item: #1 of 481 id: cubo-1137 author: Abbas, Saïd; Benchohra, Mouffak; Lazreg, Jamal-Eddine; N’Guérékata, Gaston M. title: Hilfer and Hadamard functional random fractional differential inclusions date: 2017-03-01 words: 7891 flesch: 80 summary: The Caputo fractional derivative of order r ∈ (0, 1] of a function w ∈ AC(I) is defined by (cDr0w)(t) = ! ∈ [0, 1], γ = α + β − αβ, and w ∈ L1(I). keywords: a.e; abbas; benchohra; continuous; convex; cubo; definition; derivative; differential; equations; existence; exists; f(t; following; fractional; function; g(t; generalized; hadamard; hilfer; hyers; inclusions; integral; math; measurable; multivalued; n(w)u; n’guérékata; operator; order; point; problem; random; rassias; set; solution; space; stability; stable; theorem; tγ−1; u(t; u(w; ulam; v(t; w)(t; γ(1; γ(α; γ(γ; φ(w cache: cubo-1137.pdf plain text: cubo-1137.txt item: #2 of 481 id: cubo-1139 author: Rosas, E.; Carpintero, C.; Salas, M.; Sanabria, J.; Vásquez, L. title: Almost ω-continuous functions defined by ω-open sets due to Arhangel’ski ̆ı date: 2017-03-01 words: 7168 flesch: 88 summary: The set of all ω-open sets of (X,τ) containing a point x ∈ X is denoted by ωO(X, x). A point x ∈ X is called a condensation point of A if for each U ∈ τ with x ∈ U, the set U ∩ A is uncountable. keywords: closed; continuous; definition; f(u; f(x; following; function; f−1(v; int(cl(v; open; open set; point; proof; regular; sense; set; sets; subset; theorem; topology; u ∈; weakly; ωo(x cache: cubo-1139.pdf plain text: cubo-1139.txt item: #3 of 481 id: cubo-1142 author: Antón Marval, Gabriel M.; Castillo, René E.; Ramos-Fernández, Julio C. title: Maximal functions and properties of the weighted composition operators acting on the Korenblum, α-Bloch and α-Zygmund spaces date: 2017-03-01 words: 5263 flesch: 78 summary: The case of weighted composition operators acting on cer- tain growth spaces We consider first the case of weighted composition operators Wu,φ from H ∞ vlog to H∞ β . A similar result for weighted composition operators from Hardy spaces into logarithmic Bloch spaces was obtained by Colonna and Li in [8]. keywords: analytic; a∈d; banach; bloch; compact; compactness; composition; composition operators; continuity; continuous; cubo; fernández; functions; holomorphic; lim; math; maximal; new; operators; properties; ramos; result; spaces; sup; theorem; vlog; weighted cache: cubo-1142.pdf plain text: cubo-1142.txt item: #4 of 481 id: cubo-1143 author: Dragomir, S. S.; Boldea, M. V.; Megan, M. title: Inequalities for Chebyshev functional in Banach algebras date: 2017-03-01 words: 7778 flesch: 87 summary: Using (3.7) and (3.8) we have K (i) = P̄i ⎛ ⎝Pi+1ai+1 − i+1∑ j=1 pjaj ⎞ ⎠ + Pi ⎛ ⎝ n−1∑ j=i+1 pj+1aj+1 − P̄i+1ai+1 ⎞ ⎠ = P̄iPi+1ai+1 − PiP̄i+1ai+1 − P̄i i+1∑ j=1 pjaj + Pi n−1∑ j=i+1 pj+1aj+1 = [(Pn − Pi) Pi+1 − Pi (Pn − Pi+1)] ai+1 + Pi n−1∑ j=i+1 pj+1aj+1 − P̄i i+1∑ j=1 pjaj 62 S. S. Dragomir, M. V. Boldea, M. Megan CUBO 19, 1 (2017) If we define Pi := i∑ k=1 pk, P̄i := Pn − Pi, i ∈ {1, ..., n − 1} , Ai (p) := i∑ k=1 pkak, Āi (p) := An (p) − Ai (p) , i ∈ {1, ..., n − 1} , then we have the identity Tn (p; a, b) = n−1∑ i=1 det ( Pi Pn Ai (p) An (p) ) ∆bi (3.3) keywords: 1≤i≤n−1; = ∣; algebras; appl; banach; boldea; chebyshev; cubo; det; dragomir; exp; functional; grüss; i=0; i=1; identity; inequalities; inequality; j=1; k=1; math; max; max1≤i≤n−1; megan; min{i; n∑ i=1; n−1∑; power; proof; p̄i; s. s.; series; spaces; šev; theorem; type; |pk|; ∣ =; ∣ ∣; ∣p̄max{i; ∥ q)1; ∥ ∥; ∥tn; ∥y∥; ∥∆ai∥; ∥∆bi∥ cache: cubo-1143.pdf plain text: cubo-1143.txt item: #5 of 481 id: cubo-1144 author: Venkatesha; G., Divyashree title: Three dimensional f-Kenmotsu manifold satisfying certain curvature conditions date: 2017-03-01 words: 2490 flesch: 82 summary: From the above relation it follows that R(X, Y)R(U, V)W − R(R(X, Y)U, V)W − R(U, R(X, Y)V)W (5.2) −R(U, V)R(X, Y)W = fR[(X ∧g Y)R(U, V)W − R((X ∧g Y)U, V)W −R(U, (X ∧g Y)V)W On substituting X = U = ξ and using (2.10) and (2.12), (7.2) reduces to −(f2 + f′)[(f2 + f′)g(V, W)Y + R(Y, V)W − (f2 + f′)g(Y, W)V] (7.3) = f[(f2 + f′)S(Y, V)η(W)ξ − 2(f2 + f′)2g(V, W)Y − 2(f2 + f′)R(Y, V)W keywords: contact; cosymplectic; cubo; cyclic; dimensional; g(x; g(y; kenmotsu; kenmotsu manifold; manifold; pseudosymmetric; r(x; ricci; tensor; v)w; χ(mn cache: cubo-1144.pdf plain text: cubo-1144.txt item: #6 of 481 id: cubo-1145 author: Singh, Vikram; Pandey, Dwijendra N title: Weighted pseudo Almost periodic solutions for fractional order stochastic impulsive differential equations date: 2017-03-01 words: 8388 flesch: 87 summary: − t1)y1 + ∫t t0 (t − s)α−1J (t − s)G(s, y(s))ds + ∫ t t0 (t − s)α−1J (t − s)F(s, y(s), ∫ s −∞ K(s − ξ)g(ξ, y(ξ))dξ)dw(s), t ∈ (t1, t2]; ... + ∫ t t0 (t − s)α−1J (t − s)G(s, y(s))ds + ∫ t t0 (t − s)α−1J (t − s)F(s, y(s), ∫ s −∞ K(s − ξ)g(ξ, y(ξ))dξ)dw(s), t ∈ (tk, tk+1], (3.1) where I(t) = ∫ ∞ 0 Nα(θ)S(t αθ)dθ, J (t) = α ∫ ∞ 0 θNα(θ)S(t αθ)dθ, and for θ ∈ (0, ∞) Nα(θ) = 1 α θ−1− 1 α ωα(θ − 1 α ) ≥ 0, ωα(θ) keywords: 2(p; anal; aσi(t; cubo; d(aσ; definition; denote; differential; dwijendra; equations; existence; fractional; functions; g(t; impulsive; k(t; l2(p; lemma; lim; math; mean; mild; nα(θ; operator; order; pandey; pc(r; periodic; piecewise; processes; pseudo; s)g(s; s)α−1j; sequence; set; singh; solutions; space; square; stochastic; system; theorem; vikram; weighted; wpapρ(r; y(t; z(t; µ(γ; λ(2−2σ; ρ(t)dt; ∈ papρ(r; ∈ r; − s cache: cubo-1145.pdf plain text: cubo-1145.txt item: #7 of 481 id: cubo-1147 author: Tunc, Cemil title: Instability to vector lienard equation with multiple delays date: 2015-03-01 words: 2196 flesch: 80 summary: Making Y = X ′ in equation (1.1), we obtain X ′ = Y, Y ′ = −F(X, Y) − G(X) = x(t + s), −r ≤ s ≤ 0, t ≥ 0. keywords: constant; cubo; delays; differential; equation; i=1; instability; krasovskii; lienard; lyapunov; multiple; solution; tunc; vector; ∣ ∣ cache: cubo-1147.pdf plain text: cubo-1147.txt item: #8 of 481 id: cubo-1148 author: Chadha, Alka; Pandey, Dwijendra N title: Periodic BVP for a class of nonlinear differential equation with a deviated argument and integrable impulses date: 2015-03-01 words: 6078 flesch: 84 summary: − Q2(τ1)‖ ≤ H(τ2 − τ1) 2 + H (τ2 − τ1) 2 2 . (3.51) For τ2, τ1 ∈ (sm, tm+1], m = 1, · · · , δ with τ2 > τ1, ‖Q2(τ2) − Q2(τ1)‖ ≤ H(τ2 − τ1) 2 + H (τ2 − τ1) 2 2 . keywords: 1.1)-(1.3; banach; boundary; bvp; chadha; class; conditions; continuous; contraction; cubo; differential; equations; existence; f(s; following; fractional; function; gm(s; gδ(s; impulsive; m=1; map; max; mild; nonlinear; order; pandey; periodic; point; problem; s)]))ds; s)f(s; solution; space; step; system; theorem; theory; tm+1; u ∈; u([h(u(s; u(s; u(s))ds; u(t; ∫sδ cache: cubo-1148.pdf plain text: cubo-1148.txt item: #9 of 481 id: cubo-1149 author: Rostamani, Mohadeseh; Hejazian, Shirin title: Maps preserving Fredholm or semi-Fredholm elements relative to some ideal date: 2015-03-01 words: 5531 flesch: 78 summary: Since θ is surjective up to the inessential ideal, there exist x ∈ A and y ∈ I(B) such that b = θ(x) Since θ is surjective up to the inessential ideal I(B), 34 Mohadeseh Rostamani & Shirin Hejazian CUBO 17, 1 (2015) there exist u′ ∈ A and x′ ∈ I(B) such that u = θ(u′)+x′. keywords: algebra; banach; calkin; cr(a; cr(b; cubo; directions; elements; finite; fredholm; fredholm elements; i(a; i(b; ideal; inessential; invertible; isomorphism; jordan; left; lemma; linear; map; maps; preserving; proof; relative; right; semi; set; sets; spectral; spectrum; surjective; theorem; unital; θ(1; θ(i(a cache: cubo-1149.pdf plain text: cubo-1149.txt item: #10 of 481 id: cubo-1150 author: Verma, Ram U. title: Hybrid (Φ,Ψ,ρ,ζ,θ)−invexity frameworks and efficiency conditions for multiobjective fractional programming problems date: 2015-03-01 words: 8020 flesch: 80 summary: A point x∗ ∈ Q is an efficient solution to (P) if there exists no x ∈ Q such that fi(x) gi(x) ≤ fi(x ∗) gi(x ∗) Let x∗ ∈ Q, let fi, gi for i ∈ {1, · · ·, p} with fi(x ∗ ) gi(x ∗) ≥ 0, gi(x ∗) > 0 and Hj for j ∈ {1, · · ·, m} be twice continuously differentiable at x∗ ∈ Q, and let there exist u∗ keywords: conditions; cubo; differentiable; duality; efficiency; fi(x; fractional; functions; generalized; gi(x; hj(x ∗; hybrid; invex; invexity; j=1v ∗; multiobjective; order; problems; programming; ren; second; verma; x∗)‖2; x∗)‖θ(x; ζ(x; ρ(x; σmj=1v; ∗ j; ∗ ∈; ∗)z cache: cubo-1150.pdf plain text: cubo-1150.txt item: #11 of 481 id: cubo-1151 author: Anastassiou, George A. title: Spline left fractional monotone approximation involving left fractional differential operators date: 2015-03-01 words: 2964 flesch: 94 summary: + 2j−αj Γ (j − αj + 1) C∗2 nσ−j−1 ωm−σ+1 ( f(σ−1), 1 n ) = C∗2ωm−σ+1 ( f(σ−1), 1 n )     k∑ j=h l j 2 j−α j Γ ( j − α j + 1 ) 1 nσ−j−1   · (28) ( h−j∑ λ=0 2h−αj−λ λ!Γ (h − αj − λ + 2j−αj Γ (j − αj + 1) 1 nσ−j−1 ] ≤ C∗2ωm−σ+1 ( f(σ−1), 1 n ) 1 nσ−k−1     k∑ j=h l j 2j−αj Γ ( j − α j + 1 )   · (29) ( h−j∑ λ=0 2h−αj−λ λ!Γ (h − αj − λ keywords: c∗2; f(σ−1; j −; nσ−j−1; ωm−σ+1; ∗−1; ∣ ∣ cache: cubo-1151.pdf plain text: cubo-1151.txt item: #12 of 481 id: cubo-1152 author: Sanabria, José; Acosta, Edumer; Carpintero, Carlos; Rosas, Ennis title: Continuity via ΛsI-open sets date: 2015-03-01 words: 4949 flesch: 82 summary: Given an ideal I on a topological space (X, τ), a subset A ⊂ X is said to be ΛsI-closed if A = U ∩ F where U is a Λ s I-set and F is a τ⋆-closed set. (1) ⇒ (3) Let x ∈ X and V any open set in (Y, σ) such that f(x) keywords: closed; compact; connected; continuous; function; ideal; irresolute; open; proof; quasi; semi; set; sets; space; topological; λ s; λsi cache: cubo-1152.pdf plain text: cubo-1152.txt item: #13 of 481 id: cubo-1153 author: Aghajani, A.; O'Regan, D.; Shole Haghighi, A. title: Measure of noncompactness on Lp(RN) and applications date: 2015-03-01 words: 4044 flesch: 89 summary: Let us choose u ∈ X and for x,h ∈ BT with ‖h‖RN ≤ ǫ, we have |(Fu)(x) − (Fu)(x + h)| ≤ ∣ ∣ ∣ f(x,u(x)) A mapping µ : ME −→ R+ is said to be a measure of noncompactness in E if it satisfies the following conditions: 1◦ The family kerµ = {X ∈ ME : µ(X) = 0} is nonempty and kerµ ⊆ NE. keywords: aghajani; applications; conditions; cubo; equation; f(x; functional; haghighi; integral; k(x; lim; lp(rn; measure; noncompactness; nonlinear; point; satisfies; shole; solutions; space; theorem; u(x; µ(x; ‖x‖lp(rn\bt cache: cubo-1153.pdf plain text: cubo-1153.txt item: #14 of 481 id: cubo-1154 author: Banerjee, Amar Kumar; Saha, Pratap Kumar title: Semi Open sets in bispaces date: 2015-03-01 words: 3935 flesch: 87 summary: Keywords and Phrases: bispaces, semi open sets, τ1 semi open sets with respect to τ2. 2010 AMS Mathematics Subject Classification: 54A05, 54E55, 54E99 100 Amar Kumar Banerjee & Pratap Kumar Saha CUBO 17, 1 (2015) 1 Introduction The notion of a σ space or simply a space was introduced by A.D.Alexandroff [1] in 1940 generalising the idea of a topological space where only countable unions of open sets were taken to be open. Their complementary sets are called open sets. keywords: bispace; bitopological; collection; condition; numbers; open; s.o.w.r.to; semi; set; sets; theorem; union; τ1 open; τ1int(τ1s.o.(x)τ2; τ1inta; τ2clo cache: cubo-1154.pdf plain text: cubo-1154.txt item: #15 of 481 id: cubo-1155 author: Dyavanal, Renukadevi S.; Hattikal, Ashwini M.; Mathai, Madhura M. title: Uniqueness of meromorphic functions sharing a set in annuli date: 2016-12-01 words: 4916 flesch: 84 summary: For any constant a, we say that f and g share a Counting Multiplicity(CM), provided that f − a and g − a have the same zeros with same multiplicities. December 2016 Uniqueness of meromorphic functions sharing a set in annuli Renukadevi S. Dyavanal, Ashwini M. Hattikal, Madhura M. Mathai Department of Mathematics, Karnatak University, Dharwad - 580003, India renukadyavanal@gmail.com, ashwinimhmaths@gmail.com, madhuramathai@gmail.com ABSTRACT The purpose of this article is to investigate the uniqueness of meromorphic functions sharing a set with counting multiplicity and also with weight 1 in annuli. keywords: admissible; annuli; annulus; cubo; functions; j=1; lemma; let; lim; meromorphic; n0(r; non; r→∞,r∈i; s(r; set; sup; t0(r; theorem; uniqueness cache: cubo-1155.pdf plain text: cubo-1155.txt item: #16 of 481 id: cubo-1156 author: Chen, Peng; Ding, Hui-Sheng; N’Guérékata, Gaston M. title: Positive asymptotically almost periodic solutions of an impulsive hematopoiesis model date: 2016-12-01 words: 4442 flesch: 86 summary: − tk| ∈ [ 1 2 , 1], p = lim t−s→+∞ i(s, t) + ϕn(s − τ) ds + ∑ tk 0 such that, given any initial state x0, the solution satisfies ‖ x(t) ‖≤ β(‖ x0 ‖, t − t0) + r ∀t ≥ t0, then the system (1) is globally uniformly practically asymptotically stable. Then, for all t0 ≥ 0, s ≥ 0 and t ≥ t0 ∫t t0 φ ≤ N + L(t − t0) (6) where N = ∫s 0 φ + Ms p and L = p−1 p Ms with Ms =‖ φ|[s,+∞) ‖p . keywords: bellman; continuous; cubo; function; gronwall; hammami; inequalities; inequality; piecewise; solution; stability; stable; sup; systems; theorem; time; type; x(t; x(t0; ∫t t0 cache: cubo-1163.pdf plain text: cubo-1163.txt item: #24 of 481 id: cubo-1164 author: Lusares, Gina; Rodado Amaris, Armando title: Parametrised databases of surfaces based on Teichmüller theory date: 2016-12-01 words: 6809 flesch: 63 summary: The following properties which are proved in [2] establish the relationship between generic graphs and the Teichmüller space. Then, we showed that the face constraint of the systems associated to generic graphs for the genus two case are consequence of the equations and angle constraints of the systems, which allow us to claim that there are exactly 10 realizable generic graphs associated to Riemann surfaces of genus two. Proposition 5.1. keywords: a(s; amaris; angle; armando; associated; case; ce(g; cell; circle; complex; cone; connected; constraints; contraction; corresponding; cubo; databases; decomposition; delaunay; edge; faces; figure; generic; genus; gina; graphs; hyperbolic; hyperelliptic; l(g; linear; lusares; marked; mathematical; metric; moduli; moves; new; number; pattern; points; polytope; problem; proposition; realizable; riemann; riemann surfaces; rodado; set; solutions; space; sphere; structure; surface; system; teichmüller; theory; triangles; vertex; vertices; voronoi; weierstrass; whitehead cache: cubo-1164.pdf plain text: cubo-1164.txt item: #25 of 481 id: cubo-1165 author: Sudo, Takahiro title: Computing the Laplace transform and the convolution for more functions adjoined date: 2015-10-01 words: 5808 flesch: 80 summary: − µ)g(τ − s)dτ restricted to the sub-interval [s, t − µ] of [0, t], so that we may call the convolution in the statement the sub-convolution. − fn ∗ gn| + |fn ∗ gn − hn ∗ kn| + |hn ∗ kn − lim(hn ∗ kn)|, which go to zero as n → ∞. We denote by G(R) the algebra generated by A(R) and the set {e−λt 2 | λ keywords: algebra; algebraic; compute; convolution; cos; cubo; delta; denote; eµt; e−u; e−λt; functions; g(r; integral; laplace; lemma; lim; proof; shifted; sin; transform; λ+µ; ρ))(t cache: cubo-1165.pdf plain text: cubo-1165.txt item: #26 of 481 id: cubo-1172 author: Soltani, Fethi title: Reproducing inversion formulas for the Dunkl-Wigner transforms date: 2015-06-01 words: 4056 flesch: 86 summary: The Dunkl translation operators τx, x ∈ Rd, [18] are defined on L2(µk) by Fk(τxf)(y) = Ek(ix, y)Fk(f)(y), y ∈ Rd. For y ∈ Rd, the initial problem Dju(., y)(x) keywords: = ∫; cubo; dunkl; ek(ix; extremal; formulas; function; f∗λ; hs(µk; iii; inversion; kernel; l2 rad; l2(µk; l2rad(µk; math; operators; proof; proposition; rad; soltani; space; theorem; transform; vg(f)(x; wigner; |z|2)s; λ(1; ‖g‖2 cache: cubo-1172.pdf plain text: cubo-1172.txt item: #27 of 481 id: cubo-1174 author: Chettaoui, Chirine title: An other uncertainty principle for the Hankel transform date: 2015-06-01 words: 4132 flesch: 87 summary: (4.7) On the other hand, for f ∈ L2(dµα) and t > 0, we denote by ft the dilated of f defined by ft(r) In the following, we shall prove the uncertainty principle in terms of entropy for f ∈ L1(dµα)∩ L2(dµα) such that ||f||2,µα = 1. keywords: 2t2; bessel; chettaoui; chirine; cubo; dµα(r; entropy; fourier; function; hankel; hα(f; inequality; k→+∞; l2(dµα; lim; ln2; math; operator; principle; product; proof; p−1; terms; theorem; transform; uncertainty; weyl; |f(r)|2; ||f||2,µα; ταr; ∫+∞ cache: cubo-1174.pdf plain text: cubo-1174.txt item: #28 of 481 id: cubo-1175 author: Dragomir, S.S. title: Refinements of the generalized trapezoid inequality in terms of the cumulative variation and applications date: 2015-06-01 words: 5710 flesch: 89 summary: Lb (b − t) β for any t + 1 Lb (b − t) β+1 (2.12) for any x ∈ keywords: = ∣; a+b; applications; bounded; constant; cubo; dragomir; etx; function; generalized; inequalities; inequality; math; m−0; proof; refinements; s.s; selfadjoint; trapezoid; variation; ∣ ∣; ∣ ≤ cache: cubo-1175.pdf plain text: cubo-1175.txt item: #29 of 481 id: cubo-1176 author: Leiva, Hugo; Matute, Jesús; Merentes, Nelson; Sánchez, José title: On a type of Volterra integral equation in the space of continuous functions with bounded variation valued in Banach spaces date: 2015-06-01 words: 7677 flesch: 85 summary: Let us note that ∣∣F(x)(t + h) − F(x)(t) ∣∣ = ∣∣∣∣ ∫t+h a K(t + h, s)f(x(s))ds − ∫t a K(t, s)f(x(s))ds ∣∣∣∣ ≤ ∫t a ∥∥K(t + h, s) − K(t, s) ∥∥ · ∣∣f(x(s)) = x0 ∈ X, where B : F −→ F is an adequate function, F denotes the space of continuous functions of bounded variation defined from the interval [a, b] into any fixed normed space X and the expression K(t, s)x(s) in the integral part means that the continuous linear operator K(t, s) : X −→ X is evaluated in x(s). keywords: b(g)(s)ds; banach; bounded; b−δ; continuous; controllability; cubo; definition; equation; formula; function; i=1; integral; interval; josé; k(t; leiva; linear; matute; max; nelson; nonlinear; number; operator; pair; problem; proof; proposition; r(b; r(t; real; riemann; sánchez; section; solution; space; system; s∈[a; t(s; theorem; type; variation; volterra; x(a; x(t; ∣∣∣∣∣ cache: cubo-1176.pdf plain text: cubo-1176.txt item: #30 of 481 id: cubo-1177 author: Gokmen Yildiz, Onder; Ersoy, Soley; Masal, Melek title: A note on inextensible flows of curves on oriented surface date: 2014-10-01 words: 3443 flesch: 83 summary: 2 Preliminaries Let S be an oriented surface in three-dimensional Euclidean space E3 and α(s) be a curve lying on the surface S. Suppose that the curve α(s) is spatial then there exists the Frenet frame { −→ T , −→ N, −→ B } at each points of the curve where −→ T is unit tangent vector, −→ N is principal normal vector and −→ B is binormal vector, respectively. In this frame −→ T is the unit tangent of the curve, −→ n is the unit normal of the surface S and −→ g is a unit vector given by −→ g = −→ n × −→ T . keywords: cubo; curvature; curve; darboux; f1kn; f2τg; flows; following; frame; g ∂t; geodesic; inextensible; oriented; surface; ∂ −→; ∂f2; ∂f3; ∂f3 ∂s; ∂kn; ∂s2 cache: cubo-1177.pdf plain text: cubo-1177.txt item: #31 of 481 id: cubo-1178 author: Anastassiou, George A. title: Higher order multivariate Fuzzy approximation by basic neural network operators date: 2014-10-01 words: 4896 flesch: 85 summary: ∈ N. Suppose that sup r∈[0,1] max ( x (r) i , y (r) i ) ∈ R, for i = 1, ..., m. − f (x ′ 1, ..., x ′ m)| . keywords: anastassiou; approximation; continuous; cubo; definition; function; fuzzy; i=1; max; multivariate; n1−α; neural; operators; order; sup; ∣∣∣ cache: cubo-1178.pdf plain text: cubo-1178.txt item: #32 of 481 id: cubo-1179 author: Miranville, Alain title: On an anisotropic Allen-Cahn system date: 2015-06-01 words: 4012 flesch: 85 summary: Keywords and Phrases: Allen-Cahn equation, Willmore regularization, anisotropy effects, well- posedness 2010 AMS Mathematics Subject Classification: 35B45, 35K55 74 Alain Miranville CUBO 17, 2 (2015) 1 Introduction The Allen-Cahn equation, ∂u ∂t − ∆u + f(u) = 0, (1.1) where u is the order parameter and f(s) = s3 −s, describes important processes related with phase separation in binary alloys, namely, the ordering of atoms in a lattice (see [1]). dx, (1.2) where Ω is the domain occupied by the material and, typically, F(s) = 1 4 (s2 − 1)2. keywords: alain; allen; anisotropic; cahn; case; cubo; div(δ′; energy; equation; existence; f(u; f(u)∇u; free; h2(ω; hilliard; landau; miranville; particular; problem; regularization; solutions; system; uniqueness; |s|2; |∇u|; |∇u|2; ∂u ∂t cache: cubo-1179.pdf plain text: cubo-1179.txt item: #33 of 481 id: cubo-1180 author: Benchohra, Mouffak; Bennihi, Omar; Ezzinbi, Khalil title: Existence Results for Some Neutral Partial Functional Differential Equations of Fractional order with State-Dependent Delay date: 2014-10-01 words: 5524 flesch: 81 summary: − t)u(s − ρ1(t)ρ2( ∫π 0 a2(θ)|u(t,θ)| 2dθ),ξ)ds] = ∂ 2 u(t,ξ) ∂ξ2 + a0(t,ξ)u(t,ξ) + ∫0 −∞ a1(s − t)u(s =    ϕ(t), t ∈ (−∞,0], g(t,xρ(t,xt)) keywords: 0,b; abstract; appl; benchohra; bennihi; cn)ds; conditions; continuous; cubo; d(a; definition; delay; denote; dependent; differential; differential equations; equations; evolution; example; existence; ezzinbi; family; fixed; fractional; fréchet; function; g(t; infinite; kn|z(s)|; math; mild; m̂kn; m̄0lkn; neutral; nonlinear; norm; operator; order; partial; point; problem; resolvent; results; semi; solution; space; state; unique; yρ(s; yρ(t; zρ(s cache: cubo-1180.pdf plain text: cubo-1180.txt item: #34 of 481 id: cubo-1181 author: Nuray, Fatih; Patterson, Richard F. title: Submatrices of four dimensional summability matrices date: 2015-06-01 words: 2186 flesch: 68 summary: In this paper, firstly we will obtain a general correspondance between RH-regular matrices and ℓ′′ − ℓ′′ matrices by proving that every RH-regular matrix gives rise to an ℓ′′ − ℓ′′ matrix by the removing of appropriate rows. Secondly we prove that a matrix from double bounded sequences to double bounded sequences contains a row-submatrix is conservative. keywords: convergent; dimensional; double; limm; math; matrix; patterson; pringsheim; regular; row; sequence; submatrix; summability; theorem; |am; ℓ′′ cache: cubo-1181.pdf plain text: cubo-1181.txt item: #35 of 481 id: cubo-1182 author: Aranda, Carlos Cesar title: Spacetime singularity, singular bounds and compactness for solutions of the Poisson’s equation date: 2015-06-01 words: 8627 flesch: 83 summary: ∈ R, and g ∈ C∞(R) (see the C∞ Urysohn Lemma page 245, [14]). |= r ∈ [r0, R), (24) we deduce − limj→∞ ∆Pj = limj→∞ Hj(Pj) keywords: = ∫; analysis; aranda; b(0; b(x0,r; b(x0,δ; ball; black; bounds; c2(ω; carlos; cesar; compactness; concentration; continuous; cubo; derivative; differential; discontinuity; distributions; domain; elliptic; equation; f1,j; function; gravity; green; hj(pj; hole; j=1; journal; j→∞; lemma; lim; limj→∞; markarian; mathematical; mean; measure; messier; newtonian; ngc; non; page; poisson; potentials; press; problem; proof; proposition; qso; results; s=0; satisfies; sdss; second; sequence; set; simple; singular; singularity; solid; solution; spaces; spacetime; springer; support; theorem; theory; ∂xi; − ∫ cache: cubo-1182.pdf plain text: cubo-1182.txt item: #36 of 481 id: cubo-1183 author: Selmi, Belgacem title: Calderón’s reproducing Formula For q-Bessel operator date: 2015-06-01 words: 5264 flesch: 84 summary: Fα,q(f) is an isomorphism of L 2 α,q(Rq,+), we have ||Fα,q(f)||2,α,q = ||f||2,α,q, for f ∈ L 2 α,q(Rq,+) and F−1α,q(f) = 132 Belgacem Selmi CUBO 17, 2 (2015) (iii) Fα,q(T α q,xf)(ξ) = jα(ξx;q 2)Fα,q(f)(ξ); f ∈ L 1 α,q(Rq,+). keywords: belgacem; bessel; calderón; convolution; cubo; cµ,α; dqt; dqx; f ∈; f(x; finite; formula; fourier; function; integral; l1α; lim; logq; measure; operator; proof; q(f; q(rq,+; q(rq,+,dqσ(x; selmi; space; theorem; transform; tαq; δ(x; ∈ l cache: cubo-1183.pdf plain text: cubo-1183.txt item: #37 of 481 id: cubo-1184 author: Dimbour, William; Mado, Jean-Claude title: S-asymptotically ω-periodic solution for a nonlinear differential equation with piecewise constant argument in a Banach space date: 2014-10-01 words: 3085 flesch: 80 summary: A function f ∈ BC(R+,X) is called S-asymptotically ω-periodic if there exists ω such that lim t→∞ (f(t + ω) − f(t)) and δǫ,K > 0 such that ||f(t,x) − f(t,y)|| < ǫ for all t ≥ Lǫ,K and all x,y ∈ K with ||x − y|| < δǫ,K. 58 William Dimbour & Jean-Claude Mado CUBO 16, 3 (2014) Theorem 2. keywords: argument; banach; constant; continuous; cubo; definition; differential; dimbour; equation; f(t; function; lim; nonlinear; operator; periodic; piecewise; s)a0φ([s])ds; sapω(x; solution; space; t(t; theorem; x(t; ||a0|| cache: cubo-1184.pdf plain text: cubo-1184.txt item: #38 of 481 id: cubo-1185 author: Bültel, Oliver title: On the supersingular loci of quaternionic Siegel space date: 2014-10-01 words: 8303 flesch: 74 summary: In subsections 2.2 we explain techniques needed to understand supersingular Dieudonné modules. We apply these techniques to supersingular Dieudonné modules with the particular additional structure under consideration in the subsections 2.3- 2.4. keywords: abelian; additional; algebra; basis; bültel; closed; corollary; crisdisc(m; cubo; decomposition; degenerate; dieudonné; dieudonné module; direct; divisible; dual; elements; equal; fact; following; form; group; i=1; invariant; isogeny; isomorphism; isotropic; lemma; linear; loci; locus; maximal; module; non; notice; odd; oliver; oort; orthogonal; pairing; particular; perfect; points; prime; proof; quaternionic; rank; s0(m; satisfies; shimura; siegel; skp; space; structure; sum; supersingular; supersingular dieudonné; superspecial; symmetric; theorem; type; varieties; variety; volume; w(fp2; w(k; φ(x cache: cubo-1185.pdf plain text: cubo-1185.txt item: #39 of 481 id: cubo-1186 author: Moudafi, Abdellatif title: Computing the resolvent of composite operators date: 2014-10-01 words: 3909 flesch: 67 summary: + 〈u,y − x〉 for all y ∈ H2} as usual). x + JA1 (y − x). keywords: algorithm; applications; approach; composite; compute; computing; continuous; converges; convex; cubo; example; fact; fixed; following; image; mapping; maximal; method; monotone; moudafi; operator; point; problem; proximity; resolvent; sequence; set; sum; λy1 cache: cubo-1186.pdf plain text: cubo-1186.txt item: #40 of 481 id: cubo-1187 author: Sudo, Takahiro title: Computing the inverse Laplace transform for rational functions vanishing at infinity date: 2014-10-01 words: 6618 flesch: 84 summary: − (k + m)(µ2 − µ1) (µ2 − µ1) 2 + (λ1 ± λ2)2 ∫t 0 τk+m−1e(µ2−µ1)τ sin(λ1t − (λ1 ± λ2)τ)dτ − (k + m)(λ1 ± λ2) (µ2 − µ1) 2 + (λ1 ± λ2)2 ∫t 0 τk+m−1e(µ2−µ1)τ cos(λ1t − (λ1 ± λ2)τ)dτ, where the last two integrals are denoted by Ik+m−1,sin and Ik+m−1,cos respectively, and the integrals can be inductively reduced to the cases of Ij,sin and Ij,cos for 1 ≤ j ≤ k + m − 2 and finally to the case of I0,sin and I0,cos that are given by I0,sin ≡ ∫t 0 e(µ2−µ1)τ sin(λ1t − (λ1 ± λ2)τ)dτ = µ2 − µ1 (µ2 − µ1) 2 + (λ1 ± λ2)2 {e(µ2−µ1)t sin(∓λ2t) − sin(λ1t)} + λ1 ± λ2 (µ2 − µ1) 2 + (λ1 ± λ2)2 {e(µ2−µ1)t cos(∓λ2t) − cos(λ1t)} and I0,cos ≡ ∫t 0 e(µ2−µ1)τ cos(λ1t − (λ1 ± λ2)τ)dτ = µ2 − µ1 (µ2 − µ1) 2 + (λ1 ± λ2)2 {e(µ2−µ1)t cos(∓λ2t) − cos(λ1t)} − λ1 ± λ2 (µ2 − µ1) 2 + (λ1 ± λ2)2 {e(µ2−µ1)t sin(∓λ2t) − sin(λ1t)} Other cases of convolution products of general monomials with sin and cos changed are also computed similarly, but omitted. keywords: a(r; case; compute; convolution; cos; cubo; eµt; functions; integral; inverse; k=0; laplace; l−1; m+1∑; product; r0(c; rational; real; sin; sin(λ1; theorem; transform; λ(t; λ2)2; λ2l(k; λτdτ; − λ; −1)(l−1)k cache: cubo-1187.pdf plain text: cubo-1187.txt item: #41 of 481 id: cubo-1274 author: Diagana, Toka; Ezzinbi, Khalil; Miraoui, Mohsen title: Pseudo-almost periodic and pseudo-almost automorphic solutions to some evolution equations involving theoretical measure theory date: 2014-06-01 words: 10779 flesch: 81 summary: If in the finite sequence of λk there exist λnk = 0 for k = 1, 2, ...l with am ∈ X − {0} for all m ̸= nk (k = 1, 2, ..., l), it can be easily shown that M(f, µ,ν) = θµν l∑ k=1 ank = θµνM(f). ≤ KF∥u − v∥, for all u, v ∈ X and t ∈ R, then the equation (1.1) has a unique bounded mild solution u : R #→ X given by u(t) = ∫ R Γ(t, s)F(s, u(s))ds, t ∈ R, where the operator family Γ(t, s), called Green’s function corresponding to U and P(.), is given by { Γ(t, s) = U(t, s)P(s), keywords: a(t; abstract; analysis; applications; assumptions; automorphic; banach; compact; conditions; continuous; cubo; definition; denote; diagana; differential; e(r; equations; evolution; existence; ezzinbi; f(t; family; following; follows; form; functions; g ∈; g(t; h(t; h1(t; journal; khalil; lemma; lim; mathematical; measure; mild; miraoui; mohsen; new; nonautonomous; nonlinear; n’guérékata; pap(r; partial; periodic; periodicity; proof; pseudo; s ∈; set; solutions; spaces; theorem; theory; toka; u(t; u(τ))dτ; unique; v(t; weighted; µ(qr; µ,ν; ν(qr; ∥f(t)∥dµ(t; ∫+∞ cache: cubo-1274.pdf plain text: cubo-1274.txt item: #42 of 481 id: cubo-1275 author: Anastassiou, George title: Voronovskaya type asymptotic expansions for multivariate quasi-interpolation neural network operators date: 2014-06-01 words: 4274 flesch: 89 summary: Φ (nx − k) V (x) − f (x) = m−1∑ j=1 ⎛ ⎝ ∑ |α|=j ( fα (x) ∏N i=1 αi! ) ⎞ ⎠ (∑⌊nb⌋ k=⌈na⌉ Φ (nx − k) (∏N i=1 ( ki n − xi )αi )) ∞∑ k=−∞ Φ (nx − k) := ∞∑ k1=−∞ ∞∑ k2=−∞ ... ∞∑ kN=−∞ Φ (nx1 − k1, ..., nxN − kN) = 1, ∀ x ∈ RN; keywords: i=1; k n; k=⌈na⌉; max; multivariate; neural; ∥ ∥; ∥fα∥ cache: cubo-1275.pdf plain text: cubo-1275.txt item: #43 of 481 id: cubo-1276 author: Sudo, Takahiro title: K-theory for the group C*-algebras of a residually finite discrete group with Kazhdan property T date: 2014-06-01 words: 1316 flesch: 71 summary: Keywords and Phrases: Group C*-algebra, K-theory, discrete group, projection. 2010 AMS Mathematics Subject Classification: 46L05, 46L80, 19K14. Because if it is zero, then K0(C ∗ r(SLn(Z))) ∼= Z, which implies that C∗r(SLn(Z)) does not contain non-trivial projections. keywords: c∗-algebras; direct; discrete; finite; group; k0(c; k1(c; kazhdan; math; non; property; r(γ; residually; sum; theory; trivial; ∗(γ cache: cubo-1276.pdf plain text: cubo-1276.txt item: #44 of 481 id: cubo-1277 author: Li, Fang; Yang, Zuodong title: Existence of blow-up solutions for quasilinear elliptic equation with nonlinear gradient term. date: 2014-06-01 words: 5605 flesch: 85 summary: ≤ 0, x ∈ D+σ, △mu − − b(x)(u−)p(1 + |∇u−|q) ≥ 0, x ∈ D−σ. (3.16) Let u be any nonnegative solution of (1.1) and M1(δ) = R − |x − x0| keywords: asymptotic; b(x; blow; boundary; condition; constant; cubo; d(x)→0; domain; elliptic; equation; existence; fang; function; gradient; large; lemma; lim; lower; nonlinear; nonnegative; problem; proof; quasilinear; r)−α; results; r→r; solutions; theorem; u(x; upper; weak; yang; zuodong; αm−1−q(α; ψ(x cache: cubo-1277.pdf plain text: cubo-1277.txt item: #45 of 481 id: cubo-1279 author: Tunc, Cemil title: On the uniform asymptotic stability to certain first order neutral differential equations date: 2014-06-01 words: 2617 flesch: 88 summary: − g(x(t − τ))) − g(x(t − τ))}, Then, the zero solution of Eq. (1.2) is uniformly asymptotically stable. Remark. keywords: asymptotic; differential; equations; g(x(t; neutral; solution; stability; tanh; tanh x(t; x(s)ds; x(t; ∗ ∗; ⎢ ⎢; ⎥ ⎥ cache: cubo-1279.pdf plain text: cubo-1279.txt item: #46 of 481 id: cubo-1280 author: Aghanians, Aris; O’Regan, Donal; Fallahi, Kamal; Nourouzi, Kourosh title: Some coupled coincidence point theorems in partially ordered uniform spaces date: 2014-06-01 words: 5268 flesch: 84 summary: For given comparable elements (g(x), g(y)) and (g(u), g(v)) of X × X, where x, y, u, v ∈ X, write r1 = ρ(g(x), g(u)) and r2 = ρ(g(y), g(v)) and take ε > 0. For given comparable elements (g(x), g(y)) and (g(u), g(v)) of X × X, where x, y, u, v ∈ X, write r1 = ρ(F(x, y), g(x)) and r2 = ρ(F(u, v), g(u)) keywords: coincidence; comparable; f(u; f(x; f(xn; g(u; g(x; g(xn; g(xn+1; g(y; g(yn; point cache: cubo-1280.pdf plain text: cubo-1280.txt item: #47 of 481 id: cubo-1281 author: Kumar Mohanta, Sushanta title: Coupled coincidence points for generalized (ψ, ϕ)-pair mappings in ordered cone metric spaces date: 2014-06-01 words: 5418 flesch: 88 summary: A map T : (X, d) → (X, d) is called sequentially continuous if xn ∈ X, xn → x implies Txn → Tx. Lemma 2. [3] An element (x, y) ∈ X × X is called a coupled fixed point of the mapping F : X × X → X if x = F(x, y) and y = F(y, x). keywords: coincidence; cone; cubo; f(u; f(x; g(x; let; mappings; metric; monotone; point; property; sequence; space; theorem cache: cubo-1281.pdf plain text: cubo-1281.txt item: #48 of 481 id: cubo-1282 author: Al-Islam, Najja title: Diagana space and the gas absorption model date: 2014-06-01 words: 3681 flesch: 78 summary: = 0 for all x ∈ [0, 1] and t ∈ R. Suppose inf x∈[0,1],t∈R a(x, t) = 4 Example To illustrate the main result of this paper(Theorem 3.2), consider the following nonlinear hyperbolic second-order partial differential equation ⎧ ⎪⎪⎨ ⎪⎪⎩ uxt(x, t) + ! P(x) + sin t ux(x, t) = H(t) sin(u(x, ⌊t⌋)) u(0, t) = 0 = ϕ(t) (4.1) where P(x) = n∑ k=0 akx k for x keywords: a(x; absorption; anal; ap(r; cubo; diagana; differential; equations; existence; functions; gas; islam; lim; nonlinear; norm; pap0(r; periodic; periodicity; proof; pseudo; solutions; space; weighted; µ(r cache: cubo-1282.pdf plain text: cubo-1282.txt item: #49 of 481 id: cubo-1283 author: Galeano, Rafael; Ortega, Pedro; Cantillo, John title: Stationary Boltzmann equation and the nonlinear alternative of Leray-Schauder type date: 2014-03-01 words: 2452 flesch: 82 summary: + ∥ ∥ ∥ Q(un, un) − Q(u, u) ∥ ∥ ∥ L1(Ω×B 3R (0)) + ∥ ∥ ∥ ∥ ∥ n∑ i=1 vi ∂ ∂xi (un − u) ∥ ∥ ∥ ∥ ∥ L1(Ω×B 3R (0)) + n∑ i=1 ∥ ∥ ∥ ∥ vi ∂ ∂xi (un − u) ∥ ∥ ∥ ∥ E ≤ r∗R + R + nR∗∗ keywords: alternative; b 3r; boltzmann; equation; i=1; j(u; l1(ω×b; l1(ω×b 3r; nonlinear; q(u; q(un; stationary; type; u(x; |un(x; ∂xi; ∣ ∣; ∣ ∫; ∥ ∥ cache: cubo-1283.pdf plain text: cubo-1283.txt item: #50 of 481 id: cubo-1284 author: Aoyama, Koji; Kimura, Yasunori title: Viscosity approximation methods with a sequence of contractions date: 2014-03-01 words: 5168 flesch: 79 summary: Then it is easy to verify that (η′)2 < 2κ′, µA is κ′-strongly monotone and η′-lipschitzian, and moreover, 〈y − z, Az〉 ≥ 0 is equivalent to 〈y − z, µAz〉 ≥ 0 for every y, A set-valued mapping A of H into H, which is denoted by A ⊂ H×H, is said to be a monotone operator if 〈x − y, x′ − y′〉 ≥ 0 for all (x, x′), (y, y′) keywords: approximation; common; condition; convergence; convex; cubo; fixed; following; iterative; lemma; lim; mappings; math; method; monotone; n=1; nonempty; nonexpansive; point; problem; sequence; subset; sup; theorem; viscosity; yokohama cache: cubo-1284.pdf plain text: cubo-1284.txt item: #51 of 481 id: cubo-1285 author: Abbas, Syed title: Weighted pseudo almost automorphic solutions of fractional functional differential equations date: 2014-03-01 words: 5039 flesch: 75 summary: Keywords and Phrases: Fractional differential equation, Fixed point theorem, Almost auto- morphic functions, Abstract differential equations. A : D(A) ⊂ X → X is a linear densely defined operator of sectorial type on a complex Banach space X. With motivation coming from a wide range of engineering and physical applications, fractional differential equations have recently attracted great attention of mathematicians and scientists. keywords: abbas; anal; applications; automorphic; automorphic solutions; continuous; cubo; differential; differential equations; equations; existence; f(t; fractional; functions; g(t; lim; lipschitz; m(r; math; nonlinear; n’guérékata; operator; order; periodic; problem; pseudo; sectorial; set; solutions; space; stepanov; syed; sα(t; t ∈; theorem; type; u(s),us)ds; u(t; vol; weighted; wpaa(x; αsin cache: cubo-1285.pdf plain text: cubo-1285.txt item: #52 of 481 id: cubo-1286 author: Suresh, G.; Vasavi, Ch; Rao, T.S.; Murty, M.S.N. title: Existence of Ψ-Bounded Solutions for Linear Matrix Difference Equations on Z+ date: 2014-03-01 words: 3658 flesch: 78 summary: The existence and uniqueness of solutions of matrix difference equation (1) was studied by Murty, Anand and Lakshmi Prasannam [17]. Recently [10, 18, 19], extended the concept of Ψ-boundedness of the solutions to Lyapunov matrix differential equations. keywords: a(n; cubo; definition; difference; differential; equations; existence; f(n; function; fundamental; journal; kumar; lemma; lim; linear; matrices; matrix; n=1; operator; proof; rm×m; solution; summable; theorem; x(n; y(n; z(n;   cache: cubo-1286.pdf plain text: cubo-1286.txt item: #53 of 481 id: cubo-1287 author: Lahiri, Indrajit; Mandal, Nintu title: On a result of Q. Han, S. Mori and K. Tohge concerning uniquesness of meromorphic functions. date: 2014-03-01 words: 4887 flesch: 90 summary: f ′ |≥ 2) = S(r), (vii) N(r, 0; g′ |≥ 2) = S(r), (viii) N(r, 0; f′ |≥ 2) = S(r), (ix) N(r, 0; f − g |≥ 2) = S(r), (x) N(r, 0; f − g | f = ∞) = S(r), where N0(r, 0; g ′ |≥ 2)(N0(r, 0; f ′ |≥ 2)) is the counting function of those multiple zeros of g′(f′) which are not the zeros of f(f − 1) and N(r, 0; f − g | f = ∞) is the counting function of those zeros of f − g which are poles of f. 3 Proof of Theorem 1.1 Proof. This shows that z3 is at most a simple pole of H. Since a simple zero of f − a is a zero of H and N(r, 0; F | f = t) ≤ N(r, 0; f − g |≥ 2) for t = 0, 1 and F = (f − a) keywords: bilinear; following; functions; lahiri; lemma; meromorphic; n(r; n0(r; result; s(r; share; sharing; t(r; theorem; transformation cache: cubo-1287.pdf plain text: cubo-1287.txt item: #54 of 481 id: cubo-1288 author: Sahin, Ilker; Telci, Mustafa title: A Common Fixed Point Theorem for Pairs of Mappings in Cone Metric Spaces date: 2014-03-01 words: 3523 flesch: 88 summary: [3] Di Bari, C. and Vetro P., ϕ- pairs and common fixed points in cone metric spaces, Rend. [5] Ilić, D. and Rakočević, V., Common fixed points for maps on cone metric space, J. Math. Anal. keywords: common; complete; cone; d(x; fixed; inequalities; mappings; metric; point; sequence; space; theorem; x2n+1; ∣ ∣ cache: cubo-1288.pdf plain text: cubo-1288.txt item: #55 of 481 id: cubo-1289 author: Sirovnik, Nejc title: On certain functional equation in semiprime rings and standard operator algebras date: 2014-03-01 words: 2966 flesch: 83 summary: Ring derivations on standard operator algebras, J. Funct. Jordan derivations on prime rings, Bull. keywords: