedling; soil; solanum
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        item: #19 of 40
          id: m-530
      author: Pandey, Himanshu; Rao, Arun Kumar
       title: BAYESIAN ESTIMATION OF SHAPE PARAMETER OF TOPP-LEONE DAGUM DISTRIBUTION
        date: 2021
       words: 4273
      flesch: 93
     summary:  212 2 1 2 1 1 1 1 n a i i E n d n d log x                           .                
    keywords:  
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        item: #20 of 40
          id: m-541
      author: Hima, Lina Rihatul; Sari, Lilin Nur Indah; *, Samijo
       title: PROCRASTINATION OF STUDENTS IN WORKING MATHEMATICS
        date: 2021
       words: 3689
      flesch: 47
     summary: Likewise, what happened in high school, in this study the researchers focused on class XI high school students. The delay in collecting the assignments indicated that there was procrastination in class XI high school students.
    keywords: assignments; female; math; procrastination; students
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        item: #21 of 40
          id: m-591
      author: Hamed, Abdulaziz Babiker Mohamed; Bawa, Bulama Adamu
       title: Mathematical modeling of Climate change and Desertification: A case study of Yobe State, Nigeria.
        date: 2022
       words: 7232
      flesch: 41
     summary: ��(����������)� �������√������(�������) Where � is the slope. Hence the depth of the river is ℎ = � − � it is based on the principle conservation of mass for the substrate, and may be written as (1 − �) �� �� + ∇. � = �� IJO - INTERNATIONAL JOURNAL OF MATHEMATICS Volume 5 | Issue 09 | September 2022 | https://www.ijojournals.com/index.php/m/index 16 3.3.2 St Venant equation The Navier-Stokes equations is also written in this case of two-dimensional flow ��+�� = 0 ��(����������)� ����������(�������)
    keywords: africa; change; climate; desertification; https://www.ijojournals.com/index.php/m/index; ijo; international; issue; journal; land; mathematics; mathematics volume; september; volume; − �; � �
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        item: #22 of 40
          id: m-598
      author: Hamed, Abdulaziz Babiker Mohamed; Abu Aasha, Younis Ahamed.
       title: Using Energy Conservation Concept and Basic Mathematical Modeling Techniques to Study the Effect of Greenhouses Gases to Earth's Climate System.
        date: 2022
       words: 4230
      flesch: 49
     summary: According to conservation of the energy and thermal equilibrium state, the incoming energy equal to out coming energy and Stefan Boltzmann Law, such that E�� = E���, Thus T = � �(���) ��� � � � ≈ 282.9K Interpretation: The value of β = 0.66 gives a climate model that correctly predicts the current global average temperature T ≈ 282.9K, which equivalent to 9.64 degrees Celsius, this gives reasonable approximate value to the Earth's surface temperature. At thermal equilibrium, the incoming energy (temperature) must equal to outgoing energy and with use Stefan Boltzmann Law, such that ��� = ���� Therefore the mathematical model represent the following equation ���� = 4������ ⇒ � = 4��� TO solve the equation for T, thus � = ( � �� ) � � Where � = 5.67 × 10��and � = 1376.6 The value of � = ( ����.
    keywords: climate; earth; energy; model; surface; system; temperature; � =; � �
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        item: #23 of 40
          id: m-605
      author: Fauzi, M. Amin; Siregar, Hasratuddin; Siregar, Budi Halomoan; Sari, Dwi Novita
       title: A Problems Solving and Thinking Critical Ability Student Through Realistic Approach Based on Problem Non-routine by Blended Learning in the Department Mathematics, Faculty Mathematics and Natural Science, Medan State University
        date: 2022
       words: 4740
      flesch: 54
     summary: And, by chart could seen that ability solving problem student who was given learning with based realistic approach problem non-routine more than every group on learning normal online. So that could concluded that no there is interaction Among learning with ability beginning to ability solution problem mathematical student.
    keywords: ability; class; learning; non; problem; routine; student; thinking
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        item: #24 of 40
          id: m-613
      author: Siregar N, Hasratuddin; Rambe, Titin Rahmayanti; Rola, Fasti; Pratiwi, Siti Habsari; Pratama, Anggili; Dongoran, Jhohas
       title: LEARNING PROCESS CONTROL MTsN 1 MEDAN
        date: 2023
       words: 2500
      flesch: 56
     summary: ���(�)��(� − ��). ���(�)��(� − ��) a)
    keywords: english; mathematics; value; � =; � �
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        item: #25 of 40
          id: m-616
      author: Siregar N, Hasratuddin; Hayati, Rahmi; Karim, Asrul; *, Facrurazi; *, Marzuki; Marianus, Sumarlin Mangandar
       title: CONTROL OF THE LEARNING PROCESS AT DISTRICT 5 JULY ELEMENTARY SCHOOL, BIREUEN
        date: 2023
       words: 1948
      flesch: 47
     summary: | https://www.ijojournals.com/index.php/m/index 10  Largest predicted value from each Indonesian language value to each Mathematica value:����� = 3,652 + 0,568���  The magnitude of the predictive value assigned to each English-language numeric by the mathematical values is as follows:����� = 1,343 + 0,841����  Each value of natural science and mathematics is accompanied by a significant predictive value. The highest percentage, as calculated above, is for the subject of mathematics 94.85% ( ��.������� ��.����� )) while the lowest is for the subject of Indonesian language study (67.49%)( �.��������� �.������� ).