a(x; algebra; case; derivation; f(x; i=0; jordan; l(x; linear; math; n−1; n−2; operator; relation; rings; semiprime; standard; theorem; vukman cache: cubo-1289.pdf plain text: cubo-1289.txt item: #56 of 481 id: cubo-1290 author: El-Sayed Ahmed, A.; Kamal, A.; Yassen, T.I. title: Characterizations for certain analytic functions by series expansions with Hadamard gaps date: 2014-03-01 words: 3872 flesch: 88 summary: p (1 − r)q ωp(1 − r) × { 1 2π ∫2π 0 K(g(reiθ,a))dθ } rdr ≤ sup a∈D ∫1 0 ( ∞∑ k=1 nk |ak|r (nk−1) )p (1 − r)q ωp(1 − r) K ( log 1 r ) rdr by Theorem 2.7,we obtain ||f||QK,ω(p,q) . By Lemma 2.6, Theorem 2.7 and Theorem 3.2, we have ∫δ 0 ( ∞∑ k=1 nk |ak|r (nk−1) )p (1 − r)q ωp(1 − r) ∫2π 0 K(g(z,a))rdrdθ ≤ ∫δ 0 ( ∞∑ k=1 nk |ak|r (nk−1) )p (1 − r)q ωp(1 − r) K ( log 1 |a| ) keywords: 0,∞; 1 r; ahmed; analytic; condition; cubo; functions; k(log; k=1; lemma; n=0; r)q; r)α−1; satisfy; series; spaces; theorem; |z|; ω(p; ωp(log cache: cubo-1290.pdf plain text: cubo-1290.txt item: #57 of 481 id: cubo-1291 author: Soltani, Fethi title: \(L^p\) local uncertainty inequality for the Sturm-Liouville transform date: 2014-03-01 words: 2774 flesch: 81 summary: Keywords and Phrases: Sturm-Liouville transform; local uncertainty principle; Donoho-Stark’s uncertainty principle. [11] S. Omri, Local uncertainty principle for the Hankel transform, Int. keywords: 2α+2; cubo; f(f; function; inequality; k(a; liouville; local; math; measurable; operator; principle; sturm; theorem; transform; trimèche; uncertainty; ν(e; ‖xaf‖lp(µ cache: cubo-1291.pdf plain text: cubo-1291.txt item: #58 of 481 id: cubo-1292 author: Djebali, Smaïl; Saifi, Ouiza title: Upper and lower solutions for φ−Laplacian third-order BVPs on the half-Line date: 2014-03-01 words: 3878 flesch: 90 summary: ≤ 0, t ∈ R+ (β − x)(0) = µ(β − x)′(0), (β − x)′(+∞) t ∈ R+ which means that (β − x)′ is nonincreasing in R+. keywords: a(t; boundary; cubo; djebali; existence; f(t; f(τ; g(t; lemma; lim; lower; order; point; positive; problem; s)φ−1; singular; solution; upper; value; x(0; x(t; φ−1; φ−laplacian; ∫+∞;  cache: cubo-1292.pdf plain text: cubo-1292.txt item: #59 of 481 id: cubo-1293 author: Matsumoto, Akio; Szidarovszky, Ferenc title: An Elementary Study of a Class of Dynamic Systems with Single Time Delay date: 2013-10-01 words: 2281 flesch: 73 summary: There is a large literature on delayed equations with one delay (see for example, Hayes (1950) and Burger (1956) for the earliest studies), however only very few studies are devoted to multiple delays (see for example, Hale and Huang (1993) and Piotrowska (2007)). − Ae−∆∆′ = 0 showing that ∆′ = e−∆ Ae−∆ − 1 = ∆ A∆ + A = iβ iβA + A = iβ(A − iβA) A2β2 + A2 with real part β2/(Aβ2+A) > keywords: case; class; cubo; delay; delayed; dynamic; elementary; equation; f(β; models; positive; real; sin; single; solution; stability; systems; value; ẋ(t; π/2 cache: cubo-1293.pdf plain text: cubo-1293.txt item: #60 of 481 id: cubo-1294 author: Choudhury, Binayak; Kundu, Subhajit title: Approximating a solution of an equilibrium problem by Viscosity iteration involving a nonexpansive semigroup date: 2013-10-01 words: 4548 flesch: 89 summary: − βn)(1 − θ)αn)‖xn − p‖ 2 + α2nM0 + θα 2 nM0 + 2αnηn ≤ (1 − 2(1 − θ)αn)‖xn − p‖ 2 + (α2nM0 + θα 2 nM0 + 2αnηn) keywords: banach; convergence; convex; cubo; ep(f; equilibrium; f(p; fix(s; hilbert; iteration; lemma; lim; mapping; nonexpansive; nonlinear; n→∞; point; problem; real; semigroup; set; space; sup; viscosity; xn−1; |rn−rn−1|; − p cache: cubo-1294.pdf plain text: cubo-1294.txt item: #61 of 481 id: cubo-1295 author: El-Sayed Ahmed, A.; Bakhit, M. A. title: Composition operators in hyperbolic general Besov-type spaces date: 2013-10-01 words: 4387 flesch: 83 summary: ∞. Moreover, we say that f ∈ F∗(p, q, s) belongs to the class F∗0(p, q, s) if lim |a|→1 ∫ D (f∗(z))p(1 − |z|2)qgs(z, a)dA(z) = 0. CUBO 15, 3 (2013) Composition operators in hyperbolic general Besov-type spaces 21 The usual general Besov-type spaces F(p, q, s) (defined using the conventional derivative f′ instead of f∗) and their norms are denoted by the same symbols but with f′. Yamashita was probably the first one considered systematically hyperbolic function classes. ∞, the hyperbolic class F∗(p, q, s) consists of those functions f ∈ B(D) for which (see [7]) ‖f‖ p F∗(p,q,s) = sup a∈D ∫ D (f∗(z))p(1 − |z|2)qgs(z, a)dA(z) < keywords: a)da(z; a∈d; besov; bloch; bounded; b∗α; classes; compact; composition; cubo; d(f; fnj; function; f∗(p; general; hyperbolic; metric; operators; spaces; sup; type; |z|2)qgs(z; |φ(z)|2)αp; ∣ ∣ cache: cubo-1295.pdf plain text: cubo-1295.txt item: #62 of 481 id: cubo-1296 author: Chauhan, Sunny; Pant, B. D.; Imdad, Mohammad title: Coincidence and common fixed point theorems in Non-Archimedean Menger PM-spaces date: 2013-10-01 words: 6003 flesch: 89 summary: [15, Example 0.1℄ wherein it an be easily seen that involved mappings do not have a oin iden e or ommon �xed point in the underlying spa e. CUBO 15, 3 (2013) Coin iden e and ommon �xed point theorems in N.A. Menger . Thus we on lude that z is a ommon �xed point of A, B, S and T. The uniqueness of ommon �xed point is an easy onsequen e of inequality (2). keywords: by(t; cubo; g(fsx; g(fz; himedean; iden; imdad; ipro; lim; mappings; math; max; menger; metri; n.a; non; n→∞; ommon; ompatible; ontinuity; ontinuous; pair; pant; point; self; sequen; spa; sub; theorems; xed; xed point; z(t cache: cubo-1296.pdf plain text: cubo-1296.txt item: #63 of 481 id: cubo-1298 author: Fosner, Maja; Marcen, Benjamin; Sirovnik, Nejc title: On centralizers of standard operator algebras with involution date: 2013-10-01 words: 2638 flesch: 86 summary: Given an integer n ≥ 2, a ring R is said to be n-torsion free if for x ∈ R, nx = 0 implies x Re all that a ring R is prime if for a, b ∈ R, aRb = (0) implies that either a = 0 or b = 0, and is semiprime in ase aRa = (0) implies a = 0. keywords: a(x; additive; ase; entralizer; f(x; kosi; l(x; left; mapping; math; omplex; operator; relation; right; ring; semiprime; spa; standard; ulbl; vukman; xed cache: cubo-1298.pdf plain text: cubo-1298.txt item: #64 of 481 id: cubo-1299 author: Patil, P. G.; Rayanagoudar, T. D.; Benchalli, S. S. title: Generalization of new continuous functions in Topological spaces date: 2013-10-01 words: 3859 flesch: 91 summary: The following statements are eqivalent for bije tive fun tion f : (X, τ) → (Y, σ) (1) f is somewhat ωα-open fun tion (2) If F is losed subset of X su h that f(F) 6= Y, then there exists a ωα- losed subset D of Y su h that D 6= Y and f(F) (1) ⇒ (2):Let F be a losed subset of X su h that f(F) keywords: example; fun; fun tion; f−1(u; ontinuous; open; set; sin; somewhat; spa; subset; theorem; tion; topologi; ωαlosed cache: cubo-1299.pdf plain text: cubo-1299.txt item: #65 of 481 id: cubo-1300 author: Prakasha, D.G.; Nagaraja, H.G. title: On quasi-conformally flat and quasi-conformally semisymmetric generalized Sasakian-space-forms date: 2013-10-01 words: 4305 flesch: 86 summary: an write the equation (1) as C̃(X, Y, Z, W) = a 1 − 2n f2[g(Y, Z)g(X, W) − g(X, Z)g(Y, W)] +af2[g(X, φZ)g(φY, W) − g(Y, φZ)g(φX, W) + 2g(X, φY)g(φZ, W)] + 3a 1 − 2n f2[g(Y, W)η(X)η(Z) Now with the help of (19) and (20) the equation (21) gives [a + (2n − 1)b][ r 2n + 1 − 2n(f1 − f3)] keywords: 3f2; cubo; form; g(x; g(y; generalized; generalized sasakian; m(f1; manifold; onta; r(x; s(x; sasakian; semisymmetri; spa; spa e; tensor; theorem; urvature; y)z cache: cubo-1300.pdf plain text: cubo-1300.txt item: #66 of 481 id: cubo-1301 author: Saluja, G. S. title: Convergence theorems for generalized asymptotically quasi-nonexpansive mappings in cone metric spaces date: 2013-10-01 words: 6404 flesch: 89 summary: O tober 2013 Convergen e theorems for generalized asymptoti ally quasi-nonexpansive mappings in one metri spa es G. S. Saluja Department of Mathemati s and Information Te hnology, Govt. The mapping T is said to be quasi-nonexpansive if F(T) 6= ∅ and d(Tx, p) � d(x, p) (4) for all x ∈ X and p ∈ F(T). keywords: ally; appl; asymptoti; convergen; cubo; errors; generalized; mappings; math; metri; metri spa; n=1; nonexpansive; normal; onstant; onvex; point; pro; quasi; results; said; sequen; spa; spa e; theorems; type; xed; ‖d(xn cache: cubo-1301.pdf plain text: cubo-1301.txt item: #67 of 481 id: cubo-1302 author: Saleh, M. H.; Amer, S. M.; Mohamed, M. A.; Abdelrhman, N. S. title: Approximate solution of fractional integro-differential equation by Taylor expansion and Legendre wavelets methods date: 2013-10-01 words: 3465 flesch: 86 summary: = 2t1.25 Γ(2.25) − t4 − t5 4 + t2y(t) + ∫t 0 tsy(s) ds , (5.1) with the initial ondition y(0) − t4 − t2et 5 y(t) keywords: approximate; cubo; equation; erential; example; expansion; fra; fra tional; fun; integro; k−1; legendre; m=0; method; m−1∑; n.s.abdelrhman; n=1; order; results; s.m.amer; solution; taylor; tional; tional integro; y(s; y(t;   cache: cubo-1302.pdf plain text: cubo-1302.txt item: #68 of 481 id: cubo-1303 author: Sîntamarian, Alina title: Euler's constant, new classes of sequences and estimates date: 2013-10-01 words: 6713 flesch: 97 summary: CUBO 15, 3 (2013) Euler's onstant, new lasses of sequen es and estimates 119 We have �un+1 − �un = �αn+1 − �αn + 127 30720(n + �c)8 − 127 30720(n + �c − 1)8 . In part (i) of Theorem 2.2 we have proved that lim n→∞ n8(γ − �αn) = 127 30720 . keywords: alina; b2k; best; cubo; estimates; euler; fun; h(x; k=1; lasses; lim; math; ned; new; onstant; proof; property; reasing; remark; rian; sequen; stri; sînt; theorem; tion; γ(a cache: cubo-1303.pdf plain text: cubo-1303.txt item: #69 of 481 id: cubo-1304 author: Sudo, Takahiro title: K-theory for the group C*-algebras of nilpotent discrete groups date: 2013-10-01 words: 4445 flesch: 78 summary: [Z3 ⊗ Z3] ∼= Z 18, K1(C ∗ (G × G)) Our theorem tells us that K0(C ∗ (G × G)) keywords: ase; bott; cubo; c∗(g; c∗-algebra; dire; dis; elements; generalized; generators; group; indu; k0(c; k1(c; lass; lasses; m2(c; nilpotent; non; ommutative; produ; proje; rete; set; theory; tion; torsion; unitary cache: cubo-1304.pdf plain text: cubo-1304.txt item: #70 of 481 id: cubo-1305 author: Anastassiou, George A.; Mezei, Razvan A. title: Uniform convergence with rates of general singular operators date: 2013-06-01 words: 5153 flesch: 92 summary: It holds, for n = 1 |Tr,ξ(f; x) − f(x)| ≤ 3 2π ξ3 ∫∞ −∞ G1(t) ( sin (t/ξ) t )4 dt, (43) and, for n = 2 ∣ ∣ ∣ ∣ Tr,ξ(f; x) − f(x) − f′′(x) 2 δ2c2,ξ − f(4)(x) 24 δ4c4,ξ − f(6)(x) 720 δ6c6,ξ ∣ ∣ ∣ ∣ (62) ≤ 1663200 655177π ξ11 ∫∞ −∞ G6(t) ( sin (t/ξ) t )12 dt. ∣ ∣ ∣ ∣ Tr,ξ(f; x) − f(x) keywords: = ∣; f(x; general; operators; proof; sin; sin t; singular; t t; theorem; ξ(f; ωr(f; ∣ =; ∣ tr; ∣ ∣; ∣ ∫∞; ∣ ≤; ∥ ∥ cache: cubo-1305.pdf plain text: cubo-1305.txt item: #71 of 481 id: cubo-1306 author: Wang, Weihui; Yang, Zuodong title: Nonnegative solutions of quasilinear elliptic problems with sublinear indefinite nonlinearity date: 2013-06-01 words: 3922 flesch: 81 summary: − ur+1λ − (r + 1)u r λu +] (i) let u+ ∈ W 1,p 0 (Ω+a ), and for ‖u +‖ sufficiently small, we have Iλ(u) ≥ 1 p ∫ Ω |∇(uλ + u)| p − 1 p ∫ |Ω∇(uλ + u +)|p + 1 p ∫ Ω |∇uλ| p + ∫ Ω gλ(x, uλ)u + CUBO 15, 2 (2013) Nonnegative solutions of quasilinear elliptic problems ... 29 then, Iλ(u) ≥ 1 p ∫ Ω |∇uλ| p + ∫ Ω gλ(x, uλ)u + ≥ 1 p ∫ Ω |∇uλ| p = Iλ(0) (ii) let v1 ∈ W 1,p 0 (Ω+ b ), v1 ≥ 0, v1 6≡ 0,such that ∫ Ω b(x)vr+1 1 > 0. q < p − 1 < keywords: 1,p; a(x; a(x)u; b(x; cubo; eigenvalue; elliptic; equations; existence; gλ(x; m(x; nonnegative; positive; problem; proof; quasilinear; results; solution; yang; zuodong cache: cubo-1306.pdf plain text: cubo-1306.txt item: #72 of 481 id: cubo-1307 author: Narain, Dhruwa; Yadav, Sunil title: On Weak concircular Symmetries of Lorentzian Concircular Structure Manifolds date: 2013-06-01 words: 3197 flesch: 75 summary: Thus the Lorentzian manifold M together with unit time like concircular vector field ξ, it’s associate 1-form η and (1, 1)–tensor field φ is said to be Lorentzian concircular structure manifolds (briefly (LCS)2n+1-manifold) In [1] De and Ghose introduced the notion of weakly concircular Ricci symmetric manifolds. keywords: a(x; concircular; cubo; field; following; form; g(x; k −; lorentzian; lorentzian concircular; m2n+1; manifold; n −; ricci; riemannian; structure; symmetric; tensor; vector; weakly; weakly concircular; yadav cache: cubo-1307.pdf plain text: cubo-1307.txt item: #73 of 481 id: cubo-1308 author: Wolf, Elke title: Isometric weighted composition operators on weighted Banach spaces of holomorphic functions defined on the unit ball of a complex Banach space date: 2013-06-01 words: 3083 flesch: 85 summary: In this article we are interested in weighted composition operators Cφ,ψ : Hv(BY) → Hw(BY), f 7→ ψ(f ◦ φ). [17] M. Lindström, E. Wolf, Essential norm of differences of weighted composition operators, Monatsh. keywords: analytic; banach; bonet; complex; composition; condition; cubo; functions; h(d; holomorphic; hv(bx; isometric; lindström; math; norm; operators; proof; soc; spaces; sup; ṽ(φ(xn; weighted; wolf; ‖f‖v cache: cubo-1308.pdf plain text: cubo-1308.txt item: #74 of 481 id: cubo-1309 author: Minkevicius, S. title: About cumulative idle time model of the message switching system date: 2013-06-01 words: 3606 flesch: 84 summary: Keywords and Phrases: mathematical models of technical systems, queueing theory, multiphase queueing systems, a law of the iterated logarithm, cumulative idle time of a customer. The works on cumulative idle time for the multiphase queueing systems and open Jackson networks in heavy traffic are also sparse. keywords: 0≤l≤n; a(n; cubo; cumulative; customer; example; f̂j; heavy; i=1; idle; iterated; law; lim; logarithm; max; message; model; multiphase; queueing; queues; switching; system; ŝi; theorem; time; traffic; ẑj cache: cubo-1309.pdf plain text: cubo-1309.txt item: #75 of 481 id: cubo-1310 author: Noiri, Takashi; Popa, Valeriu title: A note on modifications of \(rg\)-closed sets in topological spaces date: 2013-06-01 words: 1414 flesch: 82 summary: the condition ”sCl(A) ⊂ V whenever A ⊂ V and V ∈ RO(X, τ)” does not define a subset like regualr generalized semi-closed sets. [15] means nothing to the family of semi-open sets. RESUMEN Destacamos que una modificación de conjuntos cerrados regulares generalizados debido a Palaniappan and keywords: closed; generalized; math; open; semi; sets; space; subset; topological cache: cubo-1310.pdf plain text: cubo-1310.txt item: #76 of 481 id: cubo-1311 author: Franssens, Ghislain R. title: On the impossibility of the convolution of distributions date: 2013-06-01 words: 2656 flesch: 59 summary: [7] G.R. Franssens, Convolution product formula for associated homogeneous distributions on R, Math. Notice that F′ is again allowed to be a subset of D′. For Schwartz’ set of distributions D′, the convolution defined on D′ Z − is not prolonged to D′, so condition (ii) does not hold, and this allows the existence in D′ of a derivation X and a distribution 1 6= 0 : δ(1) ∗ 1 = 0 (e.g., 1 = X2 ( −πη(1) ) ). keywords: algebra; associated; associative; convolution; derivation; distributions; franssens; functions; homogeneous; impossibility; multiplication; product; schwartz; set; subset; theorem; x2f; δ(1 cache: cubo-1311.pdf plain text: cubo-1311.txt item: #77 of 481 id: cubo-1312 author: Cerin, Zvonko title: Squares in Euler triples from Fibonacci and Lucas numbers date: 2013-06-01 words: 3920 flesch: 87 summary: Since B2 = 5A2, A2 = F2n+3 and C3 = D3 = L2n+5, the product 1 5 A2 B2 C3 D3 is the square of F2n+3L2n+5. k = 5, the infi- nite sequences of triples A = (F2n+1, F2n+3, F2n+5), B = (F2n+1, 5F2n+3, F2n+5), C = (L2n+1, L2n+3, L2n+5), keywords: components; cubo; f2n+3; f4n+6; following; hold; l2n+5; numbers; products; proof; relations; second; sequences; similar; square; sums; theorem; triples; true cache: cubo-1312.pdf plain text: cubo-1312.txt item: #78 of 481 id: cubo-1313 author: Saleh, M.H.; Mohammed, D.Sh. title: Numerical solution of singular and non singular integral equations date: 2013-06-01 words: 3570 flesch: 79 summary: Keywords and Phrases: Linear Hypersingular integral equations, nonlinear integral equations, Chebyshev polynomial, shifted Chebyshev polynomial, Approximate solution. 2010 AMS Mathematics Subject Classification: 45E05; 65R20; 78W23. In part I, we study the approximate solution of Hypersingular integral equations by means of Chebyshev polynomial. keywords: approximate; chebyshev; cubo; equation; f(x; following; hypersingular; integral; k(x; numerical; polynomial; singular; solution; substituting; φ(x; ϕ(t;  ;   cache: cubo-1313.pdf plain text: cubo-1313.txt item: #79 of 481 id: cubo-1314 author: Singh Thakur, Balwant title: An iterative method for finite family of hemi contractions in Hilbert space date: 2013-06-01 words: 1889 flesch: 83 summary: − T1)x‖ 2 + λ ‖(I − T2)x‖ 2 − λ(1 − λ) ‖(T1 Sjxj‖ 2 ≤ ∞∑ j=1 ( ‖xj−1 − p‖ 2 − ‖xj − p‖ 2 ) = ‖x0 − p‖ 2 implies, δ2 ∞∑ j=1 ‖xj−1 − keywords: hemicontractive; hilbert; i=1; iteration; mappings; math; nonexpansive; point; pseudocontractive; snxn‖; space; ‖(i; ‖xn−1 cache: cubo-1314.pdf plain text: cubo-1314.txt item: #80 of 481 id: cubo-1315 author: Farag, M. H.; Talaat, T. A.; Kamal, E. M. title: Existence and uniqueness solution of a class of quasilinear parabolic boundary control problems date: 2013-06-01 words: 2637 flesch: 75 summary: A larage amount of the theoretical concept which governed by quasilinear parabolic equations [1-5] has been investigated in the field of optimal control problems. The study and determination of the optimal regimes of heat conduction processes at a long interval of the change of temperture gives rise to optimal control problems with respect to a quasilinear equation of parabolic type. keywords: class; control; cubo; equation; existence; f(x; i=1; j0(v; optimal; parabolic; problem; quasilinear; solution; theorem; uniqueness; y(x; ωt1; ∂xi; ∂δy; ∆bi cache: cubo-1315.pdf plain text: cubo-1315.txt item: #81 of 481 id: cubo-1316 author: Benchohra, Mouffak; Mostefai, Fatima-Zohra title: Weak Solutions of Fractional Order Pettis Integral Inclusions with Multiple Time Delay in Banach Spaces date: 2013-03-01 words: 4415 flesch: 87 summary: u ∈ V} ≤ β {∑m i=1 gi(x, y)u(x − ξi, y − µi); u ∈ V } +β { 1 Γ(α1)Γ(α2) ∫x 0 ∫y 0 (x − s)α1−1(y − t)α2−1υ(s, t)dsdt; υ(x, y) ∈ F(x, y, u), u ∈ V } ≤ ∑m i=1 β({gi(x, y)u(x − ξi, y − µi); y ∈ keywords: banach; benchohra; closed; cubo; differential; equations; f(x; fractional; function; gi(x; i=1; integral; math; order; pettis; point; s)α1−1(y; solutions; space; t)dsdt; theorem; u(x; weak; weakly; y)u(x; γ(α1)γ(α2; − t cache: cubo-1316.pdf plain text: cubo-1316.txt item: #82 of 481 id: cubo-1317 author: Bohner, Martin; Heim, Julius; Liu, Ailian title: Solow models on time scales date: 2013-03-01 words: 5812 flesch: 86 summary: We also need the set Tκ which is defined in the following way: If T has a left-scattered maximum m, then Tκ = T − {m}. If t ∈ Tκ, then f∆(t) is defined as the number (provided that it exists) such that for every ε > 0, there exists a neighborhood U of t (i.e., U = (t − δ, t keywords: a(t)n(t; ailian; bohner; capital; cobb; conditions; constant; continuous; cubo; douglas; dynamic; equation; example; function; f̃(x; growth; gxα−1; heim; julius; k(t; lim; liu; martin; model; population; production; proof; r)(t; rate; s(t; scales; section; solow; solution; technological; theorem; time; y(t; z(x; µ(t; α−1; δ(t; δ̃κ; σ(t cache: cubo-1317.pdf plain text: cubo-1317.txt item: #83 of 481 id: cubo-1318 author: Gal, Ciprian G.; Gal, Sorin G. title: On Fokker-Planck and linearized Korteweg-de Vries type equations with complex spatial variables date: 2013-03-01 words: 5075 flesch: 85 summary: t ∈ = ea(t)+d(t)[c(t)d(t)+b(t)+z] 2 √ πc(t) ∫∞ −∞ e−[u+b(t)+2c(t)d(t)] 2 /(4c(t))f(ze−iu)du, z ∈ DR. keywords: akz; analytic; a∗(dr; c(t; ciprian; complex; convergent; cos(uτ; cubo; equations; f(z; fokker; gal; integral; k=0; korteweg; planck; proof; real; solutions; sorin; spatial; theorem; t̃k; u(t; variable; vries; ∫+∞ cache: cubo-1318.pdf plain text: cubo-1318.txt item: #84 of 481 id: cubo-1319 author: Chitioui, Taoufik; Ezzinbi, Khalil; Rebey, Amor title: Existence and stability in the α-norm for nonlinear neutral partial differential equations with finite delay date: 2013-03-01 words: 9293 flesch: 88 summary: − Pv(t)|α 6 ‖D2G(t,xt)‖L(Cα,Xα) ‖ut − vt‖α +Mα ∫t 0 ‖D2F(s,xs)‖L(Cα,X)‖us − vs‖α ds (t − s)α 6 ( Lg + MαLf a1−α 1 − α ) − T(t1))A α(ϕ(0) − G(0,ϕ))‖ + kMα‖β‖∞ ∫t2 t1 (t2 − s) −αds +‖(T(t2 − t1) keywords: 0,a; adimy; amor; analysis; analytic; banach; bounded; chitioui; compact; conditions; continuous; cubo; d(a; d(aα; delay; differential; equations; equilibrium; existence; ezzinbi; following; functional; g(0,ϕ; g(t; khalil; lemma; lipschitz; mild; neutral; nonlinear; norm; operator; partial; point; positive; proof; rebey; s)f(s; s)α; semigroup; set; solution; space; stability; stable; strict; sup; t(t; taoufik; theorem; u(t; v(t; v(t))t≥0; x(t; x̃s)ds; z(t; ϕ(0; ϕ2‖α; ‖ϕ‖α cache: cubo-1319.pdf plain text: cubo-1319.txt item: #85 of 481 id: cubo-1320 author: Liu, Junwei; Zhang, Chuanyi title: Existence and stability of almost periodic solutions to impulsive stochastic differential equations date: 2013-03-01 words: 7432 flesch: 85 summary: ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ 2 =E ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∑ 0 n1−β Φ (nx − k) < ( e2 − 1 2 ) = Gn (f, x) − f (x) − N−1∑ j=1 f(j) (x) j! Gn ( (· − x) j ) (x) = θ∗n (x) , (27) where θ∗n (x) := 1 Γ (α) V (x)    ⌊nx⌋∑ k=⌈na⌉ Φ (nx − k) ∫x k n ( J − k n )α−1 Dαx−f (J) dJ + ⌊nb⌋∑ k=⌊nx⌋+1 Φ (nx − k) ∫ k n x ( k n − J )α−1 Dα∗xf (J) dJ    . keywords: anastassiou; f(j; fractional; k n; k=⌈na⌉; neural; α−1; ∞,[a; ∣ ∣ cache: cubo-1332.pdf plain text: cubo-1332.txt item: #98 of 481 id: cubo-1333 author: Mohanta, S.K.; Mohanta, Srikanta title: A common fixed point theorem in G-metric spaces date: 2012-10-01 words: 5060 flesch: 88 summary: x, y ∈ X} = inf { 1 2 | x − y | + 1 2 | x − T(x) |: x, y ∈ X } = 0. x, y ∈ X with y 6= T(y)} = inf {G(x, y, y) + G(x, T(x), T(x)) : keywords: common; complete; corollary; fixed; g(t(x; g(x; g(xn; g(y; inf; metric; point; space; t(x; t(y; t2(x; theorem cache: cubo-1333.pdf plain text: cubo-1333.txt item: #99 of 481 id: cubo-1334 author: Matsumoto, Akio; Szidarovszky, Ferenc title: An elementary study of a class of dynamic systems with two time delays date: 2012-10-01 words: 3298 flesch: 83 summary: cos(υγ1)[υγ2 − ω(γ2 − γ1) sin(υγ1)] − ω)) is strictly increasing in υ, γ2 is strictly decreasing in υ. keywords: 2kπ; 2nπ; 2υω; analysis; case; class; cos(υγ1; cubo; curves; delays; dynamic; elementary; equation; l1(k; l2(k; region; segment; sin(υγ1; sin−1; stability; switches; systems; υγ2; − ω;   cache: cubo-1334.pdf plain text: cubo-1334.txt item: #100 of 481 id: cubo-1335 author: Rao, K.P.R.; Kishore, G.N.V.; Van Luong, Nguyen title: A unique common coupled fixed point theorem for four maps under ψ - φ contractive condition in partial metric spaces date: 2012-10-01 words: 3645 flesch: 92 summary: Regarding the concept of coupled fixed points introduced by Bhaskar and Lakshmikantham [17], in [4], Aydi proved some coupled fixed point theorems for the mappings satisfying contractive conditions in partial metric spaces. Using concept of coupled fixed points, Luong and Thuan in [18] proved some coupled fixed point theorems for a mapping F : X × X → X satisfying the following contractive condition in the partially ordered metric spaces (X,d,≤) ψ(d(F(x,y),F(u,v))) keywords: cauchy; common; cubo; f(x; fixed; lim; luong; max{ps(z2mk; metric; nguyen; n→∞; p(fu; p(fv; p(v; p(w2n; p(x; p(xn; partial; point; spaces; theorem; unique; w2n; w2nk; z2n; z2n−1; ψ(p(u cache: cubo-1335.pdf plain text: cubo-1335.txt item: #101 of 481 id: cubo-1336 author: Ibrahim, Rabha W. title: Existence of deviating fractional differential equation date: 2012-10-01 words: 4389 flesch: 79 summary: Thus we have ‖Pu − Pv‖B ≤ L̂‖u − v‖B, which shows that P is Lipschitzian, hence continuous. − f(τ, v(τ), v(v(τ)))|dτ ≤ ∫t 0 (t − τ)α−1 Γ(α) keywords: banach; cauchy; convex; cubo; differential; equations; existence; expansive; f(τ; fixed; fractional; function; ibrahim; initial; iteration; iterative; liouville; mapping; math; non; operators; order; point; problem; rabha; riemann; solutions; space; subset; t2|; theorem; u(t; u(τ; value; |t1; γ(α; τ)α−1; ∣∣∣ cache: cubo-1336.pdf plain text: cubo-1336.txt item: #102 of 481 id: cubo-1337 author: Banerjee, Shrabani; Choudhury, Binayak S. title: Weak and strong convergence theorems of a multistep iteration to a common fixed point of a family of nonself asymptotically nonexpansive mappings in banach spaces date: 2012-10-01 words: 9558 flesch: 94 summary: − an1 − bn1)xn + an1T1(PT1) n−1yn+r−2 +bn1T1(PT1) n−1yn+r−3] (1.8) where {ani}, {bni}, {1 − ani − bni} are appropriate real sequences in [0, 1] for i − λm−1)( λm 1 − λ1 − λ2 − .... keywords: a1ni)(1 −; banach; banerjee; binayak; bnj; convergence; convex; cubo; exists; follows; i=1; infn→∞; iteration; iterative; j(p1 −; k=1; kin; lemma; lim; limn→∞; mappings; math; multistep; n(r−1; n2 −; n=1; nonempty; nonexpansive; nonself; nr −; n−1xn −; p[(1 −; point; real; s.choudhury; sequence; shrabani; space; strong; subset; theorems; uniformly; weak; λ1 −; ‖xn+1 −; − a1n(r−1; − bnr)g1(‖tr(ptr; − p2; − q‖; − t)p1; − xn‖; − y‖; − λ2; − λm−1 cache: cubo-1337.pdf plain text: cubo-1337.txt item: #103 of 481 id: cubo-1338 author: Raj, Kuldip; Sharma, Sunil K. title: Some generalized difference double sequence spaces defined by a sequence of Orlicz-functions date: 2012-10-01 words: 9800 flesch: 91 summary: Let lim i→∞ xik,l = xk,l, say for k, l = 1, 2, ...., nm. Proceeding in this way inductively, we have lim i→∞ xik,l = xk,l exists for each k, keywords: cubo; difference; double; inf; kl)−suk; l h; l k; l pk; l δ; l ρ; l ρ1; l ρ2; l=1; let; lim; lim k; lmk; math; m′′k; numbers; orlicz; positive; proof; sequence; spaces; sup; sup k; zn−1||; ∆mn; ∆mn xk cache: cubo-1338.pdf plain text: cubo-1338.txt item: #104 of 481 id: cubo-1339 author: Verma, Ram U. title: The ϵ−Optimality conditions for multiple objective fractional programming problems for generalized (ρ, η)−invexity of higher order date: 2012-06-01 words: 4400 flesch: 75 summary: Let S∗ ∈ Q, let Fi, Gi, i ∈ {1, ..., p}, and Hj, j ∈ {1, ..., m}, be differentiable at S∗ ∈ Λ, and let there exist u∗ Let S, S∗ ∈ X, let the function F : X → ℜn with components Fi for i ∈ {1, ..., n}, be differentiable at S ∗. Definition 2.1. keywords: conditions; fi(s; function; generalized; gi(s; higher; invex; order; η(s; ∗ ∈ cache: cubo-1339.pdf plain text: cubo-1339.txt item: #105 of 481 id: cubo-1340 author: Ouaro, Stanislas title: Weak and entropy solutions for a class of nonlinear inhomogeneous Neumann boundary value problem with variable exponent date: 2012-06-01 words: 8994 flesch: 92 summary: Then, ( |u1| p(x)−2 u1 − |u2| p(x)−2 u2 ) Tk(u1 − u2) ≥ 0, ∀x ∈ Ω and ∀k > 0. then (u − ϕ) ∈ T 1,p(.) tr (Ω) and tr(u − ϕ) = tr(u) keywords: + ∫; = ∫; a(x,∇u1).∇(u1; a.e; boundary; class; converges; cubo; entropy; existence; exponent; following; follows; function; inequality; j(u; l(p−; lemma; lp(.)(ω; math; meas(ω; measurable; measure; neumann; nonlinear; ouaro; p(x)dx; p(x)−2; problem; proof; proposition; result; section; solution; space; stanislas; theorem; tk(un; u2)dx; uniqueness; v)dx; variable; w1,p(.)(ω; weak; |u2|; |u|p(x)−2; ‖f‖l1(ω; − ∫; ∣ ∣; ≤ ∫ cache: cubo-1340.pdf plain text: cubo-1340.txt item: #106 of 481 id: cubo-1341 author: Gamara, Najoua; Ben Ahmed, Ali; Amine, Aribi title: A New proof of the CR Pohožaev Identity and related Topics date: 2012-06-01 words: 5638 flesch: 79 summary: Given a piecewise C1 bounded domain Ω ⊂ Hn, we say that it is δ−starshaped with respect to a point ξ0 ∈ Ω, if denoting by N the outer unit normal to the boundary of τξ−1 0 (Ω), we have X.N ≥ 0 Hn be a bounded and connected domain such that 0 = (0, 0, 0) ∈ Ω and Ω is δ−starshaped with respect to this point. keywords: ahmed; ali; amine; aribi; a∇u; ben; boundary; br(ξ̄; c(ω; critical; cubo; domain; dvθ0; equation; existence; following; function; g(u; gamara; group; heisenberg; identity; lemma; najoua; new; non; pohoz̆aev; positive; problem; proof; respect; result; semilinear; solution; theorem; vector; yamabe; |∇hnu|; ω u; ∂xi; −∆hu cache: cubo-1341.pdf plain text: cubo-1341.txt item: #107 of 481 id: cubo-1342 author: Luna, M. E.; Shapiro, M.; Struppa, D. C.; Vajiac, A. title: Bicomplex Numbers and their Elementary Functions date: 2012-06-01 words: 7198 flesch: 75 summary: M.E. Luna-Elizarrarás, M. Shapiro Departamento de Matemáticas, E.S.F.M del I.P.N., México. and D.C. Struppa1, A. Vajiac Schmid College of Science and Technology, Chapman University, Orange California, 1 email: struppa@chapman.edu ABSTRACT In this paper we introduce the algebra of bicomplex numbers as a generalization of the field of complex numbers. Instead of considering (z1,z2) as a point in C 2 we now consider, in analogy with what we did in the case of R2, a new space whose elements are of the form Z = z1 + jz2, where j is a new imaginary unit (i.e. j 2 = −1), which commutes with the original imaginary unit i. This creates a new algebra, the algebra of bicomplex numbers, and as we will CUBO 14, 2 (2012) Bicomplex Numbers and their Elementary Functions 63 show in the next sections, such an algebra enjoys most of the properties one would expect from a good generalization of the field of complex numbers. keywords: algebra; algebraic; bicomplex; bicomplex numbers; case; component; cos(z2; cosz; cubo; d.c; definition; elementary; elizarrarás; equation; example; exponential; ez1; following; form; formula; functions; holomorphic; idempotent; imaginary; inverse; invertible; jz2; limit; logarithm; luna; m.e; new; numbers; p(z; polynomials; properties; real; representation; roots; set; shapiro; sin(z2; solutions; structure; struppa; system; theory; trigonometric; vajiac; variable; z21 cache: cubo-1342.pdf plain text: cubo-1342.txt item: #108 of 481 id: cubo-1343 author: D’alessandro, Paolo title: An immediate derivation of maximum principle in Banach spaces, assuming reflexive input and state spaces date: 2012-06-01 words: 4087 flesch: 70 summary: But, also, ζ ∈ Rρ implies ∃u s.t.‖u‖ ≤ email: dalex@mat.uniroma3.it ABSTRACT We consider a standard setting for the norm optimal problem in Banach spaces and show that with a simple argument which invokes some appropriately selected powerful general Theorems for Banach spaces a straightforward derivation of the Maximum Principle is obtained. RESUMEN Consideramos una formulación estándar keywords: banach; case; closed; condition; cone; continuous; control; convex; cubo; extreme; fattorini; functionals; interior; linear; maximum; norm; optimal; points; principle; reachable; reflexive; set; sets; setting; spaces; state; support; theorem; void cache: cubo-1343.pdf plain text: cubo-1343.txt item: #109 of 481 id: cubo-1344 author: Breteaux, Sébastien title: Higher order terms for the quantum evolution of a Wick observable within the Hepp method date: 2012-06-01 words: 11849 flesch: 78 summary: Writing T = L + A with L the C-linear and A the C-antilinear part of T we obtain |T∗z| 2 − |z| 2 = 〈L∗z,L∗z〉 + 〈A∗z,A∗z〉 + 〈L∗z,A∗z〉 + 〈A∗z,L∗z〉 − 〈z,z〉 = 〈z,LL∗z〉 + 〈z,AA∗z〉 + 〈LA∗z,z〉 + 〈z,LA∗z〉 − 〈z,z〉 = 〈z,2AA∗z〉 + 〈 v,z∨ 2 〉 + 〈 z2,v 〉 with v ∈ ⊗2 Z the vector such that for all z1, z2 ∈ Z, 〈z1 ⊗ z2,v〉 = 〈z1,LA∗z2〉. ,Qσ}(2)Wick U(σ,0)dσ holds as an equality of continuous operators from D(〈N〉m/2) to H, with 〈N〉 = (N2 + 1)1/2. keywords: adjoint; antilinear; application; associated; bogoliubov; breteaux; case; classical; comm; conjugation; continuous; cubo; definition; dimension; equality; equation; estimate; evolution; example; expansion; family; field; finite; flow; following; formula; fourier; general; hfin; higher; hilbert; implementable; lemma; limit; linear; math; mean; operator; order; parameter; phys; polynomial; proof; proposition; p≤m; quadratic; quantization; quantum; remark; respect; result; schmidt; second; section; self; semiclassical; set; sébastien; solution; space; symbol; symplectic; symplectomorphism; terms; theorem; time; transform; transformations; u(t; use; vector; weyl; wick; |z|2; ε/2; πε/2; ϕ(t; ϕ(t,0; ∂2z cache: cubo-1344.pdf plain text: cubo-1344.txt item: #110 of 481 id: cubo-1345 author: Grove, E. A.; Lapierre, E.; Tikjha, W. title: On the global behavior of 𝑥ᵤ₊₁ = |𝑥ᵤ|− 𝑦ᵤ − 1 and 𝑦ᵤ₊₁ = 𝑥ᵤ +|𝑦ᵤ| date: 2012-06-01 words: 10175 flesch: 99 summary: x8K+3 + |y8K+3| = 24K+1x0 − 2 4K+1y0 + 2DK − 2 4K+1x0 − 2 4K+1y0 − 6DK − 1 = −24K+2y0 Hence x8K+2 = |x8K+1| − y8K+1 − 1 = 24Kx0 + 2 4Ky0 + 3DK + 1 − 2 4Kx0 + keywords: 22k; 22m+2; = −; behavior; case; claim; cubo; cycle; e.a; global; grove; integer; lapierre; lemma; period-3; period-3 cycle; proof; solution; statement; tikjha; true; xn+1; xn+2; xn+3; yn+1; yn+2; ≤ − cache: cubo-1345.pdf plain text: cubo-1345.txt item: #111 of 481 id: cubo-1346 author: Kian, Yavar title: Local energy decay for the wave equation with a time-periodic non-trapping metric and moving obstacle date: 2012-06-01 words: 7723 flesch: 85 summary: According to (1.7), Rψ1,ψ2(θ) is a family of bounded operators analytic with respect to θ on {θ ∈ C : I(θ) > AT}. Then, Rψ1,ψ2(θ) admits a meromorphic continuation from {θ ∈ C : I(θ) > keywords: a(t; arguments; continuation; cubo; c∞0; decay; divx(a(t; energy; equation; estimate; existence; e−idθf′; finite; following; i(θ; kian; lemma; local; math; meromorphic; metrics; mixed; non; o(t; obstacle; odd; operator; p(t; periodic; perturbations; petkov; problem; proof; q(t; respect; results; rψ1,ψ2(θ; s)ψ2)(t; section; solution; theorem; time; trapping; u(t; u(t,0; v(t; wave; yavar; θ)dθ cache: cubo-1346.pdf plain text: cubo-1346.txt item: #112 of 481 id: cubo-1347 author: Kovalevsky, Alexander A.; Nicolosi, Francesco title: On a condition for the nonexistence of \(W\)-solutions of nonlinear high-order equations with L\(^1\) -data date: 2012-06-01 words: 2639 flesch: 78 summary: For instance, if p < 2 − m/n, y ∈ Ω, v : Ω → R is a function such that for every x ∈ Ω\{y}, v(x) = ln |x − y|, B is a closed ball in Rn with the center y such that B ⊂ Ω, ψ1 ∈ C ∞ 0 (Ω) and ψ1 = 1 in B, then vψ1 ∈ ◦ Wm,p1(Ω)\L∞(Ω). (2.2) Then there exists f ∈ L1(Ω) such that problem (Pf) does not have W-solutions. Proof. keywords: a(x; condition; data; equations; function; hand; l1(ω; nonlinear; order; problem; solutions; α∈λ cache: cubo-1347.pdf plain text: cubo-1347.txt item: #113 of 481 id: cubo-1348 author: Sudo, Takahiro title: K-theory for the C*-algebras of continuous functions on certain homogeneous spaces in semi-simple Lie groups. date: 2012-06-01 words: 4176 flesch: 89 summary: ∼= K0(C) ∼= Z, K1(C ∗(R2n)) ∼= K0(C) ∼= Z, K0(C ∗(Tn)) keywords: case; continuous; cubo; c∗-algebras; exact; following; functions; group; homogeneous; k0(c; k1(c; k−1; n−1)n; odd; product; quotient; r)+; sequence; short; sn−1; so(n; space; sudo; theory; ←−−−−; −−−−→ cache: cubo-1348.pdf plain text: cubo-1348.txt item: #114 of 481 id: cubo-1349 author: Anastassiou, George A. title: Univariate right fractional Ostrowski inequalities date: 2012-03-01 words: 1914 flesch: 92 summary: ∫b x (J − x) m−α−1 (b − J) α−m dJ = α(α − 1) ...(α − m + 1) Γ (m − α) ∫b x (b − J) (α−m+1)−1 (J − x) (m−α)−1 dJ = α(α − 1) ...(α − m + 1) Γ (m − α) Γ (α − m + 1)Γ (m − α) Γ (1) = α(α − 1) ...(α − m + 1)Γ (α − m − 1) (α − 2) ...(α − m + 2) (α − m keywords: f(b; f(x)dx; fractional; inequalities; ostrowski; right; |f(x; α−1; ∣∣∣∣∣; ∥∥dαb−f∥∥∞,[a cache: cubo-1349.pdf plain text: cubo-1349.txt item: #115 of 481 id: cubo-1350 author: Wolf, Elke title: Integral composition operators between weighted Bergman spaces and weighted Bloch type spaces date: 2012-03-01 words: 3455 flesch: 85 summary: Lemma 2 yields that for every f ∈ Av,p and every h, z ∈ D with z + h ∈ D, we have |f(z + h) − f′(w)| ≤ C 1 p M 1 p 1 M 2 p +1 2 v(0) 1 p |ϕw(z)|r‖f‖v,p (r − |ϕw(z)|)2(1 − |w|2) 2 p +1 v(w) 1 p ≤ 4C 1 p M 1 p 1 M 2 p +1 2 v(0) 1 p ρ(z, w)‖f‖v,p r(1 − |w|2) 2 p +1 v(w) 1 p . keywords: bergman; bloch; composition; condition; cubo; functions; h(d; integral; lemma; math; max; operators; p +1; spaces; sup; type; v(0; v(w; v(z; weighted; weights; wolf; |w|2; |z|2; ρ(z; ‖f‖v cache: cubo-1350.pdf plain text: cubo-1350.txt item: #116 of 481 id: cubo-1351 author: Bernardino, A. Thiago title: Remarks on cotype and absolutely summing multilinear operators date: 2012-03-01 words: 2005 flesch: 78 summary: If Xj has finite cotype sj ≥ 2, j = 1, ..., k and 1 ≤ 1/s1 + · · · + 1/sk, then Πnp;p1,...,pk,q,...,q (X1, ..., Xn; Y) j Π n r;r1,...,rk,q,...,q (X1, ..., Xn; Y) , where pj = p and rj = r for all j = 1, ..., k, for all r [15] D. Popa, Reverse inclusions for multiple summing operators, J. Math. keywords: cotype; multilinear; operators; pellegrino; spaces; summing; theorem cache: cubo-1351.pdf plain text: cubo-1351.txt item: #117 of 481 id: cubo-1352 author: Dimassi, Mouez; Zerzeri, Maher title: Spectral shift function for slowly varying perturbation of periodic Schrödinger operators date: 2012-03-01 words: 7221 flesch: 79 summary: March 2012 Spectral shift function for slowly varying perturbation of periodic Schrödinger operators. Paris 13, LAGA, (UMR CNRS 7539), F-93430 Villetaneuse, France, email: zerzeri@math.univ-paris13.fr ABSTRACT In this paper we study the asymptotic expansion of the spectral shift function for the slowly varying perturbations of periodic Schrödinger operators. keywords: absorption; assume; assumption; asymptotic; class; classical; cubo; c∞0; dimassi; domain; ej,−+(z; energy; expansion; f(µ; following; function; hamiltonian; identity; l2(t∗; lemma; math; neighborhood; non; operator; p(h; p(k; periodic; perturbation; perturbed; potential; proof; proposition; pseudodifferential; r;h; r;z; recall; respect; scattering; schrödinger; semi; shift; simple; small; spectral; ssf; subsection; theorem; theory; trace; zerzeri; λ(k; λp(k; ϕ(x cache: cubo-1352.pdf plain text: cubo-1352.txt item: #118 of 481 id: cubo-1353 author: Danchev, Peter title: Units in Abelian Group Algebras Over Direct Products of Indecomposable Rings date: 2012-03-01 words: 1847 flesch: 77 summary: [Dc] P. V. Danchev, Warfield invariants in commutative group rings, J. Algebra Appl. Mollov and N. A. Nachev, Unit groups of commutative group rings, Commun. keywords: abelian; algebras; commutative; cubo; danchev; direct; exp(g0; finite; group; indecomposable; isomorphism; mixed; prime; rings; u(rg; units cache: cubo-1353.pdf plain text: cubo-1353.txt item: #119 of 481 id: cubo-1354 author: Burton, T. A.; Zhang, Bo title: Bounded and periodic solutions of integral equations date: 2012-03-01 words: 7305 flesch: 91 summary: = D(t, s)(t − s)2 ∣∣∣t b + 2 ∫t b D(t, s)(t − s)ds = −D(t, b)(t − b)2 + 2 ∫t b D(t, s)(t − s)ds for each b < t. Since D(t, s) ≥ 0 and Ds(t, s) ≥ 0, letting b → −∞, we see that∫t −∞Ds(t, s)(t − s) ≤ p ≤ T, and for s ≤ hn we have ∫hn s |g(x(v))|dv ≤ ∫tn+1 s |g(x(v))|dv ≤ M(tn+1 − s). keywords: a(t; boundedness; burton; c(t; constant; continuous; convex; ct(t; cubo; d(t; ds(t; equations; functional; g(x(u))du; hold; integral; liapunov; periodic; proof; s)ds; s)g(x(s))ds; solution; sup; t)g(x; theorem; t−h; v(t; x(t; xg(x; zhang; |cs(t; |x|; ∣∣∣∣; ∫t s; ∫t t−h; ∫tn cache: cubo-1354.pdf plain text: cubo-1354.txt item: #120 of 481 id: cubo-1355 author: Goswami, Anjali title: Special recurrent transformation in an NPR-Finsler space date: 2012-03-01 words: 3487 flesch: 83 summary: (4.19) Now £Hijk = LH i jk + µH i jkrv r − µrH r jkv i + µjH i rkv r + µkH i jrv r. Transvecting (4.19) by vm and using (3.2) in the above equation, we get = (δih − l ilh)lrv r + li(ghr − lhlr)v r. Contracting the indices i and h and using δii = n and l rlr = 1, we get (n − 1)lrv r = 0. keywords: affine; bjµk; commutation; cubo; curvature; differentiating; field; finsler; formula; hijk; jkh; kind; motion; npr; pandey; recurrent; respect; space; special; tensor; transformation; transvecting; vector; view; ẋi; µjk cache: cubo-1355.pdf plain text: cubo-1355.txt item: #121 of 481 id: cubo-1356 author: Georgiev, S.; Morais, J.; Spross, W. title: New Aspects on Elementary Functions in the Context of Quaternionic Analysis date: 2012-03-01 words: 6048 flesch: 76 summary: [f(p)]3k, where the coordinate-functions [f]i (i = 0,1,2,3) are real-valued functions defined in H. As in the case with complex functions we have the standard operations on quaternion functions. The proof is a consequence of Theorem 3.6. 4 Trigonometry revisited In this section we define quaternion trigonometric functions. keywords: 0,±1,±2; analysis; arccos; arg(p; aspects; complex; context; cos(p; cosine; cubo; definition; elementary; exponential; following; follows; functions; general; georgiev; hyperbolic; inequality; inverse; lim; ln(1; ln(p; logarithm; loge; morais; multiple; n=1; natural; new; number; n−→∞; p20; proof; properties; quaternion; real; sequence; sgn(p; spröß; theorem; trigonometric; value; |p|; |p|2; ν=1; ∣∣∣1 cache: cubo-1356.pdf plain text: cubo-1356.txt item: #122 of 481 id: cubo-1357 author: Maher, Philip J.; Sal Moslehian, Mohammad title: More on approximate operators date: 2012-03-01 words: 2266 flesch: 75 summary: − I‖ ≤ � there corresponds a unitary operator U such that ‖T − U‖ < �. f∥∥ ≤ �‖f‖p (a) and ‖ [ T2T∗ − T ] f‖ ≤ �‖f‖p (b) 114 Philip J. Maher and Mohammad Sal Moslehian CUBO 14, 1 (2012) for given � > 0 and a real number p. keywords: approximate; b(h; cubo; exact; example; generalized; i]f‖; inverse; isometries; isometry; lemma; moslehian; operator; partial; proof; real; ‖f‖p cache: cubo-1357.pdf plain text: cubo-1357.txt item: #123 of 481 id: cubo-1358 author: Eljamal, E. A.; Darus, M. title: Majorization for certain classes of analytic functions defined by a new operator date: 2012-03-01 words: 2011 flesch: 84 summary: + (D0f(z))′ zλ1 p + λ2(k − p) = zp + Σ∞k=p+1 [ p + (λ1 + λ2)(k − p) p + λ2(k − p) ] akz k, and D2n,λ1,λ2,p = D 1 n,λ1,λ2,p f(z) 121 = zp + Σ∞k=p+1 [ p + (λ1 + λ2)(k − p) p + λ2(k − p) ]2 akzk. keywords: analytic; class; darus; derivative; f(z; functions; majorization; nλ1,λ2,pg(z; operator; p+1; p+λ2(k−p; λ2(k cache: cubo-1358.pdf plain text: cubo-1358.txt item: #124 of 481 id: cubo-1359 author: Argyros, Ioannis K.; Hilout, Saïd title: On the semilocal convergence of Newton–type methods, when the derivative is not continuously invertible date: 2011-10-01 words: 4124 flesch: 84 summary: ‖ ≤ ‖ x − y ‖ (2 γ + 3 (‖ x ‖ + ‖ y ‖)) 8 ≤ ‖ x − y ‖ (2 γ + 6 R + 6 ‖ u0 ‖) 8 = γ + 6 R + 3 4 ‖ x − y ‖, ‖ F′(x) − F′(u0) On the semilocal convergence of Newton–type · · · 11 Concerning the error estimates, if: (L − 2 L0) η + 2 (a + 1) 1 − L0 η (1 − η) + L η < 1 + 2 a, (3.6) then, we have v0 = t0, v1 = t1, v2 = t2, t3 − t2 < v3 − v2. keywords: argyros; banach; convergence; cubo; equation; hilout; hold; methods; newton; operator; q(s; semilocal; sequence; solution; space; theorem; tk+1; tm+1; type; u(x0; xm+1; xn+1 cache: cubo-1359.pdf plain text: cubo-1359.txt item: #125 of 481 id: cubo-1360 author: Mezei, Razvan A. title: Applications and Lipschitz results of approximation by smooth Picard and Gauss-Weierstrass type singular integrals date: 2011-10-01 words: 10298 flesch: 98 summary: γ ≤ 1, for any δ > 0.Then ‖∆(x)‖p ≤ (Γ (p (r − 1 + γ + n) + 1)) 1 p 2(r+γ+n)K [ (n − 1)!q 1 q p r− 1 q +γ+n (q(n − 1) + 1) 1 q (p (r − 1 + γ) keywords: condition; corollary; cubo; f(x; lipschitz; proof; proposition; section; singular; theorem; |t|; ξ(f; ω2(f cache: cubo-1360.pdf plain text: cubo-1360.txt item: #126 of 481 id: cubo-1361 author: Kumar Saraf, Ratnesh; Caldas, Miguel title: On strongly Fβp-irresolute mappings date: 2011-10-01 words: 3194 flesch: 84 summary: Define fuzzy sets A(a) [22] Yalvac T.H., Fuzzy sets and functions on fuzzy spaces, J. Math Anal. keywords: closed; continuous; cubo; f(a; f(xt; fpo(x; fuzzy; fuzzy β; fβp; f−1(v; irresolute; mapping; math; open; point; preirresolute; resp; saraf; set; sets; spaces; theorem; topological cache: cubo-1361.pdf plain text: cubo-1361.txt item: #127 of 481 id: cubo-1362 author: Banerjee, Abhijit title: Some uniqueness results on meromorphic functions sharing three sets II date: 2011-10-01 words: 5043 flesch: 92 summary: We say that f and g share a CM, provided that f − a and g − a have the same zeros with the same multiplicities. Similarly, we say that f and g share a IM, provided that f − a and g − a have the same zeros ignoring multiplicities. keywords: + s(r; constant; definition; functions; g share; integer; lemma; let; meromorphic; multiplicity; n +; n(r; non; points; proof; share; sharing; theorem; uniqueness cache: cubo-1362.pdf plain text: cubo-1362.txt item: #128 of 481 id: cubo-1363 author: Massamba, Fortune title: Lightlike geometry of leaves in indefinite Kenmotsu manifolds date: 2011-10-01 words: 8916 flesch: 75 summary: Y − 2g(φ X, Y)φ − v(ANX)E − v(A ∗ EX)N + φ(ANX) + τ(X)U, (4.8) keywords: b(x; bundle; c(x; civita; connection; contact; cubo; curvature; distribution; field; follows; form; fundamental; g(x; g(y; geodesic; geometry; hypersurface; indefinite; integrable; kenmotsu; killing; leaf; leaves; levi; lie; lightlike; lightlike hypersurface; local; m(c; manifolds; massamba; metric; non; parallel; proof; respect; riemannian; s(tm; sasakian; screen; second; semi; space; structure; submanifolds; tangent; tensor; theorem; umbilical; vector; φ(n(tm; φ(tm⊥ cache: cubo-1363.pdf plain text: cubo-1363.txt item: #129 of 481 id: cubo-1364 author: Khaled, Hleili; Slim, Omri; Rachdi, Lakhdar title: Uncertainty principle for the Riemann-Liouville operator date: 2011-10-01 words: 8050 flesch: 88 summary: respectively q. Let us pick d1,d2 ∈ R, such that d1 > 2α + 3 and d2 > 2. If ∫ ∫ Γ+ ∫ keywords: = ∫; beurling; cubo; dm2(r; dγ̃α(µ,λ; dνα(r; e |(r; fourier; function; hleili; hörmander; khaled; lakhdar; liouville; measurable; omri; operator; polynomial; principle; proof; r |f(r; rachdi; real; relation; respect; riemann; slim; theorem; transform; uncertainty; variable; x)dm2(µ,λ; x)||(µ,λ)|; |f(r; |wα(f)(r; ∫ +; ∫ r cache: cubo-1364.pdf plain text: cubo-1364.txt item: #130 of 481 id: cubo-1365 author: Diagana, Toka; Mohamed, Ahmed title: Pseudo-almost automorphic solutions to some second-order differential equations date: 2011-10-01 words: 8100 flesch: 82 summary: = P(t), u ∈ Rn, t ∈ R, (1.1) where A is an n×n-matrix whose eigenvalues are positive, c,d,k are positive constants, H : Rn 7→ R n is a locally Lipschitz function, P : In this paper, using techniques developped in [36], we obtain some reasonable sufficient con- ditions, which do guarantee the existence of pseudo-almost automorphic solutions to u′′(t) + au′(t) + bAu = f(t,u), t ∈ R, (1.2) where A : D(A) keywords: abstract; ahmed; anal; applications; automorphic; banach; continuous; cubo; d(a; diagana; differential; equations; evolution; existence; f(t; following; functions; lim; linear; math; mohamed; n=1; norm ∥; operator; order; parabolic; partial; periodic; pseudo; second; sectorial; semigroup; solutions; space; theorem; toka; ∣ ∣; ∥ ds; ∥ eju; ∥ f1(s; ∥ k−1n; ∥ t(t)px; ∥ u(t; ∥ v(s; ∥ β; ∥ ψ(t; ∥ ∥; ∥ ;   cache: cubo-1365.pdf plain text: cubo-1365.txt item: #131 of 481 id: cubo-1366 author: Kumar Hui, Shyamal title: On weak concircular symmetries of trans-Sasakian manifolds date: 2011-10-01 words: 4074 flesch: 85 summary: [ (2n − 1){α2 − (ξβ) −β2} − n − 2 n(n − 1) r ] + [ α 2 − (ξβ) − β2 − r n(n − 1) ] η(U)D(ξ). [ (2n − 1){(α2 − β2)η(U) − (Uβ)} − ((φU)α) − n−2 n(n−1) rη(U) (2n − 1){α2 − (ξβ) − β2} − n−2 n(n−1) r ] − 2n{2α(ξα) − 2β(ξβ) − (ξ(ξβ))} keywords: a(x; associated; concircular; forms; manifold; n(n −; r n; ricci; sasakian; symmetric; tensor; trans; weakly; ξ(ξβ; − 1){(xβ; − dr(x; − n−2; − r; − β2 cache: cubo-1366.pdf plain text: cubo-1366.txt item: #132 of 481 id: cubo-1367 author: Holm, Michael title: Sum and Difference Compositions in Discrete Fractional Calculus date: 2011-10-01 words: 10980 flesch: 87 summary: [ µ + 1 Γ (ν) t−ν∑ s=a+µ (t − σ(s))ν−1(s − a)µ − (t − ν + 1 − a)µ+1 ] . − ∆k−1f(a) Γ (ν) (t − a)ν−1 = ∆2−νa ∆ k−2 f(t) − ∆k−1f(a) Γ (ν) (t − a)ν−1 − ∆k−2f(a) Γ (ν − 1) (t − a)ν−2 = · · · · · · · · · · · · · · · · · · · · · · ·· = ∆k−νa f(t) − k∑ i=1 ∆k−if(a) Γ (ν − i + 1) (t − a)ν−i = ∆k−νa f(t) keywords: a+m−µ∆; af(t; calculus; case; compositions; cubo; definition; difference; domains; f(a +; f(s; f(t; fractional; function; general; holm; i=0; i=1; initial; j +; k=0; m −; michael; n −; na+n−ν; na+µ+ν; na+ν; n−1∑; order; p=0; paper; power; problem; proof; r =; rule; solution; sum; sums; t −; theorem; t−ν∑; value; y(t; ν −; νth; σ(s))ν−1(s −; ∆−νa; − a)µ; − a)ν−1; − k; − k−1∑; − m−1∑; − p; − µ; − σ(s))ν−1 cache: cubo-1367.pdf plain text: cubo-1367.txt item: #133 of 481 id: cubo-1368 author: Verma, Ram U. title: Linear convergence analysis for general proximal point algorithms involving (H, η) − monotonicity frameworks date: 2011-10-01 words: 3467 flesch: 68 summary: if 〈u∗ − v∗, u − v〉 ≥ ‖u The map M is said to be: (i) (η)− monotone if 〈u∗ − v∗, η(u, v)〉 ≥ 0 keywords: algorithm; analysis; applications; constant; convergence; cubo; generalized; graph(m; h(x∗)‖; journal; mapping; monotone; monotonicity; nonlinear; point; problems; proximal; variational; verma; η)− cache: cubo-1368.pdf plain text: cubo-1368.txt item: #134 of 481 id: cubo-1369 author: Rachdi, L.T.; Rouz, A. title: Homogeneous Besov spaces associated with the spherical mean operator date: 2011-06-01 words: 11218 flesch: 95 summary: Rn (∫b a f ∗ φt ∗ φt(s,y) dt t ) τ(r,−x)ψ̌(s,y) dνn(s,y), and by Fubini’s theorem, we obtain f ∗ ψ(r,x) = lim a→0+ b→ +∞ ∫b a (∫ +∞ 0 ∫ From i) of Proposition 8, we deduce that the function f ∗ φt ∗ φt belongs to the space E∗ ( R × keywords: + ∞; 1,νn; 2n+1; = +; = ∫; a.rouz; besov; cubo; dt t; dνn(s; function; g(t; homogeneous; l.t.rachdi; lp(dνn; math; mean; operator; proof; relation; s1∗,0(r; space; spherical; s∗(r; theorem; transform; µ,λ; φt(r; φρs; ∈ r; ∥∥φ; ∥∥ψ; ∫ + cache: cubo-1369.pdf plain text: cubo-1369.txt item: #135 of 481 id: cubo-1370 author: Gal, Sorin G. title: Remarks on the generation of semigroups of nonlinear operators on p-Fréchet spaces, 0 < p < 1 date: 2011-06-01 words: 9348 flesch: 86 summary: One of the main result in [5] is the Chernoff-type formula etA(x) = ĺımn→ ∞ ( I − t n A )−n (x), for A a bounded linear operator on a p-Fréchet space with 0 < ∈ lp, the real functions gk,r(x)(t) are differentiable (in the classical sense) with respect to t ∈ keywords: a(0; affine; banach; case; cauchy; compact; continuous; convergent; convex; corollary; cubo; denote; dissipative; family; follows; fréchet; functions; gal; generation; jn t; k ∈; l1)∗; limit; limk→; lipschitz; lp[0; nk t; nonlinear; norm; operator; problem; proof; remarks; result; semigroups; sequence; solution; sorin; space; subsequence; subsets; t n; t)(x; theorem; u(t; uk(x)(t; un(t; |gnk; ||(i; ∈ l cache: cubo-1370.pdf plain text: cubo-1370.txt item: #136 of 481 id: cubo-1371 author: Shelah, Saharon title: On λ strong homogeneity existence for cofinality logic date: 2011-06-01 words: 5633 flesch: 85 summary: ,aεn−1, b̄]}; note that Pβ(xε)) t(ε,β) ∈ Γ when β < α,ε < ζ and t(ε,β) is the truth value of aε ∈ M 2 β. 3) M is sequence (∆,κ)-homogeneous when: ∆ ⊆ L(τM) and if ζ < κ,ā ∈ ζM,b̄ ∈ ζM and tp∆(ā,∅,M) = tp∆(b̄,∅,M) then for every c ∈ M for some d keywords: beth; cardinality; cofinality; cubo; definition; demostración; existence; kec; kecα; logic; m(m̄; model; order; property; quantifier; saharon; sequence; set; shelah; strongly; theory; type; use; ≤kα cache: cubo-1371.pdf plain text: cubo-1371.txt item: #137 of 481 id: cubo-1372 author: D’alessandro, Paolo title: Closure of pointed cones and maximum principle in Hilbert spaces date: 2011-06-01 words: 4834 flesch: 74 summary: z ∈ Rρ} The existence of solutions of this linear program derive from the fact that Rρ is convex and weakly compact and the functional is continuous (and hence also weakly continuous). z ∈ Rρ} Call the maximum m, then m = ρ ‖L∗ Γ n‖ (n, GΓ n) = ρ(n, GΓ n) 1/2 = ρ‖L∗Γ n‖ 1/2 84 Paolo d’Alessandro CUBO 13, 2 (2011) Recall that m > 0. keywords: case; closed; closure; cone; continuous; control; convex; cubo; fact; hilbert; interior; known; linear; maximum; minimum; norm; normal; origin; point; pointed; polar; principle; quasi; r∧ρ; set; space; support; theorem; topology; unique; vectors cache: cubo-1372.pdf plain text: cubo-1372.txt item: #138 of 481 id: cubo-1373 author: Brackx, F.; De Schepper, H.; Soucek, V. title: Differential forms versus multi-vector functions in Hermitean Clifford analysis date: 2011-06-01 words: 10980 flesch: 73 summary: For A = {ii, ..., ir} ⊂ M we denote dXA\{ij} = dXi1 ∧ ... ∧ dXij−1 ∧ [dXij ∧] dXij+1 ∧ ... = ej • (ei1 ∧ ... ∧ eir ) = r∑ k=1 (−1)kδjik eA\{ik} with eA\{ik} = ei1 ∧ ... ∧ eik−1 ∧ [eik ∧] eik+1 ∧ ... ∧ eir while for the outer product    ej ∧ eA = ej ∧ (ei1 ∧ ... ∧ eir ) keywords: = −; action; algebra; analysis; basis; brackx; c2n; clifford; complex; cubo; derivative; differential; differential forms; dirac; dot; dxj; dzcj; er(g; euclidean; euler; ez⌉; following; follows; forms; functions; fundamental; hermitean; hodge; i=1; identification; iii; inner; j=1; j=1 ej; j=1 f; kählerian; monogenic; monogenicity; multi; multivector; n∑ j=1; open; operators; product; properties; property; proposition; r0,m; real; schepper; setting; smooth; souček; space; structure; system; values; vector; way; wedge; witt; ∂xj; ∂zc; ∂z†; ∂∗c cache: cubo-1373.pdf plain text: cubo-1373.txt item: #139 of 481 id: cubo-1374 author: Chen, Yuqing; O’Regan, Donal; P. Agarwal, Ravi title: Degree theory for the sum of VMO maps and maximal monotone maps date: 2011-06-01 words: 2961 flesch: 89 summary: ∈ Ω ∩ D(T ), gn ∈ − f|dy < β 2 (2.2) for all ǫ < ǫ0, x ∈ Ω and ǫ < d(x,∂Ω) 2 . keywords: brezis; bǫ(y; d(t; degree; maps; math; maximal; monotone; open; pag; proof; theory; vmo; ∂ωǫ cache: cubo-1374.pdf plain text: cubo-1374.txt item: #140 of 481 id: cubo-1375 author: Ebrahimi Bagha, D.; Amini, M. title: Module amenability for Banach modules date: 2011-06-01 words: 4647 flesch: 79 summary: Keywords and phrases: Banach modules, module amenability, weak module amenability, semi- group algebra, inverse semigroup. June 2011 Module amenability for Banach modules D. Ebrahimi Bagha Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran. email: d.ebrahimibagha@iauctb.ac.ir and M. Amini Department of Mathematics, Tarbiat Modares University, P.O.Box 14115-175, Tehran, Iran. keywords: algebra; amenability; amenable; amini; approximate; a⊗̂a; banach; bimodule; bounded; case; closed; commutative; compact; cubo; dense; derivation; diagonal; example; group; homomorphism; ideal; identity; l1(g; module; module amenability; point; proof; proposition; range; right; semigroup; weak; ∆(e cache: cubo-1375.pdf plain text: cubo-1375.txt item: #141 of 481 id: cubo-1376 author: Benchohra, Mouffak; Hamidi, Naima title: Fractional Order Differential Inclusions via the Topological Transversality Method date: 2011-06-01 words: 3811 flesch: 79 summary: ∈ F(t,y(t)), t ∈ J := ∈ F(t,y), t ∈ J := keywords: anal; benchohra; boundary; bounded; c(j; caputo; compact; continuous; convex; cubo; derivative; differential; equations; existence; f(t; fractional; function; inclusions; irn; map; math; nonlinear; order; point; problems; results; set; solutions; theorem; topological; transversality; usc; value; y(t; γ(α cache: cubo-1376.pdf plain text: cubo-1376.txt item: #142 of 481 id: cubo-1377 author: Khosravi, B.; Khatami, M.; Akhlaghi, Z. title: Some new characterizations for PGL(2, q) date: 2011-06-01 words: 5544 flesch: 91 summary: Now using the classification of finite simple groups and the results in Tables 1-3 in [10], we consider the following cases. [15] W. Shi, Pure quantitative characterization of finite simple groups (I), Progr. keywords: abelian; case; conjecture; contradiction; cubo; divides; finite; frobenius; graph; group; hand; lemma; new; non; odd; order; pgl(2; prime; proof; q′2; shi; simple; subgroup; theorem cache: cubo-1377.pdf plain text: cubo-1377.txt item: #143 of 481 id: cubo-1378 author: Devi, R.; Selvakumar, A.; Parimala, M.; Jafari, S. title: On strongly α-𝘐-𝘖𝑝𝑒𝑛 sets and a new mapping date: 2011-03-01 words: 3983 flesch: 90 summary: 2 R.Devi, S.Jafari, A.Selvakumar and M.Parimala CUBO 13, 1 (2011) 1 Introduction The notion of α-open sets was introduced and investigated by Njastad [16]. The following theorem gives a characterization of open sets in terms of strongly α-I-open sets and AI -sets. keywords: continuous; cubo; ideal; open; open set; pre; proof; set; sets; space; subset; theorem; topological; −1(v cache: cubo-1378.pdf plain text: cubo-1378.txt item: #144 of 481 id: cubo-1379 author: Manaka, Hiroko; Takahashi, Wataru title: Weak convergence theorems for maximal monotone operators with nonspreading mappings in a Hilbert space date: 2011-03-01 words: 5570 flesch: 84 summary: Thus we have 0 ≤ (1 − d)a(2α − d) Since B is monotone, we have that for (u, v) ∈ B, 〈 yn − u, 1 λn (xn − yn − λnAxn) keywords: closed; convergence; convex; cubo; hilbert; inverse; lim; mapping; maximal; monotone; nonempty; nonexpansive; nonspreading; operator; points; real; set; space; subset; takahashi; theorem; weak; ‖axn cache: cubo-1379.pdf plain text: cubo-1379.txt item: #145 of 481 id: cubo-1380 author: Yamaleev, Robert M. title: Evolutionary method of construction of solutions of polynomials and related generalized dynamics date: 2011-03-01 words: 6672 flesch: 64 summary: − k − 1) 2 RkP n−k−2 1 + Rn−2. − k)! . keywords: algorithm; case; coefficients; construction; cubic; cubo; degree; dp1; dynamics; eigenvalues; elliptic; energy; eq.(2.1; eq.(2.4; equal; equations; evolution; evolutionary; expression; field; following; formula; functions; generalized; invariant; k=2; method; motion; n−1∑; order; original; p(x; parameter; polynomial; potential; problem; process; proof; quadratic; r.m.yamaleev; related; relativistic; respect; robert; roots; section; set; simultaneous; solutions; theory; translations; weierstrass; yamaleev cache: cubo-1380.pdf plain text: cubo-1380.txt item: #146 of 481 id: cubo-1381 author: Argyros, Ioannis K.; Hilout, Saïd title: On the solution of generalized equations and variational inequalities date: 2011-03-01 words: 4963 flesch: 84 summary: Then, since −f (u) ∈ g(u), and −f (v) ∈ g(v), it follows from (1.2) that: α ‖u − v‖2 ≤ (f (v) − f (u), u − v) = −(f (u) − f (v) − f ′(u0)(u − v), u − v) − (f ′(u0) ‖um − um−1‖ ≤ tm − tm−1, (2.28) ‖um − u0‖ ≤ tm, (2.29) ‖u − um‖ ≤ t⋆ − tm. keywords: argyros; condition; cubo; equations; generalized; hilout; induction; inequalities; ioannis; kantorovich; l0 l; lemma; let; math; newton; nonlinear; operator; problem; säıd; solution; theorem; tk+1; uko; unique; variational cache: cubo-1381.pdf plain text: cubo-1381.txt item: #147 of 481 id: cubo-1382 author: Anastassiou, George A. title: 𝘲− fractional inequalities date: 2011-03-01 words: 3230 flesch: 90 summary: x − qx , (x 6= 0) , (5) (Dqf ) (0) = lim x→0 (Dqf ) (x) , (6) and the q−derivatives of higher order: D 0 q f = f, D n q f = Dq ( D n−1 q f ) , n = 1, 2, 3, ... (7) In the case of a = xqn, then (9) becomes ∫ x xqn f (t) dqt = x (1 − q) n−1 ∑ k=0 f ( xq k ) q k , (10) see also keywords: dqt; q t; w1q; w2q; wqn; α−1; ∣ ∣ cache: cubo-1382.pdf plain text: cubo-1382.txt item: #148 of 481 id: cubo-1383 author: Diagana, Toka title: Existence of pseudo almost automorphic solutions to a nonautonomous heat equation date: 2011-03-01 words: 9821 flesch: 84 summary: Define for all n = 1, 2, ..., the sequence of integral operators 90 Toka Diagana CUBO 13, 1 (2011) Φn(t) = ∫ n n−1 U(t,t − s)P(t − s)φ(t − s)ds, and Ψn(t) − s)U(t,t − s)P(t − s)φ(t − s)ds and Ψn(t) keywords: = ∫; a(t; abstract; acquistapace; anal; applications; assumptions; automorphic; banach; c(r; c(α; collection; composition; continuous; cubo; definition; diagana; differential; equations; evolution; existence; f(t; family; following; functions; lim; linear; lp((0; math; nonlinear; n−1; operators; p((0; paap(x; parabolic; periodic; proof; pseudo; s)ds; s)p(s)x; s)p(t; s)−α; sequence; solutions; space; theorem; toka; t−n+1; u ∈; u(t; uniformly; τnk; φn(t; − ∫; ∥∥∥; ∥∥∥ ≤ cache: cubo-1383.pdf plain text: cubo-1383.txt item: #149 of 481 id: cubo-1384 author: Kreinovich, Vladik title: Engineering design under imprecise probabilities: computational complexity date: 2011-03-01 words: 6845 flesch: 72 summary: [b, b] of possible values of b. [b, b] of possible values of b; • we want to describe the set of all values of a for which f (a, b) keywords: algorithm; backcalculation; bounds; box; boxes; c(x; case; complexity; computational; constraints; corresponding; cubo; c̃0; c̃1; c̃i; design; engineering; example; fc(x; following; form; general; guarantee; hard; imprecise; inequalities; inequality; interval; kreinovich; max; possible; probabilities; probability; problem; s=1; smallest; solution; terms; values; vladik cache: cubo-1384.pdf plain text: cubo-1384.txt item: #150 of 481 id: cubo-1385 author: Liu, Xiaoling; Yuan, Dehui; Yang, Shengyun; Lai, Guoming; Xu, Chuanqing title: Multiple objective programming involving differentiable (𝛨ᵨ, 𝘳)-invex functions date: 2011-03-01 words: 4888 flesch: 71 summary: For convenience, we assume that S be a Hp-invex set, Hp is right differentiable at 0 with respect to variable λ for each given pair x, u ∈ S, and T denotes the right derivative of Hp at 0 with respect to variable λ for each given pair x, u ∈ S; ▽f (x) , (▽1f (x), . . . keywords: analysis; conditions; cubo; differentiable; efficient; feasible; fi(x̄; functions; h′p(x; j=1; journal; mathematical; mfp; optimality; problem; programming; r)-invex; set; solution; theorem; vop cache: cubo-1385.pdf plain text: cubo-1385.txt item: #151 of 481 id: cubo-1386 author: Singh Saluja, Gurucharan; Kumar Nashine, Hemant title: Strong convergence of an implicit iteration process for a finite family of strictly asymptotically pseudocontractive mappings date: 2011-03-01 words: 3438 flesch: 85 summary: There holds the following identities: (i) ‖x − y‖ 2 = ‖x‖ 2 − ‖y‖ 2 − 2〈x − y, y〉 ∀ x, y ∈ H. (ii) ‖tx + (1 − t)y‖ 2 = t ‖x‖ 2 + (1 − t) ‖y‖ 2 − t(1 − t) − p‖ ≤ (1 + dn) 1/2 ‖xn − p‖ . keywords: common; convergence; cubo; family; finite; hilbert; i=0; implicit; iteration; mappings; n=1; process; pseudocontractive; sequence cache: cubo-1386.pdf plain text: cubo-1386.txt item: #152 of 481 id: cubo-1388 author: Chu, Wenchang; Wang, Chenying; Zhang, Wenlong title: Partial fractions and 𝘲-binomial determinant identities date: 2010-10-01 words: 3892 flesch: 81 summary: Similarly, the q-binomial relation [ X i + Y j j ][ A + X i − j n − j ] = q (Y j −A) j [ n j ][ A + X i n ] (q−X i −Y j ; q) j (q−A−X i ; q) j leads us to the following binomial determinant evaluation formulae det 0≤i, j≤n [ [X i+Y j j ][ A+X i j ] = ∏ 0≤i< j≤n(x j − xi )(a − c/xi x j) ∏n k=0 (axk|γ)n(c/xk|γ)n n ∏ ℓ=1 γ ℓ ℓ−1. keywords: 0≤i; binomial; chu; coefficients; corollary; cubo; determinant; evaluation; factorials; formula; fractions; identity; j≤n; k=0; n+1; numbers; partial; q)n+1n; q1+x; q−x; relation; shifted; y j cache: cubo-1388.pdf plain text: cubo-1388.txt item: #153 of 481 id: cubo-1389 author: Precioso, Juliana Conceição title: A Family of Stationary Solutions to the Euler Equations and Generalized Solutions date: 2010-10-01 words: 6081 flesch: 88 summary: y = y(t,γ,δ) the solution of    d x d t = u11(x, y) = cos(x) sin( y) Then, we obtain ˆ D2 ˆ T 0 (ˆ D2 c(t, x, y,α1,α2)dα1 dα2 − 1 ) keywords: 1(x(t; 2πi n; c(t; cubo; c∞0; d y; dβ2; equations; euler; family; field; g(t; generalized; i=0; incompressible; juliana; measures; n y; n−1∑; precioso; problem; solutions; stationary; t)d; tdα1; u11(x(t; x(t; y(t; yn(t; ˆ d2; α1,β2; α1,β2),γ; α1,γ; β2 n; − 2πi; ∣∣∣∣ cache: cubo-1389.pdf plain text: cubo-1389.txt item: #154 of 481 id: cubo-1390 author: Benchohra, Mouffak; N’Guérékata, Gaston M.; Seba, Djamila title: Measure of noncompactness and nondensely defined semilinear functional differential equations with fractional order date: 2010-10-01 words: 4289 flesch: 79 summary: ∈ J |N( y)(t)| = ∣ ∣ ∣ ∣ 1 Γ(r) d dt ˆ t 0 (t − s)r−1 S(t − s) f (s, ys )ds ∣ ∣ ∣ ∣ CUBO 12, 3 (2010) Semilinear Fractional Differential Equations 43 ≤ [16] DIETHELM, K. AND FORD, N.J., Analysis of fractional differential equations, J. Math. Anal. keywords: anal; banach; benchohra; c([−ρ; continuous; cubo; definition; differential; equations; existence; fractional; function; integral; integrated; noncompactness; nonlinear; n’guérékata; operator; point; problem; s)r−1; satisfies; semigroup; semilinear; solutions; space; theory; γ(r cache: cubo-1390.pdf plain text: cubo-1390.txt item: #155 of 481 id: cubo-1391 author: Banyaga, Augustin title: On the group of strong symplectic homeomorphisms date: 2010-10-01 words: 7531 flesch: 84 summary: = (γγ ′ , (H + H ′ , u + u ′ ◦γ+ v)) We saw that for any X ∈ s ym p(M,ω), i X ω = H X + du X and we wrote H X = ∑ λi hi . keywords: ameo(m; banyaga; basis; cauchy; cubo; distance; following; group; h t; hamiltonian; harmonic; homeomorphisms; isotopies; lemma; m s; m t; m(µ̇; metric; n s; n t; norm; osc(u; p(m; peo(m; peo0; proof; proposition; s ym; sequence; so(m; space; strong; symplectic; theorem; topology; vector; ym peo(m; µ n; φ m; φ n; φ t cache: cubo-1391.pdf plain text: cubo-1391.txt item: #156 of 481 id: cubo-1392 author: O’Regan, Donal; Saadati, Reza title: ℒ -Random and Fuzzy Normed Spaces and Classical Theory date: 2010-10-01 words: 4262 flesch: 96 summary: For t > 0 we define the open ball B(x, r, t) with center x and radius r ∈ L \ {0L , 1L } as B(x, r, t) = { y ∈ X : P (x − y, t) >L N (r)}. ∈ L there exists γ ∈ L, such that Eλ,P ((xm + ym) keywords: -fuzzy; -random; cauchy; complete; cubo; definition; sequence; space; theorem cache: cubo-1392.pdf plain text: cubo-1392.txt item: #157 of 481 id: cubo-1393 author: Dasgupta, Aparajita; Wong, M.W. title: The semigroup and the inverse of the Laplacian on the Heisenberg group date: 2010-10-01 words: 4577 flesch: 81 summary: The function F on H× (0,∞) given by F(z, t, u) = (e−u∆H f )(z, t), (z, t) ∈ H, u > 0, is in fact the solution of the initial value problem    ∂F ∂u (z, t, u) = −(∆HF)(z, t, u), F(z, t, 0) = f (z, t), (z, t) ∈ H, u > 0, (z, t) ∈ H, for the Laplacian ∆H. Using the same techniques as in [1], we get for all f ∈ L2(H) and u > 0, (e −u∆H f )(z, t) = (2π)−1/2 ˆ ∞ −∞ e −itτ (e −uL̃τ f τ)(z) dτ, (z, t) ∈ H, (1.1) where L̃τ, τ ∈ R \ {0}, is given by L̃τ = −∆+ 1 4 (x 2 + y2)τ2 − i ( x ∂ ∂y − y ∂ ∂x ) τ+τ2 and f τ is the function on C given by f τ (z) = (2π)−1/2 ˆ ∞ −∞ e itτ f (z, t) dt, z ∈ C, provided that the integral exists. So, by (6.1)–(6.3), Fubini’s theorem and Parseval’s identity, (L̃ −1 τ f , g) = 2π ∞∑ k=0 1 (2k + 1 +|τ|)|τ| ∞∑ j=0 (W τ f̂ e τ k , e τ j )(e τ j , W τ ĝ e τ k ) keywords: cubo; e τ; fourier; functions; inverse; k=0; l2(c; l2(r; l2s; laplacian; m.w; proof; semigroup; theorem; transforms; weyl; wigner; wong; τ j; τ k; ‖l2 cache: cubo-1393.pdf plain text: cubo-1393.txt item: #158 of 481 id: cubo-1394 author: Sushch, Volodymyr title: Self-Dual and Anti-Self-Dual Solutions of Discrete Yang-Mills Equations on a Double Complex date: 2010-10-01 words: 9192 flesch: 87 summary: From Proposition 4.4 F is su(2)-valued if and only if Mi (ki k j + k j ) − M j (ki k j + ki ) The quaternions are formed from real numbers by adjoining three symbols i, j, k and an arbitrary quaternion x can be written as x = x1 keywords: analog; anti; arbitrary; basis; c(4; complex; continual; cubo; curvature; dimensional; discrete; dual; e k; elements; equations; f 4; following; form; form f; gauge; instanton; j k; k f; k k; k −; mills; operator; proof; proposition; quaternionic; s k; self; solutions; su(2; sushch; theory; volodymyr; x k; xk1; xk2; xk3; yang; |κ|2; ε k; τ1 k; τ2 k; τ3 k; τ4 k; − f cache: cubo-1394.pdf plain text: cubo-1394.txt item: #159 of 481 id: cubo-1395 author: De Malafosse, Bruno; Rakočević, Vladimir title: Calculations in new sequence spaces and application to statistical convergence date: 2010-10-01 words: 6581 flesch: 93 summary: Wτ = Wλµτ. (v) As above X ∈ [ C+, C+ ] Wτ if and only if C+ ( µ ) X ∈ Wτ ( C+ (λ) ) and the condition τ = Wλµτ and we have shown (ii). (iii) For any given X ∈ [ C+,∆ ] Wτ we have ∆ ( µ ) X ∈ Wτ ( C+ (λ) ) and for τ ∈ Γ+ we have Wτ ( C+ (λ) ) keywords: convergence; cubo; i=1; k=1; lim; m=1; malafosse; math; sequence; sets; spaces; sup; wλτ; λµτ; τ ∈; ∣∣∣∣∣ cache: cubo-1395.pdf plain text: cubo-1395.txt item: #160 of 481 id: cubo-1396 author: Dhage, Bapurao C. title: Some Generalizations of Mulit-Valued Version of Schauder’s Fixed Point Theorem with Applications date: 2010-10-01 words: 4520 flesch: 77 summary: ∈ P cl,bd (E), where ψ(0) = 0. = ⋃ x∈A T x for all subsets A of E. Let E1 and E2 be two Banach spaces and let Q : E1 → P p (E2) be a multi-valued operator. keywords: banach; closed; compact; continuous; contraction; convex; cubo; definition; dhage; inclusion; mappings; multi; noncompactness; nonlinear; operator; p cl; point; semi; set; solution; space; subset; theorem; theory; upper cache: cubo-1396.pdf plain text: cubo-1396.txt item: #161 of 481 id: cubo-1397 author: Guo, Chengjun; O’Regan, Donal; Agarwal, Ravi P. title: Existence of Periodic Solutions for a Class of Second-Order Neutral Differential Equations with Multiple Deviating Arguments date: 2010-10-01 words: 3762 flesch: 91 summary: = ´ T 0 G(t, s)ϕ(s)ds, where G(t, s)    w(t − s), (k − 1)T ≤ s ≤ t ≤ kT w(T + t − s), (k − 1)T ≤ t − cx ′′ (s −τ) + p(s) −g(s, x(s −τ1 (s)), x(s −τ2 (s))··· , x(s −τn (s)))]ds + cx ′′ (t −τ), (2.12) where G t(t, s)    w̃(t − s), (k − 1)T ≤ s ≤ t ≤ kT w̃(T + t − s), (k − 1)T ≤ t keywords: a(s))x(s; class; cubo; differential; equations; existence; g(t; guo; lemma; mapping; math; max; neutral; p(s; periodic; solutions; t −τ; theorem; t∈[0,t]|x; x(s; x(t; −g(s; −τ1; −τ2; −τn cache: cubo-1397.pdf plain text: cubo-1397.txt item: #162 of 481 id: cubo-1398 author: Paolo, Boggiatto; Giuseppe, De Donno; Alessandro, Oliaro; Kien Cuong, Bui title: Generalized spectrograms and τ-Wigner transforms date: 2010-10-01 words: 5313 flesch: 75 summary: In [3], the two window spectrogram has been introduced and studied: it depends on two windows and it is defined by the skew-linear form S pφ,ψ( f , g)(x, w) = Vφ( f )Vψ( g)(x, w); (2.6) when φ = ψ, f = g, formula (2.6) becomes the classical spectrogram. and repeat the argument above with x replaced by ω. From (4.9), (4.10), and the equality supp( f g) = supp f ∩ supp g, we obtain the “support” property of the parameterized two window spectrogram. keywords: boggiatto; case; class; cohen; cubo; distribution; following; fourier; frequency; g)(x; generalized; parameterized; particular; properties; proposition; representation; signal; spectrogram; supp; time; transform; wigner; window; ′(r2d cache: cubo-1398.pdf plain text: cubo-1398.txt item: #163 of 481 id: cubo-1399 author: Sawano, Yoshihiro title: Modulation Spaces with A-loc-∞ -Weights date: 2010-10-01 words: 5007 flesch: 84 summary: f : M s,W p,q ∥ ∥ ∥ ϕ2 (1.5) holds for f ∈ C∞c 3.3 Proof of Lemma 1 Instead of dealing with 〈f ,ψ〉 directly, we have only to deal with ψ∗ f (0), which is justified by the isomorphism ψ 7→ ψ(−·). keywords: aloc∞; analysis; condition; cubo; c∞c; decomposition; enη|y|; function; lemma; loc; l∈zn; m s; modulation; m∈zn; norm; operators; proof; proposition; result; sawano; spaces; sup; theorem; w p; weight; weighted; y)|η; yoshihiro; λml; ∥ ∥ cache: cubo-1399.pdf plain text: cubo-1399.txt item: #164 of 481 id: cubo-1400 author: Yoshino, Kunio title: Analytic continuation and applications of eigenvalues of Daubechies’ localization operator date: 2010-10-01 words: 2255 flesch: 75 summary: Making use of generating functions, we will establish the reconstruction formula of symbol functions of Daubechies’ localization operators with ro- tational invariant symbol. Then (i) The Hermite functions hm (x) are eigenfunctions of the operator PF : PF (hm )(x) = λm hm (x), m ∈ N. (ii) Secondly, λm = 1 m! keywords: analytic; cubo; daubechies; eigenvalues; functions; f̃(2s; g(t; localization; m=0; operator; proof; proposition; transform; λ(w cache: cubo-1400.pdf plain text: cubo-1400.txt item: #165 of 481 id: cubo-1401 author: Cordero, Elena; Zucco, Davide title: Strichartz estimates for the Schrödinger equation date: 2010-10-01 words: 10554 flesch: 78 summary: Then, for 1 ≤ p ≤ ∞, the potential space [4] is defined by W p s = { f ∈ S ′, 〈∆〉s f ∈ L p} with norm ‖f ‖ W p s = ‖〈∆〉 s f ‖L p . The original version of Strichartz estimates in L p spaces, closely related to restriction problem of Fourier transform to surfaces, was elaborated by Robert Strichartz [36] in 1977(who, in turn, had precursors in [31, 41]). keywords: admissible; amalgam; analysis; applications; banach; case; cauchy; classical; conditions; cordero; cubo; davide; definition; different; dispersive; elena; equation; estimates; f l; fixed; following; fourier; function; homogeneous; i(t−s)∆; interpolation; it∆; l p; l q; lebesgue; lemma; linear; lrx; math; modulation; nonlinear; norm; operator; particular; problem; proof; proposition; q s; q t; r d; r é; result; r×r; s =; schrödinger; section; sobolev; solution; spaces; strichartz; strichartz estimates; study; t f; t l; theorem; time; transform; wiener; zucco; ∥∥∥ cache: cubo-1401.pdf plain text: cubo-1401.txt item: #166 of 481 id: cubo-1402 author: Oka, Yasuyuki title: On the Weyl transform with symbol in the Gel’fand-Shilov space and its dual space date: 2010-10-01 words: 4692 flesch: 88 summary: Then U(x, t) ≡ ˆ Rd E(x − y, t)ϕ( y)d y ∈ S r,Br,a (R d ) , t > 0 and U(x, t) → ϕ(x) in ∈ S r,Br,a (R d ) as t → 0. S r,B ′ r,a′ (Rd2 ), for any a, B ∈ (0,∞)d1 and a′, B′ ∈ (0,∞)d2 , B(ϕ,ψ) = 〈kψ,ϕ〉 , ϕ ∈ S r,Br,a (Rd1 ) , ψ ∈ S r,B′ r,a′ (Rd2 ) is separately continuous. keywords: 0,∞)d; cubo; following; gel’fand; kernel; l2(rd; proposition; r d; r r; s r; s rr; schwartz; shilov; space; symbol; theorem; transform; weyl; ∣ ∣ cache: cubo-1402.pdf plain text: cubo-1402.txt item: #167 of 481 id: cubo-1403 author: Abada, Nadjet; Benchohra, Mouffak; Hammouche, Hadda title: Existence Results for Semilinear Differential Evolution Equations with Impulses and Delay date: 2010-06-01 words: 5916 flesch: 83 summary: ,m (2) y(t) = φ(t), t ∈ t ∈ [−r, 0] , (6) keywords: 0,b; a.e; abada; applications; b],e; banach; benchohra; conditions; continuous; cubo; definition; differential; equations; evolution; existence; f(t; functional; hammouche; impulsive; k=1; let; mild; new; nonlocal; operator; pc([−r; point; problem; section; semilinear; set; solution; space; systems; t t; theorem; y(t cache: cubo-1403.pdf plain text: cubo-1403.txt item: #168 of 481 id: cubo-1404 author: Wolf, Elke title: Differences of weighted composition operators between weighted Banach spaces of holomorphic functions and weighted Bloch type spaces date: 2010-06-01 words: 3148 flesch: 86 summary: For the study of the compactness of the difference ψ1Cφ1 − ψ2Cφ2 we need the following result. 