    keywords: analysis; data; indonesian; mathematics; process; � �
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        item: #26 of 40
          id: m-618
      author: LAWAL, Ruth Folake; OLUWOLE, Deborah Oyeronke; OLANIYI-OJOAWO, Inioluwa Damilola
       title: Predicting Students’ Study Habits through Attitude to Mathematical Mistakes in Alimosho Local Government Area, Lagos State.
        date: 2022
       words: 3379
      flesch: 38
     summary: As well, study habits was observed to increase significantly with students’ advancement in class level and a positive attitude towards mathematical mistakes. Keywords: Study habits, attitude, mistakes, mathematics IJO - INTERNATIONAL JOURNAL OF MATHEMATICS Volume 5 | Issue 12 | December 2022 | https://www.ijojournals.com/index.php/m/index 1 mailto:femifolawal256@gmail.com mailto:deboronke@yahoo.com mailto:deboronke65@gmail.com mailto:inioluwaojoawo@gmail.com Introduction Individuals are daily faced with circumstances, concepts and situations to which a person mustrespond positively or negatively.
    keywords: attitude; class; habits; journal; mathematics; mistakes; students; study
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        item: #27 of 40
          id: m-684
      author: *, Rosita; *, Hasratuddin; Aziz, Tian Abdul
       title: Ability Solving Problem And Think Critical Mathematical Through Problem based Flipped classroom Help Videos
        date: 2023
       words: 3753
      flesch: 50
     summary: A question become problem student if his students This not own method the solution. Which state that flipped classroom learning model is effective in order to increase comprehension skills concepts and solving student problems.
    keywords: ability; class; classroom; control; learning; mathematics; model; problem; solving; students
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        item: #28 of 40
          id: m-750
      author: Siregar N, Hasratuddin; Fauzi, Amin; Siregar, Nurhasanah
       title: The Students' Mathematical Creative Thinking Ability Strategy Mathematical Habits Of Mind Based
        date: 2023
       words: 5883
      flesch: 54
     summary: In accordance with objective study This that is For analyze ability think creative given student _ learning geometry with based Mathematical Habits of Mind (MHM) strategy problem , then following describe the process and results . So so that can concluded that there is difference ability think creative given student learning MHM strategy geometry with given students learning normal .
    keywords: ability; facet; learning; lecturer; mathematics; mhm; question; strategy; student; think; thinking
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        item: #29 of 40
          id: m-757
      author: Maulida, Rizki; Hutasuhut, Riska Fadhilah; Tindaon, Juwita; Restella, Rika; *, Hasratuddin
       title: LEARNING PROCESS ANALYSIS MIS GUPPI PADANG HILIR (Using a Multivariate Analysis Approach)
        date: 2023
       words: 2305
      flesch: 59
     summary: Process data is seen in 2019 -2020 with the results of the highest correlation value is 8.265306, namely in Indonesian and mathematics subjects. The research conducted by Antoro found that a larger portion of student learning was experienced by students who were in fullday class learning, students who studied with a larger portion had a high average score.
    keywords: correlation; data; learning; science; subjects
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        item: #30 of 40
          id: m-769
      author: John, Michael N.; Otobong. G, Udoaka,
       title: Algebraic and Topological Analysis of Enveloping Semigroups in Transformation Groups: Proximal Equivalence and Homomorphic Image
        date: 2023
       words: 4787
      flesch: 44
     summary: In the latter part, the study extends to the analysis of homomorphic images of transformation groups through their enveloping semigroups. The study of transformation groups with compact Hausdorff phase spaces has significant implications in various mathematical and applied fields.
    keywords: enveloping; group; issue; journal; transformation; volume
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        item: #31 of 40
          id: m-782
      author: John, Michael N.; Okeke, Stephen I.; Nwala, Boniface O.; G., Udoaka Otobong.
       title: Para-G Relations and Hirsch Length in Residually Nilpotent Groups
        date: 2024
       words: 4401
      flesch: 55
     summary: Therefore, �� is the inverse limit of polycyclic groups, and it is locally polycyclic. Nilpotent groups in cryptographic key exchange protocol for N≥ 1.