1 6 ( 3 2 1 vφ1(zn)(z) 2 − vφ1(zn)(φ1(zn)) vφ1(zn)(z) 3 )− 2 3 · · ( − v′ φ1(zn) (z) vφ1(zn)(z) 3 + vφ1(zn)(φ1(zn)) vφ1(zn)(z) 4 v′φ1(zn)(z) ) for every n ∈ N. By Proposition 3, the fact that ψ1Cφ1 − ψ2Cφ2 is compact yields ‖(ψ1Cφ1 − ψ2Cφ2 )gφ1(zn)‖Bw → 0 if n → ∞. Finally, ‖(ψ1Cφ1 − ψ2Cφ2 )gφ1(zn)‖Bw ≥ w(zn) ∣ ∣ ∣ ∣ ∣ ψ′1(zn) v(φ1(zn)) 1 2 ϕ2φ2(zn)(φ1(zn)) keywords: analytic; composition; differences; functions; holomorphic; math; max; operators; spaces; sup; supz∈d; v(φ1(z; vφ1(p)(z; vφ1(zn)(z; w(z; weighted; weights; z∈d; φ1(p; φ2(p; ψ1cφ1; ψ2cφ2; ∣ =; ∣ ∣ cache: cubo-1404.pdf plain text: cubo-1404.txt item: #169 of 481 id: cubo-1405 author: Saleh, M. H.; Amer, S. M.; Ahmed, M. H. title: The method of Kantorovich majorants to nonlinear singular integral equations with Hilbert Kernel date: 2010-06-01 words: 4063 flesch: 88 summary: To prove the Frechet derivative B̀(ϕ) satisfies Lipschitz condition in the sphere S(ϕ 0 ,R) = {ϕ :‖ ϕ − ϕ 0 ϕ ∈ X,‖ ϕ − ϕ 0 ‖< R}, in a Banach space X into a Banach space Y. keywords: ahmed; amer; b̀(ϕ; cot; cubo; equations; g ϕ; g(t; gv(t; hilbert; integral; iλxv(s; kantorovich; kernel; method; nonlinear; s,ϕ(s; sg(t; singular; solution; theorem; v(s))k; v(s))k ϕ; v(t; σ,ϕ(σ cache: cubo-1405.pdf plain text: cubo-1405.txt item: #170 of 481 id: cubo-1406 author: Renukadevi, V. title: On subsets of ideal topological spaces date: 2010-06-01 words: 5390 flesch: 94 summary: if and only if int(cl⋆(A)) = int(A) and so semi⋆ − I−closed sets are nothing but t − I−sets. Since t − I−sets are semi⋆ − I−closed sets, SIcl(V ) = keywords: bi−set; example; ideal; int(cl⋆(a; int(cl⋆(int(a; int(v; i−closed; i−open; proof; resp; semipre⋆; semi⋆; set; sets; sicl(a; space; subset; sβio(x; theorem cache: cubo-1406.pdf plain text: cubo-1406.txt item: #171 of 481 id: cubo-1407 author: Levstein, Fernando; Maldonado, Carolina title: Generalized quadrangles and subconstituent algebra date: 2010-06-01 words: 7386 flesch: 82 summary: Denoting λ0 = r(k − 2), λ1 = k − r − 1, λ2 = k − 2, λ3 = −r S satisfies the equation (S − λ0I22) (S − λ1I22) (S − λ2I22) (S − λ3I22) = 0 Proof. − r)QtQ − r(r − 1)J22 + r(k − 2)S keywords: -submodules; 1)2; algebra; association; atx; block; column; cubo; decomposition; definition; equation; following; generalized; graph; ideals; irreducible; j22; j=1; left; lemma; let; levstein; line; maldonado; matrices; matrix; parameters; point; proof; proposition; quadrangles; r(k; regular; row; set; simple; subconstituent; terwilliger; vertices;   cache: cubo-1407.pdf plain text: cubo-1407.txt item: #172 of 481 id: cubo-1408 author: Albeverio, S.; Belopolskaya, Ya. title: Generalized solutions of the Cauchy problem for the Navier-Stokes system and diffusion processes date: 2010-06-01 words: 8092 flesch: 82 summary: − ηx,k−1(τ)‖2) 1 2 dτ + ∫ t 0 1 σ √ t − τ e R t τ α(θ)dθ(E‖∇pk+1(τ,ψkt,τ(x)) + (t − τ) keywords: 0,t; albeverio; approach; belopolskaya; cauchy; compact; conditions; continuous; cubo; denote; diffusion; equation; estimates; e‖ηx; fields; following; formula; functions; g t; g(τ; generalized; inequality; initial; interval; k t; lemma; leray; lipschitz; loc; navier; norm; p(t; positive; probabilistic; problem; processes; proof; r t; representation; results; satisfies; set; solution; space; stochastic; stokes; sup; system; t τ; t,0(x; theorem; theory; u(t; vector; weak; θ)dθ; λ(t; τ(x; ψgt; ψkt; ψk−1t; ψut,0; ∇ug(t; − ∫ cache: cubo-1408.pdf plain text: cubo-1408.txt item: #173 of 481 id: cubo-1409 author: Rump, Wolfgang title: The tree of primes in a field date: 2010-06-01 words: 14002 flesch: 94 summary: ⊂ P + P ⊂ P , which gives P̃ + P̃ ⊂ P̃. We call a prime P of a field K algebraic if P + P ⊂ P , that is, (P4) holds for d = 1, otherwise transcendental. keywords: 0,∞; algebraic; ap̃; arbitrary; a−1; b ∈; c+p; compact; contradiction; corollary; cubo; definition; d−1p; f ∈; f(a; fact; field; field k; finite; follows; form; formula; fp[x; function; g(a; haar; i(f; i(f0; i=1; integral; krull; lemma; math; minimal; monotonous; n ∈; non; normalized; number; open; p n; prime; prime p; product; proof; proposition; pseudo; respect; rump; satisfies; set; topology; transcendental; tree; trivial; unique; v(a; valuation; wolfgang; yields; ◦ ⊂ cache: cubo-1409.pdf plain text: cubo-1409.txt item: #174 of 481 id: cubo-1410 author: Jafari, Saeid; Mohammad Latif, Raja; Moshokoa, Seithuti P. title: A note on generalized topological spaces and preorder date: 2010-06-01 words: 2082 flesch: 86 summary: Then G is a subset of X × X, we shall refer to G as the graph of the preorder. That is, a subset B of X × X is (µ × µ)-open if for every (x, y) ∈ B there exist µ-open sets U and V, such that (x, y) ∈ U × V ⊂ B, where U and V contain x and y, respectively. keywords: cµi(a; i(g; preorder; subset; µ-closed; µ-open cache: cubo-1410.pdf plain text: cubo-1410.txt item: #175 of 481 id: cubo-1411 author: Koike, Naoyuki title: Examples of a complex hyperpolar action without singular orbit date: 2010-06-01 words: 9192 flesch: 78 summary: Here the curvature-adaptedness means that, for each normal vector v of the submanifold, the Jacobi operator R(·, v)v preserves the tangent space of the submanifold invariantly and the restriction of R(·, v)v to the tangent space commutes with the shape operator Av, where R is the curvature tensor of G/K. Furthermore, as a subclass of the class of complex equifocal submanifolds, we [15] defined that of the proper complex equifocal submanifolds in G/K as a complex equifocal submanifold whose lifted submanifold to H0([0, 1], g) (g := Lie G) through some pseudo-Riemannian submersion of H0([0, 1], g) onto G/K is proper complex isoparametric in the sense of [13], where we note that H0([0, 1], g) is a pseudo-Hilbert space consisting of certain kind of paths in the Lie algebra g of G. Let G/K be a symmetric space of non-compact type and H be a closed subgroup of G which admits an embedded complete flat submanifold meeting all H-orbits orthogonally. [14] N. Koike, Complex equifocal submanifolds and infinite dimensional anti-Kaehlerian isopara- metric submanifolds, Tokyo J. Math. 28 (2005) 201-247. keywords: abelian; action; adapted; anti; aξiti; compact; complex; complex equifocal; complex hyperpolar; cosh(|λi|ti; cubo; curvature; decomposition; denote; equifocal; examples; field; flat; following; geodesic; group; gλi; h0([0; hyperpolar; i=1; invariant; isoparametric; kaehlerian; koike; lemma; lie; math; non; normal; orbit; parallel; principal; projection; proof; proper; resp; respect; rhλi; sb,̄l1; section; set; shape; singular; space; statement; subalgebra; submanifold; symmetric; theorem; type; vector; x =; |λi|; γξ1; θξi cache: cubo-1411.pdf plain text: cubo-1411.txt item: #176 of 481 id: cubo-1412 author: Delanghe, Richard title: On homogeneous polynomial solutions of generalized Moisil-Théodoresco systems in Euclidean space date: 2010-06-01 words: 9633 flesch: 83 summary: ∈ IR m}, let us recall that for a smooth s-form ωs =∑ |A|=s ω s Adx A(0 ≤ s ≤ m If i1 6= 0, then {i1, ..., is} ⊂ {1, ..., m} and eAe ◦ M = ±e ◦ M\A ∈ IR (m−s) keywords: 0,3; 0,4; 0,m+1; algebra; basis; case; clifford; conjugate; cubo; degree; degree k; delanghe; euclidean; following; functions; generalized; h(m; harmonic; homogeneous; ir+0,4; ir0,m+1; ir3; irm+1; k+1; k+2; ker; lemma; let; m t; moisil; monogenic; odd; operator; p r; p r−1; p(m; polynomial; properties; r k; r+2j; r+2q; r+2q k; richard; r−1; section; solutions; space; surjective; system; theorem; théodoresco; type; ṽk; ∂x0; ∂xw cache: cubo-1412.pdf plain text: cubo-1412.txt item: #177 of 481 id: cubo-1413 author: Bauer, Claus title: A new solution algorithm for skip-free processes to the left date: 2010-06-01 words: 7149 flesch: 84 summary: N − 1. Y (C0 − 1) −1 )−1 , (3.1) πk = π ∗ 0 ∑ bl k E(bm−1, ..., b1), 1 ≤ k ≤ N − 1, (3.2) keywords: algorithm; bauer; bm−1; calculation; claus; cm−x; complexity; computational; cubo; degree; e(bm−1; eqn; equations; finite; free; k=1; l=1; l=2; left; lemma; levels; linear; matrix; method; models; m−1; new; number; n−1; order; polynomial; probability; processes; proof; real; relation; roots; set; skip; solution; state; steady; sum; summation; system; theorem; time; transition; u=1; x=1;  ;   cache: cubo-1413.pdf plain text: cubo-1413.txt item: #178 of 481 id: cubo-1414 author: Malonek, Helmuth R.; Peña, Dixan; Sommen, Frank title: Fischer decomposition by inframonogenic functions date: 2010-06-01 words: 2838 flesch: 74 summary: June 2010 Fischer decomposition by inframonogenic functions Helmuth R. Malonek1, Dixan Peña Peña2 Department of Mathematics, Aveiro University, 3810-193 Aveiro, Portugal 1email: hrmalon@ua.pt 2email: dixanpena@ua.pt, dixanpena@gmail.com and Frank Sommen Department of Mathematical Analysis, Ghent University, 9000 Gent, Belgium email: fs@cage.ugent.be ABSTRACT Let ∂x denote the Dirac operator in R m. In this paper, we present a refinement of the biharmonic functions and at the same time an extension of the monogenic functions by considering the equation ∂xf ∂x = 0. The solutions of this “sandwich” equation, which we call inframonogenic functions, are used to obtain a new Fischer decomposition for homogeneous polynomials in Rm. RESUMEN Denotemos por ∂x el operador de Dirac en R m. keywords: appl; clifford; cubo; decomposition; fischer; functions; harmonic; homogeneous; inframonogenic; j=1; left; math; operator; p(k; peña; pk(x; polynomials; proposition; r0,m; right; sommen; vector; xp(k; ∂xf cache: cubo-1414.pdf plain text: cubo-1414.txt item: #179 of 481 id: cubo-1415 author: O’Regan, Donal title: Fixed point theory for compact absorbing contractions in extension type spaces date: 2010-06-01 words: 8983 flesch: 86 summary: Given a map F : X → 2 X and α ∈ Cov (X), a point x ∈ X is said to be an α–fixed point of F if there exists a member U ∈ α such that x ∈ U and F(x) ∩U 6= ∅. Since X ∈ ANES(compact) there exists an open neighborhood Uα of K⋆ in T and fα : Uα → X a continuous function such that fα|K⋆ and s −1 are α′–close and as a result fα jUα s : K → X and i : K → X are α–close keywords: admissible; class; closed; compact; continuous; cubo; endomorphism; following; hausdorff; juα; lefschetz; map; maps; note; pair; point; remark; result; space; subset; theorem; theory; topological; uniform;   cache: cubo-1415.pdf plain text: cubo-1415.txt item: #180 of 481 id: cubo-1416 author: Castro, L. P.; Silva, A. S. title: Fredholm property of matrix Wiener-Hopf plus and minus Hankel operators with semi-almost periodic symbols date: 2010-06-01 words: 6389 flesch: 73 summary: Therefore, AP W is precisely the (proper) subclass of all functions ϕ ∈ AP which can be written in an absolutely convergent series of the form: ϕ = ∑ j ϕj eλj , λj ∈ R , ∑ j |ϕj| < ∞ . If ϕ ∈ AP , then the limit M (ϕ) := lim α→∞ 1 |Iα| ∫ Iα ϕ(x) dx exists, is finite, and is independent of the particular choice of the family {Iα}. keywords: 2n×2n; canonical; case; castro; cubo; det; equivalence; extension; factorization; following; fourier; fredholm; functions; fφ2; gsap; hankel; hopf; hφ2; ind[wφ1; matrix; minus; n×n; operators; periodic; present; property; relation; right; right ap; sap; semi; symbols; theorem; wiener; wφ1; φ̃2r; φ−12 cache: cubo-1416.pdf plain text: cubo-1416.txt item: #181 of 481 id: cubo-1417 author: Tung, Chia-chi title: On Semisubmedian Functions and Weak Plurisubharmonicity date: 2010-06-01 words: 12394 flesch: 73 summary: An upper semicontinuous function φ : Y → [−∞,∞) is said to be spherically (respectively, solidly) monotone at z ∈ Y if there exists a pseudoball U at z of radius r0 such that [φ⌋U]z,r ≤ An upper semicontinuous map φ : Y → [−∞,∞) is called nearly subharmonic at z ∈ Y if there exists a pseudoball U at z of radius r0 such that 〈φ⌋U〉z,r ≤ keywords: analytic; assertion; case; chi; chia; complex; component; consequently; constant; continuous; contradiction; covering; cubo; denote; domain; formula; function; induced; inequality; integrable; lemma; lim; local; map; mapping; math; maximum; mean; monotone; neighborhood; nonnegative; normal; open; peak; plurisubharmonic; point; principle; proof; property; proposition; pseudoball; psh; radius; real; regularized; relation; riemann; semicontinuous; semiharmonic; semisubmedian; sequence; set; small; solid; space; spherical; standard; subharmonic; subharmonicity; submean; submedian; subset; theorem; thin; tung; unramified; upper; value; weakly; yreg; φ(z; φ̃k cache: cubo-1417.pdf plain text: cubo-1417.txt item: #182 of 481 id: cubo-1418 author: Sudo, Takahiro title: Real and stable ranks for certain crossed products of Toeplitz algebras date: 2010-06-01 words: 5986 flesch: 85 summary: ⊗ t)∗ = txt∗ ⊗ tyt∗ for x ⊗ y ∈ F ⊗ F. Denote it by C∗(H2,1) = (F ⊗ F) ⋊α⊗α N the crossed product of F ⊗ F by α ⊗ α of N. In what follows, we often omit the symbol for actions in crossed products. → (F ⊗ K) ⋊ N → C∗(H2,1) → (F ⊗ C(T)) keywords: action; algebras; c(t; c(tn−l; certain; connected; crossed; cubo; c∗(hn,1; c∗-algebra; discrete; estimate; exact; extensions; group; isomorphic; j=0; m2(c; map; note; products; proof; proposition; rank; real; real rank; remark; sequence; stable; stable rank; structure; theorem; theory; toeplitz cache: cubo-1418.pdf plain text: cubo-1418.txt item: #183 of 481 id: cubo-1419 author: Palin, V. V.; Radkevich, E. V. title: The Maxwell problem and the Chapman projection date: 2010-06-01 words: 9446 flesch: 81 summary: 1This work was supported by the Russian Foundation of Basic Researches (grant no. 09-01-00288) 2Corresponding author 276 V. V. Palin and E. V. Radkevich CUBO 12, 2 (2010) Key words and phrases: closure, the state equation, the Chapman projection, matrix equation, dynamic separation, inertional manifold AMS (MOS) Subj. [14] V. V. Palin, On the solvability of quadratic matrix equations [in Russian] Vestn. MGU, Ser. 1, No. 6, 36-42 (2008). keywords: assertion; assumptions; basis; case; cauchy; chapman; condition; conservation; constants; continuous; corresponding; cubo; data; denote; divx; eigenvalues; equation; estimate; following; form; fourier; hyperbolic; inequality; initial; kinetic; laws; lemma; matrix; matrix equation; matrix λ; maxwell; nonlinear; norm; order; p21; palin; parameter; problem; projection; proof; q0(t; quadratic; radkevich; relaxation; required; respect; russian; set; small; solution; solvable; space; system; t(1; terms; theorem; variables; vector; ∫ +; ∫ t cache: cubo-1419.pdf plain text: cubo-1419.txt item: #184 of 481 id: cubo-1421 author: Sánchez P., Joss title: Characterization of the Banzhaf value using a consistency axiom date: 2010-03-01 words: 2236 flesch: 77 summary: Pintores s/n, Col. B. del Estado 78213, San Luis Potośı, México email : joss.sanchez@uaslp.mx ABSTRACT One of the important properties characterizing cooperative game solutions is consistency. Reduced games describe what games are played between the remaining players, i.e. what is earned by coalitions of the remaining players after one player has left the game. keywords: axiom; banzhaf; consistency; function; game; j},v; n\{k; payoff; person; players; reduced; set; solution; v(s; v({i; value cache: cubo-1421.pdf plain text: cubo-1421.txt item: #185 of 481 id: cubo-1422 author: Minkevicius, Saulius title: Analysis of the Component-Based Reliability in Computer Networks date: 2010-03-01 words: 2641 flesch: 76 summary: Limit theorems on the extreme queue length and extreme virtual waiting time in open queueing networks in heavy traffic are derived and applied to a reliability model for computer networks where we relate the time of failure of a computer network to the system parameters. In this paper, we will first briefly review the works related to using the queueing theory of computer system reliability, and then present some new results on the estimation of the time of failure of a computer network. keywords: computer; i=1; j=1; lim; network; probability; queueing; reliability; station; sup; system; theorem; time cache: cubo-1422.pdf plain text: cubo-1422.txt item: #186 of 481 id: cubo-1423 author: Bhowmik, B.; Wirths, K.-J.; Ponnusamy, S. title: On some problems of James Miller date: 2010-03-01 words: 2491 flesch: 82 summary: If f (z) ∈ Σ∗(p, w0), then the second coefficient is given by a2(f ) = 1 2 w0 ( b2 − p 2 − 1 p2 − 1 w02 ) where b2 is the second coefficient of a function in P(b1), i.e. the region of variability for a2(f ) is contained in the disc ∣ ∣ ∣ ∣ a2(f ) Let f ∈ Σ∗(p, w0) having the expansion (1.3). keywords: 2c1p; a2(f; class; coefficient; disc; functions; math; meromorphic; miller; region; starlike; theorem; variability; σ∗(p; ∣ ∣ cache: cubo-1423.pdf plain text: cubo-1423.txt item: #187 of 481 id: cubo-1424 author: Boni, Théodore K.; Nabongo, Diabaté title: Quenching for discretizations of a nonlocal parabolic problem with Neumann boundary condition date: 2010-03-01 words: 6467 flesch: 83 summary: − U (n) K , K ∈ Γ, where U (n) h is the solution of (5)-(6). i − U (n) i ∆tn = I−1∑ l=0 hJ(xi − xl) ( U (n+1) l − U (n+1) i ) −(U (n) i ) −p−1U (n+1) keywords: boni; boundary; cubo; diabaté; diffusion; discrete; discretizations; equations; estimate; fact; finite; hmin; inequality; j(xk; lemma; l∈γ∗; m −; math; n+1; nabongo; nonlocal; numerical; p+1; parabolic; problem; proof; quenches; quenching; section; solution; theorem; théodore; time; time t; u(x; use cache: cubo-1424.pdf plain text: cubo-1424.txt item: #188 of 481 id: cubo-1425 author: Kaikina, Elena I.; Guardado-Zavala, Leonardo; Ruiz-Paredes, Hector F.; Juarez Zirate, S. title: Korteweg-de Vries-Burgers equation on a segment date: 2010-03-01 words: 6286 flesch: 88 summary: −β dτ ∫ 1 0 (t − τ )β f (y, t − τ ) From (4.4) and estimates (2.31) of Lemma 2.2 we obtain for n = 0, 1 ∥∥∥u(n)x (·, t) ∥∥∥ L2 ≤ Ce−ξ0t ‖u (·, 1)‖ L2 + ∫ t 1 dτ ∫ x 0 |uuy(y, τ )| ‖∂nx F1 (·, y, t − τ )‖L∞ dy + ∫ t 1 dτ ∫ 1 x |uuy(y, τ ) keywords: 2πi; asymptotics; boundary; burgers; cubo; data; e.i; equation; estimate; e−φj; initial; j=1; kaikina; korteweg; large; problem; respect; small; solutions; sup; theorem; time; t∈(0,t; u(0; u(x; value; vries; ̃(−ξ0; φ(p; ‖u0‖l2; − △ cache: cubo-1425.pdf plain text: cubo-1425.txt item: #189 of 481 id: cubo-1426 author: Popa, Valeriu title: Weakly Picard pairs of multifunctions date: 2010-03-01 words: 3010 flesch: 93 summary: ≤ 0 holds for all x, y ∈ X, where F ∈ F and FT1 6= Φ or FT2 6= Φ, then FT1 = FT2 . Proof. If (1) holds for all x, y ∈ X, where F ∈ F, then T1 and T2 have a common fixed point and FT1 = FT2 ∈ P cl(X). Proof. keywords: d(x1; d(x2; d(yn; ft1; ft2; multifunctions; picard; t1(x; t2(x1; weakly cache: cubo-1426.pdf plain text: cubo-1426.txt item: #190 of 481 id: cubo-1427 author: Raymond, Nicolas title: Uniform spectral estimates for families of Schrödinger operators with magnetic field of constant intensity and applications date: 2010-03-01 words: 4374 flesch: 81 summary: For the lower bound, we apply Theorem 1.1 to the subfamily C(τ) of A and, using (5.10), we get: µ∗(q,τ) qτ ≥ Θ0 − C ( 1 (qτ)1/2−2ǫ + 1 (qτ)2ǫ + c0 (qτ)x (qτ)1/2−2ǫ ) . We let: Ωγ = {y ∈ Ω : d(y,∂Ω) ≥ γ}. keywords: boundary; c(τ; case; constant; crystals; cubo; estimates; families; field; large; lemma; liquid; magnetic; neumann; nicolas; order; problem; proof; raymond; section; spectral; study; superconductivity; surface; theorem; uniform; y3>0; |(i∇y; µ(q cache: cubo-1427.pdf plain text: cubo-1427.txt item: #191 of 481 id: cubo-1428 author: Mustafa, Zead; Obiedat, Hamed title: A fixed point theorem of Reich in \(G\)-Metric spaces date: 2010-03-01 words: 4417 flesch: 91 summary: Suppose that T satisfies condition (2.1), then for all x, y ∈ X, we have G(T x, T y, T y) ≤ k[G(x, T x, T x) + 2G(y, T y, T y)], and (2.2) G(T y, T x, T x) keywords: condition; continuous; fixed; g(u; g(xn; metric; point; space; t x; t y; xn+1 cache: cubo-1428.pdf plain text: cubo-1428.txt item: #192 of 481 id: cubo-1429 author: Kosi-Ulbl, Irena; Vukman, Joso title: An identity related to derivations of standard operator algebras and semisimple H∗ -algebras date: 2010-03-01 words: 2802 flesch: 85 summary: = A + P AP − (AP + P A). A2 ) − 2 ((n − 2) + (n − 3) + (n − 4) + · · · + 3 + 2 + 1) (AD (A) P + P D (A) A) − 4 (1 · (n − 2) + 2 · (n − 3) + 3 · (n − 4) + · · · + (n − 3) · 2 + (n − 2) · 1) AD(P )A− 2 (n − 1) (AD (A) + D (A) A) = 0, and fn−1 (A, P ) = nD keywords: a(x; ad(p; algebra; case; d(a; d(p; derivation; j=1; l(x; linear; operator; relation; ring; standard; theorem cache: cubo-1429.pdf plain text: cubo-1429.txt item: #193 of 481 id: cubo-1430 author: Ballico, E. title: Brill-Noether Theories for Rank 1 Sheaves on Mg date: 2010-03-01 words: 6242 flesch: 83 summary: Let X be a reduced and quasi-projective curve, P ∈ X, and F a sheaf on X with pure rank 1 and depth 1. We don’t touch a very important topic: the limit linear series introduced by D. Eisenbud and J. Harris for nodal curves of compact type, i.e. such that ‖X‖ has no loop and no multiple edge ([11]). keywords: assume; b(x; brill; components; connected; cubo; curve; deg(f; degree; depth; free; genus; h0(x; irreducible; lemma; line; map; math; nodal; node; noether; ordinary; point; projective; pure; rank; section; set; sheaf; sheaves; sing(f; spanned; stable; theorem; torsion; ♯(s cache: cubo-1430.pdf plain text: cubo-1430.txt item: #194 of 481 id: cubo-1431 author: Rozenblum, Grigori; Shirokov, Nikolay title: Entire Functions in Weighted 𝘓₂ and Zero Modes of the Pauli Operator with Non-Signdefinite Magnetic Field date: 2010-03-01 words: 7305 flesch: 80 summary: ≤ C ∫∫ Γ1 |z2w−4|dµ(w) ≤ C. (3.8) For Q ∈ Q1,2, w ∈ Q, we note that 5|z| ≥ |z − w|, |z + w| ≥ |z|2 , therefore the quantity w2(3w2 − z2)/(w2 − z2)2 is bounded and we again arrive at (3.7). If Q is a square we take the center of Q as aQ. Otherwise we choose aQ so that ∫ Q (z − aQ)dµ keywords: a2q; analytical; arg; b(x; case; constant; construction; cubo; denote; domain; entire; equation; estimate; f(z; field; form; function; grigori; half; homogeneous; infinite; integral; log; magnetic; mapping; modes; negative; nikolay; non; plane; point; poisson; positive; proposition; rozenblum; sector; set; shirokov; sign; sin; small; solution; space; term; u(z; upper; vǫ(z; wǫ(z; |z|2; φ(z; ∣∣∣∣ cache: cubo-1431.pdf plain text: cubo-1431.txt item: #195 of 481 id: cubo-1432 author: Ouaro, Stanislas title: Well-Posedness results for anisotropic nonlinear elliptic equations with variable exponent and 𝘓¹ -data date: 2010-03-01 words: 5813 flesch: 85 summary: We introduce the numbers q = N(p̄ − 1) N − 1 , q∗ = Nq N − q = N(p̄ − 1) N − p̄ . p−i < p̄(N − 1) N − p̄ , N ∑ i=1 1 p−i > 1 and p+i keywords: 1,p; = ∣; a(x; ai(x; anisotropic; constant; cubo; entropy; existence; exponent; fluids; following; function; i=1; inequality; l1(ω; lebesgue; lemma; math; norm; ouaro; pi(x; problem; proof; results; sobolev; solution; spaces; u ∣; v)dx; variable; ∂ ∂xi; ∂xi u; − −; ∣ =; ∣ ∂; ∣ ∣; ∣ ∫; ∣ ≤;  ;  ;  ;  ;   cache: cubo-1432.pdf plain text: cubo-1432.txt item: #196 of 481 id: cubo-1433 author: Argyros, Ioannis K. title: An improved convergence and complexity analysis for the interpolatory Newton method date: 2010-03-01 words: 3097 flesch: 85 summary: : ei+1 = ‖xi+1 − α‖ ≤ { 1 2 + 3 2 ( 1 2 )k } ei, (2.15) ei+1 ≤ ci,ne n i (2.16) where, ci,n = ( 1 + e∗i+1 ei ) ‖xi+1 − α‖ ≤ ‖xi+1 − x ∗ i+1‖ + ‖x ∗ i+1 − α‖ ≤ ( 1 2 )k ‖z0 − x ∗ i+1‖ + 1 2 ‖xi − α‖ ≤ [ 3 2 ( 1 2 )k + 1 2 ] ‖xi − α‖ ≤ 7 8 ‖xi − α‖, (2.39) which shows xi ∈ U and (2.15) hold true. keywords: analysis; argyros; banach; complexity; convergence; cubo; i+1; improved; local; method; newton; n−1; theorem; x∗i+1; ′(α)−1f cache: cubo-1433.pdf plain text: cubo-1433.txt item: #197 of 481 id: cubo-1434 author: Argyros, Ioannis K.; Hilout, Saïd title: Convergence conditions for the secant method date: 2010-03-01 words: 4458 flesch: 89 summary: [F (x) − F (y) − F ′(u)(x − y)] ≤ η; ‖ A [δF (x, y) − F ′(z)] keywords: argyros; banach; conditions; convergence; cubo; equations; hilout; lemma; lipschitz; math; method; newton; operator; secant; sequence; solution; space; tk+1; tk+2; unique; xk+1; x−1; − tk cache: cubo-1434.pdf plain text: cubo-1434.txt item: #198 of 481 id: cubo-1435 author: Hidalgo, Rubén A. title: A short note on 𝑀-symmetric hyperelliptic Riemann surfaces * date: 2010-03-01 words: 2020 flesch: 74 summary: The Necessary Part Let us consider a planar extended Schottky group G of rank g ≥ 2, say generated by the reflections τ1,..., τg+1 on a collection of (g+1) pairwise disjoint round circles on the Riemann sphere, say C1,..., Cg+1, bounding a common domain D of connectivity (g + 1). Federico Santa Maŕıa, Valparáıso, Chile email : ruben.hidalgo@usm.cl ABSTRACT We provide an argument, based on Schottky groups, of a result due to B. Maskit which states a necessary and sufficient condition for the double oriented cover of a planar compact Klein surface of algebraic genus at least two to be a hyperelliptic Riemann surface. keywords: circle; extended; fixed; group; hyperelliptic; involution; order; oval; planar; points; rank; riemann; schottky; surface; transformation cache: cubo-1435.pdf plain text: cubo-1435.txt item: #199 of 481 id: cubo-1436 author: Shaikh, A.A.; Bagewadi, C.S. title: On 𝘕(𝑘)-Contact Metric Manifolds date: 2010-03-01 words: 4383 flesch: 82 summary: (since the torsion tensor T (X, Y ) = ∇X Y − ∇Y X − March 2010 On N (k)-Contact Metric Manifolds A.A. Shaikh Department of Mathematics, University of Burdwan, Golapbag, Burdwan-713104, West Bengal, India email : aask2003@yahoo.co.in and C.S. Bagewadi Department of Mathematics, Kuvempu University, Jana Sahyadri, Shankaraghatta-577 451, Karnataka, India email : prof bagewadi@yahoo.com ABSTRACT The object of the present paper is to study a type of contact metric manifolds, called N (k)- contact metric manifolds admitting a non-null concircular and torse forming vector field. keywords: 2n+1; concircular; cubo; distribution; field; following; form; g(x; k)-contact; manifold; metric; metric manifold; non; product; r(x; riemannian; sasakian; theorem; torse; vector; vector field; virtue cache: cubo-1436.pdf plain text: cubo-1436.txt item: #200 of 481 id: cubo-1437 author: Rojas, Jacqueline; Mendoza, Ramon; da Silva, Eben title: Projective Squares in ℙ² and Bott’s Localization Formula date: 2010-03-01 words: 9404 flesch: 88 summary: − w0)(2w2 − w0 − w1) Making a cyclic permutation of x′is in the table above, we will obtain all the 30 contributions to (5.1) determined by the 6 fixed points w11 = ([ℓ 2, ℓℓ1], ℓℓ 2 2) ∈ W 1 (cf. − w0)(2w1 − w0 − w2) w23 = (w 1 1, x̃ 2 1x 2 2) (5w0 + w1 + 2w2) keywords: answer; bott; c[x0; contribution; cubic; cubo; degree; description; dimensional; eben; enumerative; fact; fixed; following; formula; g2(f2; general; geometry; hilbert; homogeneous; ideal; intersection; jacqueline; lines; math; mendoza; note; o(e; p(f; plane; points; polynomial; projective; ramón; rojas; silva; space; squares; t(w2−w0; tangent; variety; vector; w0)(w0; x0x1; x0x2; ℓ1 ℓ; ℓ1ℓ; ℓ2 ℓ; ℓ31; ℓℓ1; ℓℓ2; ℓℓ22 cache: cubo-1437.pdf plain text: cubo-1437.txt item: #201 of 481 id: cubo-1438 author: Farajzadeh, A.P.; Amini-Harandi, A.; O’Regan, D.; Agarwal, R.P. title: Strong vector equilibrium problems in topological vector spaces via KKM maps date: 2010-03-01 words: 5023 flesch: 81 summary: We denote the duality pairing between X∗ and X, by 〈., .〉, and the open line segment joining between x, y ∈ K by ]x, y[. + ‖ x − f (x) ‖, ∀x, y ∈ K, and let W (x) = [−∞, 0) ⊂ Y = R, for all x ∈ K. The function F is concave in the second variable with respect to the set (Y \W (x)) keywords: bifunction; c(x; closed; compact; cone; continuous; convex; cubo; equilibrium; following; kkm; mapping; nonempty; problems; proof; sign; strong; subset; svep; t x; theorem; topological; vector; −c(x)\{0 cache: cubo-1438.pdf plain text: cubo-1438.txt item: #202 of 481 id: cubo-1440 author: Helffer, Bernard; Pan, Xing-Bin title: On Some Spectral Problems and Asymptotic Limits Occuring in the Analysis of Liquid Crystals date: 2009-12-01 words: 7038 flesch: 76 summary: This is a consequence of λN1 (qn) = Θ0 qτ + O((qτ) 2/3 ) , (7.2) with O((qτ)2/3) uniform with respect to n ∈ C(τ) and τ ∈ (0,τ0] . We hope to give in [HP3] a two-term asymptotic of µ∗(q,τ) and consequently of Qc3(κ,τ) for large κ (with τ ∈ (0,τ0]). keywords: analysis; asymptotic; bclp; bernard; bin; c(κ; c(τ; case; constants; critical; crystals; cubo; curl; elastic; energy; field; following; functional; g[ψ; gennes; ginzburg; helffer; hp2; inf; l2(ω; l4(ω; landau; large; liquid; magnetic; math; minimizers; neumann; nqτ; number; pan; phase; phillips; problems; proof; proposition; reduced; results; smectic; spectral; state; superconductivity; surface; vector; wave; x.b; xing; λn1 cache: cubo-1440.pdf plain text: cubo-1440.txt item: #203 of 481 id: cubo-1441 author: Bony, Jean-François; Bruneau, Vincent; Briet, Philippe; Raikov, Georgi title: Resonances and SSF Singularities for Magnetic Schrödinger Operators date: 2009-12-01 words: 5576 flesch: 79 summary: Here H̃0 := H0 + v0 where v0 = v0(x3) decays fast enough at infinity, while H̃ := H̃0 + V where V satisfies (1.1). Then H̃0 := H0,⊥ ⊗ I‖ + I⊥ ⊗ H‖ = H0 + I⊥ ⊗ v0 is the Hamiltonian of a non-relativistic spinless quantum particle subject to a classical electromag- netic field (E, B) with B = (0, 0,b) and E = −(0, 0,v′0). keywords: 0,∞; adjoint; asymptotic; bony; briet; bruneau; cubo; decay; eigenvalues; extension; fix; function; h̃,h̃0; h̃0; infinite; j.-f; ker; landau; levels; magnetic; math; multiplicity; o(1; operator; proposition; raikov; resonances; satisfies; satisfy; schrödinger; section; set; shift; singularities; spectral; ssf; theorem; theory; ξ(2bq cache: cubo-1441.pdf plain text: cubo-1441.txt item: #204 of 481 id: cubo-1442 author: Ammari, Kaïs; Vodev, Georgi title: Boundary Stabilization of the Transmission Problem for the Bernoulli-Euler Plate Equation date: 2009-12-01 words: 3629 flesch: 89 summary: Then O = Ω\Ω1 is a bounded, connected domain with boundary ∂O = Γ1 ∪Γ. We are going to study the following mixed boundary value problem    (∂2t Write f = f ♭ +f♮, where f♭ = φ(G/z)f, f♮ = (1 − φ)(G/z)f. keywords: ammari; boundary; cubo; c∂ν; energy; equation; estimate; following; function; l2(γ; l2(ω; math; plate; problem; satisfies; stabilization; theorem; transmission; vodev; ‖gf‖h; ‖v1‖l2(ω1; ‖v2‖l2(o; ∂νu1|γ1; ∆u2|γ1; ∥∥∥ cache: cubo-1442.pdf plain text: cubo-1442.txt item: #205 of 481 id: cubo-1443 author: Hess, Patrícia; Melo, Severino T. title: K-Theory of an Algebra of Pseudodifferential Operators on a Noncompact Manifold date: 2009-12-01 words: 2060 flesch: 74 summary: For each ϕ ∈ R, let Uϕ be the operator on L 2 (S1) given by Uϕf (z) = z −ϕf (z), z ∈ S1, and let Yϕ := FdUϕF −1 d , where Fd : L 2 (S1) → ℓ2(Z) is the discrete Fourier transform. Therefore, the class of generators LΛ can be replaced by the operator 1 i ∂ ∂β Λ, β ∈ S1, since S1 has trivial tangent bundle. keywords: algebra; c*-algebra; cubo; functions; k0(a; k1(a; l2(ω; melo; operators; pseudodifferential; sequence; symbol; theorem; theory cache: cubo-1443.pdf plain text: cubo-1443.txt item: #206 of 481 id: cubo-1444 author: Cardoso, Fernando; Cuevas, Claudio; Vodev, Georgi title: Dispersive Estimates for the Schrödinger Equation with Potentials of Critical Regularity date: 2009-12-01 words: 5230 flesch: 88 summary: Rn K̃h(|x − ξ|, t − τ)Kh(|y − ξ|,τ)V (ξ)dξdτ, where K̃h denotes the kernel of the operator e itG0ψ1(h 2G0). ∣∣∣ ∣∣∣∂α2ξ ah(|y − ξ|, t/µ) ∣∣∣ ∣∣∣∂α3ξ Q(ξ) ∣∣∣ ≤ Ch−k−ε(t/µ)k+ε ∑ |α1|+|α2|+|α3|=|α| |x − ξ|−|α1||y − ξ|−|α2|−k−ε ∣∣∣∂α3ξ Q(ξ) ∣∣∣ , (3.28) ∣∣∂µ∂αξ W(µ,ξ) ∣∣ ≤ tµ−2 ∣∣∂αξ (ã ′ h(|x − ξ|, t(µ − 1)/µ)ah(|y − ξ|, t/µ)Q(ξ)) ∣∣ +tµ−2 ∣∣∂αξ (ãh(|x − ξ|, t(µ − 1)/µ)a ′ h(|y − ξ|, t/µ)Q(ξ)) ∣∣ ≤ Ctµ−2 ∑ |α1|+|α2|+|α3|=|α| ∣∣∣∂α1ξ ã ′ h(|x − ξ|, t(µ − 1)/µ) ∣∣∣ ∣∣∣∂α2ξ ah(|y − ξ|, t/µ) ∣∣∣ ∣∣∣∂α3ξ Q(ξ) keywords: cardoso; claudio; cubo; cuevas; dimensions; dispersive; equation; estimates; function; georgi; l1→l∞; log; n/2; potentials; proof; proved; regularity; satisfying; schrödinger; sup; t(µ; theorem; vodev; ∣∣∣ cache: cubo-1444.pdf plain text: cubo-1444.txt item: #207 of 481 id: cubo-1445 author: McDowall, Stephen title: Optical Tomography for Media with Variable Index of Refraction date: 2009-12-01 words: 10019 flesch: 80 summary: If x,y ∈ M then simplicity of (M,g) ensures there exists a unique geodesic from x to y; let d(x,y) be the geodesic distance between x and y, and let v(x,y) be the tangent vector at x of this geodesic. If y ∈ M, consider z = zy(t,v) = γ(y,v)(t) defined from the “polar” coordinates (t,v) ∈ R × ΩyM. Let Jy(z) denote the Jacobian determinant | det ∂z/∂(t,v)| −1 of this change of variables. keywords: albedo; boundary; case; change; constant; cubo; cκm; definition; denote; determination; determined; diam; dimensions; dµ(x′,v′; equation; estimate; euclidean; final; following; form; function; geodesic; index; inverse; kernel; lemma; m(x; mcdowall; measurements; media; metric; neighborhood; operator; optical; particles; point; problem; proof; proposition; ray; results; riemannian; scattering; section; series; simple; sin; small; solution; stationary; stephen; tangent; terms; theorem; tomography; transform; transport; v)(t; v)(−τ−(x; variables; vectors; volume; γ(x; γ(y; θ̃(x; τ−(x; ωxm; ωym; ∣∣∣ cache: cubo-1445.pdf plain text: cubo-1445.txt item: #208 of 481 id: cubo-1446 author: Bleyer, Ismael; Leitão, A. title: On Tikhonov Functionals Penalized by Bregman Distances date: 2009-12-01 words: 6496 flesch: 81 summary: ∈ ∂h (u) } , where ∂h (u) denotes the subdifferential of h at u and D ξ h (v,u) = h (v) − h (u) − 〈ξ , v − u〉 . (11) Notice that ∥∥Fuδα ∥∥2 − ‖Fu‖2 = ∥∥F ( uδα − u + αω )∥∥2 − ‖F (u − u + αω)‖2 + 2 〈 Fuδα − Fu , Fu − αFω 〉 H . keywords: assumption; banach; bregman; condition; convergence; cubo; d(f; data; definition; distance; estimate; existence; functionals; hold; inequality; method; minimizer; nonlinear; operator; problems; proof; rates; regularization; section; solution; source; step; theorem; tikhonov; uk+1; uδα; ∥∥2 cache: cubo-1446.pdf plain text: cubo-1446.txt item: #209 of 481 id: cubo-1447 author: Gil, Juan B. title: Structure of Resolvents of Elliptic Cone Differential Operators: A Brief Survey date: 2009-12-01 words: 4211 flesch: 72 summary: [T (λ)(A − λ)] : Dmax/Dmin → C d, and AD − λ is invertible if and only if FD(λ) = F (λ)|D/Dmin is invertible. Thus, for every domain D with Dmin ⊂ D ⊂ Dmax and all λ ∈ C, AD − λ : D → x −m/2L2b(M ; E) is Fredholm with ind(AD − λ) = ind AD. keywords: asymptotic; a∧,d∧; b(λ; boundary; case; closed; cone; cubo; differential; dimensional; dmax; dmin; domain; elliptic; extension; family; function; gil; growth; invertible; juan; math; minimal; near; operator; parameter; ray; res(a∧; resolvent; sector; set; space; spectral; spectrum; stationary; structure; theorem; x−m/2l2b; −m/2l2b cache: cubo-1447.pdf plain text: cubo-1447.txt item: #210 of 481 id: cubo-1448 author: Guillarmou, Colin title: Scattering Theory on Geometrically Finite Quotients with Rational Cusps date: 2009-12-01 words: 18851 flesch: 73 summary: If moreover θ,θ ′ are chosen satisfying supp(θ) ∩ ck = ∅ and θθ ′ = 0 then θ′RXk (λ)θ ∈ ρ λρ′ λ R−1c C ∞ (X̄k × X̄k), θRXk (λ)θ ′ ∈ ρλρ′ λ R′c −1 C∞(X̄k × X̄k) (4.3) Proof : clearly, it is enough to show the lemma with θ,θ′ which are independent of the variable z ∈ T k. We recall from [8] that the explicit formula for the resolvent on Xk can be obtained by Fourier analysis on the z ∈ T k variable, RXk (λ) admits a meromorphic continuation to C and its Schwartz kernel can be written RXk (λ) = ∑ m∈Zk eiωm.(z−z ′)Rm(λ) (4.4) for λ /∈ For the term R0(λ), it is clear, using (4.6) and (4.7) that θR0(λ)θ ′ ∈ ρλρ′ λ R′c −1 C∞(X̄k × X̄k) 150 Colin Guillarmou CUBO 11, 5 (2009) which concludes the proof of (4.3) using the symmetry of the resolvent kernel. keywords: 0,∞; acc; blow; boundary; case; class; colin; compact; compactification; conformal; consequence; constant; construction; coordinates; cubo; cusps; c∞(x̄; defining; density; derivatives; differential; dvolh0; e(λ; eisenstein; equation; expansion; expression; extension; finite; flat; function; graham; guillarmou; hn+1; hyperbolic; ĥ0; infinity; kernel; k∞(λ; l2(b; laplacian; lemma; manifold; mapping; math; maximal; mazzeo; melrose; meromorphic; metric; model; multiplicity; m̄k; neighbourhood; non; n−k; odd; operator; order; parabolic; perry; point; poisson; poles; positive; previous; problem; proof; properties; proposition; pseudo; quotients; r(λ; rank; recall; resolvent; resonance; respect; restriction; results; rn−k; r′c; r−1c; s(λ; satisfies; satisfying; scattering; schwartz; section; sense; set; singularity; smooth; space; straightforward; structure; study; subgroup; submanifolds; support; t k; term; theorem; theory; vanishing; variable; view; volume; x̄k; |y|2 cache: cubo-1448.pdf plain text: cubo-1448.txt item: #211 of 481 id: cubo-1449 author: Caldas, M.; Hatir, E.; Jafari, S.; Noiri, T. title: A New Kupka Type Continuity, λ-Compactness and Multifunctions date: 2009-09-01 words: 6738 flesch: 82 summary: If F(x) 6= ∅ for every point x ∈ X, then there exists a nonempty, λ-closed set C of X such that F(C) = C. Proof. A net ξ = {xα | α ∈ Λ} λ-accumulates at a point x ∈ X if the net is frequently in every U ∈ λO(X,x), i.e. for each U ∈ λO(X,x) and for each α0 ∈ Λ, there is some α ≥ α0 such that xα ∈ keywords: accumulation; card; closed; compact; compactness; continuity; continuous; cover; f(x; finite; function; irresolute; kupka; lower; n)-λ; open; point; proof; set; sets; space; subset; theorem; topological cache: cubo-1449.pdf plain text: cubo-1449.txt item: #212 of 481 id: cubo-1450 author: Venkov, George title: Small Data Global Existence and Scattering for the Mass-Critical Nonlinear Schrödinger Equation with Power Convolution in ℝ³ date: 2009-09-01 words: 5162 flesch: 84 summary: Key words and phrases: Nonlinear Schrödinger equation, power convolution, Hartree equation, local and global existence. [5] Ginibre, J. and Velo, G., On a class of nonlinear Schrödinger equations with nonlocal interaction, Math. Zeitschr. keywords: admissible; b2r; critical; cubo; data; equation; estimate; existence; following; global; hartree; inequality; initial; l2(r3; lemma; local; mass; math; nonlinear; operator; pair; posedness; problem; proof; scattering; schrödinger; small; solution; space; strichartz; theorem; time; u(t; venkov; wave cache: cubo-1450.pdf plain text: cubo-1450.txt item: #213 of 481 id: cubo-1451 author: Antoine, Xavier; Besse, Christophe; Szeftel, Jérémie title: Towards accurate artificial boundary conditions for nonlinear PDEs through examples date: 2009-09-01 words: 7923 flesch: 68 summary: email: jszeftel@math.princeton.edu ABSTRACT The aim of this paper is to give a comprehensive review of current developments re- lated to the derivation of artificial boundary conditions for nonlinear partial differential equations. 1 Introduction The subject of designing artificial boundary conditions for linear scalar and systems of Partial Dif- ferential Equations (PDEs) has been studied since more than thirty years now. keywords: = −; a(x; abc; absorbing; accurate; antoine; approximation; artificial; artificial boundary; besse; boundary; boundary conditions; calculus; case; christophe; coefficients; computational; conditions; cubo; domain; e −i; equation; error; figure; functions; jérémie; linearization; math; n u; n+1; nonlinear; numerical; operator; order; point; potential; problem; pseudodifferential; relative; schemes; schrödinger; section; solution; strategy; symbols; szeftel; t u; time; transparent; variable; wave; xavier; α(u; β(u; ∂ n; ∂xu; −i π; ∞[×{xr cache: cubo-1451.pdf plain text: cubo-1451.txt item: #214 of 481 id: cubo-1452 author: Le Peutrec, D. title: Small singular values of an extracted matrix of a Witten complex date: 2009-09-01 words: 3304 flesch: 74 summary: Consider a linear application B(h) depending on h ∈ (0, h0]: B(h) : We will apply this corollary in the particular case when C and D depend on h ∈ (0, h ′ 0 ] and are quasi-unitary: C(h) keywords: a0(h; analysis; b(h; case; complex; cubo; diffusion; eigenvalues; forms; induction; j(k; laplacians; linear; matrices; matrix; operator; oε(e−; processes; quasi; remark; singular; small; theorem; unitary; witten; η h; ∣∣∣ cache: cubo-1452.pdf plain text: cubo-1452.txt item: #215 of 481 id: cubo-1453 author: Cuccu, Fabrizio; Popivanov, Petar; Porru, Giovanni title: Estimates for solutions to nonlinear degenerate elliptic equations date: 2009-09-01 words: 4283 flesch: 86 summary: If h(r) = π for r ≤ ρ ≤ R we can replace E by the ball h(r) π for r ≤ ρ ≤ R. Define the set Gτ = {r ≤ ρ ≤ R, −τ ≤ θ ≤ τ}, with τ such that ∫ E |x|γdx = ∫ Gτ |x|γdx. keywords: 2πλ; case; condition; cubo; elliptic; equation; estimates; h(ρ; inequality; integral; p−1; rβ+1; rγ+2; solutions; special; sup; λ|x|βds; λ|x|γdx; ψ(x cache: cubo-1453.pdf plain text: cubo-1453.txt item: #216 of 481 id: cubo-1454 author: Combescure, Monique title: Circulant Matrices, Gauss Sums and Mutually Unbiased Bases, I. The Prime Number Case date: 2009-09-01 words: 4690 flesch: 79 summary: Proof : For any j = 0, ...,d − 1, one has d−1∑ l=0 |ĉl|2ω−jl = 1 d d−1∑ l=0 ω −jl d−1∑ k=0 c̄kω −lk d−1∑ k′=0 ck′ω k′l = d−1∑ k,k′=0 c̄kck′ 1 d d−1∑ l=0 ω l(k′−k−j) = d−1∑ k=0 c[j+k]c̄k since d −1 d−1∑ l=0 ω l(k′−j−k) = δk′,[j+k] It is known ( [4], [13]) that circulant unitary Hadamard matrices are in one-to-one correspon- dance with bi-unimodular sequences c = (c0,c1, ...,cd−1). It is trivial to show that if the orthonormal bases Bk are the column vectors of an unitary matrix Ak, then the property that must satisfy the Ak’s in order that {1l,B1, ...,Bm} are MUB’s is that all Ak, k = 1, ...,m and A∗kAk′, k 6= k′ = 1, ...,m are unitary Hadamard matrices. keywords: bases; case; cd−1; circulant; combescure; cubo; dimension; discrete; d−1∑; exp; fourier; gauss; hadamard; j(j+1; k=0; matrices; matrix; mub; number; odd; prime; problem; proof; property; proposition; sequences; set; sums; transform; unbiased; unimodular; unitary; −1/2 cache: cubo-1454.pdf plain text: cubo-1454.txt item: #217 of 481 id: cubo-1455 author: Toft, Joachim title: Pseudo-differential operators with smooth symbols on modulation spaces date: 2009-09-01 words: 8276 flesch: 79 summary: In order to prove this, assume first that N1 = N, N2 = 0, f ∈ M̃0, and choose open sets Ω0 = {ξ ∈ Rd ; |ξ| < 2 }, and Ωj = {ξ ∈ Rd ; 1 < |ξ| < d|ξj| }. [1,∞] and ω ∈ P(R2d). keywords: applications; at(x; banach; constant; continuity; continuous; cubo; definition; differential; feichtinger; following; fourier; function; gröchenig; invariant; joachim; lemma; math; moderate; modulation; modulation spaces; operators; p(r2d; proof; properties; pseudo; pseudodifferential; remark; respect; result; set; smooth; spaces; symbols; t ∈; theorem; toft; translation; w p; weight; wiener; ω(x; ∈ r; ∈ s cache: cubo-1455.pdf plain text: cubo-1455.txt item: #218 of 481 id: cubo-1456 author: Pereira Gomes, Luiz Antonio; Brandani da Silva, Eduardo title: A Characterization of the Product Hardy Space 𝐻¹ date: 2009-09-01 words: 5102 flesch: 86 summary: To prove 3.2(3), since the map u ∈ IR −→ (ϕi(u)f(u); −n ≤ One of ingredients for the proof of the H1 characterization obtained in this work, consists of the theorems about singular integral vector operators contained in [12]. 2 Spaces H1(IR × IR) and HP,Q S (IR × IR) in the Product Case 2.1 Notations. keywords: 1,2; characterization; constant; cubo; f(x; functions; gomes; h1(ir; h1,2; hardy; hilbert; i=−∞; ir2; ir×ir; i∈zz; j∈zz; l2(ir; l∞c; math; measurable; norm; operators; product; proof; silva; space; test; theorem; triebel; ‖f‖h1(ir×ir cache: cubo-1456.pdf plain text: cubo-1456.txt item: #219 of 481 id: cubo-1457 author: Riihentaus, Juhani title: On an inequality related to the radial growth of subharmonic functions date: 2009-09-01 words: 3676 flesch: 79 summary: Generalizamos el resultado de Pavlović a las así llamada funciones subarmónicas casi-cercanas definidas en dominios bastante generales en Rn, n ≥ 2. Key words and phrases: Subharmonic function, quasi-nearly subharmonic function, accessible boundary point, approach region, integrability condition, radial order. Observe that Gehring, Hallenbeck and Stoll in fact considered subharmonic functions and that the limit in (2) was uniform in Stolz approach regions (in Stoll’s result in even more general regions). keywords: bn(x; boundary; constant; cubo; dhd(ζ; functions; general; inequality; lebesgue; let; math; pavlović; proof; quasi; radial; result; riihentaus; subharmonic; sup; theorem; u(x; u(y; δ(x; δ(x)n+γ; ϕ−1(δ(x))]−du(x cache: cubo-1457.pdf plain text: cubo-1457.txt item: #220 of 481 id: cubo-1459 author: Becker, Leigh C. title: Uniformly Continuous 𝐿¹ Solutions of Volterra Equations and Global Asymptotic Stability date: 2009-08-01 words: 8407 flesch: 86 summary: Integrating, we obtain V (t) − V (τ) ≤ −k ∫ t τ x 2 (s) ds. x 2 (t) ∫ t 0 | cos s| (1 + t)2 ds ≤ − ( 1 − 1 1 + t − t (1 + t)2 ) x 2 (t), which simplifies to V ′ (t) ≤ keywords: a(s; a(t; asymptotic; b(t; becker; c[0; conditions; constant; continuous; cubo; equations; f(t; functions; initial; l1[0,∞; leigh; lemma; liapunov; positive; proof; s)x(s; s)|du; solution; stability; stable; t s; t t0; theorem; volterra; x(t; |b(u; |ϕ|t0; ϕ(t; − ∫ cache: cubo-1459.pdf plain text: cubo-1459.txt item: #221 of 481 id: cubo-1460 author: Wang, Tingxiu title: Some General Theorems on Uniform Boundedness for Functional Differential Equations date: 2009-08-01 words: 5702 flesch: 91 summary: For k = 0, integrating (iii) from t0 to t ∈ I0, we have V (t, Xt) Therefore for each k = 0, 1, 2, · · · , there is a qk ∈ Ik such that V (qk, Xqk ) < ∆. Now for each t ≥ t0, V (t, Xt) ≤ ∆ if t ∈ I0 (see(3)), CUBO 11, 3 (2009) Some General Theorems on Uniform Boundedness ... 33 or if t ∈ Ik, k = 1, 2, 3, · · · , (iii) implies V (t, Xt) ≤ V (qk, Xqk ) keywords: boundedness; continuous; cubo; d(u; differential; equations; iii; solutions; stability; t t−h; theorem; t−h; u.b; uniform; wang; xu)du cache: cubo-1460.pdf plain text: cubo-1460.txt item: #222 of 481 id: cubo-1461 author: Zhang, Bo title: Boundedness and Global Attractivity of Solutions for a System of Nonlinear Integral Equations date: 2009-08-01 words: 4404 flesch: 85 summary: + ∫ t 0 e A(t−s) ˜G(s,x(s))ds (1.7) with a view of proving the existence and qualitative behavior of solutions by applying fixed point theorems. = ∫ t 0 ( ∫ t s g(v,x(v))dv )T Ds(t,s) ( ∫ t s g(v,x(v))dv ) ds + ( ∫ t 0 g(v,x(v))dv )T D(t, 0) keywords: = ∣; attractivity; boundedness; burton; cubo; d(t; differential; equations; function; g(t; g(v; global; h(t; integral; levin; liapunov; nonlinear; s)g(s; solutions; x(s))ds; x(t; x(v))dv; ‖ds(tn; ∣ ∣; ∣ ∫ cache: cubo-1461.pdf plain text: cubo-1461.txt item: #223 of 481 id: cubo-1462 author: Furumochi, Tetsuo title: Periodic Solutions of Periodic Difference Equations by Schauder’s Theorem date: 2009-08-01 words: 3099 flesch: 71 summary: In this paper, we give some new existence results of periodic solutions for periodic difference equations by using Schauder’s fixed point theorem and a convex Liapunov function, and show that the existence problem of periodic solutions of a periodic difference equation with infinite delay can be reduced to the existence problem of periodic solutions of an auxiliary difference equation with finite delay. 3 Periodic difference equations with finite delay In this section, concerning the existence of periodic solutions of periodic difference equations with finite delay, we state some known results. keywords: continuous; convex; delay; difference; differential; equations; existence; f(n; functional; furumochi; periodic; periodic difference; periodic solutions; point; set; solutions; theorem; x(n cache: cubo-1462.pdf plain text: cubo-1462.txt item: #224 of 481 id: cubo-1463 author: Kirk, C.M. title: A Localized Heat Source Undergoing Periodic Motion: Analysis of Blow-Up and a Numerical Solution date: 2009-08-01 words: 4791 flesch: 68 summary: A brief survey is presented of the literature concerning numerical studies of nonlinear Volterra integral equations with weakly singular kernels that exhibit blow-up solutions. In fact, the numerical modeling of nonlinear Volterra integral equations with blow-up solutions can be a difficult problem. keywords: amplitude; analysis; appl; behavior; blow; brunner; collocation; continuous; cubo; diffusive; equations; exp; frequency; heat; integral; k(t; kirk; localized; math; methods; motion; nonlinear; numerical; olmstead; periodic; problem; results; singular; solution; source; theorem; ti+1; time; tn+1; tn+1−s; u(t; volterra; w.e; weakly; −a2[cos(ωtn+1)−cos(ωs cache: cubo-1463.pdf plain text: cubo-1463.txt item: #225 of 481 id: cubo-1464 author: Henderson, J.; Ntouyas, S.K.; Purnaras, I.K. title: Positive Solutions for Systems of Three-point Nonlinear Boundary Value Problems with Deviating Arguments date: 2009-08-01 words: 7039 flesch: 90 summary: ≤ 1 1 − αη ∫ 1 0 (1 − s)y(s)ds, for all t ∈ − αη ∫ 1 η (1 − s)y(s)ds. keywords: boundary; bvp; cubo; henderson; i.k; lim; max; min; nonlinear; ntouyas; point; positive; problems; s.k; solutions; systems; theorem; u(t; v(t; value; − αη cache: cubo-1464.pdf plain text: cubo-1464.txt item: #226 of 481 id: cubo-1465 author: Grimmer, Ronald; He, Min title: Fixed Point Theory and Nonlinear Periodic Systems date: 2009-08-01 words: 4685 flesch: 81 summary: Based on semigroup theory, when A(ε) generates a C0-semigroup T (t, ε), the weak solution of (1.6) will have the form z(t, ε) = T (t, ε)z0 + ∫ t 0 T (t − s, ε)F (s, z(s, ε), ε) ds. = T (t, ε)z0 + ∫ t 0 T (t − s, ε)F (s, ε) ds. keywords: a(ε; continuity; continuous; cubo; equation; f2(t; nonlinear; operator; parameters; periodic; point; proof; semigroup; solution; theorem; unique; z(t cache: cubo-1465.pdf plain text: cubo-1465.txt item: #227 of 481 id: cubo-1466 author: Islam, Muhammad N.; Raffoul, Youssef N. title: Bounded Solutions and Periodic Solutions of Almost Linear Volterra Equations date: 2009-08-01 words: 2685 flesch: 85 summary: Multiply both sides of (3.7) with e−H ∫ t 0 a(s)ds and then integrate both sides from t − T to t, to obtain x(t)[e −H ∫ t t−T a(s)ds − 1]e−H ∫ t−T 0 a(s)ds = ∫ t t−T [ − Ha(u)x(u) + a(u)h(x(u)) + ∫ t −∞ C(t,s)g(x(s))ds + p(t), t ∈ (−∞,∞). keywords: a(s)ds; a(t; assume; c(t; continuous; equations; integral; linear; resolvent; solution; theorem; t−t; t−t a(s)ds; volterra; x(t cache: cubo-1466.pdf plain text: cubo-1466.txt item: #228 of 481 id: cubo-1467 author: Griechisch, Erika title: Some Theoretical Issues Concerning Hamming Coding date: 2009-05-01 words: 1911 flesch: 85 summary: In this case 〈A〉 = 〈B〉 = G. In 1970 L. Rédei conjectured if G = AB is a normalized factorization of G and G is of type (p, p, p), then either 〈A〉 6= G or 〈B〉 6= G has the Rédei property if from each normalized factorization G = AB it follows that either 〈A〉 6= G or 〈B〉 6= G. keywords: case; factorization; groups; property; rank; rédei; subgroup; table; type; x1x cache: cubo-1467.pdf plain text: cubo-1467.txt item: #229 of 481 id: cubo-1468 author: Szilagyi, Miklos N. title: 𝑁-Person Games with Crossing Externalities date: 2009-05-01 words: 2401 flesch: 65 summary: In this short paper we look at other N -person games with crossing payoff functions. May 2009 N-Person Games with Crossing Externalities Miklos N. Szilagyi Department of Electrical & Computer Engineering, University of Arizona, Tucson, AZ 85721-0104 email: szilagyi@ece.arizona.edu ABSTRACT We report computer simulation experiments based on our agent-based simulation tool to model uniform N -person games with crossing payoff functions for the case when the agents are greedy simpletons who imitate the action of that of their neighbors who received the highest payoff for its previous action. keywords: -person; action; agents; array; behavior; changes; chicken; cooperators; crossing; cubo; defectors; figure; functions; game; greedy; lines; number; para; payoff; point; ratio; simpletons; simulation; szilagyi; total; value; xcross; xfinal cache: cubo-1468.pdf plain text: cubo-1468.txt item: #230 of 481 id: cubo-1469 author: Dal Forno, Arianna; Merlone, Ugo title: Optimal Effort in Heterogeneous Agents Population with Global and Local Interactions date: 2009-05-01 words: 7988 flesch: 67 summary: Figure 1: Fixed vs Committed As the number of committed players approaches the whole population, their effort approx- imates e C and, the higher is the effort provided by fixed effort agents, the lower is the optimal effort supplied by committed players. Furthermore, when few committed agents face a population of fixed effort agents, they will expect a low probability of facing another committed agent. keywords: agents; arianna; best; committed; composition; coordination; cubo; dal; e c; eco; effort; equilibrium; figure; fixed; following; forno; game; heterogeneous; incentive; individual; interaction; local; max; merlone; model; nash; neighborhood; optimal; particular; policy; population; problem; profit; ranking; rational; results; second; section; set; strategies; theorem; ugo cache: cubo-1469.pdf plain text: cubo-1469.txt item: #231 of 481 id: cubo-1470 author: Szidarovszky, Ferenc; Zhao, Jijun title: The Dynamic Evolution of Industrial Clusters date: 2009-05-01 words: 6913 flesch: 65 summary: To react to the higher price of supplies and higher labor price, the producers cut their production levels and labor usage. 3 Conclusions This paper first introduced a static model of describing the mechanism of industrial clusters including sup- pliers and final product producers. keywords: behavior; bjl; c =; case; changes; clusters; cubo; decrease; dynamic; evolution; ferenc; figure; final; final products; firms; function; group; higher; increase; industrial; initial; innovation; ĩj; jijun; labor; level; limit; linear; market; model; oscillations; output; patterns; price; producers; productivity; products; profit; results; simulation; suppliers; supply; szidarovszky; time; trajectories; usage; value; xij; zhao cache: cubo-1470.pdf plain text: cubo-1470.txt item: #232 of 481 id: cubo-1471 author: Szidarovszky, Ferenc; Smith, Vernon L.; Rassenti, Steven title: Cournot Models: Dynamics, Uncertainty and Learning date: 2009-05-01 words: 12004 flesch: 73 summary: = xl(B − εkQ) − (αlxl + βl), (7.24) so the best believed output choice is xl = B − αl εk − Q, and the believed total production of the industry is Q (k) = N B − ∑N l=1 αl (N + 1)εk . In this further special case relation (3.10) simplifies to the following: N r 1 − r > −1 which can be rewritten as r > −1 N − 1 . keywords: = −; actual; behavior; believed; best; case; ck(xk; classical; conditions; cost; cournot; cubo; denote; different; dynamic; economic; environment; equation; equilibrium; experimental; ferenc; firm; firm k; following; function; game; industry; information; k=1; l=1; learning; market; models; nash; negative; new; notice; oligopoly; output; price; process; production; profit; r(n; rassenti; real; response; results; roots; session; simple; smith; special; stability; stable; state; steady; steven; subject; system; szidarovszky; t k; theory; time; true; uncertainty; unit; value; vernon; xk(t cache: cubo-1471.pdf plain text: cubo-1471.txt item: #233 of 481 id: cubo-1472 author: Chiarella, Carl; Szidarovszky, Ferenc title: Dynamic Oligopolies and Intertemporal Demand Interaction date: 2009-05-01 words: 6046 flesch: 77 summary: [ (h̄ − K)2 − (n − 1)K2r ] K(nhr̄ + h̄) + (Kz − h̄) < 0 which can be simplified as (Kz − h̄)(h̄ − K) + T ( (h̄ − K)2 − (n − 1)K2r ) keywords: = −; ak(λ; assume; bk(λ; carl; case; chiarella; conditions; critical; cubo; cycle; demand; dynamic; equation; equilibrium; ferenc; figure; firm; information; interaction; intertemporal; k=1; negative; nhkr̄; oligopolies; oligopoly; positive; real; roots; stability; stable; state; steady; szidarovszky; theorem; time; value; xkf cache: cubo-1472.pdf plain text: cubo-1472.txt item: #234 of 481 id: cubo-1473 author: Chiarella, Carl; Szidarovszky, Ferenc title: A Multiobjective Model of Oligopolies under Uncertainty date: 2009-05-01 words: 3034 flesch: 68 summary: The derivative of the objective function (2.4) with respect to qj can be given as qj f ′ (Q) + f (Q) − C′j (qj ) − αj qj σ 2 j . We can rewrite equation (2.11) as qj f ′ (Q) + f (Q) − C′j (qj ) = αj qj σ 2 j . keywords: best; chiarella; conditions; cubo; demand; equation; equilibrium; expected; firm; function; hand; left; model; multiobjective; oligopoly; output; product; profit; response; solution; szidarovszky; theorem; time; uncertainty; unique cache: cubo-1473.pdf plain text: cubo-1473.txt item: #235 of 481 id: cubo-1474 author: Kapolyi, László title: Network Oligopolies with Multiple Markets date: 2009-05-01 words: 3500 flesch: 76 summary: Notice that ∂Πk ∂xki = pi + xki ∂pi ∂si + ∑ j 6=i xkj ∂pj ∂si − C′k − T ′ ki = pi + M ∑ l=1 xkl ∂pl ∂si − C′k − T ′ ki, (3) furthermore ∂ 2 Πk ∂x 2 ki = 2 ∂pi ∂si + xki ∂ 2 pi ∂s 2 i + ∑ j 6=i xkj ∂ 2 pj ∂s 2 i − C′′k − T ′′ ki (4) and ∂ 2 Πk ∂xki∂xkj = ∂pi ∂sj + ∂pj ∂si + M ∑ l=1 xkl ∂ 2 pl ∂si∂sj − C′′k . and Lki − xki ≥ 0. keywords: case; ck(qk; conditions; cost; cubo; equilibrium; firm; function; i=1; k=1; linear; lki; markets; matrix; model; multiple; network; oligopolies; positive; price; problem; profit; solution; stability; system; uki; vki; xki; xkj; ∂si; ∂πk;   cache: cubo-1474.pdf plain text: cubo-1474.txt item: #236 of 481 id: cubo-1475 author: Kugler, Tamar; Szidarovszky, Ferenc title: An Inter-Group Conflict and its Relation to Oligopoly Theory date: 2009-05-01 words: 3772 flesch: 72 summary: The concavity of fk implies that the best response of player k is given as Rk(Qk) =      0 if ∂fk ∂xk |xk=0≦ 0 Lk if ∂fk ∂xk |xk=Lk ≧ 0 z ∗ k otherwise (8) where z∗k is the unique solution of equation ∂fk ∂zk = AQk (zk + Qk) 2 − βk = 0 In summary, the best response function of player k is equivalent with the following: R̄k(Q) =      0 if Q = 0 or Q ≧ keywords: best; case; conflict; contribution; cubo; equation; equilibrium; figure; firm; function; game; good; group; inter; k=1; kugler; members; oligopoly; players; public; q(1; relation; response; r̄k(q; szidarovszky; theory; unique; xki; yki cache: cubo-1475.pdf plain text: cubo-1475.txt item: #237 of 481 id: cubo-1476 author: Qiao, Haiyan; Edwards, Brandon title: A General Purpose Platform for Data Clustering Analysis date: 2009-05-01 words: 3390 flesch: 53 summary: In the analysis of complex survey data, cluster analysis is usually the crucial step to dis- cover patterns that will be used in the decision-makings such as the target audience for a product, the development of new products etc. A few platforms for cluster analysis have been developed for some CUBO 11, 2 (2009) A General Purpose Platform for Data Clustering Analysis 141 special contexts or purposes; see [4, 5]. keywords: algorithms; analysis; brandon; centroid; clustering; clusters; cubo; data; data clustering; density; development; different; display; distance; easy; edwards; figure; general; haiyan; hierarchical; important; interface; knowledge; linkage; matlab; means; methods; metric; netbeans; noise; number; parameters; platform; point; problem; procedure; purpose; qiao; results; sciences; set; similarity; single; social; user; visual cache: cubo-1476.pdf plain text: cubo-1476.txt item: #238 of 481 id: cubo-1477 author: Constales, D.; De Almeida, R.; Krausshar, R.S. title: A Generalization of Wiman and Valiron’s theory to the Clifford analysis setting date: 2009-03-01 words: 6667 flesch: 72 summary: (7) 3 Order of growth of monogenic functions in Rn+1 In this overview paper we restrict us to treat entire monogenic functions. Notice that Taylor series actually are a natural method to construct and to define entire monogenic functions. keywords: algebra; almeida; analysis; asymptotic; behavior; c(n; cauchy; central; cl0n; classes; classical; clifford; complex; constales; cos; cubo; differential; dimensional; entire; equations; f(z; following; formula; function; generalization; generalized; growth; higher; index; inf; integral; kraußhar; left; lim; log; log(r; m(r; maximum; monogenic; order; partial; polynomials; r.s; real; riemann; rn+1; series; sin; solutions; sup; taylor; term; theorem; theory; type; valiron; wiman; |m|; |ν(r)|; µ(r; ρ(f cache: cubo-1477.pdf plain text: cubo-1477.txt item: #239 of 481 id: cubo-1478 author: Tolksdorf, Jürgen title: Dirac Type Gauge Theories – Motivations and Perspectives date: 2009-03-01 words: 13028 flesch: 68 summary: In fact, the former should be considered as a functional of a specific class of Dirac type operators on (31) and hence as a specific restriction of a much more general functional (c.f. our discussion in the next section). The form (43) of the Einstein-Hilbert action makes it most explicit how the metric gM can be replaced by (a specific class of) Dirac type operators and hence how the Einstein-Hilbert functional determines a Clifford action γ on a twisted Grassmann bundle (31). keywords: action; algebra; anti; appropriate; associated; bundle; c.f; case; chosen; class; clifford; complex; connection; considered; contrast; corresponding; covariant; cubo; curvature; d(eλ; differential; dirac; dirac action; dirac operators; dirac type; dvolm; einstein; electromagnetic; end(e; end(eλ; equations; field; following; form; functional; gauge; general; generalized; geometrical; grassmann; group; hand; hermitian; hilbert; i/∂; jürgen; laplacian; like; loc; local; manifold; matter; maxwell; mills; module; motivations; note; operator; order; particle; particular; pauli; perspectives; potential; pp̄; principal; real; respect; riemannian; sec(m; section; semi; space; specific; spinor; square; structure; terms; theories; tolksdorf; tre; twisted; type; underlying; universal; vector; yang; γ(fa cache: cubo-1478.pdf plain text: cubo-1478.txt item: #240 of 481 id: cubo-1479 author: Brackx, Fred; De Schepper, Hennie; Sommen, Frank; Van de Voorde, Liesbet title: Discrete Clifford analysis: an overview date: 2009-03-01 words: 6874 flesch: 74 summary: Key words and phrases: discrete Clifford analysis, discrete function theory, discrete Cauchy formula. − f(x − ej), j = 1, . . . keywords: algebra; analysis; backward; basis; brackx; case; cauchy; clifford; complex; cubo; definition; degree; dimensional; dirac; discrete; e −; e(x; f(x; forward; function; fundamental; graph; gt(x; homogeneous; inner; j e; j=1; k e; laplacian; metric; model; monogenic; operator; order; overview; pk(x; points; polynomial; r0,m; scalar; schepper; section; set; sommen; space; spherical; support; theorem; theory; van; vectors; voorde cache: cubo-1479.pdf plain text: cubo-1479.txt item: #241 of 481 id: cubo-1480 author: Gürlebeck, K.; Morais, J. title: On mapping properties of monogenic functions date: 2009-03-01 words: 10511 flesch: 73 summary: March 2009 On mapping properties of monogenic functions K. Gürlebeck and J. Morais Institute of Mathematics / Physics, Bauhaus-University, Weimar, Germany. email: guerlebe@fossi.uni-weimar.de email: jmorais@mat.ua.pt ABSTRACT Main goal of this paper is to study the description of monogenic functions by their geometric mapping properties. keywords: analytic; associated; ball; bohr; case; class; coefficients; complex; conformal; constants; cos; cubo; degree; derivative; dimensional; expansion; f(0; f(ξ; following; fourier; functions; generalized; gürlebeck; harmonics; homogeneous; hyperholomorphic; inequality; inner; integrable; l2(br; left; lemma; linear; m,†; m,† n; m=1; mapping; monogenic; monogenic functions; morais; n+1; n+1 n; operator; orthogonal; point; polynomials; previous; product; proof; properties; proposition; quaternionic; radius; real; relations; remark; resp; respect; result; sc(y; series; space; spherical; square; study; sup; theorem; theory; unit; |sc; |ξ|≤r; α0 n; ‖l2(br;a;r; ‖l2(s;a;r; ‖sc(x cache: cubo-1480.pdf plain text: cubo-1480.txt item: #242 of 481 id: cubo-1481 author: Ludkovsky, S.V. title: Wrap groups of fiber bundles and their structure date: 2009-03-01 words: 13264 flesch: 80 summary: ∈ N. Take δ = δm = 1/m and f = fm ∈ H ∞ p such that < fm >t,H= g 1/m. On the other hand, jg1/m = gj/m for each j < mǫ, j ∈ N, hence fj/m(M) = f1/m(M) for each j < mǫ, since f ∨ h(M ∨ M) = f(M) ∨ h(M) and using embedding η of (SMN)t,H into (W MN)t,H. CUBO 11, 1 (2009) Thus there exists the quotient uniform space Ht p (M,{X0,q : q = 1, ...,k}; W,y0)/Rt,H =: (S ME)t,H. In view of [30, 31] DifH t p (M) is the group of diffeomorphisms for t ≥ [m/2] + 1. keywords: -diffeomorphic; -differentiable; arcwise; associative; bundles; canonical; case; charts; class; closed; commutative; compact; complete; conditions; connected; continuous; corners; cubo; definition; difh; dimensional; element; embedding; equivalence; family; fiber; functions; groups; h t; ht p; iii; infinite; isomorphic; k(x; limn→∞; loop; ludkovsky; m,{s0,q; manifolds; mapping; marked; neighborhood; non; octonion; open; parallel; plot; points; principal; product; pseudo; q=1,; quadrants; quaternion; quotient; real; relative; s.v; s0,q; separable; sequence; sme)t; space; structure; subset; t p; topological; transport; uniform; uniformity; wedge; wme)t; wrap cache: cubo-1481.pdf plain text: cubo-1481.txt item: #243 of 481 id: cubo-1482 author: Perotti, Alessandro title: Regular quaternionic functions and conformal mappings date: 2009-03-01 words: 7966 flesch: 79 summary: email: perotti@science.unitn.it ABSTRACT In this paper we study the action of conformal mappings of the quaternionic space on a class of regular functions of one quaternionic variable. Every element of Holp(Ω, H) is regular, but there exist regular functions that are not holomorphic for any p. keywords: alessandro; biregular; c1(ω; cauchy; class; complex; composition; conformal; constant; corollary; cubo; dimensional; d|2; e(f; energy; example; following; fueter; function; holomorphic; holomorphicity; holp(ω; hyperholomorphic; identity; kernel; left; m(f; mappings; maps; matrix; p(z; perotti; proof; properties; quadric; quaternionic; r(ω; rank; real; regular; regular function; regularity; remark; respect; result; rota; rotation; rotγ(a; space; structure; theorem; transformation; unit; w.r.t; z̄1; γ(a; γ(b; ;  cache: cubo-1482.pdf plain text: cubo-1482.txt item: #244 of 481 id: cubo-1483 author: Sproessig, Wolfgang; Thu Hoai, Le title: On a new notion of holomorphy and its applications date: 2009-03-01 words: 5169 flesch: 83 summary: = −e2e1 = e3 , e2e3 Then the general operators L,T and P are given by L := D + iα (Dirac operator with mass), (Tu)(x) := − 1 σ3 ∫ G eiα(x keywords: applications; boundary; corollary; cubo; discrete; following; formula; fractional; functions; general; gontcharov; hoai; holomorphy; i=1; integral; ker; m−1∑; new; notion; operator; order; proof; property; ptru; right; set; sproessig; taylor; teodorescu; theorem; thu; tlu; trace; transform; tru; type; u(t; value; wolfgang; γ(α cache: cubo-1483.pdf plain text: cubo-1483.txt item: #245 of 481 id: cubo-1484 author: Park, Sehie title: Remarks on KKM Maps and Fixed Point Theorems in Generalized Convex Spaces date: 2008-12-01 words: 5164 flesch: 78 summary: Since 1993, the author has initiated the study of the KKM theory on generalized convex spaces (or G-convex spaces) (X, D; Γ) as a common generalization of various general convexities without linear structures due to other authors. [12] S. Park, Elements of the KKM theory for generalized convex spaces, Korean J. Comput. keywords: abstract; authors; closed; continuous; convex; convex space; cubo; definition; function; generalized; kkm; map; maps; math; nonempty; park; point; property; set; space; theorem; theory; topological; type; φa}a∈〈d cache: cubo-1484.pdf plain text: cubo-1484.txt item: #246 of 481 id: cubo-1485 author: Shinzato, Rinko; Takahashi, Wataru title: A Strong Convergence Theorem by a New Hybrid Method for an Equilibrium Problem with Nonlinear Mappings in a Hilbert Space date: 2008-12-01 words: 4918 flesch: 87 summary: Azni − Auni〉 − 〈v − zni , zni − uni λni 〉 ≥ −‖v − zni‖‖Azni − Auni‖ − ‖v − u‖ − ‖yn − u‖) ≤ (‖xn − u‖ + ‖yn − u‖)‖xn keywords: convergence; convex; cubo; equilibrium; hilbert; i(c; inequality; inverse; mapping; monotone; nonexpansive; problem; set; solutions; space; strong; takahashi; theorem; variational; zni; ‖xn; ‖yn; − u‖ cache: cubo-1485.pdf plain text: cubo-1485.txt item: #247 of 481 id: cubo-1486 author: Andres, Jan; Pastor, Karel; Snyrychov´a, Pavla title: Simple Fixed Point Theorems on Linear Continua date: 2008-12-01 words: 6580 flesch: 83 summary: Introduction (Fixed point theorems in low dimensions) [G1] L. Górniewicz, Present state of the Brouwer fixed point theorem for multivalued map- pings, Ann. Sci. keywords: andres; closed; connected; connectivity; continua; continuous; cubo; example; fixed; graph; interval; lemma; linear; maps; math; multivalued; orbit; pastor; point; relation; sharkovskii; simple; šnyrychová; theorem; upper; values; ϕ(x; ∈ n;  ;  ;  ;  ;   cache: cubo-1486.pdf plain text: cubo-1486.txt item: #248 of 481 id: cubo-1487 author: Petrus¸el, Adrian; Rus, Ioan A.; S¸erban, Marcel Adrian title: Fixed Points for Operators on Generalized Metric Spaces date: 2008-12-01 words: 9073 flesch: 87 summary: Moreover, if x ∈ X, then there exists i(x) +∞; iii) there exist x ∈ X and n (x) ∈ N such that d ( f n(x) (x) , f n(x)+1 (x) ) < keywords: adrian; complete; contraction; cubo; d(x; definition; f n; fixed; following; generalized; generalized metric; i.a; lemma; let; metric; multivalued; operator; petruşel; picard; point; proof; rus; sequence; set; space; theorem; weakly; xi(x0; xn)n∈n cache: cubo-1487.pdf plain text: cubo-1487.txt item: #249 of 481 id: cubo-1488 author: Rhoades, B.E. title: A Fixed Point Theorem for Certain Operators date: 2008-12-01 words: 1767 flesch: 91 summary: − xn‖ ≤ g(max{‖xn − p‖, ‖xn − T xn‖, ‖p − T p‖, ‖xn − T p‖, ‖p − T xn‖}) → p. Again using (3), ‖T p − T xn‖ ≤ g(max{‖p − xn‖, ‖p − T p‖, ‖yn‖, ‖p − T xn‖, ‖xn − T p‖}). keywords: cubo; d(p; d(t; fixed; lim; maps; point; satisfying; theorem; xn‖ cache: cubo-1488.pdf plain text: cubo-1488.txt item: #250 of 481 id: cubo-1489 author: Balaj, Mircea; O’Regan, Donal title: An Intersection Theorem and its Applications date: 2008-12-01 words: 4449 flesch: 83 summary: Suppose that the following conditions are satisfied: (i) one of the following requirements is fulfilled: (i1) for each z ∈ Z the set {x ∈ X : p(x, z) < α} is open; (i2) p is marginally upper semicontinuous in x and for each y ∈ Y the set {z ∈ Z : q(y, z) ≥ β} is closed; (ii) for each x ∈ X the set {z ∈ Z : p(x, z) < α} is convex; (iii) q is (y, z)-quasiconvex; (iv) for x ∈ X, y ∈ Y and z ∈ Z the following implication holds: p(x, z) < α and q(y, z) < β ⇒ t(x, y) < in z; (ii) p is quasiconvex in z; (iii) q is (y, z)-quasiconvex; (iv) for x ∈ X, y ∈ Y and z ∈ Z the following implication holds: keywords: c(z; closed; compact; convex; following; map; maps; p(x; q(y; semicontinuous; set; space; t(x; theorem; topological; values; vector cache: cubo-1489.pdf plain text: cubo-1489.txt item: #251 of 481 id: cubo-1490 author: V¨ath, Martin title: A Disc-Cutting Theorem and Two-Dimensional Bifurcation of a Reaction-Diffusion System with Inclusions date: 2008-12-01 words: 6568 flesch: 76 summary: Now we can apply the disc-cutting theorem with S = Q ∩ Bglobal(d∗). = Ω ∩ Q, Ω4 := (Q \ Ω) ∩ Q = Q \ Ω, R := Q0 \ keywords: assume; bifurcation; boundary; case; compact; connected; cubo; cutting; disc; following; functions; global; interior; intersects; open; point; set; theorem;   cache: cubo-1490.pdf plain text: cubo-1490.txt item: #252 of 481 id: cubo-1491 author: Suzuki, Tomonari title: Browder Convergence and Mosco Convergence for Families of Nonexpansive Mappings date: 2008-12-01 words: 3188 flesch: 85 summary: It is easy to verify that for u ∈ C, P(α,t)u is the unique point satisfying x = (1 − α) T (t)x + αu. December 2008 Browder Convergence and Mosco Convergence for Families of Nonexpansive Mappings Tomonari Suzuki* Department of Mathematics, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan email: suzuki-t@mns.kyutech.ac.jp ABSTRACT We study the relationship between Browder’s strong convergence and Mosco conver- gence of fixed-point set for families of nonexpansive mappings. keywords: banach; browder; convergence; converges; f(p; f(sn; f(t; let; limn; mapping; math; mosco; nonexpansive; opial; point; property; sequence; space; theorem; weakly; ‖uk cache: cubo-1491.pdf plain text: cubo-1491.txt item: #253 of 481 id: cubo-1492 author: Moussaoui, Toufik; Precup, Radu title: Positive Solutions for Elliptic Boundary Value Problems with a Harnack-Like Property date: 2008-12-01 words: 2765 flesch: 85 summary: u ≤ r and x Then T has a fixed point with r ≤ ‖u‖ ≤ R. 2 Existence results for Problem 1.1 In this section, E is the Banach space C0(Ω, R) = {u ∈ C(Ω, R) : u = 0 on ∂Ω} endowed with norm ‖.‖ 0 , and C is the cone C = {u ∈ C0(Ω, R+) : u(x) keywords: elliptic; positive; problem; theorem; ‖u‖0 cache: cubo-1492.pdf plain text: cubo-1492.txt item: #254 of 481 id: cubo-1493 author: Heikkila, Seppo title: Fixed Point Results for Set-Valued and Single-Valued Mappings in Ordered Spaces date: 2008-12-01 words: 8316 flesch: 81 summary: Moreover, it follows from (O) that the functions F |CF , F ∈ C, considered as relations in P × P , are nested. ∈ P and for every y ∈ P . keywords: br(c; center; chain; complete; cubo; element; f(x; finite; fixed; following; g(x; g[c; greatest; inf; lemma; maximal; minimal; nonempty; normed; ordered; point; proof; proposition; results; sequences; set; solution; spaces; subset; sup{c; upper cache: cubo-1493.pdf plain text: cubo-1493.txt item: #255 of 481 id: cubo-1494 author: Fakhar, M.; Zafarani, J. title: A New Version of Fan’s Theorem and its Applications date: 2008-12-01 words: 4017 flesch: 79 summary: X. Suppose that Γ : K ⇉ K is a set-valued mapping such that the following conditions are satisfied: (i) Γ is a KKM map; (ii) for all A ∈ < K >, Γ is transfer closed-valued on conv(A); (iii) for all x, y ∈ K, clK ( ⋂ u∈[x,y] Γ(u)) ∩ [x, y] = ( ⋂ u∈[x,y] Γ(u)) Let K be a nonempty convex subset of a (t.v.s.) X and S : K ⇉ K a set-valued map such that: (i) for each A ∈< K >, S− is transfer open valued on conv(A); (ii) for each x, y ∈ K; int   ⋃ z∈[x,y] S−(z)   ∩ [x, y] =   ⋃ z∈[x,y] S−(z)   ∩ [x, y]; (iii) there exist a nonempty convex compact subset B of K and a nonempty compact subset D of K such that, for each y ∈ K \ D there exists x keywords: clk; closed; compact; condition; conv(a; convex; fan; fixed; map; nonempty; point; subset; theorem; transfer; γ(u; γ(x cache: cubo-1494.pdf plain text: cubo-1494.txt item: #256 of 481 id: cubo-1495 author: Aslam Noor, Muhammad; Inayat Noor, Khalida title: Proximal-Resolvent Methods for Mixed Variational Inequalities date: 2008-10-01 words: 4430 flesch: 66 summary: For a positive constant α, we consider u = u − αR(u) = u − α{u − Jϕ[u − ρT u]}, which is another fixed point problem. zn = Jϕ[un − ρnT wn] (7) un+1 = un − α(un − zn), n = 0, 1, 2, . . . keywords: algorithm; appl; approximate; aslam; closed; convergence; convex; cubo; equivalent; formulation; function; inequalities; inequality; iterative; jϕ[un; known; math; methods; mixed; mixed variational; new; noor; operator; point; problems; projection; proximal; resolvent; set; solution; un −; un+1; variational; variational inequalities; − ρt cache: cubo-1495.pdf plain text: cubo-1495.txt item: #257 of 481 id: cubo-1496 author: Anastassiou, George A. title: Poincar´e Type Inequalities for Linear Differential Operators date: 2008-10-01 words: 1871 flesch: 97 summary: p < 1, q < 0 : 1 p + 1 q = 1, ν > 0. Assume H (x, t) ≥ 0 for x0 ≤ t ≤ x, and Ly = h is of fixed sign and nowhere zero. (4) When ν = q we have 2) ‖y‖ Lq (x0,b) ≤ ( ∫ b x0 ( ∫ x x0 |H (x, t)| p dt )q/p dx )1/q ‖Ly‖ Lq (x0,b) . keywords: t)|; ‖ly‖; ∣ ∣ cache: cubo-1496.pdf plain text: cubo-1496.txt item: #258 of 481 id: cubo-1497 author: Agarwal, Ravi P.; Filippakis, Michael E.; O’Regan, Donal; Papageorgiou, Nikolaos S. title: Multiple Solutions for Doubly Resonant Elliptic Problems Using Critical Groups date: 2008-10-01 words: 7195 flesch: 87 summary: + c|x| for a.a. z ∈ Z, all x ∈ R, with a ∈ L∞(Z)+,c > 0, ⇒ |f(z,xn(z))| ‖xn‖ ≤ a(z) ‖xn‖ + c|yn(z)| for a.a. z ∈ Z, all n ≥ 1, (3.1) ⇒ { f(·,xn(·)) ‖xn‖ } n≥1 ⊆ L2(Z) is bounded. − λ1 for a.a. z ∈ Z and all 0 < |x| ≤ δ. keywords: a.e; agarwal; condition; contradiction; critical; cubo; double; e(λ1; e(λ2; elliptic; f(z; groups; hypothesis; l2(z; lemma; multiple; n(z)dz; nontrivial; point; problem; proof; proposition; ravi; resonance; robinson; rumbos; semilinear; solutions; theorem; xn(z; z f(z; ‖xn‖; ∣ ∣; ∣ ≤ cache: cubo-1497.pdf plain text: cubo-1497.txt item: #259 of 481 id: cubo-1498 author: Ichigi, Ippei; Shimomura, Katsumi title: The Modulo Two Homotopy Groups of the 𝐿₂-Localization of the Ravenel Spectrum date: 2008-10-01 words: 5498 flesch: 88 summary: → T (m), where ṽ1 : Σ 8T (m) → T (m) is the composite ṽ1 : Σ 8 T (m) = S8 ∧ T (m) T (m) ∧ T (m)wv1∧T (m) Then, d(w) = 0 in the cobar complex ˜Ω 3 Σm(2) Em(2)∗/(2), and we see that s⊗4 1 cobounds s2 3 ⊗ s1 ⊗ s1 + v1w 2 ⊗ s2 + (r1 ⊗ s1 + s1 ⊗ r1 + v1r1 ⊗ r1) ⊗ s2 (in which we set v2 = 1). keywords: adams; cofiber; cubo; denote; element; groups; homotopy; ichigi; km−1(2)∗[u; l2vm(1; lemma; map; math; mod; modulo; novikov; permanent; proof; proposition; ravenel; ring; sequence; shimomura; spectral; spectrum; term; theorem; vm(0; vm(1; σm(2 cache: cubo-1498.pdf plain text: cubo-1498.txt item: #260 of 481 id: cubo-1499 author: Kaji, Shunsuke title: The Extension of the Formula by Dupire date: 2008-10-01 words: 2410 flesch: 90 summary: Finally, we compute from (2) that the right-hand side of (4) is = ∫ ∞ 0 e −rT E[(XxT − K) 2 x2 ∂2u ∂x2 + (r − δ)x ∂u ∂x − ru = 0, (t,x) ∈ [0,T ) × (0,∞); u(t,x,T,K)|t=T = (x − K) keywords: 0,∞; a(t; c(i1×i2; c(x; cubo; dupire; e−rt; hand; price; |z|≥1; φh(t; ϕ(t; ∂2ϕ; ∂k2 cache: cubo-1499.pdf plain text: cubo-1499.txt item: #261 of 481 id: cubo-1500 author: Matsuo, Miki; Nishimura, Kazuo; Sakagami, Tomoya; Venditti, Alain title: Equilibrium Cycles in a Two-Sector Economy with Sector Specific Externality date: 2008-10-01 words: 5985 flesch: 76 summary: [ [ β 1 K −ρ yt + β2L −ρ yt + et ]− 1 ρ − kt+1 ] + rt (kt − Kct − Kyt) In the equilibrium the equation (2) is rewritten as Lyt = ( y −ρ t − (β1 + b) K −ρ yt β 2 − b )− 1 ρ . keywords: 1+ρ; = −; b β; capital; cubo; cycles; economy; equation; equilibrium; following; good; indeterminacy; kt+1; kyt; lct; local; lyt; perspective; proposition; sector; state; steady; α1β2; α2β1 cache: cubo-1500.pdf plain text: cubo-1500.txt item: #262 of 481 id: cubo-1501 author: Brito, Francisco title: Many-Ended Complete Minimal Surfaces Between Two Parallel Planes in ℝ³ date: 2008-10-01 words: 3144 flesch: 77 summary: Meanwhile N.Nadirashvili proved in [4] the existence of bounded complete minimal surfaces in R3. Another way for rendering complete minimal surfaces between two parallel planes in R3 was developed in [1]. keywords: complete; cubo; exp; functions; holomorphic; lemma; minimal; parallel; planes; points; proof; series; surfaces; theorem cache: cubo-1501.pdf plain text: cubo-1501.txt item: #263 of 481 id: cubo-1502 author: Ferreira de Lima, Pedro; Toom, Andr´e title: Dualities Useful in Bond Percolation date: 2008-10-01 words: 5403 flesch: 75 summary: Let (G, G′) be a dual pair of oriented finite graphs. Whitney [W.1932, W.1933] proved some state- ments about dual graphs. keywords: avoiding; closed; connected; contour; curve; direction; dual; duality; edges; facts; finite; good; graph; infinite; left; lemma; main; non; open; oriented; pair; path; percolation; plane; reachable; representation; self; theorem; type; vertex; vertices;  ;  ;  ;  ;   cache: cubo-1502.pdf plain text: cubo-1502.txt item: #264 of 481 id: cubo-1503 author: Sudo, Takahiro title: The Flip Crossed Products of the 𝐶*-Algebras by Almost Commuting Isometries date: 2008-10-01 words: 4866 flesch: 91 summary: Moreover, Kj((⊗ m+1 ε F) ⋊σ Z2) ∼= Kj((⊗ m+1F) ⋊σ Z2) for j = 0, 1. Proof. Z2 ∼= Eε ⋊αε∗β (N ∗ Z2), where N ∗ Z2 is the free product of N and Z2, and the action β on Eε is given by β(tn) keywords: action; continuous; crossed; cubo; c∗-algebra; emε; flip; isometries; isomorphic; k z2; product; theory; universal; z)p; ←−−−−; −−−−→; ∗σ⊗id; ⋊αε; ⋊ρ∧ε; ⋊σ z2;   cache: cubo-1503.pdf plain text: cubo-1503.txt item: #265 of 481 id: cubo-1504 author: Gaiko, Valery A. title: Limit Cycles of Li´enard-Type Dynamical Systems date: 2008-10-01 words: 9172 flesch: 68 summary: October 2008 Limit Cycles of Liénard-Type Dynamical Systems Valery A. Gaiko∗ Department of Mathematics, Belarusian State University of Informatics and Radioelectronics, L. Beda Str. 6-4, Minsk 220040 – Belarus email: valery.gaiko@yahoo.com ABSTRACT In this paper, using geometric properties of the field rotation parameters, we present a solution of Smale’s Thirteenth Problem on the maximum number of limit cycles for Liénard’s polynomial system, generalize the obtained results for special classes of polynomial systems, and complete the global qualitative analysis of a piecewise linear dynamical system approximating a Liénard-type polynomial system with an arbitrary number of finite singularities. 