    keywords: group; issue; john; journal; volume
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        item: #32 of 40
          id: m-792
      author: James, Etim, Uduak; John, Eno; Lawson, Dr. Tombotamunoa W. J.; Monday, Udo Ukemeobong
       title: ADVANCEMENTS IN LINEAR MULTI-STEP METHOD FOR SOLVING THIRD ORDER ORDINARY DIFFERENTIAL EQUATIONS
        date: 2024
       words: 9859
      flesch: 49
     summary: Etim, Uduak James* https://ijojournals.com/index.php/index Volume 07 Issue 01 || January., 2024 || ℎ(�) = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ ����������������������������������������������������������������������������� ����������������������������������������������������������������� ������������������������������������������������������������������������ ����������� �������������������������������������������������������������� ����������������������������� ���������������������������������� ���������������� ������������������������������ ������������������������� ���������������������������������������������� ���������������� �������������������������������� �������������������������������� ���������� ����������������� ��������������������� ����� ������������������������������ ���������������� ������������������������ ���� ��������������������� ���������������� ���������������������������� ������������������������������������������� ������������� ��������������� ������������������������� ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡ ��������������������������������������������������� ������������� ������������������������������������������������� �������������������������������������������������� �������������������������������������������������������������������������� ���������������������������������� �������������������������������������� ������������������������� ���������������������������� ������������������������������������������������������������������� �������������������������������������� ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ . = 120[�� − 2�� + 2� − 1] �� + 56�� + 126�� + 56� + 1 (3.8) byDeMoiveries’s theorem �� = ���� = ����� + ������ where ����� is the real part of ���� and ����� is the imaginary part of����, but here we will replace �� with �� .
    keywords: + �; ℎ �; − �; � −; � �
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        item: #33 of 40
          id: m-806
      author: Akpan, I.U. Udo-; Chukwuchekwa, J. U.
       title: ON A-TWO-PARAMETER DYNAMIC BUCKLING OF A VISCOUSLY DAMPED BUT CLAMPED COLUMN STRESSED BY A STEP LOAD
        date: 2024
       words: 21797
      flesch: 47
     summary: where, �� = ����� � ��� + �� � � � + ������ �� ��� ��� � � �� (6.54c) �� = �������� � − �������� �� � � ��� ��� ��� � � ��� (6.54d) �� = ���� ��� �� − ������� �� � � ��� ��� ����� � � ���� (6.54e) where, ��(0) = �����, �� = ��� ��� + �� ����� � � ��� (6.54f) ��(0) = �����, �� = 9 � � �� + � ��� � � ��� � (6.54g) ��(0) = ������, ��� = � ��� − �� ����� � � ���� (6.54h) https://zenodo.org/doi/10.5281/zenodo.10726874 IJO JOURNALS Volume 07 | Issue 02 | February 2024 | https://ijojournals.com/index.php/m/index 14 IJO - INTERNATIONAL JOURNAL OF MATHEMATICS (ISSN: 2992-4421 ) I.U. Udo-Akpan1 * https://ijojournals.com/ Volume 07 Issue 02 || February, 2024 || ON A-TWO-PARAMETER DYNAMIC BUCKLING OF A VISCOUSLY DAMPED BUT CLAMPED COLUMN STRESSED BY A STEP LOAD On solving (6.54a,b), we get U�� (��) = �� cos ����̂ + �� sin ����̂ + �� ��� ��� ��� � � �� + �� ��� ���� ��� � � ��� + �� ��� ���� ��� � � ��� (6.55a) ��(0) = ������� ����� ������ = � (5.9a)
    keywords: + �; u �; ̂ �; − �; � +; � cos; � ̂; � −; � �
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        item: #34 of 40
          id: m-815
      author: K. K, Venuprasad; Shivashankara, Prof. K.; D. S, Dhananjaiah; P, Prakasha.
       title: Mathematical study of MHD Convective flow with chemical reaction through a porous medium in a vertical wavy channel
        date: 2024
       words: 4174
      flesch: 49
     summary: Venuprasad K. K.1 * https://ijojournals.com/ Volume 07 Issue 03 || March, 2024 || Mathematical study of MHD Convective flow with chemical reaction through a porous medium in a vertical wavy channel Mathematical study of MHD Convective flow with chemical reaction through a porous medium in a vertical wavy channel Venuprasad K. K.1, Prof. K. Shivashankara2, Dhananjaiah D. S3, Prakasha. Venuprasad K. K.1 * https://ijojournals.com/ Volume 07 Issue 03 || March, 2024 || Mathematical study of MHD Convective flow with chemical reaction through a porous medium in a vertical wavy channel to an external magnetic field.
    keywords: chemical; flow; ijo; issue; march; mhd; temperature; volume;  
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        item: #35 of 40
          id: m-817
      author: D.S, Dhananjaiah; Shivashankara, Prof. K.; K. K, Venuprasad; P, Prakasha.