116 Valery A. Gaiko CUBO 10, 3 (2008) Key words and phrases: Planar polynomial dynamical system, Liénard’s polynomial system, generalized Liénard’s cubic system, piecewise linear Liénard-type dynamical system, Hilbert’s six- teenth problem, Smale’s thirteenth problem, field rotation parameter, bifurcation, limit cycle. keywords: bifurcations; case; cubo; curve; cycle; domain; dynamical; field; focus; gaiko; global; input; inside; liénard; limit; limit cycle; multiplicity; origin; parameters; point; polynomial; principle; problem; regions; rotation; saddle; semi; separatrix; singular; stable; stable limit; system; theorem; trajectories; type; unstable; values; vector; y =; µ2k+1 cache: cubo-1504.pdf plain text: cubo-1504.txt item: #266 of 481 id: cubo-1505 author: Steuding, J¨orn title: The Fibonacci Zeta-Function is Hypertranscendental date: 2008-10-01 words: 1392 flesch: 64 summary: In the case of Fibonacci numbers this is usually the correspond- ing Lambert series; however, in the recent past also the generating Dirichlet series was studied; this function is more interesting with respect to its analytic properties. References [1] C. Elsner, S. Shimomura and I. Shiokawa, Algebraic relations for reciprocal sums of Fibonacci numbers, Acta Arith., 130 (2007), 37–60. keywords: analytic; cubo; difference; differential; dirichlet; equation; fibonacci; function; hypertranscendence; integers; math; non; numbers; reich; series; theorem; zeta cache: cubo-1505.pdf plain text: cubo-1505.txt item: #267 of 481 id: cubo-1506 author: Lellis Thivagar, M.; Athisaya Ponmani, S.; Raja Rajeswari, R.; Ekici, Erdal title: On Some Bitopological 𝛾-Separation Axioms date: 2008-10-01 words: 2865 flesch: 82 summary: A map f :(X, τ 1, τ 2) → (Y, σ1, σ2) is called (i, j)-γ-open if the image of each τ i- open set in X is (i, j)-γ-open in Y , i, j = 1, 2, i 6= j. Recall that a map f :(X, τ 1, τ 2) → (Y, σ1, σ2) is called (i, j)-pre-open if for each τ Definition 1 A subset A of X is called pre-open set [11] if A ⊂ int(cl(A)). keywords: definition; j)-γ; net; open; preopen; proof; sets; space; theorem cache: cubo-1506.pdf plain text: cubo-1506.txt item: #268 of 481 id: cubo-1507 author: Appleby, John A.D.; Gleeson, James P.; Rodkina, Alexandra title: Asymptotic Constancy and Stability in Nonautonomous Stochastic Differential Equations date: 2008-10-01 words: 5100 flesch: 86 summary: = ∫ t 0 σ2(s) ds. Let T ∗ be given by T ∗ = ∫ ∞ 0 σ2(s) ds, (2.3) where we define T ∗ = ∞ if σ 6∈ L2([0, ∞); R). [0, T ∗), where T ∗ is defined as in (2.3), and define X(t) = X̃ ( ∫ t 0 σ2(s)ds ) , t ≥ 0. keywords: a.s; asymptotic; b̃(t; case; cubo; differential; equation; h(x̃(t; l(ξ; l2([0; lim; log; m〉(t; non; proposition; result; solution; stochastic; strong; sup; s̃0(ξ; theorem; time; v(x; x(t; x̃(s; σ2(s; ∗ − cache: cubo-1507.pdf plain text: cubo-1507.txt item: #269 of 481 id: cubo-1508 author: Blot, J.; Pennequin, D.; N’Gu´er´ekata, Gaston M. title: Existence and Uniqueness of Pseudo Almost Automorphic Solutions to Some Classes of Partial Evolution Equations date: 2008-10-01 words: 3038 flesch: 80 summary: A continuous function f : R × X 7→ X is said to be almost automorphic in t ∈ R for each u ∈ X if every sequence of real numbers (σn)n∈N contains a subsequence (sn)n∈N such that g(t,u) := lim n7→∞ f(t + sn,u) is well defined for each t ∈ R and each u ∈ X and, f(t,u) = lim n7→∞ g(t − sn,u) exists for each t ∈ R and u ∈ X. 164 J. Blot et al. CUBO 10, 3 (2008) t ∈ R, (1.1) where the functions f(t,u) and g(t,u) are almost automorphic in t, for each u. keywords: automorphic; banach; bc(r; continuous; cubo; differential; equations; evolution; existence; e−ω(t−s)γ(t; f(t; functions; g(t; g.m; math; mild; n’guérékata; operator; paa(r; pseudo; solutions; space; u(t; uniqueness cache: cubo-1508.pdf plain text: cubo-1508.txt item: #270 of 481 id: cubo-1509 author: Chen, Yuqun; Shao, Hongshan; Shum, K.P. title: Rosso-Yamane Theorem on PBW Basis of 𝑈ԛ(𝐴ɴ) date: 2008-10-01 words: 8724 flesch: 98 summary: On the other hand, the universal enveloping algebra U (L) = k〈X|xixj − xjxi − ∑ αkij xk, i > j, xi, xj , xk ∈ X〉 is the associative algebra presented by the same set X and the defining relations S(−) (we rewrite S using [xy] = xy − yx). [xilxmn − (q 2 − q−2)xinxml] +(q2 − q−2)2xkn[xilxmj − (q 2 − q−2)xij xml] ≡ 0. keywords: algebras; basis; bokut; case; chen; cubo; enveloping; g)w; gröbner; l.a; lie; pbw; q −2(q2; q(q; qxin; qxkj; q−2)xinxklxmj; q−2)xkj; q−2)xknxij; q−2)xknxmlxij; rosso; shirshov; similar; subcases; theorem; uq(an; xij; xil; xil]xmn; xkl −; xklxij; xklxmn; xklxmnxij; xml; xmn; xmnxij; xmnxkl; yamane; yuqun; − q−2)xknxml]xij; −(q2; −2(q2; −2xij cache: cubo-1509.pdf plain text: cubo-1509.txt item: #271 of 481 id: cubo-1510 author: Detomi, Eloisa; Lucchini, Andrea title: On the Structure of Primitive 𝓃-Sum Groups date: 2008-10-01 words: 8430 flesch: 83 summary: As N = X is a homomorphic image of G, we get G = N . [4] M. Aschbacher and R. Guralnick, On abelian quotients of primitive groups, Proc. keywords: abelian; assume; chief; contradiction; corollary; cover; cubo; cyclic; degree; elements; equivalent; factor; finite; group; image; isomorphic; lemma; maximal; minimal; monolithic; non; normal; odd; order; prime; primitive; product; proof; proper; proposition; set; simple; soc(g; soc(xi; solvable; subgroup; theorem; σ(g cache: cubo-1510.pdf plain text: cubo-1510.txt item: #272 of 481 id: cubo-1511 author: Vukman, Joso; Kosi-Ulbl, Irena title: On Two-Sided Centralizers of Rings and Algebras date: 2008-10-01 words: 4872 flesch: 82 summary: = P T (P )P, which gives T (P )P = P T (P ). T (A) − ( nm nm ) T (A) P − ( nm nm−1 ) BA− ( m m−1 )( (n−1)m (n−1)m ) AB − ( m m )( (n−1)m (n−1)m ) P T (A)P − ( m m )( (n−1)m (n−1)m−1 ) BA − · · · − ( m m )( (n−1)m (n−1)m−1 ) AB − ( m m )( (n−1)m (n−1)m ) P T (A)P − ( m m−1 )( (n−1)m (n−1)m ) BA− ( nm nm−1 ) AB − ( nm nm ) P T (A) = 0. keywords: a(x; additive; algebras; banach; case; centralizers; cubo; element; form; kosi; left; mapping; math; n−1)m; p t; proof; relation; right; ring; semiprime; semisimple; sided; theorem; theory; ulbl; vukman cache: cubo-1511.pdf plain text: cubo-1511.txt item: #273 of 481 id: cubo-1512 author: Cardoso, F.; Vodev, G. title: Semi-Classical Dispersive Estimates for the Wave and Schr¨odinger Equations with a Potential in Dimensions 𝓃 ≥ 4 date: 2008-07-01 words: 5200 flesch: 85 summary: ≤ k ≤ (n − 3)/2 such that the operators ≤ k ≤ (n − 3)/2 such that the operators Fj satisfy the estimate ‖Fj (t, keywords: cardoso; case; cjh; classical; cubo; dispersive; equation; estimates; group; h)dτ; h)v; h)‖l1→l∞; l1→l2; l1→l∞; operators; potentials; proof; satisfying; schrödinger; semi; theorem; vodev; wave; ∥∥∥ cache: cubo-1512.pdf plain text: cubo-1512.txt item: #274 of 481 id: cubo-1513 author: Belishev, M.I. title: Dynamical Inverse Problem for the Equation 𝒰ᵼᵼ − Δ𝒰 − ∇ln𝜌 · ∇𝒰 = 0 (the BC Method) date: 2008-07-01 words: 6325 flesch: 77 summary: [T − ξ, T ], so that fξ is an element of the subspace F T, ξ . − 1 2 f (γ, T − ξ) θ1 (t − (T − ξ) − τ ) + w(x, t) θ2 (t − (T − ξ) − τ ) , (13) where x = x(γ, τ ) in the l.h.s. and w is a smooth function. keywords: amplitude; belishev; boundary; control; cubo; density; dynamical; equation; f t; f ξ; form; function; inverse; jump; k=1; m.i; method; operator; problem; r2 t; relation; response; subdomain; surface; system; t t; t σ; time; tube; u ξ; velocity; w t; wave; x(γ; ξ k; ρ0(γ; ρdx; ∣∣∣∣ cache: cubo-1513.pdf plain text: cubo-1513.txt item: #275 of 481 id: cubo-1514 author: Ikehata, Masaru title: A Remark on the Enclosure Method for a Body with an Unknown Homogeneous Background Conductivity date: 2008-07-01 words: 5370 flesch: 79 summary: However, integration by parts yields ∫ ∂Ω γ ∂u ∂ν vds = γ ∫ ∂Ω u ∂v ∂ν ds − γ ∫ ∂D u ∂v ∂ν ds (2.1) and we have already studied the asymptotic behaviour of the second term as described in Intro- duction (see (1.2)). Then Cm(f ) = 0 for m ≥ N + 2 and from (2.4) and (2.9) we obtain ∫ ∂Ω uv(ν1 − iν2)ds = 2πab ( 1 2πz )1/2 eize−iπ/4 × {( 1 + 1 8iz ) keywords: background; band; body; boundary; case; cm(f; condition; conductivity; cos; cubo; data; domain; enclosure; formula; fourier; function; hd(ω; ikehata; inverse; iω2; limited; m=1; method; problem; remark; satisfies; set; sin; solution; unknown; valid; ∣∣∣∣ cache: cubo-1514.pdf plain text: cubo-1514.txt item: #276 of 481 id: cubo-1515 author: Sushch, Volodymyr title: Green Function for a Two-Dimensional Discrete Laplace-Beltrami Operator date: 2008-07-01 words: 4824 flesch: 82 summary: and k 6= m, s = n. Check the case k = m, s > n. The proof for the case k = m, s < n (or k 6= m, s = n) is similar. keywords: analog; basis; c(2; case; complex; cubo; differential; dimensional; discrete; elements; equation; following; forms; function; g(x; green; k(2; laplacian; math; n k; operator; proof; set; sushch; µ)ϕ; τ s cache: cubo-1515.pdf plain text: cubo-1515.txt item: #277 of 481 id: cubo-1516 author: Ezzinbi, Khalil; Nelson, Valerie; N’Gu´er´ekata, Gaston title: 𝐶⁽ⁿ⁾-Almost Automorphic Solutions of Some Nonautonomous Differential Equations date: 2008-07-01 words: 4659 flesch: 81 summary: f (t), t ∈ R where the oper- ator A generates a quasi-compact semigroup in a Banach space, and in both cases f is C(n)-almost automorphic. f (t), t ∈ R, A(t) es τ keywords: aa(n)(x; automorphic; banach; bc(r; c(n)-almost; compact; continuous; cubo; definition; differential; equations; ezzinbi; following; function; gaston; khalil; lim; linear; math; nelson; norm; n’guérékata; operator; periodic; proof; proposition; result; semigroup; set; solution; space; spu(f; theorem; uniform; valerie cache: cubo-1516.pdf plain text: cubo-1516.txt item: #278 of 481 id: cubo-1517 author: Sudo, Takahiro title: Spectral Rank for 𝐶*-Algebras date: 2008-07-01 words: 2705 flesch: 80 summary: = n. Let C∗(Fn) be the full group C ∗ -algebra of the free group Fn with n generators. Nn with n generators, i.e., keywords: c(t; cubo; c∗-algebra; dim; dimension; direct; generators; group; limit; product; proof; proposition; rank; spectral; spr(a; sudo; unital; universal cache: cubo-1517.pdf plain text: cubo-1517.txt item: #279 of 481 id: cubo-1518 author: Brackx, F.; De Schepper, H. title: The Hilbert Transform on a Smooth Closed Hypersurface date: 2008-07-01 words: 8693 flesch: 76 summary: The so–called Kerzman–Stein operator, defined by A = 1 2 (H − H∗) measures the ”non–selfadjointness” of the Hilbert transform. = P⊥[E(x − ζ)]. keywords: = −; analysis; boundary; brackx; c −; c(ζ; c[u](x; cauchy; clifford; cubo; d −; decomposition; dimensional; dirac; direct; dσζ; e(ζ; extension; f(x; follows; function; h2(ω; hardy; harmonic; hilbert; h∗[h; iii; integral; kernel; l2(∂ω; left; lim; means; monogenic; n(x; operator; orthogonal; p[f; particular; projections; proof; properties; proposition; r0,m; related; s(ζ; schepper; similar; singular; space; sum; szegö; theory; transform; u(ζ; u(ξ; unit; value; vector; ν(ζ; − −; − −→ cache: cubo-1518.pdf plain text: cubo-1518.txt item: #280 of 481 id: cubo-1520 author: Leit˜ao, A.; Zubelli, J.P. title: Iterative Regularization Methods for a Discrete Inverse Problem in MRI date: 2008-07-01 words: 3612 flesch: 67 summary: It is worth noticing that the local tangential cone condition is a standard assumption in the convergence analysis of adjoint type methods (Landweber, steepest descent, Levenberg-Marquardt, asymptotical regularization) for nonlinear inverse problems [3, 4, 6, 9, 10, 11, 13]. Pura e Aplicada, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro – Brasil email: zubelli@impa.br ABSTRACT We propose and investigate efficient numerical methods for inverse problems related to Magnetic Resonance Imaging (MRI). keywords: analysis; assumption; convergence; cubo; data; discrete; ill; image; imaging; inverse; iteration; iterative; kaczmarz; kernels; leitão; llk; lsdk; magnetic; methods; mri; nonlinear; operators; problem; regularization; results; rnum; satisfied; sensitivity; zubelli; δ k cache: cubo-1520.pdf plain text: cubo-1520.txt item: #281 of 481 id: cubo-1521 author: Hua, Xinhou; Vaillancourt, R´emi title: Prime Factorization of Entire Functions date: 2008-03-01 words: 2807 flesch: 81 summary: ≤ 1. Lemma 4 ([16]) Let f (z) and g(z) be prime entire functions. [5] F. Gross, C. C. Yang, Further results on prime entire functions, Trans. keywords: case; complex; cubo; entire; example; factorizable; factorization; functions; g(z; h(z; hua; lemma; linear; math; meromorphic; nonconstant; number; prime; theorem; transcendental; yang cache: cubo-1521.pdf plain text: cubo-1521.txt item: #282 of 481 id: cubo-1522 author: Ujevi´c, Nenad title: Error Inequalities for a Taylor-like Formula date: 2008-03-01 words: 2332 flesch: 93 summary: [a, x] then |f (x) − F (x, a)| ≤ (Γn − Tn) (n + 1)(x − a)n+1 4nn! . = (t − 3a+x 4 ) n−1 n! keywords: a)n+1; formula; function; n+1; t)dt; taylor; ∣ ∣ cache: cubo-1522.pdf plain text: cubo-1522.txt item: #283 of 481 id: cubo-1523 author: Yano, Syouji title: On the Index of Clifford Algebras of Quadratic Forms date: 2008-03-01 words: 5693 flesch: 84 summary: In a similar fashion, if q is a quadratic form with discriminant algebra Z 6≃ F × F and ν(qZ) If q is a quadratic form with discriminant algebra Z 6≃ F × F and ν(qZ) keywords: 0,q; algebra; arf; c(q; case; ch(f; clifford; cubo; dimensional; dimensional quadratic; dimf; discriminant; field; form; gp2(f; indc(q; index; invariant; m2(d4; norm; quadratic; quadratic form; space; table; theorem; trivial cache: cubo-1523.pdf plain text: cubo-1523.txt item: #284 of 481 id: cubo-1524 author: Palanichetty, G.; Balasubramanian, G. title: On Some What Fuzzy Faintly Semicontinuous Functions date: 2008-03-01 words: 4311 flesch: 89 summary: 34 G. Palanichetty and G. Balasubramanian CUBO 10, 1 (2008) 1 Introduction The concept of fuzzy sets was introduced by Zadeh Based on the concept of fuzzy sets, C.L.Chang keywords: functions; fuzzy; proof; proposition; semicontinuous; semidense; semiopen; set; spaces; topological; −1(λ cache: cubo-1524.pdf plain text: cubo-1524.txt item: #285 of 481 id: cubo-1525 author: Seenivasan, V.; Balasubramanian, G.; Thangaraj, G. title: Somewhat Fuzzy Semi 𝛼-Irresolute Functions date: 2008-03-01 words: 4364 flesch: 91 summary: [7]: A function f from a fuzzy topological space (X, T ) to a fuzzy topological space (Y , S) is said to be fuzzy semi α-irresolute if f −1(λ) is fuzzy semi-open set in (X, T ) for each fuzzy α-open set λ in (Y , S). λ is called fuzzy α-open set [2] if λ ≤ int cl intλ 2. λ is called fuzzy semi-open set keywords: functions; fuzzy; fuzzy semi; fuzzy α; irresolute; let; open; open set; semi; set; −1(λ cache: cubo-1525.pdf plain text: cubo-1525.txt item: #286 of 481 id: cubo-1526 author: Bounkhel, Messaoud title: Arc-wise Essentially Tangentially Regular Set-valued Mappings and their Applications to Nonconvex Sweeping Process date: 2008-03-01 words: 9172 flesch: 87 summary: We will say that C is arc-wise essentially tangentially regular and we will write C ∈ AWET R(I,X), if for each x ∈ AC(I,X), the set {t ∈ I : x(t) Indeed, for any x ∈ AC(I,X) we can easily check that µ ( {t ∈ keywords: a.e; arc; banach; bounkhel; c(t; c(t0; class; closed; concept; continuous; cubo; differentiable; direction; example; exist; existence; f(t; fn(t; following; function; kc(t)(x(t; lim; lipschitz; mapping; math; messaoud; nonconvex; process; proof; proposition; recall; regular; resp; s.d; set; sets; smooth; space; sweeping; t n; tc(t)(x(t; theorem; values; vol; wise; x(0; x(t; x(t0 cache: cubo-1526.pdf plain text: cubo-1526.txt item: #287 of 481 id: cubo-1527 author: Fattorini, H. O. title: Regular and Strongly Regular Time and Norm Optimal Controls date: 2008-03-01 words: 5466 flesch: 81 summary: ≤ t ≤ T, whereas a merely regular control may “oscillate” at the endpoint T of the control interval. ≤ t ≤ T equipped with the norm ‖z‖Z∞(T ) keywords: banach; conditions; continuous; control; cubo; d(a; dense; equivalent; fattorini; implies; interval; lemma; linear; maximum; norm; optimal; principle; proof; regular; reversible; rp(t; r∞(t; s(t; satisfies; semigroup; space; theorem; time; ū(t; y(t; σ)u(σ)dσ cache: cubo-1527.pdf plain text: cubo-1527.txt item: #288 of 481 id: cubo-1528 author: Yurko, Vjacheslav A. title: Recovering Higher-order Differential Operators on Star-type Graphs from Spectra date: 2008-03-01 words: 3260 flesch: 77 summary: 95 Fix s = 1,p − 1, k = 1,n − 1, µ = k,n. Let Λskµ := {λlskµ}l≥1 be the set of the eigen- values of the boundary value problem Lskµ for equation (1) with the boundary conditions y (ν−1) s (0) = 0, = ∆skµ(λ) ∆sk(λ) , s = 1,p − 1, k = 1,n − 1, µ = k + 1,n, (11) where ∆skµ(λ) := ∆sksµ(λ), ∆sk(λ) := ∆skk(λ). keywords: 1,n; 1,p; boundary; conditions; cubo; differential; edge; equation; functions; inverse; matrix; operators; order; potential; problem; solution; spectra; system; type; weyl; ν−1 cache: cubo-1528.pdf plain text: cubo-1528.txt item: #289 of 481 id: cubo-1529 author: Sudo, Takahiro title: Continuous or Discontinuous Deformations of C*-Algebras date: 2008-03-01 words: 5885 flesch: 69 summary: We find that it is easy to have degenerate continuous deformations of C ∗ -algebras, some of which are useful to provide some examples with non-Hausdorff spectrums, and it is not easy to construct nondegenerate continuous deformations of C ∗ -algebras. Continuous deformations of C ∗ -algebras are in a particular case of continuous fields of C ∗ -algebras in the sense that their base spaces are the closed interval [0, 1] and the fibers on the half open interval (0, 1] are the same (cf. keywords: -algebras; action; at}t∈[0,1; c ∗; c(t; c0(r; continuous; continuous deformation; crossed; cubo; c∗-algebra; deformation; discontinuous; example; field; group; isometries; nondegenerate; operator; product; proof; proper; theorem; trivial; unital; unitary; γ([0 cache: cubo-1529.pdf plain text: cubo-1529.txt item: #290 of 481 id: cubo-1530 author: Anastassiou, George A. title: Converse Fractional Opial Inequalities for Several Functions date: 2008-03-01 words: 7990 flesch: 99 summary: Here x, x0 ∈ [a, b] : x ≥ x0. (x − x0) keywords: j=1 ∣; v x0; w x0; x0 fj; x0 p; x0 q; γ1 x0; λv p; ∣ =; ∣ p; ∣ λv; ∣ λα; ∣ λα+1; ∣ λα+λv; ∣ ∣ cache: cubo-1530.pdf plain text: cubo-1530.txt item: #291 of 481 id: cubo-1531 author: Anastassiou, George A. title: Fuzzy Taylor Formulae date: 2005-12-01 words: 4310 flesch: 97 summary: = n∑∗ i=1 (zi − x0i) � d dt ( ∂f (x1, . . . , xn) ∂xi ) = n∑∗ i=1 (zi − x0i) �   n∑∗ j=1 ∂2f (x1, . . . keywords: anastassiou; continuous; formula; function; fuzzy; george; i=1; lemma; n−1; taylor; theorem; x01; x0i; ∂xi cache: cubo-1531.pdf plain text: cubo-1531.txt item: #292 of 481 id: cubo-1532 author: Corduneanu, Constantin title: Some special classes of neutral functional differential equations date: 2005-12-01 words: 4174 flesch: 79 summary: Class.: 34K40 1 Introduction In several recent papers of the author [3], [4], [5], as well as in some joint papers with M. Mahdavi [7], [8], certain types of neutral functional equations (including functional–differential ones) have been investigated in regard to the existence of so- 16 Constantin Corduneanu 7, 3(2005) lutions. The literature on neutral functional equations is very rich, and a good amount of references can be found in our book [6]. keywords: c([0; causal; condition; continuous; corduneanu; differential; equation; existence; following; form; functional; g(t; hand; initial; irn; local; neutral; operator; problem; right; solution; sup; theorem; x(t; y(s)ds; y(t cache: cubo-1532.pdf plain text: cubo-1532.txt item: #293 of 481 id: cubo-1533 author: Fattorini, H. O. title: Sufficiency of the maximum principle for time optimality date: 2005-12-01 words: 3239 flesch: 85 summary: T−δ 0 S(T − δ − σ)u(σ)dσ = ȳ − S(T )ζ . T−δ 0 S(T − δ − σ)u(σ)dσ = ȳ − S(T )ζ , thus v(t) drives from ζ to ȳ in time T. keywords: condition; control; cos; d(a; drives; fattorini; maximum; norm; optimal; optimality; principle; s(t; sin; space; sufficiency; t)∗z; time; ū(t; y(t; σ)u(σ)dσ; σ)∗z cache: cubo-1533.pdf plain text: cubo-1533.txt item: #294 of 481 id: cubo-1534 author: Ganikhodjaev, Nasir; Temir, Seyit; Akin, Hasan title: The exact solution of the Potts models with external magnetic field on the Cayley tree date: 2005-12-01 words: 3489 flesch: 83 summary: Key words and phrases: Cayley tree, Potts model, Competing interactions, External magnetic field. Theorem 1 For Potts model (1) with null external field, a phase transition occurs when, θ > k + 2q keywords: akin; case; cayley; equation; exact; exp; external; field; following; interactions; j=1; level; magnetic; model; neighbors; n−1; phase; potts; solution; system; transformation; tree; δσ(x)σ(y cache: cubo-1534.pdf plain text: cubo-1534.txt item: #295 of 481 id: cubo-1535 author: Blackmore, Denis L.; Prykarpatsky, Yarema A.; Samoilenko, Anatoliy M.; Prykarpatsky, Anatoliy K. title: The ergodic measures related with nonautonomous hamiltonian systems and their homology structure. Part 1 date: 2005-12-01 words: 6722 flesch: 69 summary: S is any continuous arc joining these two chosen points x̃, ỹ ∈ Lt0 (H) × S, and ã (1) j ∈ H 1(Lt0 (H); R) are the corresponding liftings to Lt0 (H) of 1-forms a(1)j ∈ H 1(Lt0 (H); R), j = 1,r. ∈ Mt0 (H). keywords: 1,m; a(1; a(τ; class; compact; convex; corresponding; curves; domain; equality; ergodic; field; floer; flow; following; form; function; h1(lt0; hamiltonian; homology; hyperbolic; invariant; lagrangian; lim; lnt0; m2n; manifolds; mather; measure; metric; mt0; neighborhood; nonautonomous; points; properties; pt0; related; respect; results; satisfies; set; space; structure; submanifold; supp; symplectic; systems; t(lt0; theorem; theory; type; zt0; µ̄j; α(1; γt0; ρt0; σt0 cache: cubo-1535.pdf plain text: cubo-1535.txt item: #296 of 481 id: cubo-1536 author: Sun, Ziqi title: Conjectures in Inverse Boundary Value Problems for Quasilinear Elliptic Equations date: 2005-12-01 words: 3486 flesch: 68 summary: Key words and phrases: Inverse boundary value problem. [I1] V. Isakov, On uniqueness in inverse problems for semilinear parabolic equa- tions, Arch. keywords: a(x; anisotropic; boundary; c3,α(γ; case; coefficient; conformal; conjecture; diffeomorphisms; dimensional; directions; elliptic; equations; family; independent; information; inverse; math; matrix; nonlinear; problem; proof; quasilinear; solution; sun; suu1; system; uhlmann; uniqueness; value; vector cache: cubo-1536.pdf plain text: cubo-1536.txt item: #297 of 481 id: cubo-1537 author: Matsutani, Shigeki title: Relations of al Functions over Subvarieties in a Hyperelliptic Jacobian date: 2005-12-01 words: 3173 flesch: 77 summary: 2 + f′(am+1)(al (m) r (v (m)))2(al(m)s (v (m)))2(ar − as) (am+1 − ar)(am+1 − as)(al (m) m+1(v (m)))4(Q(2)′m (am+1))2 + · · · · · · + f′(ag)(al (m) r (v (m)))2(al(m)s (v (m)))2(ar − as) (ag − ar)(ag − as)(al(m)g (v(m)))4(Q (2) m (ag)′)2 . From (2.7), we will consider the following formula instead of (3.1) without loss of generality, ∂ ∂v (m) 1 ∂ ∂v (m) 2 log Fm(a1) Fm(a2) = 2 Fm(a1)Fm(a2) (a1 − a2) ( f′(a1) Fm(a1)2(Q (2) m (a1))2 + f′(a2) Fm(a2)2(Q (2) m (a1))2 + f′(am+1)(a1 − a2)2 (am+1 − a1)(am+1 − a2)Fm(am+1)2(Q (2)′ m (am+1))2 + · · · + f′(ag)(a1 − a2)2 (ag − a1)(ag − a2)Fm(ag)2(Q (2)′ m (ag))2 ) . keywords: al(m)r; article; ba2; complex; corollary; curve; equation; functions; gordon; hyperelliptic; jacobian; log; math; matsutani; proof; q(2)m; relations; shigeki; sine; subvarieties; subvariety; theorem; weierstrass cache: cubo-1537.pdf plain text: cubo-1537.txt item: #298 of 481 id: cubo-1538 author: Buong, Nguyen title: Convergence rates in regularization for ill-posed variational inequalities date: 2005-12-01 words: 2495 flesch: 80 summary: 〈U (xτα(δ,h) − x 0) − U (x0 − x0), xτα(δ,h) − x0〉 ≤ (δ + hg(‖xα(δ,h)‖))‖xα(δ,h) − x0‖ +α(δ, h)〈U (x0 − x0), x0 − xτα(δ,h)〉. + αnU (x τn αn − x0) keywords: banach; convergence; inequalities; lemma; mat; method; monotone; operator; principle; property; rates; regularization; solution; space; variational; xτα; α(δ cache: cubo-1538.pdf plain text: cubo-1538.txt item: #299 of 481 id: cubo-1539 author: Cordovil, Raúl; Forge, David title: Gr¨obner and diagonal bases in Orlik-Solomon type algebras date: 2005-08-01 words: 8365 flesch: 82 summary: J �∈ NBC�(M)] a contradiction. ∈ S�, the equality Flag (Jτ ) = Flag (IσI ) implies J = I. Theorem 4.8 Suppose that I� is a diagonal basis of A�. keywords: a(m; algebra; arrangement; aχ(m; basis; broken; circuit; clear; cordovil; corresponding; david; definition; diagonal; different; element; flag; following; forge; gröbner; gröbner basis; hyperplanes; i]a; ideal; iff; ind(m; independent; m([n; m(ak; math; matroid; minimal; monomials; nbc; nbc(m; note; order; oriented; orlik; permutation; piσ; proof; proposition; raul; reduced; remark; residue; resp; respect; set; sets; sgn; solomon; space; t(a; terao; term; theorem; type; vector; χ(m; −1)pχ(u; � = cache: cubo-1539.pdf plain text: cubo-1539.txt item: #300 of 481 id: cubo-1540 author: Mahmudov, E. N.; C¸i¸cek, G. title: Optimization of differential inclusions of Bolza type with state constraints and duality date: 2005-08-01 words: 5647 flesch: 82 summary: Conversely, if we have the last inclusion then z0 ∈ z + KM (z) or there are such z1 ∈ M and a number γ > 0, that z0 − z = γ(z1 − z) ∈ KM (z). In other words, there exists a vector z̄1(z̄1 �= 0) such that < z∗1, z̄1 >< 0, z̄1 ∈ KM (z), ∀z ∈ M or < z∗1, z̄1 >< 0, z̄1 ∈ ⋂ z∈M KM (z), i.e. z ∗ 1 �∈ ( ⋂ z∈M KM (z)) keywords: admissible; a∗(y∗; closed; condition; cone; conjugate; continuous; control; convex; definition; differential; dual; following; function; gfa; inclusions; inf; k∗m; lemma; mahmudov; mapping; optimal; optimization; point; problem; proof; relation; set; sup; t1 t0; theorem; trajectory; wa(x; x̃(t; z∈m cache: cubo-1540.pdf plain text: cubo-1540.txt item: #301 of 481 id: cubo-1541 author: Ammar, Boukhemis title: On the classical 2−orthogonal polynomials sequences of Sheffer-Meixner type date: 2005-08-01 words: 4820 flesch: 83 summary: + 1 = Pn+1(x + ω) −Pn+1(x) (n + 1)ω , n ≥ 0 (3.2) and {F̃n}n≥0 the dual sequence associated to the sequence {Qωn}n≥0, then we have ∇ωF̃n=Δ−ωF̃n = −(n + 1)Fn+1; [∫ r(x)dx ] , then equation (5.11) may be written (x + k)2 d2W(x) dx2 − σ2 α2 keywords: ammar; boukhemis; case; classical; deg; d−orthogonal; equation; following; functional; integral; lim; math; meixner; monic; pn}n≥0; polynomials; proof; properties; relation; representation; respect; sequences; sheffer; theorem; type; x−σ0 cache: cubo-1541.pdf plain text: cubo-1541.txt item: #302 of 481 id: cubo-1542 author: Spr¨ossig, Wolfgang title: Quaternionic analysis and Maxwell’s equations date: 2005-08-01 words: 2829 flesch: 72 summary: Key words and phrases: Maxwell equations, quaternionic analysis, operator calculus. Math. ∈ Ω− = IR3 \G . keywords: 1+βiν; analysis; borel; boundary; calculus; chiral; conditions; domain; ek+1; equations; field; formula; functions; gürlebeck; ih(c; ir3; iν)g̃k+1; kravchenko; lνμ0jk; maxwell; medium; operator; pompeiu; quaternionic; representation; sprössig; teodorescu; time; trγt−iνfiν; value; vol; wolfgang; yukawa; ν2ek; −dfk; −ek; −lνdhk cache: cubo-1542.pdf plain text: cubo-1542.txt item: #303 of 481 id: cubo-1543 author: Blesgen, Thomas title: Two-Phase Structures as Singular Limit of a one-dimensional Discrete Model date: 2005-08-01 words: 3767 flesch: 77 summary: W n(un) := { +∞ if uni+1 = uni for some i,∑3 k=1 W n k (u n) else where W n1 (u n) := n−2∑ i=0 nα 3∏ k=1 ∣∣∣sk − u n i+2 −uni+1 uni+1 −uni ∣∣∣2, W n2 (u n) := n−3∑ i=0 ∣∣∣1 − uni+3 −uni+2 uni+1 −uni ∣∣∣2, W n3 (u n) : The concept behind the ansatz for W n is the following. keywords: 2hn; boundedness; case; convergence; dimensional; discrete; energy; functional; h1,2(ω; hsn; ihn; l2(ω; large; lattice; limit; n(un; o(1; phase; sequence; singular; structures; uni+1; w(u; βni; ϕn(ihn; −uni; ∣∣∣1; ∣∣∣2 cache: cubo-1543.pdf plain text: cubo-1543.txt item: #304 of 481 id: cubo-1544 author: Liu, Dongsheng title: A note on discrete monotonic dynamical systems date: 2005-08-01 words: 2192 flesch: 89 summary: A note on discrete monotonic dynamical systems Dongsheng Liu 1 Department of Applied Mathematics, Nanjing University of Science & Technology Nanjing, 210094, Jiangsu, Peoples R China d.liu@lancaster.ac.uk ABSTRACT We give a upper bound of Lebesgue measure V (S(f, h, Ω)) of the set S(f, h, Ω) of points q ∈ Qdh for which the triple (h, q, Ω) is dynamically robust when f is monotonic and satisfies certain condition on some compact subset Ω ∈ Rd. RESUMEN Damos una cota superior de la medida de Lebesgue V (S(f, h, Ω)) del conjunto S(f, h, Ω) de puntos q ∈ Qdh para los cuales el tŕıo (h, q, Ω) es dinámicamente robusto cuando f es monótona y satisface ciertas condiciones en algunos subcon- juntos compactos Ω ∈ Rd. keywords: compact; f(x; following; k(h; monotonic; q(x; qdh; s(f; set cache: cubo-1544.pdf plain text: cubo-1544.txt item: #305 of 481 id: cubo-1545 author: Sedaghat, Hassan title: Global Attractivity, Oscillations and Chaos in A Class of Nonlinear, Second Order Difference Equations date: 2005-08-01 words: 8501 flesch: 77 summary: − xn = f (xn − xn−1) (7) From this it is evident that the standard vectorization of (7) is semiconjugate to the real factor f relative to the link map H(x, y) . − f (s)| ≤ a|t keywords: absorbing; attractivity; behavior; case; chaos; conditions; converges; corollary; cycle; difference; equation; equilibrium; fact; figure; fixed; following; function; global; goodwin; hassan; increasing; interval; investment; lemma; models; non; nonlinear; order; origin; oscillations; period; periodic; persistent; point; positive; problem; proof; puu; result; section; sedaghat; sequence; solution; stable; theorem; unique; xn−1; x̄j cache: cubo-1545.pdf plain text: cubo-1545.txt item: #306 of 481 id: cubo-1546 author: Moskowitz, Martin title: Symmetric Spaces of Noncompact type date: 2005-08-01 words: 14320 flesch: 81 summary: As we saw earlier, this is {p2; p ∈ P}. For a point p ∈ P and x = log p, since dp(x,y) ≤ keywords: abelian; action; adjoint; adk0; adx; algebraic; analytic; cartan; case; commute; compact; complex; conjugate; connected; corollary; decomposition; definite; definition; det; diagonal; diffeomorphic; dim; eigenvalues; euclidean; exp; exp(−x/2; f(c; fact; finite; following; follows; form; function; g(h+; general; geodesic; geometry; gl(n; group; hermitian; homogeneous; hyperbolic; isometries; isometry; let; lie; linear; log; manifold; map; martin; matrices; maximal; means; moskowitz; noncompact; o(n; p(t; particular; point; positive; product; proof; proposition; reader; real; result; riemannian; self; semisimple; set; sinh; so(n; space; subalgebra; subgroup; symmetric; theorem; type; u(n; unique; x(t cache: cubo-1546.pdf plain text: cubo-1546.txt item: #307 of 481 id: cubo-1547 author: Brackx, F.; Delanghe, R.; Sommen, F. title: Differential Forms and/or Multi-vector Functions date: 2005-08-01 words: 9440 flesch: 75 summary: [∂ Fr]r+1 eM = (∂ + Fr) eM and also ∂+ Gm+1−r = ∂ ∧ Gm+1−r = [∂ Gm+1−r]m+2−r = [∂ Fr ]r−1 eM = (∂− Fr) eM. 162 F. Brackx, R. Delanghe and F. Sommen 7, 2(2005) = −D̃D = d∗d−dd∗ = ̃ ∂∂̃ = −∂̃∂ = ∂−∂+ −∂+∂− = ̃ 7, 2(2005) Differential Forms and/or Multi-vector Functions 153 defined by Eωr = m∑ j=0 xj ∂xj ω r = ∑ |A|=r dxA m∑ j=0 xj ∂xj ω r A and EFr = m∑ j=0 xj ∂xj Fr = ∑ |A|=r eA m∑ j=0 xj ∂xj Fr,A is a scalar operator, measuring the degree of homogenicity of a function, and not af- fecting the order of a differential form or a multi-vector function. keywords: = ∑; action; algebra; analysis; ar+1; basis; brackx; br−1; clifford; closed; contractible; corollary; delanghe; derivative; differential; differential forms; dirac; dual; dxi; dxj; er(ω; euler; following; follows; forms; fr+1; functions; fundamental; harmonic; iii; ker; lemma; l−1e; mathematical; monogenic; multi; open; operator; poincaré; point; product; proof; r ker; r0,m+1; real; region; rm+1; r−1; section; smooth; sommen; space; vector; |a|=r; ωrk; ∂xj; ∂xk; ∂−∂+; � = cache: cubo-1547.pdf plain text: cubo-1547.txt item: #308 of 481 id: cubo-1548 author: Raikov, Georgi title: Spectral Shift Function for Schr¨odinger Operators in Constant Magnetic Fields date: 2005-08-01 words: 11588 flesch: 81 summary: If, moreover, V satisfies (1.2), then 0 ≤ W(X⊥) ≤ C′0〈X⊥〉−m0+1, X⊥ ∈ R2, with C′0 = C0 ∫ R 〈x〉−m0dx. = u0(X⊥/|X⊥|)|X⊥|−α(1 + o(1)), |X⊥|→∞, |∇U(X⊥)| ≤ C1〈X⊥〉−α−1, X⊥ ∈ R2, where α > 0, and u0 is a continuous function on S1 which is non-negative and does not vanish identically. keywords: 0,∞; 2bq; = ∫; adjoint; arctan; assumptions; asymptotics; behaviour; case; class; compact; constant; continuous; corollary; definite; discrete; eigenvalues; electric; energy; estimates; field; formula; function; general; georgi; high; hold; h±,h0; iii; inf; integral; kernel; l2(r3; landau; lemma; levels; lim; magnetic; main; math; non; n±(1; n±(s; o(1; operator; order; pair; perturbations; potential; proof; proposition; pushnitski; q ∈; raikov; results; satisfies; scattering; self; set; shift; sign; singularities; spectral; spectrum; ssf; strong; subsection; theorem; theory; tq(2bq; tq(e; type; weyl; x⊥ ∈; x⊥,x3; ξ(2bq; ξ(e; ξ(λ; τ(x⊥; φ±λ cache: cubo-1548.pdf plain text: cubo-1548.txt item: #309 of 481 id: cubo-1549 author: Bultheel, A.; Mart´ınez, H. title: An introduction to the Fractional Fourier Transform and friends date: 2005-08-01 words: 8490 flesch: 71 summary: An introduction to the Fractional Fourier Transform and friends 209 6 Windowed transform, wavelets and chirplets The short time Fourier transform or windowed Fourier transform (WFT) is defined as (Fwf)(x,ξ) = 1√ 2π ∫ ∞ −∞ f(t)w(t−x)e−iξtdt where w is a window function. Relations with the windowed or short time Fourier transform, with wavelets and chirplets can be found in Section 6. keywords: analysis; approach; bultheel; canonical; case; chirp; chirplet; classical; clear; complete; complex; convolution; cosine; cot; decomposition; definition; delta; dictionary; different; dimensional; distribution; domain; effect; eigenfunctions; example; exp; f(x; fourier; fourier transform; fractional; fractional fourier; frequency; frft; friends; function; general; group; hilbert; ieee; integral; interval; introduction; ka(ξ; kernel; l2(ir; lct; linear; mart́ınez; math; matrix; multiplication; n=0; operations; operator; proc; processing; properties; property; rate; related; representation; rotation; section; set; signal; sin; space; special; sweep; theorem; time; transform; unitary; variables; wavelets; wf)(x; wigner; ξ)-plane; −e−2iα cache: cubo-1549.pdf plain text: cubo-1549.txt item: #310 of 481 id: cubo-1550 author: Kikina, L. K.; Stavroulakis, I.P. title: A Survey on the Oscillation of Solutions of First Order Delay Difference Equations date: 2005-08-01 words: 4181 flesch: 78 summary: = 0, 1, 2, ..., en donde {pn} es una sucesión de números reales no negativos, k es un entero positivo, en especial cuando ni siquiera se satisfacen las conocidas condiciones de oscilación lim sup n→∞ n� i=n−k pi > 1 y lim inf n→∞ 1 k n−1� i=n−k pi > kk (k + 1)k+1 Key words and phrases: Oscillation, nonoscillation, delay difference equation. [2] M. P. CHEN AND Y. S. YU, Oscillations of delay difference equations with variable coefficients, Proc. keywords: appl; assume; condition; criteria; delay; difference; differential; equations; following; lim; math; n→∞; n−1∑; n−k; order; oscillate; oscillation; positive; solutions; stavroulakis; sup; theorem; zhang cache: cubo-1550.pdf plain text: cubo-1550.txt item: #311 of 481 id: cubo-1551 author: Eloe, Paul W. title: Positive Operators and Maximum Principles for Ordinary Differential Equations date: 2005-08-01 words: 8933 flesch: 71 summary: Then we shall exhibit many types of boundary value problems for which the maximum principle is valid. Second, in Section 2, we shall exhibit many types of boundary value problems (BVPs) for which the maximum principle is valid. keywords: applications; associated; assume; banach; boundary; boundary conditions; boundary value; bvp; bvps; conditions; cone; conjugate; continuous; denote; difference; differential; differential equations; eloe; equations; f(t; focal; form; function; g(t; green; henderson; impulse; inequalities; krein; lower; math; maximum; methods; monotone; nonlinear; nth; operators; order; ordinary; paul; point; positive; principle; problems; properties; respect; right; satisfies; second; section; sign; singular; soc; solutions; spaces; study; term; theorem; theory; time; type; unique; value; value