       title: A Mathematical analysis of oscillatory free convection in a vertical wavy channel with Chemical reaction
        date: 2024
       words: 3715
      flesch: 46
     summary: The study of heat transfers and mixed convection flow in enclosures of various shapes has received attention [6] O.D. Makinde, Free convection flow with thermal radiation and mass transfer past a moving vertical porous plate, Int.
    keywords: chemical; convection; flow; heat; issue; mass; reaction; transfer;  
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        item: #36 of 40
          id: m-832
      author: P, Prakasha.; K. Shivashankara, Prof.; K. K, Venuprasad; D. S, Dhananjaiah
       title: Mathematical Analysis of Effect of Viscous dissipation on Transient MHD convective Heat transfer through a porous medium in a vertical channel
        date: 2024
       words: 6118
      flesch: 69
     summary: In recent years, a great deal of interest has been generated in the area of boundary layer flow and heat transfer of a fluid over a stretching sheet In view of its numerous and wide range of applications in various fields such as polymer processing industry in particular manufacturing IJO JOURNALS Volume 07 P1* https://ijojournals.com/ Volume 07 Issue 04 || April, 2024 || Mathematical Analysis of Effect of Viscous dissipation on Transient MHD convective Heat transfer through a porous medium in a vertical channel which in the non- dimensional form reduces to 1 2 ,11,10,01,00 2 )](([ )(                yyyyyyyyy xxyy OEcEc a U      and the corresponding expressions are )()( 2 5431  OdEcddy  )()( 2 8761  OdEcddy  The local rate of heat transfer coefficient( Nusselt number Nu) on the walls has been calculated using the formula 1)( 1      y wm y Nu   Where    1 1 5.0 dym  and the corresponding expressions are )( )( )(, )( )( )( 6510 987 1 654 321 1 mEcmm mmEcm uN mmEcm mEcmm uN yy            5.
    keywords: april; dissipation; effect; flow; heat; issue; transfer; volume; π/4;  
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        item: #37 of 40
          id: m-886
      author: THIRUNIRAISELVI, DR. N.; GOPALAN, DR. M.A.
       title: Techniques to solve Diophantine Equation of Degree Ten with Six Unknowns
        date: 2024
       words: 1663
      flesch: 63
     summary: [1] has been noticed and the authors have presented only few sets of integer solutions. Substitution strategy and factorization method are applied successfully to obtain different choices of integer solutions to the considered equation.
    keywords: issue; volume
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        item: #38 of 40
          id: m-904
      author: Chow, Sengchu
       title: Algebraic Solution to Simultaneous Linear First-Order Non-Homogeneous Differential Equations with Constant Coefficients
        date: 2024
       words: 3093
      flesch: 63
     summary: − 𝑎0𝑛1𝑥 − 𝑎0𝑛0 = (𝑏0𝑚1 − 𝑎0𝑛1)𝑥 + (𝑏0𝑚0 − 𝑎0𝑛0) (30) 𝑏0𝑓 − 𝑎0𝑔 = (−1)(6) − (3)(−2) = −6 + 6 = 0 𝛼 = (2)(−1) − (3)(5) = −17 So, 𝑦′(𝑥)
    keywords: − 𝐶; 𝐶 𝐾; 𝐾 −𝐾
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        item: #39 of 40
          id: m-917
      author: Idochi, Okenwe; Udo, Osuagwu, Chidimma
       title: PERFORMANCE EVALUATION OF CANONICAL CORRELATION ANALYSIS AND REDUNDANCY ANALYSISUSING GAUSSIAN, GAMMA, EXPONENTIAL AND BETA DISTRIBUTED DATA
        date: 2024
       words: 4703
      flesch: 45
     summary: Makino's study introduced a CA formulation based on canonical correlation analysis (CCA), where correlations within and between row/column categories in a reduced dimensional space can be expressed through canonical variables. Keywords: Canonical correlation analysis,Redundancy analysis, Gaussian, Gamma, Exponential, Beta,Performance evaluation, Simulated data.
    keywords: analysis; correlation; distribution; exponential; gamma; issue; variables
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        item: #40 of 40
          id: m-930
      author: Ohaegbulem, Emmanuel Uchenna; Obi, Dr. Boniface Inalu
       title: Analytical Study of Incompressible MHD Non-Newtonian Fluid In Cylindrical Pipe With Isothermal Wall and Temperature-Dependent Viscosity
        date: 2024
       words: 3811
      flesch: 61
     summary: Massoudi and Christie [7] dealt with the effcts of variable viscosity and viscous dissipation on the flow of third grade fluid. The boundary layer equations of third grade fluid was treated by Pakdemirli
    keywords: dr dr; r r;  
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