problems; x(0; x(t cache: cubo-1551.pdf plain text: cubo-1551.txt item: #312 of 481 id: cubo-1552 author: Costa, Bruno title: Spectral Methods for Partial Differential Equations date: 2004-12-01 words: 10957 flesch: 60 summary: [8] is a good encyclopedia in spectral methods directed towards Fluid Dynamics applications, as well as the more recent monography by Fornberg [18], where a close relationship between collocation spectral methods and high order Finite Diference schemes is developed. In the past several years, the activity on both theory and application of spectral methods have been concentrated on collocation spectral methods. keywords: accuracy; applications; approximation; basis; boundary; bruno; case; characteristic; chebyshev; coefficients; collocation; computational; compute; conditions; costa; decay; derivative; differences; differential; differentiation; dimensional; discontinuity; domain; dynamics; elements; equations; error; fast; figure; finite; flow; fluid; form; fourier; functions; f̂k; galerkin; general; grid; heat; high; information; initial; instance; integration; interested; k=0; legendre; library; linear; mapping; matrix; methods; multidomain; navier; necessary; need; new; nonlinear; number; numerical; obstacle; order; partial; pde; periodic; physical; points; polynomials; problems; pseudospectral; schemes; second; section; set; siam; simple; solution; spectral; spectral methods; stokes; system; temperature; terms; time; transfinite; transformation; use; values; variables; vol; wave; way; work cache: cubo-1552.pdf plain text: cubo-1552.txt item: #313 of 481 id: cubo-1553 author: Milewski, Paul A. title: The Forced Korteweg–de Vries Equation as a Model for Waves Generated by Topography date: 2004-12-01 words: 6011 flesch: 74 summary: Topographic effects in stratified flows, Cambridge University Press [2] Choi, J.; Milewski, P. A. Resonances between surface waves and periodic topog- raphy. Figure 7: Free surface evolution of a flow over a bump according to the forced Burgers (28) equation for the case 3 2 Δh < f 2 (here f = 0.5, Δh = 0.1. keywords: bump; case; characteristics; dependent; downstream; elevation; equation; evolution; fall; figure; flow; fluid; forced; free; free surface; h(x; hole; hydraulic; kdv; large; left; milewski; obstacle; paul; periodic; plateau; problem; right; shock; similar; solutions; speed; steady; subcritical; surface; time; topography; upstream; water; waves cache: cubo-1553.pdf plain text: cubo-1553.txt item: #314 of 481 id: cubo-1554 author: Furtado, Frederico; Pereira, Felipe title: On the Scale Up Problem for Two-Phase Flow in Petroleum Reservoirs date: 2004-12-01 words: 7051 flesch: 58 summary: We believe such a characterization is an essential step in the scientific program leading to an improved understanding of the scale up problem for porous media flow. [38] F. Pereira, Stochastic geology and porous media flow: theory and simulations, State University of New York at Stony Brook, Ph.D. Thesis, 1992. keywords: analysis; anomalous; assumption; asymptotic; behavior; computational; constant; covariance; cvk; diffusion; distinct; effect; equations; exponent; felipe; field; figure; flow; fluid; fractal; frederico; function; furtado; glimm; growth; heterogeneity; heterogeneous; immiscible; laws; length; linear; log; media; mixing; new; nonlinear; nonlinearity; numerical; oil; pereira; permeability; petroleum; phase; phase flow; porous; pressure; problem; process; random; ref; regime; relative; reservoirs; results; saturation; scale; scaling; section; simulations; spe; stochastic; studies; study; theory; time; transport; unstable; values; velocity; water cache: cubo-1554.pdf plain text: cubo-1554.txt item: #315 of 481 id: cubo-1555 author: Cai, Xiao-Chuan; Dryja, Maksymilian; Sarkis, Marcus title: A Restricted Additive Schwarz Preconditioner with Harmonic Overlap for Symmetric Positive Definite Linear Systems date: 2004-12-01 words: 9600 flesch: 78 summary: Let us denote Ω(W δi,non) by Ωδi,non, then φi(xk) = 1 at xk ∈ W δi,non for the case Ωδi,non ∩ ∂Ω = ∅ since all the boundary nodes of Ωδi,non belong to W Γ δ i,in. For any given u ∈ Ṽδ, we define ui ∈ Ṽδi as ui(xk) = ⎧⎨ ⎩ u(xk) if xk ∈ W δi,in discrete harmonic if xk ∈ W δi,ovl 0 if xk ∈ W \W̃ δi . keywords: 1)h; a(u; additive; boundary; cai; case; chuan; constants �; correspondent �; discrete; dryja; element; finite; following; functions; harmonic; i=1; j �; lemma; linear; log(δ; maksymilian; marcus; matrix; nodes; non; note; operator; overlap; overlapping; ovl; paper; partition; preconditioner; problems; rasho; restricted; r̃δi; sarkis; schwarz; set; size; smaller; subdomain; subregion; symmetric; system; type; use; ṽδ; ṽδi; xiao; θi(x; φi(x; ωδi; ∂ω �; � =; � ij cache: cubo-1555.pdf plain text: cubo-1555.txt item: #316 of 481 id: cubo-1556 author: Tabak, Esteban G.; Tal, Fabio A. title: Turbulent mixing of stratified flows date: 2004-12-01 words: 5924 flesch: 57 summary: Turbulent mixing of stratified flows Esteban G. Tabak Courant Institute of Mathematical Sciences New York University Falta e-mail Fabio A. Tal 1 Courant Institute of Mathematical Sciences New York University Falta e-mail ABSTRACT A mathematical model for turbulent mixing of stratified, sheared flows is de- veloped and explored. Still another possibility is to let l evolve dynamically, following a dynamic equation modeling the cascade of turbulent energy across scales. keywords: buoyancy; cooling; critical; depth; diffusion; energy; equilibrium; esteban; evolution; fabio; figure; final; flows; fluid; flux; horizontal; initial; kinetic; layer; mathematical; mixed; mixed layer; mixing; model; momentum; number; numerical; ocean; physical; potential; processes; profile; properties; richardson; run; shear; small; state; stratification; stratified; surface; system; tabak; turbulent; turbulent energy; turbulent mixing; unstable; value; velocity; vertical; water; wind; −40 cache: cubo-1556.pdf plain text: cubo-1556.txt item: #317 of 481 id: cubo-1558 author: Chbili, Nafaa title: Sym´etries en Dimension Trois: Une Approche Quantique date: 2004-12-01 words: 11764 flesch: 79 summary: Cependant, il n’existe pas un algorithme pratique permettant de transformer un diagramme quelconque d’un entrelacs lenticulaire en un diagramme de la forme ̂T p(σ1σ2...σm−1)ms. Par 152 Nafaa Chbili 6, 4(2004) conséquent, le nœud de trèfle n’est pas 3-librement périodique. Dans le tableau de [52], il y a 84 nœuds ayant un nombre de croisements inférieur à 9. keywords: alors; approche; aussi; aux; bandes; cas; ces; cette; chbili; classes; coefficients; comme; composantes; condition; congruence; corollaire; critère; crochet; croisements; cyclique; d d; dans; dans la; dans un; de homfly; de la; de s3; des; deux; définie; définition; désigne; diagramme; dimension; donnée; d’alexander; d’autres; d’homologie; d’isotopie; d’une; effet; engendré; entier; entrelacs; entrelacs de; est; exemple; existe; été; façon; fait; fermeture; feuillets; figure; formule; groupe; homfly; impair; invariants; jones; kauffman; knots; l un; le nœud; lenticulaire; les; librement; links; l’action; l’anneau; l’ensemble; l’espace; manifolds; math; même; modulo; montre; mouvements; murasugi; n d; nafaa; nombre; non; note; notons; nous; nœuds; n’est; obtenu; orientés; où; p un; par; paragraphe; partir; pas; periodic; peut; périodiques; plusieurs; points; polynomial; polynôme; polynôme de; pour; premier; przytycki; quantique; quantum; que; question; qui; qu’on; r un; rappelons; reidemeister; relation; revêtement; résultat; seulement; simple; skein; soient; soit; sont; sous; sphère; su(3; suite; suivante; sur; symétries; tangle; techniques; tel; théorème; théorie; topology; toriques; tout; traczyk; tresse; trois; type; un entier; un entrelacs; un nombre; un nœud; une; utilisant; variétés; vol cache: cubo-1558.pdf plain text: cubo-1558.txt item: #318 of 481 id: cubo-1561 author: Martynyuk, A.A. title: Matrix Liapunov’s Functions Method and Stability Analysis of Continuous Systems date: 2004-12-01 words: 16269 flesch: 79 summary: Here the vector α can be specified as follows: (i) α = y ∈ Rm, y 6= 0; (ii) α = ξ ∈ C(Rn, Rm+ ), ξ(0) = 0; (iii) α = ψ ∈ C(Tτ × ,m, are locally Lipschitzian in x; (ii) vij (t, 0) = 0 for all t ∈ R+ (t ∈ Tτ ), i,j = 1, 2, . . keywords: = +; a.a; aiixi; aij; ajj; analysis; approach; assume; assumption; asymptotic; auxiliary; c(tτ; case; class; conditions; connected; constant; continuous; corollary; corresponding; d+v(t; decreasing; definite; definition; derivative; differential; domain; dxi; dynamical; dynamics; elements; equations; equilibrium; estimate; example; form; function; function v(t; general; hahn; hand; hold; iff; iii; invariant; investigation; large; liapunov; martynyuk; matrices; matrix; matrix liapunov; method; moscow; motion; nauka; negative; new; nonlinear; open; partial; piiaij; pij; point; positive; problem; properties; qualitative; results; rm×m; rni; satisfied; scale; section; semi; set; sign; solution; stability; stable; state x; subsystems; sup; system; terms; theorem; theory; time; total; u ∈; v(t; vector; vij; x(t; x)y; york; ytu(t; × n; ψ(t; ∈ k; ∈ r cache: cubo-1561.pdf plain text: cubo-1561.txt item: #319 of 481 id: cubo-1563 author: Avello J., Gustavo title: Una condición suficiente para que un punto encontrado por multiplicadores de Lagrange sea un extremo date: 1992-12-01 words: 802 flesch: 88 summary: = .Áj, y de la relación (go r.p)(z) = O'v' Probemos el Teorema enunciado en (A) en el caso de un mínimo, loo otros casos, con ligeras modificaciones son similares. keywords: clase; mínimo; para; punto; que; revista; sea; sobre; tal; teorema; una; vecindad cache: cubo-1563.pdf plain text: cubo-1563.txt item: #320 of 481 id: cubo-1565 author: González Aguilera, Victor title: On a pencil of 𝘒₃ surfaces date: 1992-12-01 words: 974 flesch: 79 summary: The intersection of F =O with each hyperplane H¡, i E {1 , ... , 4) , gives a Fermat's quartic of ge nus g = 3, that we denote by F¡ , i E {l , .. . , 4) . It is well known that the biggest group of proj ective automorphisms of F = O {Ferma t 's quartic surface) is isomorphic to Ge!: (7l/4Z )3 x 94 , where 9 4 is the sym· metric group. keywords: acts; curve; group; hº(p3; pencil; quartic; que; revista; section; surface; tbe; una cache: cubo-1565.pdf plain text: cubo-1565.txt item: #321 of 481 id: cubo-1566 author: Catalán, Abdón; Costa, Roberto title: Acerca de álgebras báricas satisfaciendo (𝓍²)² = 𝜔(𝓍)³𝓍 date: 1992-12-01 words: 1929 flesch: 93 summary: +'Yn-iw(x)- 1x, by the ideal E,.,(.p) de A generated by ali p(a), a E A. Different. = O se llama tren ecuación de A y n es el rango de A. Par.a estas álgebras N es un nilideal. keywords: como; ea(p; elementos; entonces; grado; ideal; ideales; las; los; p(a; p(e; p(x; para; peso; polinomio; polynomials; por; probar; que; revista; satisfacen; sea; son; suficiente; t(p; train; tren; u2v; una; uv2; w(x; álgebras cache: cubo-1566.pdf plain text: cubo-1566.txt item: #322 of 481 id: cubo-1570 author: Delgado Andrade, Victor title: Trayectorias de un sistema de control lineal en IRⁿ sobre variedades lineales de codimensión 1 y n-1. date: 1992-12-01 words: 1219 flesch: 93 summary: Trayectorias de un sistema de control Lineal en IR.n sobre variedades lineales de codimensión 1 y n-1. Si cu la proposición anteri or k = n, es deci r la última componente de m e:; -l , ento nces u= < m , Ax >.esta keywords: codimensión; con; control; cubos; del; entonces; figura; inicial; lineal; lineales; puede; que; revista; sin; sistema; una; uno cache: cubo-1570.pdf plain text: cubo-1570.txt item: #323 of 481 id: cubo-1572 author: Riquelme Sepúlveda, Roberto title: Análisis armónico sobre 𝑆𝑙(2, 𝛺), 𝛺 cuerpo p-ádico (𝑝 ≠ 2) date: 1992-12-01 words: 979 flesch: 83 summary: Teorema 2.2 G = S l (2 , !1) es generado por elem ento s d e la Jonna u(b) = ( ~ ~) pam b e n fl y el elemento w = (-~ ~). donde w(f/J) e.s el cond uctor de l/.l y q es el orden de In clase residual , entonces se verifica que Í (x ) = / (- x). keywords: carácter; con; den; denotemos; entonces; grupo; igual; los; para; por; que; representación; sea; sl(2; sobre; teorema; u(b; una cache: cubo-1572.pdf plain text: cubo-1572.txt item: #324 of 481 id: cubo-1573 author: Baeza V., R.; Benavides G., R. title: Formas Bilineales Asociativas en una Algebra Bárica date: 1992-12-01 words: 850 flesch: 85 summary: Sea J( un cuerpo de caraclerfsbica difert::nLe de Clos y Si T : N - N, con N = ke.rw, denota la mu\Liplicnció n a izquierda por d idempolente e: y U = lm-r~ , V = /( er-rk, enlonccs keywords: así; b(e; b(n; b(u; bernslein; con; forma; orden; para; por; que; sea; tenemos; una; álgebra cache: cubo-1573.pdf plain text: cubo-1573.txt item: #325 of 481 id: cubo-1575 author: Venkatesh, Akshay; Naveen Kumar, R.T. title: On some recurrent properties of three dimensional K-contact manifolds date: 2017-06-01 words: 2464 flesch: 69 summary: [8] E. Peyghan, H. Nasrabadi and A. Tayebi, On φ-recurrent contact metric manifolds, Math. [2] D.E. Blair, Contact manifolds in Riemannian geometry. keywords: contact; contact manifold; cubo; curvature; dimensional; following; form; g(x; g(y; generalized; manifold; math; metric; recurrent; ricci; semi; tensor; theorem; vector; y)z; z)x cache: cubo-1575.pdf plain text: cubo-1575.txt item: #326 of 481 id: cubo-1576 author: López, Iris A. title: On the hypercontractive property of the Dunkl-Ornstein-Uhlenbeck semigroup date: 2017-06-01 words: 6600 flesch: 84 summary: − L j kf(σix) ) = d∑ i=1 { ki 4x2i (∂2if(x) − ∂ 2 if(σix))(f(x) − f(σix)) + kj 2x2j (f(σjx) − f(x) + f(σix) − f(σjσix)) − xj(∂jf(x) − ∂jf(σix)). keywords: 2x2i; 2x2j; 4x2i; cubo; differential; dunkl; f(x; following; fractional; generalized; hermite; hypercontractive; inequalities; inequality; iris; j kf(x; j=1; j=1,j6; kf(x; ki 2x2i; kikj; kjki; l j; lemma; lkf; logarithmic; lópez; math; operator; ornstein; polynomials; property; semigroup; sobolev; spaces; theorem; uhlenbeck; x3i; zd2; γ2(f; ∂if(x; ∂jf(x; − f(σix; − f(σiσjx; − ki; − l; − ∂ cache: cubo-1576.pdf plain text: cubo-1576.txt item: #327 of 481 id: cubo-1577 author: Yadav, S. K.; Chaubey, S. K.; Suthar, D. L. title: Some geometric properties of η− Ricci solitons and gradient Ricci solitons on (𝑙𝑐𝑠)𝑛−manifolds date: 2017-06-01 words: 6091 flesch: 83 summary: + 2η(X)η(Y)ξ + η(Y)X} , (2.12) S(X, ξ) = (n − 1)(α2 − ρ)η(X), (2.13) S(φX, φY) = S(X, Y) Also from (3.18) we have δ = −α + (n − 1)(α2 − 1) = constant. keywords: 1)(α2; chaubey; concircular; constant; cubo; curvature; einstein; equation; field; g(x; geometry; lcs)n−manifold; lorentzian; manifold; math; metric; non; properties; r(e1; ricci; s(x; sasakian; soliton; structure; suthar; symmetric; tensor; theorem; vector; view; yadav; η−ricci; χ(m; −(u cache: cubo-1577.pdf plain text: cubo-1577.txt item: #328 of 481 id: cubo-1578 author: Tchuiaga, S.; Koivogui, M.; Balibuno, F.; Mbazumutima, V. title: On topological symplectic dynamical systems date: 2017-06-01 words: 8507 flesch: 76 summary: Section 4 deals with the definitions of the C0−compact open topology, the origin of strong symplectic homeomorphisms, and the definition of strong symplectic isotopies with their generators. A continuous map ξ : [0, 1] → Homeo(M) with ξ(0) = idM, is called strong symplectic isotopy if there exists a D∞−Cauchy sequence {(Fi,λi)} ⊂ T(M,ω, g) such that d̄(φ(Fi,λi),ξ) keywords: banyaga; continuous; converges; cubo; definition; denote; diffeomorphisms; displacement; dynamical; energy; flow; following; geometry; group; h1(m; hamiltonian; harmonic; hofer; homeomorphisms; isotopies; isotopy; large; like; manifold; map; max; mbazumutima; metric; norm; open; path; proof; respect; result; sequence; set; smooth; space; ssympeo(m; strong; strong symplectic; symplectic; symplectic homeomorphisms; symplectic isotopy; systems; t(m; tchuiaga; theorem; topological; topology; φ(ui; φ(vi cache: cubo-1578.pdf plain text: cubo-1578.txt item: #329 of 481 id: cubo-1579 author: Gasteratos, Ioannis; Kuruklis, Spiridon; Kuruklis, Thedore title: A Trigonometrical Approach to Morley’s Observation date: 2017-06-01 words: 5537 flesch: 69 summary: = 180◦, B′′C′′ = p sin α++ = 8R sin α− sin β− sin γ− while ∠AB′′C′′ = γ and ∠AC′′B′′ = β. = 8R sin β − sin β+; thus CC′′B = 8R sin β − sin β+ sin α++ and AC′′B = 8R sin β − sin β+ sin γ. keywords: angles; central; collinear; complete; cubo; determine; equilateral; explementary; exterior; inner; interior; intersections; kuruklis; lengths; los; meet; mix; morley; observation; p sin; parallel; peripheral; proof; proximal; sides; sin; sin β; theorem; triangle; trigonometrical; trisectors; trisectors proximal; type; vertex; ∆bac cache: cubo-1579.pdf plain text: cubo-1579.txt item: #330 of 481 id: cubo-1586 author: Prunescu, Mihai title: Concrete algebraic cohomology for the group (ℝ, +) or how to solve the functional equation 𝑓(𝑥+𝑦) - 𝑓(𝑥) - 𝑓(𝑦) = 𝑔(𝑥, 𝑦) date: 2007-12-01 words: 3604 flesch: 105 summary: und 1l{ u, r ) z, m JMtHrul111 ,,,,, O. lt fo llows 111111 \.' ii. 11 11 1 morphi..111 lw tw ('(' ll tl w r xn r t .. r o m putl' n !-n (5) T hree proofs of an identity involviog ... therefore, ,.-e have G = PAP- 1 1 c- 1 = PA - 1 P - 1 1 and 8, G = 8,(P/\P- 1 ) = (81P)/\P- 1 + P(8; A)P-1 + P/\(8,(P- 1)), c-1(8;G) = (P/\ - 1 p - ' )(8;P)/\P-1 + (P/\- 1 p - 1)(P(8,A)P- 1) keywords: china; definite; deri; hcnan; hree; identity; igi; lhe; linear; matrix; positive; proofs cache: cubo-1696.pdf plain text: cubo-1696.txt item: #343 of 481 id: cubo-1706 author: Anastassiou, George A. title: A New Expansion Formula date: 2003-01-01 words: 1242 flesch: 98 summary: lmp!icullions and applicntio ns o f tbe fo r mu la follmv. Consiclcr thc dislribution fun tions g0 ,,,.(x) : ''¡a,xl, x E a, bJi m. EN, which 1:1rc of boundl' O. Th n t.hc row vect.or (1 t ... (k¡:li )I) 'n ' for f(D). In li:l'lltrnl , R 'is f r F ( D ) may ll<' obta1111~l by r l11ci ng F t,o dia- gonaJ form by row nnd c' olu mn opcra1 ions. keywords: basis; case; columns; d(d; diagonal; f(d; form; hen; jordan; matrix; nnd; normal; ode; poly; row; solutions; system; t.he; uch cache: cubo-1783.pdf plain text: cubo-1783.txt item: #346 of 481 id: cubo-1798 author: Castro Gutierrez, F. title: Elementos Matemáticos en la Civilización Incaica date: 1999-06-01 words: 1262 flesch: 63 summary: [l ] Elementos Matemáticos en Ja Ci vilización Incaica El quipu desempeñó el rol de un in strumento de comunicación de gran capaci- dad de información en una organización política y social fuertemente centralizada. Es interesante acotar que en el caso de los incas , dos de esos elementos esenciales se estructur an en la trama de un tejido de fibr as: los puentes colgantes y el encordado del quipu. keywords: 10s; algunos; aspectos; carácter; castro; cl.e; cle; colores; comunicación; con; cual; cuerdas; del; elementos; era; esta; este; estos; fig; hoy; incas; información; juegos; las; los; matemática; más; nudos; otras; para; podemos; por; puentes; que; quipu; recurso; registros; sistema; sobre; sus; también; tejido; tra; una; uno; us0; utilizado; variables; vez; vol; vías cache: cubo-1798.pdf plain text: cubo-1798.txt item: #347 of 481 id: cubo-1803 author: Pellegrino, D. M. title: Acerca de una Definición Débil de Números Normales date: 1999-06-01 words: 1753 flesch: 90 summary: Formalmente , w, es casi g-normal si (\l k E IN ), (\lc, ... c, ; e, E {O, ... , g-1}\lj E {l , ... , k} ), 3i E JJV ; a,., _, =e,, \lj E {l , .. , k) 50 D. M. Pellegrino Est a es una condi ción débil ante la condición requerida de números g-normales. a alguna base g. Un ejemplo canónico de un número 10-normal, debido a D. G . keywords: base; cada; casi; como; con; definición; débil; dígitos; entero; entonces; esta; f(x; los; normal; normales; número; para; pero; por; proposición; que; sea; simple; son; sucesión; tal; tales; todos; una cache: cubo-1803.pdf plain text: cubo-1803.txt item: #348 of 481 id: cubo-1810 author: Mallol, Cristián title: A propos des algèbres pondérables date: 1995-05-01 words: 2361 flesch: 94 summary: qu e 'Y= WiJ.~ · b) // exist e e E A, tel qu e w;(c) = 1, pour tout i. Dómonslration. (a ) ::::} (d), il suffit de prendre E= K er(w) et choisir e E E , w(e) keywords: a(z; alg; application; b(a; c3l; car; cor; cubo; da.ns; des; deux; e e; ensemble; entre; est; existe; ker(w; les; m(e; non; par; pondémtions; pondération; pondérée; pose; pour; proposition; puis; q(e; q(x; que; qui; simple; soit; sont; sous; suit; tel; toute; type; une; w(e; w(x cache: cubo-1810.pdf plain text: cubo-1810.txt item: #349 of 481 id: cubo-1811 author: Montenegro, Eduardo title: Hamiltonety and automorphisms group of graph preserved by substitution date: 1995-05-01 words: 1840 flesch: 96 summary: no common ve rticcs 11mong t.h c mscl.t1c3 n o r wi.th G, wh ere cach S, :::::: K~_ 1 , t.hen ( i) M,.(G) is n hnmiltone.an and ( ii} A ut. Lc t G be a graph whithout i30 lated. keywords: a.nd; aut.(g; block; case; cdgc; common; complete; copy; cubo; cycle; edge; gcnerator; gmph; graph; group; interna; ion; m,(c; m,.(g; mon; preserve; proo; set; symmetry; thc; thcn; ubstitution; v(g; vcrticcs; wit.h cache: cubo-1811.pdf plain text: cubo-1811.txt item: #350 of 481 id: cubo-1813 author: Bustos V., Manuel title: Cálculo subdiferencial y conjuntos polares date: 1995-09-01 words: 2526 flesch: 104 summary: Otú.lad J E l'o(éj, z o E E .Y Si e e E., l!:'I 1111 co11j11nlO com·cxo cxn-ado que co nt iene 1\ 01 :ltlll /1 • Uf' o A UJ>ongn. keywords: 111; calc; como; con; conjunto; convexo; del; e e; e l; e n; fin; ión; nció; por; que; ubo; ulo; un11 cache: cubo-1813.pdf plain text: cubo-1813.txt item: #351 of 481 id: cubo-1817 author: Leiva Vivar, Juan title: Clasificación de las métricas invariantes a izquierda en grupos Lie date: 1995-09-01 words: 2192 flesch: 97 summary: Sean, a hora, X E e' u, V E T:i:G Cll /\lcsquicr a. Sea 8 1 = { t 1, •••• r n} ba..<:.e d e g ,ortono r mnl res¡>t'cto al 1>roduct o inte rn o < . >! keywords: ahora; bajo; base; como; con; condiciones; cubo; d e; dada; dado; del; dice; donde; e c; ele; en g; este; esto; existe; grupo; interno; invariantes; izquierda; las; lic; lie; métrica; nexo; para; por; pos; producto; puede; pues; que; queda; sea; sean; son; tal; una; y g; álgebra; única cache: cubo-1817.pdf plain text: cubo-1817.txt item: #352 of 481 id: cubo-1819 author: Figueroa Cortés, Alejandro title: Subproductos escalares no arquimedianos date: 1994-12-01 words: 1473 flesch: 90 summary: todo x , y , u en E: 8 (x + y, u) S máx(8(x, u), 8(y, u)) ( e) Paro todo x,y en E ' 8 2 (x, y) S 8(x, x )8(y,y) (f ) 8(0, 0) = o ( g) Paro todo x, y en E y a en p, 8(ax, y) = lal8(x, y). E y t odo a en F : p(ax) = la lp(z ) ( .9) keywords: anillo; b(x; b(y; con; en e; entonces; espacio; existe; figueroa; p(x; para; paro; que; sea; sean; sobre; todo; todo x; trivial; valuado; vectorial; y en cache: cubo-1819.pdf plain text: cubo-1819.txt item: #353 of 481 id: cubo-1821 author: Paredes U., Eric title: Soluciones Analíticas de un Problema de Valor Inicial y de Contorno date: 1994-12-01 words: 1491 flesch: 94 summary: Pode mos o bservar q ue : 17 (8) (9 ) (16) (11 ) P ara q ue ( 12) sea una so lución del problema ( P ) de b en s atisfacerse algunas condicio nes de integrabilidad en la.o:; fondones K , L y C: , por ejemplo: K, L y C: co ntinu as. i nicial y d e conto m keywords: a(y; c(x; contorno; cubo; del; entonces; escr; f(y; forma; inicial; l(x; obtiene; paredes; por; problema; puede; que; sean; soluciones; solución; u(x; una; valor cache: cubo-1821.pdf plain text: cubo-1821.txt item: #354 of 481 id: cubo-1825 author: Maturana, Ana María title: Modelos del Mal de Chagas date: 1991-12-01 words: 2410 flesch: 105 summary: i o n e s e n e l mo - del o serén difer e nte s ( co mo a co n llo nu ac l ó n se d e t a llan) y V(l) s e co ns ld eraró co ns tante . e ri- d as d e e s l as pi caduras. keywords: cas; cauchy; dad; del; equ; este; las; modelos; mos; nes; onde; ones; pag; para; pob; por; que; soluc; tasa; uce cache: cubo-1825.pdf plain text: cubo-1825.txt item: #355 of 481 id: cubo-1834 author: Baeza, Rodolfo title: On nuclear Bernstein algebras date: 1990-07-01 words: 1515 flesch: 91 summary: The subspacea U and V satisfy the fundamental relations u2~, uv~, v2~, vv2•o, uY-o and the fundamental identities u~-o, u1(u 1v 1 )•O, u 1 (u 2 u 3 )+u 2 (u 3 u 1 }+u 3 (u 1 u 2 ) • o (Jacobi's identity) 1 vu 1tU, v 1EV, and (xy)(zt)+(xz)(yt)+(xt)(yz) Proor , It x-ae+u+u1 u 2 be in D, then xU•O impliH aeU+uU+(u 1u 2 ) keywords: algebra; bernstein; commutative; core; finita; ideal; identity; jordan; ker(w; lemma; nilpotent; principal; proof; special; thua; train cache: cubo-1834.pdf plain text: cubo-1834.txt item: #356 of 481 id: cubo-1844 author: Alcalde, M. T.; Baeza, Ricardo; Burgueño, Cesar title: Caracterización en Álgebras de Bernstein date: 1988-12-01 words: 1263 flesch: 97 summary: O y que U V =O. El recip r oco 60 REVISTA CUl!G .. U G V un álgebra de Bernstern sobre K, en ton ces A es Normal ss1 v2:o y UV:O DEMCS!'RACION: keywords: bernstein; entonces; ker; para; por; que; sea; sobre; son; w(x; álgebra cache: cubo-1844.pdf plain text: cubo-1844.txt item: #357 of 481 id: cubo-1849 author: Henríquez Barrientos, Lionel title: Solución de la Cuártica date: 1987-12-01 words: 719 flesch: 101 summary: fina l men t e d e ( 11 ) , ob t o keywords: las cache: cubo-1849.pdf plain text: cubo-1849.txt item: #358 of 481 id: cubo-1866 author: Billeke Gonzalez, Jorge title: Solución a problemas propuestos date: 1986-12-01 words: 1393 flesch: 108 summary: Co n sideremos t:J ABC pe- d lCJO c on 8 e L l, A cl3 y C e L2 • 1- _, e e n to n ces 0 keywords: ces; log; n+l; pero; que; tal cache: cubo-1866.pdf plain text: cubo-1866.txt item: #359 of 481 id: cubo-1872 author: Hidalgo, Rubén A. title: Totally Degenerate Extended Kleinian Groups date: 2017-10-01 words: 3980 flesch: 64 summary: Basic examples of Kleinian groups are the following ones. On boundaries of Teichmüller spaces and on Kleinian groups: I. Ann. of Math. 91 (1970), 570-600. keywords: combination; component; conformal; connected; cubo; degenerate; discontinuity; element; extended; finite; fundamental; g(t; group; half; hyperbolic; invariant; isomorphism; kleinian; kleinian group; lemma; limit; maskit; möbius; non; orientation; parabolic; plane; points; quasifuchsian; region; riemann; set; theorem; transformations cache: cubo-1872.pdf plain text: cubo-1872.txt item: #360 of 481 id: cubo-1895 author: Anastassiou, George A. title: Approximation by Shift Invariant Univariate Sublinear-Shilkret Operators date: 2018-10-19 words: 4621 flesch: 92 summary: − f ( 2−k· )( 2kx )∣ ∣ψ(u)dµ(u) (14) ≤ (here ∣ ∣ ( 2kx − u ) − f ( y − u + j n )) keywords: 2kn; 2kx; approximation; cubo; f(n; n−1; operators; shift; shilkret; sup; ψ(u)dµ(u; ∣ ∣; ∣ ≤ cache: cubo-1895.pdf plain text: cubo-1895.txt item: #361 of 481 id: cubo-1896 author: Venkatesha; B., Shanmukha title: \(W_2\)-curvature tensor on generalized Sasakian space forms date: 2018-10-19 words: 3823 flesch: 74 summary: Keywords and Phrases: Generalized Sasakian space form, W2-curvature tensor, pseudosym- metric, φ-recurrent, Einstein manifold. In order to generalize such space forms in a common frame Alegre, Blair and Carriazo [1] introduced and studied generalized Sasakian space forms. keywords: cubo; curvature; equation; flat; forms; g(x; g(y; generalized; generalized sasakian; manifold; math; orthogonal; pseudosymmetric; r(x; recurrent; riemannian; sasakian; sasakian space; shanmukha; space; space forms; symmetric; tensor; theorem; v)z; vector; venkatesha; w2(u; y)z; z)x cache: cubo-1896.pdf plain text: cubo-1896.txt item: #362 of 481 id: cubo-1897 author: Jeyanthi, P.; Nalayini, P.; Noiri, T. title: Pre-regular \(sp\)-open sets in topological spaces date: 2018-10-19 words: 3064 flesch: 83 summary: α-open, semi-open, a q-set) subset of X. CUBO 20, 1 (2018) Pre-regular sp-Open Sets in Topological Spaces 33 2 pre-regular sp-open sets In this section, we define and characterize pre-regular sp-open sets and study some of their prop- erties. CUBO 20, 1 (2018) Pre-regular sp-Open Sets in Topological Spaces 35 Example 2.11. keywords: continuous; int(cl(inta; int(cla; open; pint(spcla; pre; preopen; proof; regular; regular open; regular sp; semi; sets; space; subset; theorem; topological cache: cubo-1897.pdf plain text: cubo-1897.txt item: #363 of 481 id: cubo-1898 author: Kumar Mohanta, Sushanta title: Common Fixed Point Results in C∗-Algebra Valued b-Metric Spaces Via Digraphs date: 2018-10-19 words: 9230 flesch: 87 summary: x − y |3 I for all x, y ∈ X, where I is the identity operator on H. Then (X, B(H), d) is a complete C∗-algebra valued b-metric space with the coefficient A = 4I. Let G be a digraph such that V(G) = X and E(G) A mapping f : X → X is called a C∗-algebra valued G- contraction if there exists a B ∈ A with ‖ B ‖2< 1 ‖A‖ such that d(fx, fy) � B∗d(x, y)B, for all x, y ∈ X with (x, y) ∈ E(G). keywords: b(h; cgf; coincidence; common; compatible; complete; condition; contraction; corollary; cubo; c∗-algebra; d(fx; d(u; d(x; e(g̃; fixed; g(x; graph; gxn; gxn+1; gxni; mapping; metric; metric space; n =; point; proof; property; results; sequence; set; space; theorem; theory; unique; ‖a‖+1 cache: cubo-1898.pdf plain text: cubo-1898.txt item: #364 of 481 id: cubo-1899 author: de la Maza, Ana Cecilia; Moresi, Remo title: On rigid Hermitean lattices, II date: 2018-10-19 words: 6176 flesch: 71 summary: b⊥⊥ = b c c ⊥ e a = d b⊥a ⊥ e⊥� � � � � � � � � ❅ ❅ ❅ ❅ ❅ ❅ ❅ ❅ ❅ �� �� ��❅ ❅ ❅ ❅ ❅ ❅ α1 α11 α11 α2 α3 α1 = α2 = α3 = ℵ0 r r r r r r r r r r r r r r r α12 = δ ( a ⊥ 11/a ) c = b d⊥ = a11 d I r r r r r r b a b⊥a ⊥ � � �� � � �� ❅ ❅ ❅❅ ❅ ❅ ❅❅ β4 = δ ( c/c1 ) β4 β2 β1 β1 β4 β2 r r r r r r r r r r b c c⊥ e a b⊥a⊥ e⊥� � � � ❅ ❅ ❅❅ ❅ ❅ ❅❅ � � � � ❅ ❅ ❅❅ ❅ ❅ ❅❅ β7 = δ ( c1/b ⊥⊥ ) β3 β7 β1 β1 β2 β1 β3 β3 β2 β2 β1 β1 β3 β7 r r r r rr r r r r b d⊥ d e a⊥ a e⊥ b⊥ � � �� � � �� � � �� � � �� ❅ ❅ ❅ ❅ ❅ ❅ ❅ ❅ β8 = keywords: cubo; factors; following; hermitean; lattices; maza; moresi; proof; q q; q qq; q ✟; r r; relations; rigid; theorem; α16; α17; α19; α20; α3 q; ✑ ✑; ✟ ✟; ❅ ✟; ❅ ❅; ❍ ✟; ❍ ❍ cache: cubo-1899.pdf plain text: cubo-1899.txt item: #365 of 481 id: cubo-1900 author: Danish Siddiqi, Mohd; Akif Akyol, Mehmet title: Anti-invariant ξ⊥-Riemannian Submersions From Hyperbolic β-Kenmotsu Manifolds date: 2018-10-19 words: 4997 flesch: 74 summary: On the other hand, the geometry of anti-invariant Riemannian submersions is different from the geometry of almost Hermitian sub- mersions. However, this result is not valid for anti-invariant Riemannian submersions, which was first studied by Sahin in [8]. keywords: akif; akyol; anti; contact; cubo; danish; field; following; geodesic; geometry; gm(cy; hand; harmonic; horizontal; hyperbolic; i=1; invariant; kenmotsu; kerf∗; manifold; mehmet; metric; mohd; product; proof; riemannian; section; siddiqi; submersion; tensor; theorem; vector cache: cubo-1900.pdf plain text: cubo-1900.txt item: #366 of 481 id: cubo-2045 author: del Rio, Rafael; Franco, Asaf L.; Lara, Jose A. title: An approach to F. Riesz representation Theorem date: 2018-07-31 words: 4452 flesch: 76 summary: An approach to F. Riesz representation Theorem 3 for all f ∈ C(K), where ‖ · ‖ ∞ denotes the uniform norm, that is, ‖f‖ ∞ = sup{|f(x)| : x ∈ K}. = 1 for all x ∈ K, keywords: analysis; appendix; asaf; c(k; c[a; closed; compact; constant; continuous; cubo; del; finite; franco; function; functionals; integral; interval; jose; lara; linear; measure; new; positive; proof; real; representation; result; riemann; riesz; rio; set; spaces; stieltjes; theorem; theory; use; york; µ(k cache: cubo-2045.pdf plain text: cubo-2045.txt item: #367 of 481 id: cubo-2046 author: Jeyanthi, P.; Maheswari, A. title: Odd Vertex Equitable Even Labeling of Cycle Related Graphs date: 2018-07-31 words: 3280 flesch: 86 summary: Keywords and Phrases: Odd vertex equitable even labeling, odd vertex equitable even graph, double triangular snake, subdivision of double quadrilateral snake, double alternate triangular snake, double alternate quadrilateral snake, subdivision graph. The vertex labeling f is known as vertex equitable labeling. keywords: double; edge; equitable; figure; graph; labeling; labels; nk1; odd; odd vertex; s s; snake; theorem; v(g; vertex; vertex equitable; vertices cache: cubo-2046.pdf plain text: cubo-2046.txt item: #368 of 481 id: cubo-2048 author: Georgiev, Svetlin G.; Zennir, Khaled title: New approach to prove the existence of classical solutions for a class of nonlinear parabolic equations date: 2018-07-31 words: 4398 flesch: 91 summary: [a, b], or ∫x c ∫y c ut(t, z)dzdy − u(t, x) + u(t, c) + 3lBm + lM11m ≤ B. Note that S11(u)t(t, x) = −lut(t, x) + l ∫x 0 ∫y 0 ut(t, z)dzdy −l(u(t, x) − u(t, 0) − xux(t, 0)) keywords: 7−→; boundary; classical; continuous; cubo; equation; existence; f(t; f(τ; integral; k11; new; nonlocal; problem; respect; solutions; theorem; u(t; u(τ; zennir; φ(x; φ(z; ∫x c cache: cubo-2048.pdf plain text: cubo-2048.txt item: #369 of 481 id: cubo-2049 author: Tyagi, B. K.; Luthra, Sheetal; Chauhan, Harsh V. S. title: On New Types of Sets Via γ-open Sets in (𝑎)Topological Spaces date: 2018-07-31 words: 4935 flesch: 91 summary: The complements of (m, n)-semi-open set, (m, n)-γ-semi-open set and (m, n)-γ-P-semi-open set are (m, n)-semi-closed, (m, n)-γ-semi-closed and (m, n)-γ-P-semi-closed, respectively. Then U ∩ V 6= ∅ for every (a)-γ-P-semi-open set V containing y and (a)-γ-P-semi-open set U containing x. keywords: a)-γ; a)topological; closed; example; open; open set; proof; semi; set; sets; space; theorem; topologies; α∈λ cache: cubo-2049.pdf plain text: cubo-2049.txt item: #370 of 481 id: cubo-2050 author: Barro, Moussa; Guiro, Aboudramane; Ouedraogo, Dramane title: Optimal control of a SIR epidemic model with general incidence function and a time delays date: 2018-07-31 words: 3803 flesch: 66 summary: Keywords and Phrases: SIR, general incidence, delays, optimal control, epidemic models, Hamiltonian. CUBO 20, 2 (2018) Optimal control of a SIR epidemic model with general incidence . . keywords: aboudramane; barro; conditions; control; cubo; delays; different; disease; dramane; epidemic; equations; existence; function; general; guiro; incidence; infected; model; moussa; necessary; numerical; optimal; optimal control; order; ouedraogo; population; problem; r(t; r(u1; recovered; section; set; sir; state; strategies; susceptible; time; treatment; u2(t; vaccination cache: cubo-2050.pdf plain text: cubo-2050.txt item: #371 of 481 id: cubo-2051 author: Otake, Shuichi; Shaska, Tony title: Some remarks on the non-real roots of polynomials date: 2018-07-31 words: 10902 flesch: 92 summary: t1t 0 −(n − s)tst −(n − s + 1)ts−1t . . . − s)/n from the (1,1) entry x − s(n − s)/n or by taking (a25) all anti-diagonal entries. keywords: 1)t1; bezoutian; case; complex; cubo; degree; entries; entry; equation; f(t; f(x; fact; field; form; g(x; galois; group; j≤n; j≤s; k=0; lemma; matrix; non; number; odd; otake; polynomials; prime; proof; proposition; real; remarks; roots; row; rs+1; s(n; s)rst; shaska; shuichi; s−k; t21; term; theorem; tony; vector; − 1)t; − s)t1; ∣ ∣;  ;  ;  ;   cache: cubo-2051.pdf plain text: cubo-2051.txt item: #372 of 481 id: cubo-2063 author: Anastassiou, George A. title: Quantitative Approximation by a Kantorovich-Shilkret quasi-interpolation neural network operator date: 2019-03-15 words: 2814 flesch: 84 summary: Let f ∈ C+ B ( R N,C ) , f = f1 + if2, N ∈ N, 0 < β < 1, x ∈ RN; n ∈ N with n1−β ≥ 3. http://dx.doi.org/10.4067/S0719-06462018000300001 2 George A. Anastassiou CUBO 20, 3 (2018) 1 Introduction The author here performs multivariate error function based neural network approximation to con- tinuous functions over RN, N ∈ N, and then he extends his results to complex valued functions. keywords: approximation; cubo; dµ(t; f(x; fdµ; function; k n; kantorovich; n f; neural; shilkret; sup; µ n; ∣ ∣; ∣ ≤ cache: cubo-2063.pdf plain text: cubo-2063.txt item: #373 of 481 id: cubo-2064 author: Koike, Naoyuki title: Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces date: 2019-03-15 words: 6355 flesch: 83 summary: [ξ̃1, ẽλ i ] + θ̃[ξ1, θeλi ] ) (λ − λ1 ∈ △+) 1 2 cosh(||λ1||s0) If λi ∈ △+, then we have ||λi|| = √ 2 from how to choose the metric of G/K (see Introduction). keywords: aξiti; certain; compact; cosh(||λ1||s0; cubo; curvature; denote; exp(b; ẽλ; field; flow; foliation; following; i=1; isoparametric; kind; koike; leaf; leaves; lemma; mean; minimal; mλ∑; non; proof; space; symmetric; tangent; theorem; vector; xξ0,t1; ||λi||; γξ0 cache: cubo-2064.pdf plain text: cubo-2064.txt item: #374 of 481 id: cubo-2065 author: Ballico, E. title: Postulation of general unions of lines and +lines in positive characteristic date: 2019-03-15 words: 3199 flesch: 90 summary: Since kt + (k + 1)d + z = ( r+k−1 r ) and z ≤ k, we get (k + 1)k2 − k(k + 1) − k ≥ k ( r+k−1 r−1 ) − k ≥ (r − 1) ( r + k keywords: case; general; k−1; l(r; lines; proof; r+k−1; tangent; theorem; true; union cache: cubo-2065.pdf plain text: cubo-2065.txt item: #375 of 481 id: cubo-2066 author: Chandra Mandal, Yadab; Kumar Hui, Shyamal title: Yamabe Solitons with potential vector field as torse forming date: 2019-03-15 words: 3271 flesch: 86 summary: S 0 parallel r − (n − 1){2a + 1 n π(τ)} = constant r − (n − 1){2a + 1 n π(τ)} S 0 torqued r − f − (n − 1){2a S 0 concircular r − f − (n − 1){2a + 1 n π(τ)}=constant r − f − (n − 1){2a + 1 n π(τ)} keywords: connection; constant; cubo; field; hui; math; metric; n −; respect; ricci; semisymmetric; soliton; theorem; torse; vector; yamabe; β −; γ(τ; π(τ cache: cubo-2066.pdf plain text: cubo-2066.txt item: #376 of 481 id: cubo-2067 author: Ardjouni, Abdelouaheb; Djoudi, Ahcene title: Study of global asymptotic stability in nonlinear neutral dynamic equations on time scales date: 2019-03-15 words: 5928 flesch: 90 summary: such that for t ≥ T, max { |x (t)| , |x (t − τ2 (t))| , ∣∣∣x△̃ (t − τ1 (t)) ∣∣∣ } < ε. Lg |b (t)| |x (t)| + Lf |c (t)| ∣∣∣x△̃ (t − τ1 (t)) ∣∣∣ + L1 (t) |x (t)| + L2 (t) |x (t − τ2 (t))| . 58 keywords: asymptotic; c1rd; cubo; djoudi; dynamic; equations; e⊖a; global; neutral; nonlinear; solution; stability; theorem; time; ∣∣∣ cache: cubo-2067.pdf plain text: cubo-2067.txt item: #377 of 481 id: cubo-2068 author: Argyros, Ioannis K.; George, Santhosh title: Ball comparison between Jarratt’s and other fourth order method for solving equations date: 2019-03-15 words: 4483 flesch: 88 summary: − p‖)‖x0 − p‖ ≤ ‖x0 − p‖, (2.17) so (2.10) holds for n = 0 and x1 ∈ U(p, R), where we also used the following estimates in the derivativation of (2.16): −I + 3 4 F′(y0) −1F′(x0) ω1(θ‖x − p‖)dθ‖x − p‖. (2.14) keywords: analysis; argyros; ball; bounds; comparison; conditions; convergence; cubo; equation; error; example; f(x; fourth; functions; f′(x0; f′(y0; george; ioannis; iterative; jarratt; local; mathematical; method; newton; order; radius; santhosh; set; solution; u(p; ω0(t; ω0(‖x0 cache: cubo-2068.pdf plain text: cubo-2068.txt item: #378 of 481 id: cubo-2069 author: Bochi, Jairo title: The basic ergodic theorems, yet again date: 2019-03-15 words: 5997 flesch: 75 summary: Silva and Thieullen deduce their Subadditive Ergodic Theorem Since Tn+1(x) 6∈ B and Tn+2(x) ∈ B, we have RB(T k(x)) keywords: a.e; basic; birkhoff; bochi; case; cubo; ergodic; ergodic theorem; f+1; following; function; generalized; heaviness; heavy; inequality; integrable; invariant; jairo; kac; kingman; lemma; light; math; maximal; measurable; measure; n(x; points; positive; proof; result; rokhlin; sequence; set; skyscraper; subadditive; sweeping; theorem; theory cache: cubo-2069.pdf plain text: cubo-2069.txt item: #379 of 481 id: cubo-2115 author: M.I. Belishev; A.F. Vakulenko title: On algebraic and uniqueness properties of harmonic quaternion fields on 3d manifolds date: 2019-04-01 words: 6848 flesch: 79 summary: = 1 , x ∈ Ω . Main result • Let Ω be a smooth compact oriented 3-dimensional Riemannian manifold with boundary, TΩx the tangent space at x ∈ Ω, u · v and u ∧ v the inner and vector products in TΩx. keywords: a.f.vakulenko; algebra; algebraic; banach; boundary; c(ω; case; continuous; controllability; cubo; d(ω̇; dimensional; div; fields; form; functions; g(b; harmonic; inverse; jets; lemma; m.i.belishev; manifold; mathematical; mean; method; metric; multiplication; n=1; note; point; problem; proof; properties; q(ω; quaternion; real; result; riemannian; rot; set; smooth; space; subspace; theorem; time; tωx; uniqueness; use; vector; wise; ∇wf cache: cubo-2115.pdf plain text: cubo-2115.txt item: #380 of 481 id: cubo-2116 author: Bagul, Yogesh J.; Chesneau, Christophe title: Some New Simple Inequalities Involving Exponential, Trigonometric and Hyperbolic Functions date: 2019-04-01 words: 3791 flesch: 79 summary: Keywords and Phrases: Exponential function; trigonometric function; hyperbolic function. [14] Y. Lv, G. Wang and Y. Chu, A note on Jordan type inequalities for hyperbolic functions , Appl. keywords: available; bagul; bounds; chesneau; cos(x; cubo; doi; exponential; e−x; f(x; functions; h(x; hyperbolic; increasing; inequalities; inequality; lemma; lower; new; number; positive; proof; proposition; results; sharp; simple; sin(x; tanh(x; u(x; upper; volume cache: cubo-2116.pdf plain text: cubo-2116.txt item: #381 of 481 id: cubo-2117 author: Richard, S. ; Tiedra de Aldecoa, R. title: Commutator criteria for strong mixing II. More general and simpler date: 2019-04-01 words: 4064 flesch: 73 summary: + ℓ(y) for all x,y ∈ X, (L4) if K ⊂ R+ is compact, then ℓ −1(K) ⊂ X is relatively compact. = { ϕ ∈ H | ‖ℓϕ‖ < ∞ } . keywords: adjoint; aldecoa; c1(a; commutator; compact; continuous; corollary; criteria; cubo; d(a; function; groups; hausdorff; left; length; lim; limit; mixing; net; operator; proof; proper; properties; property; representation; richard; self; set; strong; strong mixing; theorem; tiedra; topological; unitary; xj}j∈j; π(h)∗; ℓ(xj cache: cubo-2117.pdf plain text: cubo-2117.txt item: #382 of 481 id: cubo-2118 author: Haq, S. ; Nisar, K.S. ; Khan, A.H. ; Suthar, D.L. title: Certain integral Transforms of the generalized Lommel-Wright function date: 2019-04-01 words: 3122 flesch: 81 summary: Also, we have the following relations of generalized Lommel Wright functions with trigonometric functions and the generalized Bessel function and Struve function: J1,11/2,0(z) = √ ( 2 πz ) sin(z) (1.9) J1,1−1/2,0(z) [20] A.K. Rathie, A new generalization of generalized hypergeometric function, Matematiche (Catania), 52(2), (1997), 297-310. keywords: certain; corollary; cubo; following; formula; fractional; function; generalized; integral; k.s; k=0; khan; lommel; nisar; transforms; wright; µ,m; γ(λ; ν+2λ cache: cubo-2118.pdf plain text: cubo-2118.txt item: #383 of 481 id: cubo-2119 author: Aissani, Khalida ; Benchohra, Mouffak ; Benkhettou, Nadia title: On Fractional Integro-differential Equations with State-Dependent Delay and Non-Instantaneous Impulses date: 2019-04-01 words: 5770 flesch: 85 summary: − P(x)(τ2)‖ ≤ ‖Q(τ1 − si) − Q(τ2 − si)‖‖hi(si,xρ(si,xsi ) ,x(si))‖ + I1 + I2 + I3. − S((τ2 − s) qσ)‖dσds]. keywords: aissani; banach; benchohra; benkhettou; case; continuous; cubo; c∗2; delay; dependent; differential; differential equations; equations; existence; fixed; fractional; function; impulses; impulsive; instantaneous; integro; khalida; let; mild; mouffak; nadia; new; non; point; r(t; s)a(s; set; solution; space; state; sup; theorem; ti+1; t∈j; xρ(τ; y(τ; α(a; ηt(s; τ)f(τ; φ)‖φ‖b;   cache: cubo-2119.pdf plain text: cubo-2119.txt item: #384 of 481 id: cubo-2120 author: Raffoul, Youssef N. ; Yankson, Ernest title: Positive periodic solutions of functional discrete systems with a parameter date: 2019-04-01 words: 3107 flesch: 83 summary: Keywords and Phrases: Functional difference system, Positive periodic solution, Eigenvalue, Population model 2010 AMS Mathematics Subject Classification: 39A10, 39A12. CUBO 21, 1 (2019) Positive periodic solutions of functional discrete systems . . keywords: 1,2; bj(s; cj(s; continuous; cubo; difference; eigenvalue; equations; functional; j=1; lemma; min; operator; periodic; positive; proof; raffoul; s=0; s=0 cj(s; solutions; system; theorem; u=0; x(n; xu)|; |fj(u; ∏ω−1; ∏ω−1 s=0 cache: cubo-2120.pdf plain text: cubo-2120.txt item: #385 of 481 id: cubo-2153 author: Anastassiou, George A. title: Caputo fractional Iyengar type Inequalities date: 2019-08-10 words: 4303 flesch: 94 summary: The right Caputo fractional derivative of order ν is defined as Dνb−f (x) = (−1) n Γ (n − ν) ∫b x (z − x) [ f(k) (a) (t − a) k+1 − f(k) (b) (t − b) k+1 ] } − γ (ν + 1) keywords: b −; f(k; k ∣; k=0; − n−1∑; ∣ f; ∣ ∣; ∣ ≤ cache: cubo-2153.pdf plain text: cubo-2153.txt item: #386 of 481 id: cubo-2154 author: Jeyanthi, P.; Jeya Daisy, K. ; Semaničová-feňovčíková, Andrea title: \(Z_k\)-magic labeling of path union of graphs date: 2019-08-10 words: 11503 flesch: 100 summary: , r − 2, f(u1r−1v 1 r−1) = k − a, f(v11u 1 2) = k − 2a, f(v1i u 1 i+1) = k − a, for i = 2, 3, . . . , r − 1 and n is even, f(uni u n i+1) =          k − (r − 1)a, for i = 1, 3, . . keywords: b b; cubo; edge; f(u j; f(v; figure; graph; integers; j+1; k −; labeling; magic; mod; n r; odd; path; positive; r −; set; u j; u n; union; v j; v n; vertex cache: cubo-2154.pdf plain text: cubo-2154.txt item: #387 of 481 id: cubo-2155 author: Siddesha, M.S. ; Bagewadi, C.S. ; Nirmala, D. title: Totally umbilical proper slant submanifolds of para-Kenmotsu manifold date: 2019-08-10 words: 2566 flesch: 76 summary: − η(Y)PX − η(Y)FX. the fact that X and PX are orthogonal vector fields on M, we arrive at cos2θ{−‖X‖2 + η2(X)}H = −g(PX, PX)ξ − η(X)P2X − η(X)FPX + P∇PXX + F∇PXX +AFXPX − ∇ ⊥ PXFX − ∇PXPX. Then applying (3.1) and (3.2), we obtain cos2θ{−‖X‖2 + η2(X)}H = cos2θ{‖X‖2 − η2(X)}ξ + cos2θη(X){X − η(X)}ξ − η(X)FPX +P∇PXX + F∇PXX + AFXPX − ∇ ⊥ PXFX − ∇PXPX. (3.4) Taking inner product with PX in (3.4), we get 0 keywords: anti; c.s; contact; cos2θ{−‖x‖2; cubo; g(x; invariant; kenmotsu; m.s; manifold; metric; para; proper; slant; slant submanifolds; structure; submanifolds; umbilical; vector; γ(tm; σ(x cache: cubo-2155.pdf plain text: cubo-2155.txt item: #388 of 481 id: cubo-2158 author: Lampret, Vito title: The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series date: 2019-08-10 words: 4529 flesch: 87 summary: π 2 0 √ 1 − ǫ2 sin2(τ) dτ = π(a + b) 4a ( 1 + ∞∑ i=1 w2i (2i − 1)2 λ2i ) ( λ = a − b a + b ) , where the series on the right converges slightly faster than the series in (3.3). − ǫ2 ( 2ǫ + (1 − ǫ2) ln ( 1 + ǫ 1 − ǫ )) > 0 keywords: appl; approximation; cubo; ellipse; estimate; flattened; formula; functions; i=1; lampret; lim; maclaurin; math; p(a; perimeter; qn(a; ratio; series; w2i; wallis; ǫ2i cache: cubo-2158.pdf plain text: cubo-2158.txt item: #389 of 481 id: cubo-2159 author: Ammar, Aymen ; Jeribi, Aref; Mahfoudhi, Kamel title: Generalized trace pseudo-spectrum of matrix pencils date: 2019-08-10 words: 3438 flesch: 87 summary: Let U, V ∈ Mn(C), then the set of all eigenvalues of the matrix pencils of the form λV Let U, V ∈ Mn(C) and 0 < ε < 1. keywords: ammar; cubo; eigenvalues; form; generalized; jeribi; mahfoudhi; matrix; mn(c; pencils; proof; pseudo; pseudospectrum; q.e.d; set; spectrum; theorem; trace; trε(u; |tr(λv; φ(ε; ϕ(ε; ∈ c cache: cubo-2159.pdf plain text: cubo-2159.txt item: #390 of 481 id: cubo-2160 author: Kumar Yadav, Sunil ; Kushwaha, Abhishek ; Narain, Dhruwa title: Certain results for η-Ricci Solitons and Yamabe Solitons on quasi-Sasakian 3-Manifolds date: 2019-08-10 words: 7340 flesch: 80 summary: Kim [22] studied quasi-Sasakian manifold and proved that fibred Rieman- nian spaces with invariant fibers normal to the structure vector field do not admit nearly Sasakian or contact structure but a Sasakian or cosymplectic structure. [7], proved that there are no quasi-Sasakian structure of even rank, some theorems regarding Kaehlerian manifolds and existence of quasi-Sasakian manifold. keywords: abhishek; certain; condition; constant; contact; corollary; cosymplectic; cubo; curvature; cyclic; dhruwa; dimensional; equation; field; flow; following; g(u; g(v; kushwaha2; manifold; math; non; notion; parallel; proper; pseudo; quasi; results; ricci; ricci soliton; ricci tensor; riemannian; sasakian; sasakian manifold; scalar; section; soliton; special; structure; symmetric; tensor; theorem; type; v)ζ; vector; yadav1; yamabe; χ(m; −β2 cache: cubo-2160.pdf plain text: cubo-2160.txt item: #391 of 481 id: cubo-2216 author: Sudo, Takahiro title: The K-theory ranks for crossed products of C*-algebras by the group of integers date: 2020-01-08 words: 2893 flesch: 82 summary: the torsion rank of G, which is defined to be the number of direct sum components of indecomposable, finite cyclic groups in G. Set tj(A) = t(Kj(A)) for j = 0, 1, each of which we may call the j-th torsion rank of A. Recall as a fundament fact in group theory that a finitely generated abelian group H has the following direct product decomposition: H ∼= Z b(H) × For instance, there is a quotient map from G = Z to Z2 = Z/2Z, with H = 2Z, so that t(H) = t(G) keywords: abelian; b(g; b1(a; bj(a; crossed; cubo; c∗-algebras; direct; discrete; exact; free; group; map; nilpotent; product; ranks; semi; successive; sudo; t(g; theory; torsion; voiculescu; ⋊α(1 cache: cubo-2216.pdf plain text: cubo-2216.txt item: #392 of 481 id: cubo-2217 author: Hodges, Wilfrid; Shelah, Saharon title: Naturality and definability II date: 2020-01-08 words: 6682 flesch: 77 summary: ∈ P such that for all i ∈ S, pi i, every map α j f,g : λ++ → Aut(A) is constant on [i,λ++); (c) for all i,j ∈ S, ti = tj; (d) there is a condition p⋆ keywords: algebraic; aut(a; aut(b; automorphism; class; construction; cubo; definability; definable; definition; domain; elements; example; formula; generic; graph; group; hodges; homomorphism; isomorphism; lemma; map; model; natural; naturality; neat; parameters; proof; rigid; saharon; section; set; shelah; small; splitting; structure; theorem; theory; transitive; uniformisable; unitype; weakly; wilfrid; zfc; λ++)3 cache: cubo-2217.pdf plain text: cubo-2217.txt item: #393 of 481 id: cubo-2218 author: Anastassiou, George A. title: Ostrowski-Sugeno fuzzy inequalities date: 2020-01-10 words: 3266 flesch: 92 summary: We notice that f (t) = f (t) − f (x) + f (x) ≤ |f (t) − f (x)| + f (x) , then (by Theorem 2.3 (3) and Theorem 2.4 (4)) (S) ∫ keywords: fdµ; fuzzy; measure; ostrowski; sugeno; theorem; ∣ ∣; ∣ ≤ cache: cubo-2218.pdf plain text: cubo-2218.txt item: #394 of 481 id: cubo-2219 author: Raffoul, Youssef N title: Stability and boundedness in nonlinear and neutral difference equations using new variation of parameters formula and fixed point theory date: 2020-01-20 words: 7514 flesch: 89 summary: − c(t0 − 1)x(t0 − g(t0)) ] t−1 ∏ s=t0 v(s) + − g(y)| = |x − x3 − keywords: a(r; a(s; boundedness; condition; contraction; cubo; difference; equations; function; large; mapping; new; nonlinear; parameters; point; proof; r+1; raffoul; set; solution; stability; stable; t ∏; t0 v(s; t1−1; theorem; t−t; unique; v(r; v(s; v(t; variation; v−1(s; x(t; youssef; ∣ +; ∣ t−1; ∣ ∣; ∣ ≤ cache: cubo-2219.pdf plain text: cubo-2219.txt item: #395 of 481 id: cubo-2220 author: Majhi, Pradip; Kar, Debabrata title: Beta-almost Ricci solitons on Sasakian 3-manifolds date: 2020-01-20 words: 3429 flesch: 77 summary: Más aún, probamos que este tipo de variedades son isométricas a una esfera de radio √ 7. Keywords and Phrases: Ricci soliton, β-almost Ricci soliton, Sasakian 3-manifolds, Einstein. 2010 AMS Mathematics Subject Classification: 53C15, 53C25. We recall the notion of Ricci soliton according to [5]. keywords: constant; contact; contact vector; cubo; curvature; einstein; equation; field; manifolds; math; metric; non; potential; ricci; ricci soliton; sasakian; soliton; structure; tensor; theorem; trivial; vector; vector field cache: cubo-2220.pdf plain text: cubo-2220.txt item: #396 of 481 id: cubo-2221 author: Sanou, Rodrigue; Ibrango, Idrissa; Koné, Blaise; Guiro, Aboudramane title: Weak solutions to Neumann discrete nonlinear system of Kirchhoff type date: 2020-01-20 words: 4581 flesch: 85 summary: [ min 1≤i≤n (ηi) ( n∑ i=1 T+1∑ k=1 |∆ui(k − 1)| p(k−1) )α − max 1≤i≤n (νi) ] − β n∑ i=1 T∑ k=1 |ui(k)| ri(k) − βnT ≥ − B1 α(p+)α max 1≤i≤n (νi) − β n∑ i=1 T∑ k=1 |ui(k)| ri(k) − βnT ≥ − B1 α(p+)α max 1≤i≤n (νi) − β n∑ i=1 T∑ k=1 |ui(k)| r− − β n∑ i=1 T∑ k=1 |ui(k)| r+ − βnT. Using (2.16) J(u) ≥ − B1 α(p+)α max 1≤i≤n (νi) − δ0β n∑ i=1 T∑ k=1 |ui(k)| ri(k) − δ0βnT. keywords: 1)|; a(k −; cubo; discrete; existence; following; functional; i(u; i=1; j(u; k=1; k=1 a(k; kirchhoff; max; min; neumann; nonlinear; n∑ i=1; positive; problem; solutions; system; t+1∑ k=1; t∑ k=1; u(k; weak; z[0; α(p+)α; ∆ui(k −; − βnt; ≥ − cache: cubo-2221.pdf plain text: cubo-2221.txt item: #397 of 481 id: cubo-2222 author: Das, B. C.; De, Soumen; Mandal, B. N. title: Wave propagation through a gap in a thin vertical wall in deep water date: 2020-01-20 words: 4389 flesch: 64 summary: − 1 2 ) as y → a + 0, O ( (b − y) − 1 2 ) as y → b − 0, (2.1a) and CUBO 21, 3 (2019) Wave propagation through a gap in a thin vertical wall in deep water 97 g(y) =    O ( (a − y) 1 2 ) as y → a − 0, O ( (y − b) 1 2 ) as y → b + 0. (2.1b) keywords: bounds; coefficients; cubo; das; deep; different; equations; figure; galerkin; gap; incidence; increases; integral; mandal; method; normal; numerical; present; problem; reflection; results; scattering; submerged; surface; term; thin; transmission; upper; values; vertical; wall; water; wave; wavenumber; |r| cache: cubo-2222.pdf plain text: cubo-2222.txt item: #398 of 481 id: cubo-2253 author: Dragomir, Silvestru Sever title: Bounds for the generalized \( (\Phi;f) \)-mean difference date: 2020-04-17 words: 7443 flesch: 90 summary: If Φ = e, where e (t) = t, t ∈ R is the identity mapping, then we can consider the particular cases of interest, the generalized f-mean difference RG (f; w) := RG (e, f; w) = 1 2 ∫ Ω ∫ Ω w (x) w (y) |f (x) − f (y)| dν (x) dν (y) (1.3) and the generalized f-mean deviation MD (f; w) := MD (e, f; w) = ∫ Ω w (x) |f (x) − E (f; w)| dν (x) , (1.4) where E (f; w) := ∫ Ω f (y) w (y) dν (y) is the generalized f-expectation. (y)| ≤    ‖Φ′‖ [a,b],∞ |f (x) − f (y)| if p = ∞, ‖Φ′‖[a,b],p |f (x) − f (y)| 1/q if p > 1, 1 p + 1 q = 1 (3.9) for any x, y ∈ Ω. keywords: a)|; b],p; bounds; convex; cubo; difference; dragomir; f)-mean; function; generalized; gini; inequality; integral; math; mean; measurable; − ∫; ∣ ∣; ∣ ≤ cache: cubo-2253.pdf plain text: cubo-2253.txt item: #399 of 481 id: cubo-2254 author: Pahan, Sampa title: \( \eta \)-Ricci Solitons on 3-dimensional Trans-Sasakian Manifolds date: 2020-04-17 words: 4293 flesch: 81 summary: [ r 2 − (α2 − β2 − ξβ)]g(X, Y) − [ r 2 − 3(α2 − β2) + ξβ]η(X)η(Y) = (α2 − β2)(η(X)ξ − X), (2.10) S(X, ξ) = 2(α2 − β2)η(X), (2.11) R(ξ, X)Y = (α2 − β2)(g(X, Y)ξ keywords: 2(β2; condition; constants; cubo; dimensional; dimensional trans; einstein; equation; field; g(x; manifold; metric; pahan; ricci; ricci soliton; s(x; s(ξ; sasakian; sasakian manifold; satisfying; solitons; symmetric; tensor; theorem; trans; vector; z)ξ cache: cubo-2254.pdf plain text: cubo-2254.txt item: #400 of 481 id: cubo-2255 author: Hidalgo, Rubén A. title: A sufficiently complicated noded Schottky group of rank three date: 2020-04-17 words: 6544 flesch: 74 summary: J. 42 (1975), 717–724. Introduction Sufficiently complicated Noded Schottky groups Noded Schottky groups The extended region of discontinuity Neoclassical noded Schottky groups Sufficiently complicated noded Schottky groups The relative conical neighbourhood of a noded Schottky group Pinchable loops of Schottky groups Sufficiently complicated noded Schottky groups Explicit construction of a sufficiently complicated noded Schottky group A family Schottky groups of rank three A sufficiently complicated noded Schottky groups of rank three Non-classical Schottky groups of rank three The idea is to consider certain Kleinian groups, obtained as geometrically finite algebraic limits of Schottky groups of rank g, called sufficiently complicated noded Schottky groups of rank g (see Section 2). keywords: boundary; classical; classical schottky; complicated; corresponding; cubo; discontinuity; disjoint; elements; figure; fixed; fundamental; generators; genus; geodesics; geometrical; group; hidalgo; intersection; kleinian; loops; maskit; math; maximal; noded; noded schottky; non; parabolic; pinchable; point; rank; rank g; region; riemann; schottky; schottky group; set; simple; stable; surface; theorem; transformations cache: cubo-2255.pdf plain text: cubo-2255.txt item: #401 of 481 id: cubo-2256 author: Nisha, Shwet ; Parida, P. K. title: Super-Halley method under majorant conditions in Banach spaces date: 2020-04-18 words: 5328 flesch: 80 summary: − xk+1‖ ≤ − 1 (1 − Lφ(tk))φ ′(tk) − γ‖x − x̄‖)3 − 2γ (1 − γ‖x − x̄‖)3 , γ > 0 keywords: analysis; appl; assumptions; banach; conditions; convergence; converges; cubo; following; follows; function; halley; halley method; initial; kantorovich; lemma; local; lφ(t; majorant; math; method; newton; order; point; results; satisfies; sequence; smale; solution; spaces; super; theorem; tk+1; type; xk+1‖; φ(t; ‖x̄ cache: cubo-2256.pdf plain text: cubo-2256.txt item: #402 of 481 id: cubo-2257 author: Divyashree, G.; Venkatesha title: Certain results on the conharmonic curvature tensor of \( (\kappa,\mu) \)-contact metric manifolds date: 2020-04-18 words: 3987 flesch: 79 summary: − g(Y, Z)η(X)]}ξ +κ{g(Y, φZ)φhX − g(X, φZ)φhY + g(Z, φhY)φX −g(Z, φhX)φY + η(Z)[η(X)hY − η(Y)hX]} −µ{η(Y)[(1 − − η(Z){(1 − κ)[η(X)g(φY, T) − η(Y)g(φX, T)] +(1 − µ)[η(X)g(φhY, T) − η(Y)g(φhX, T)]} − 1 2n − 1 [S(Y, φZ)g(X, T) −S(X, φZ)g(Y, T) + g(Y, φZ)g(QX, T) − g(X, φZ)g(QY, T) − S(Y, Z)g(φX, T) +S(X, Z)g(φY, T) − g(Y, Z)g(QφX, T) + g(X, Z)g(QφY, T)] keywords: conharmonic; contact; cubo; curvature; einstein; flat; following; g(x; g(y; m2n+1; manifold; metric; metric manifold; n(2κ; n(x; non; r(x; riemannian; s(x; sasakian; semisymmetric; tensor; theorem; y)z; z)g(w; z)x; z)η(x; φx)ξ cache: cubo-2257.pdf plain text: cubo-2257.txt item: #403 of 481 id: cubo-2258 author: Ouaro, Stanislas; Sawadogo, Noufou title: Nonlinear elliptic \(p(u)-\) Laplacian problem with Fourier boundary condition date: 2020-04-18 words: 12687 flesch: 88 summary: Moreover, a satisfies: for all bounded subset K of R × RN, there exists a constant C(K) such that a.e. x ∈ Ω, for all (z, η), (z̃, η) ∈ K, |a(x, z, η) − a(x, z̃, η)| ≤ C(K)|z − z̃|. Ω → [p−, p+] has a representative which can be extended into a continuous function up to the boundary ∂Ω and satisfying the log-Hölder continuity assumption: ∃L > 0, ∀x, y ∈ Ω, x 6= y, − ( log |x − y| ) |π(x) − π(y)| ≤ L. (2.1) i) keywords: + ∫; = ∫; a(u; a(x; a.e; b(u)tk(u; boundary; continuous; convergence; converges; cubo; elliptic; entropy; equi; existence; exponent; following; fourier; function; hand; inequality; inf; integrable; laplacian; lebesgue; lemma; lim; lπ(.)(ω; meas(ω; measurable; measure; nonlinear; noufou; n→+∞; ouaro; p(u)−; problem; proof; proposition; results; right; sawadogo; sequence; solution; space; stanislas; term; th(v))dx; theorem; tk(u; type; u(x; un(x; uniqueness; v)dx; variable; weak; weakly; young; ||f||l1(ω; π(x; ϕ)dx; ϕ)dσ; − ϕ; − ∫; ∣ ∣; ∣ ∫; ∫ ω×rn; ≤ ∫;   cache: cubo-2258.pdf plain text: cubo-2258.txt item: #404 of 481 id: cubo-2259 author: Boucenna, Djalal; Ben Makhlouf, Abdellatif; Hammami, Mohamed Ali title: On Katugampola fractional order derivatives and Darboux problem for differential equations date: 2020-04-18 words: 4492 flesch: 84 summary: = x1−ρ1y1−ρ2ρ α1 1 ρ α2 2 Γ (1 − α1) Γ (1 − α2) D 2 x,y ∫ x a + 1 ∫ y a + 2 sρ1−1tρ2−1 (xρ1 − sρ1) α1 (yρ2 − tρ2) α2 ×u (s,t)dtds. x a + 1 ∫ y a + 2 sρ1−1tρ2−1 (xρ1 − sρ1) 1−α1 (yρ2 − tρ2) 1−α2 dtds ≤ M Γ (α1 + 1) Γ (α2 + 1) ( xρ1 − a ρ1 1 ρ1 )α1 ( yρ2 − a ρ2 2 ρ2 )α2 ≤ M ρ α1 1 ρ α2 2 Γ (α1 + 1) Γ (α2 + 1) h ρ1α1 1 h ρ2α2 2 ≤ M ρ α1 1 ρ α2 2 Γ (α1 + 1) Γ (α2 + 1) h α1 1 h α2 2 ≤ M ρ α1 1 ρ α2 2 Γ (α1 + 1) Γ (α2 + 1) kρ α1 1 ρ α2 2 Γ (α1 + 1) Γ (α2 + 1) M ≤ k. 132 Djalal Boucenna, Abdellatif Ben Makhlouf & Mohamed Ali Hammami CUBO 22, 1 (2020) keywords: a1,a2; caputo; cubo; darboux; derivative; differential; dtds; equations; existence; fractional; function; katugampola; order; problem; solutions; sρ1−1tρ2−1; theorem; uniqueness; xρ1; yρ2 cache: cubo-2259.pdf plain text: cubo-2259.txt item: #405 of 481 id: cubo-2260 author: Barro, Moussa; Traoré, Sado title: Level sets regularization with application to optimization problems date: 2020-04-18 words: 5966 flesch: 81 summary: Let U = V = R, c the standard product of R. The indicator function of R∗,i R ∗ is (c,P3)−level regular but not quasi-convex. There exists s ∈ R such that h〈〉c,P(a) > keywords: application; a〉c,1; c(a; c(u; closed; conjugacy; convex; coupling; cubo; definition; duality; epv; example; extended; follows; function; h(u; hull; inf; level; max; optimization; p v; p)−level; proof; proposition; real; regularization; set; sets; space; subset; sup; theorem; topological cache: cubo-2260.pdf plain text: cubo-2260.txt item: #406 of 481 id: cubo-2360 author: Sow, T.M.M. title: A new iterative method based on the modified proximal-point algorithm for finding a common null point of an infinite family of accretive operators in Banach spaces date: 2020-08-22 words: 7968 flesch: 85 summary: − ηAp‖‖xn − p‖ Thus, for every k ∈ N∗, we get (1 − ταn) 2βn,0βn, ‖x − y‖q − qtη〈Ax − keywords: accretive; algorithm; banach; closed; constant; continuous; convex; cubo; dql; duality; equilibrium; family; following; hilbert; inequality; inf; infinite; iterative; j(x∗; lemma; lim; lipschitzian; mapping; method; monotone; new; nonempty; nonexpansive; n→∞; operators; point; problems; proximal; qηq−1; real; sequence; smooth; solution; sow; space; subset; theorem; variational; γf(x∗; ηax∗; ηαna)yn cache: cubo-2360.pdf plain text: cubo-2360.txt item: #407 of 481 id: cubo-2362 author: Arora, Ruchi; Kumar, Dharmendra; Jhamb, Ishita; Kaur Narang, Avina title: Mathematical Modeling of Chikungunya Dynamics: Stability and Simulation date: 2020-08-22 words: 7775 flesch: 68 summary: UE = (U1,U2,U3,U4,U5,U6,U7,U8) T where U1 = ( −βBHZ ∗∗ NH + βBHZ ∗∗ S ∗∗ (NH)2 − ζ, βBHZ ∗∗ S ∗∗ (NH)2 , βBHZ ∗∗ S ∗∗ (NH)2 , βBHZ ∗∗ S ∗∗ (NH)2 , βBH Z ∗∗ S ∗∗ (NH)2 ,0,0, −βBHS ∗∗ NH ) , U2 = ( 0, −βBHZ ∗∗ S ∗∗ (NH)2 − α − ζ, −βBHZ ∗∗ S ∗∗ (NH)2 , −βBHZ ∗∗ S ∗∗ (NH)2 , −βBHZ ∗∗ S ∗∗ (NH)2 ,0,0, βBHS ∗∗ NH ) , U3 = (0,0,−γ − ζ − ζ1,0,0,0,0,0), U4 = (0,0,0,−λ − ζ − ζ2,0,0,0,0) , U5 = (0,0,0,0,−ζ,0,0,0), U6 = ( 0,0,0,0,0,− νBM(I ∗∗+R ′ ∗∗) NH − κ,0,0 ) , U7 = (0,0,0,0,0,0,−κ − ψ,0) , U8 = (0,0,0,0,0,0,0,−κ) α −γ − ζ − ζ1 0 0 0 0 keywords: 0,0; aedes; arora; avina; change; chikungunya; control; cubo; death; dfe; dharmendra; disease; dynamics; endemic; epidemic; equilibrium; existence; fig; figure; free; human; human population; infected; infection; ishita; jhamb; journal; kaur; kumar; lim; mathematical; matrix; model; modeling; mosquito; nh(t; nh)2; number; period; phase; population; rate; recovered; recovery; recuperation; reproduction; ruchi; section; stability; stable; susceptible; symptoms; time; total; transmission; t→∞; virus; βbhz; ζnh; νbm; ∗∗+r;   cache: cubo-2362.pdf plain text: cubo-2362.txt item: #408 of 481 id: cubo-2363 author: Seshagiri Rao, N.; Kalyani, K.; Khatri, Kejal title: Contractive mapping theorems in Partially ordered metric spaces date: 2020-08-22 words: 4986 flesch: 82 summary: Suppose that the self- mappings f and T on X are continuous, T is a monotone f-nondecreasing, T (X) ⊆ f(X) and satisfying the following condition d(T x, T y) ≤ α d(fx, T x) d(fy, T y) d(fx, fy) Suppose that the self- mappings f and T on X are continuous, T is a monotone f-nondecreasing, T (X) ⊆ f(X) and satisfying the following condition d(T x, T y) ≤ α d(fx, T x) d(fy, T y) d(fx, fy) keywords: coincidence; common; compatible; complete; condition; contraction; d(fx; d(fy; d(t; d(t x; f(x; f(x0; fixed; mappings; math; metric; monotone; nondecreasing; point; results; self; sequence; set; spaces; t x; t xn; t y; theorem cache: cubo-2363.pdf plain text: cubo-2363.txt item: #409 of 481 id: cubo-2364 author: Kamal, A.; Yassen, T.I. title: D-metric Spaces and Composition Operators Between Hyperbolic Weighted Family of Function Spaces date: 2020-08-22 words: 5627 flesch: 87 summary: − |z|2)αp−2(1 − |ϕa(z)| 2)sdA(z) = sup a∈D ℓp(a) ∫ D (f∗(φ(z)))p|φ′(z)|αp−2(1 − |ϕa(z)| 2)sdA(z) ≤ ||f|| p B∗ α, log sup a∈D ℓp(a) ∫ D |φ′(z)|p(1 − |z|2)αp−2(1 − |ϕa(z)| 2)s (1 − |φ(z)2|)pα(log 2 1−|z|2 ) dA(z) = ||f|| p B∗ α, log Φφ(α, p, s; a) < − |z|2)αp−2(1 − |ϕa(z)| 2)sdA(z) keywords: a∈d; b∗α; compact; complete; composition; cubo; definition; following; function; f∗(z))p(1; kamal; log; log(p; metric; operators; space; sup; z∈d; |a|2; |z|2)αp−2(1; |ϕa(z)|; ℓp(a cache: cubo-2364.pdf plain text: cubo-2364.txt item: #410 of 481 id: cubo-2365 author: Govindan, Vediyappan; Park, Choonkil; Pinelas, Sandra; Rassias, Themistocles M. title: Hyers-Ulam stability of an additive-quadratic functional equation date: 2020-08-22 words: 7904 flesch: 87 summary: x2 ∈ X. Letting x2 = 0 in (2.9), we have 2g(ax1) − cx3 − bx2) + 4g(bx2) (3.9) for x1, x2, x3 ∈ X. keywords: a(x)‖; additive; bx2; case; cubo; cx3; equation; fixed; functional; g(ax1; g(x; hyers; mapping; math; method; point; proof; q(x)‖; quadratic; rassias; replacing; satisfies; stability; theorem; ulam; unique; x3 ∈; β(x; ∥ ∥;   cache: cubo-2365.pdf plain text: cubo-2365.txt item: #411 of 481 id: cubo-2366 author: S.V., Vishnuvardhana; Venkatesha title: Results on para-Sasakian manifold admitting a quarter symmetric metric connection date: 2020-08-23 words: 5077 flesch: 78 summary: With the help of linearity property of φ and g, we have η(E1) = 1, φ2V = V − η(V )E1, g(φX, φY ) = g(X, Y ) From the above expressions and the relation of quarter symmetric metric connection and Riemannian connection, one can easily obtain the following:           ∇̃E1E1 ∇̃E1E2 ∇̃E1E3 ∇̃E1E4 ∇̃E1E5 ∇̃E2E1 ∇̃E2E2 ∇̃E2E3 ∇̃E2E4 ∇̃E2E5 ∇̃E3E1 ∇̃E3E2 ∇̃E3E3 ∇̃E3E4 ∇̃E3E5 ∇̃E4E1 ∇̃E4E2 ∇̃E4E3 ∇̃E4E4 keywords: connection; cubo; curvature; dimensional; e3)e3; e5)e5; field; manifold; metric connection; para; projectively; pseudosymmetric; quarter; r(e1; r(e2; respect; results; ricci; riemannian; r̃(x; sasakian; sasakian manifold; symmetric; symmetric metric; tensor; theorem;   cache: cubo-2366.pdf plain text: cubo-2366.txt item: #412 of 481 id: cubo-2367 author: Saluja, G. S. title: Fixed point theorems on cone \(S\)-metric spaces using implicit relation date: 2020-08-23 words: 5633 flesch: 87 summary: [8] L.-G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive map- pings, J. Math. ≤ d(x,y) for all x,y ∈ X with x 6= y and d(x,y) = 0 ⇔ x = y; (CM2) d(x,y) = d(y,x) for all x,y ∈ X; (CM3) d(x,y) ≤ keywords: complete; condition; cone; cone metric; cone s; constant; continuous; contractive; corollary; cubo; example; following; implicit; lemma; mappings; math; metric; metric spaces; normal; point; relation; results; s(x; s(xn; satisfies; sedghi; sequence; spaces; theorems; tyn; xn+1; z,0; φ(x cache: cubo-2367.pdf plain text: cubo-2367.txt item: #413 of 481 id: cubo-2464 author: Sabet, M.; Sanati, R. G. title: Topological algebras with subadditive boundedness radius date: 2020-12-07 words: 3431 flesch: 75 summary: whenver x, y ∈ A, The boundedness radius β is said to be subadditive, if for each x, y ∈ A, β(x + y) ≤ β(x) + β(y). keywords: algebra; banach; boundedness; commutative; complete; continuous; convex; cubo; lemma; norm; proof; radius; satisfies; sequential; subadditive; submultiplicative; theorem; topological; topological algebra; topology; vol; |α|; β(x cache: cubo-2464.pdf plain text: cubo-2464.txt item: #414 of 481 id: cubo-2466 author: Jeyanthi, P.; Philo, S. title: Odd Harmonious Labeling of Some Classes of Graphs date: 2020-12-07 words: 7418 flesch: 96 summary: mi − j, if i is odd and j is even, 308 P. Jeyanthi and S. Philo CUBO 22, 3 (2020) f(u j i ) =    mi − j − 2 and i is odd, f(vi,j) = 2(3m − j − 1) keywords: 2(2; 2mi −; edge; f(u; figure; graph; harmonious; induced; jeyanthi; labeling; mi −; n −; odd; philo; q q; r r; tree; vertices; vol; − j cache: cubo-2466.pdf plain text: cubo-2466.txt item: #415 of 481 id: cubo-2467 author: Abdul Khayyoom, M. Mohammed title: Characterization of Upper Detour Monophonic Domination Number date: 2020-12-07 words: 4169 flesch: 79 summary: If M is a minimal DMD set of G, then each component of G − v have an element of M. Proof. That is, each component of G − v have an element of every minimal DMD set. keywords: cardinality; connected; detour; detour monophonic; dmd; dominating; extreme; graph; minimal; minimum; monophonic; monophonic set; number; path; proof; set; sets; upper; vertex; vertices; γdm(g cache: cubo-2467.pdf plain text: cubo-2467.txt item: #416 of 481 id: cubo-2468 author: Dhage, Bapurao C. title: Existence and Attractivity Theorems for Nonlinear Hybrid Fractional Integrodifferential Equations with Anticipation and Retardation date: 2020-12-07 words: 9834 flesch: 81 summary: ∣ ∣ − m ∑ j=1 Iαj hj(t,x(t),x(η(t))) ∣ ∣ ∣ ∣ ≤ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ f(t,x(t),x(θ(t))) ∣ ∣ ∣ ( ∣ ∣ ∣ a(t0)x0 f(t0,x0,x0) ∣ ∣ ∣ − a(t0)x0 f(t0,x0,x0) ) a(t) ∣ ∣ ∣ ∣ ∣ + ∣ ∣ ∣ f(t,x(t),x(θ(t))) ∣ ∣ ∣ × × ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ a(t) ∣ ∣ − hj(t,x(t),x(η(t))) ∣ ∣ ∣ ≤ [ 4(L + F) ∣ ∣ ∣ a(t0)x0 f(t0,x0,x0) ∣ ∣ ∣ ] a(t) keywords: attractive; attractivity; bapurao; bc(j∞,r; br(0; caputo; continuous; cubo; definition; dhage; differential; equation; existence; f(t0,x0,x0; following; fractional; function; global; hfrigde; hybrid; iαj ∣; j=1; lim; mgw; mild; nonlinear; operator; point; real; results; s)q−1; solutions; sup; t t0; t0 ∣; theorem; t∈j∞; unbounded; vol; w(t; x(t; × ∣; γ(αj; ∣ =; ∣ a(t0)x0; ∣ ds; ∣ f(t; ∣ ×; ∣ ‖a‖; ∣ −; ∣ ∣; ∣ ∣f(s; ∣ ∣hj(t; ∣ ∫; ∣ ≤; ≤ ∣;   cache: cubo-2468.pdf plain text: cubo-2468.txt item: #417 of 481 id: cubo-2469 author: Oli, Abdi; Tilahun, Kelelaw; Reddy, G. V. title: The Multivariable Aleph-function involving the Generalized Mellin-Barnes Contour Integrals date: 2020-12-07 words: 2948 flesch: 85 summary: Keywords and Phrases: Hypergeometric function, Multivariable Aleph function. [1]. (3) Also, multivariable Aleph function reduces to multivariable H-function with some suitable parameters;we get the known result due to Daiya et al. keywords: 4αβ; aleph; function; generalized; i(1; i(r; j=1; k=1; multivariable; vol; ∣ ∣ cache: cubo-2469.pdf plain text: cubo-2469.txt item: #418 of 481 id: cubo-2470 author: Aouane, Abdeldjalil; Djebali, Smaïl ; Taoudi, Mohamed Aziz title: Mild solutions of a class of semilinear fractional integro-differential equations subjected to noncompact nonlocal initial conditions date: 2020-12-07 words: 5617 flesch: 81 summary: t ∈ t ∈ keywords: 1,2; abdeldjalil; aouane; aziz; banach; br0; c([0,a];e; class; conditions; continuous; cosine; cubo; cβ(t; definition; differential; djebali; equations; existence; f(t; family; fixed; following; fractional; function; i=1; lemma; lim; maa; makq; measure; mild; mohamed; n=1; noncompactness; nonlocal; operator; order; p(u; point; problem; results; semilinear; smäıl; solutions; space; subset; sup; taoudi; theorem; vol; β t; β−1; γ(β; ω(r;   cache: cubo-2470.pdf plain text: cubo-2470.txt item: #419 of 481 id: cubo-2471 author: Ballico, Edoardo title: Curves in low dimensional projective spaces with the lowest ranks date: 2020-12-07 words: 8386 flesch: 89 summary: Then there is C ∈ |h + f| such that q ∈ 〈C〉. Proof. Take C ∈ |h + f| such that q ∈ 〈C〉. keywords: 1)|; assume; component; connected; cubo; curve; degree; dim; dimensional; general; integer; integral; irreducible; lemma; line; nodal; nodes; non; plane; points; positive; projective; proof; remark; scheme; set; singular; smooth; sufficient; tangent; theorem; |oq(1; |oq(a cache: cubo-2471.pdf plain text: cubo-2471.txt item: #420 of 481 id: cubo-2474 author: Weber, Brian title: Toric, \(U(2)\), and LeBrun metrics date: 2020-12-08 words: 5958 flesch: 77 summary: (3.9) A LeBrun ansatz expression of g is obtained by setting u = log detUij = log ( U11U22 − (U12)2 ) , w = 1 U11 , and A = Aydy = U12 U11 dy (3.10) (the components Ax and Az are zero). Toric, U(2), and LeBrun metrics 409 References [1] M. Abreu, “Kähler geometry of toric varieties and extremal metrics”, International Journal of Mathematics, vol. 9, pp. keywords: ansatz; brian; compact; complex; condition; construction; coordinates; corresponding; cubo; curvature; differential; dy2; einstein; equations; exceptional; extremal; field; flat; form; functions; geometry; half; holomorphic; invariant; kähler; killing; lebrun; lebrun ansatz; manifolds; metric; page; potential; proof; proposition; scalar; structure; symmetry; symplectic; toric; u(2; variable; vol; weber; weu; −1dy cache: cubo-2474.pdf plain text: cubo-2474.txt item: #421 of 481 id: cubo-2594 author: Souza, Luciano; de O. Júnior, Wilson Rosa; de Brito, Cícero Carlos R.; Chesneau, Christophe; Fernandes, Renan L.; Ferreira, Tiago A. E. title: Tan-G class of trigonometric distributions and its applications date: 2021-04-13 words: 6753 flesch: 71 summary: The Shannon entropy, pioneered by [15], is given by SG = − ∫ With similar arguments, if x∗∗ denotes a critical point for RG(x), then it satisfies the following equation: {ln[RG(x)]} ′ |x=x∗∗ = 0, i.e.,[ g(x)′ |x=x∗∗ + π 2 g(x∗∗) 2 tan (π 4 G(x∗∗) )] keywords: = +; applications; brito; bxii; cdf; chesneau; class; cubo; data; distribution; entropy; expansion; ferreira; figure; function; g class; g(x; general; hg(x; i=1; k=1; kum; likelihood; maximum; mles; model; moments; new; order; parameters; plots; probability; proof; r=0; s s; sample; sizes; souza; statistical; table; tan; theorem; trigonometric; vol; κ =; κ(j cache: cubo-2594.pdf plain text: cubo-2594.txt item: #422 of 481 id: cubo-2596 author: Kaboré, A.; Ouaro, S. title: Anisotropic problem with non-local boundary conditions and measure data date: 2021-04-13 words: 14428 flesch: 90 summary: D (Ω̃) and∫ Ω̃ N∑ i=1 ãi(x, ∂ ∂xi u�) ∂ ∂xi ξ̃dx + ∫ Ω |u�|pM (x)−2u�ξ̃dx = ∫ Ω f�ξ̃dx + ∫ Ω F.∇ξ̃ + ∫ Γ̃Ne (d̃� − ρ̃(u�))ξ̃dσ, (3.3) for any ξ̃ ∈ W 1,~p(.)D (Ω̃) ∩L ∞(Ω). Assume (1.4)-(1.8) hold and u� be a weak solution of the problem P(ρ,µ̃�, d̃�). keywords: 1,~p; = ∂; = ∫; a.e; ai(x; anisotropic; b(u; boundary; conditions; constant; continuous; convergence; converges; cubo; data; elliptic; entropy; equations; existence; exponent; fluids; following; function; hand; i=1; inequality; inf; kaboré; l1(ω; lebesgue; lemma; lim; local; lp(.)(ω; l∞(ω; math; mdx; measurable; measure; need; nmeas(ω̃; non; nonlinear; norm; n∑ i=1; operator; ouaro; p(ρ,µ,d; problem; proof; proposition; set; sobolev; solution; spaces; study; theorem; tk(b(u; tk(u; type; uniqueness; variable; vol; x)−2u; |µ|(ω; |∇u|p; γ̃ne; ρ̃(u; ω̃\ω; ‖d̃‖l1(γ̃ne; ∂xi; ∂xi u; ∂xi v; ∂∂xitk(u �; ∂∂xiu; ∈{1; −ϕn; ∣∣∣∣; ∣∣∣∣pi(x; ∣∣∣∣∣; ; ; � =; � ‖∞; � − cache: cubo-2596.pdf plain text: cubo-2596.txt item: #423 of 481 id: cubo-2598 author: Békollè, David; Ezzinbi, Khalil; Fatajou, Samir; Danga, Duplex Elvis Houpa; Béssémè, Fritz Mbounja title: Convolutions in \((\mu,\nu)\)-pseudo-almost periodic and \((\mu,\nu)\)-pseudo-almost automorphic function spaces and applications to solve integral equations date: 2021-04-14 words: 7879 flesch: 84 summary: KF < δ 2N such that ‖F(t,u) −F(t,v)‖≤ KF‖u−v‖, for all u,v ∈ X and t ∈ R, then the equation (1.1) has a unique bounded mild solution u : R 7−→ X given by u(t) = ∫ R Γ(t,s)F(s,u(s))ds, t ∈ R, CUBO 23, 1 (2021) Convolutions in (µ,ν)-PAP and (µ,ν)-PAA Functions 79 where the operator family Γ(t,s), called Green’s function corresponding to U and P(·), is given by Γ(t,s) = U(t,s)P(s), ∀t,s ∈ R, with t (H5): We propose F : R×X 7−→ X belongs to PAP(R×X,X,µ,ν) and there exists KF > 0 such that ‖F(t,u) −F(t,v)‖≤ KF‖u−v‖, for all u,v ∈ X and t ∈ R. keywords: automorphic; banach; bc(r; békollè; continuous; convolution; cubo; d.e; danga; definition; denote; e(r; equation; evolution; existence; ezzinbi; f(t; fatajou; following; functions; hold; houpa; invariance; k(t−s; lemma; lim; mbounja; measure; mild; pap(r; periodic; proof; pseudo; r −r; respect; results; solutions; space; sup; theorem; u(t; unique; x,µ,ν; µ([−r; ν([−r; ∣∣∣∣ cache: cubo-2598.pdf plain text: cubo-2598.txt item: #424 of 481 id: cubo-2600 author: Blaga, Adara M.; Bakshi, Manoj Ray; Baishya, Kanak Kanti title: Hyper generalized pseudo \(Q\)-symmetric semi-Riemannian manifolds date: 2021-04-14 words: 2773 flesch: 84 summary: Now putting U = % in (4.2) and using (4.3) and (4.4) we get T1(%)S(Y,V ) + T2(%)g(Y,V ) = T1(Y ) (2.4) 3 Some curvature properties of (HGPQS)n manifolds In this section we prove that in a (HGPQS)n manifold, the Q-curvature tensor satisfies 2nd Bianchi’s identity, that is, (∇XQ)(Y,U,V,W) + (∇Y Q)(U,X,V,W) + (∇UQ)(X,Y,V,W) = 0. keywords: curvature; field; g(u; generalized; hgpqs)n; manifold; pseudo; riemannian; semi; symmetric; tensor; u)v; vector; ∧s)(y cache: cubo-2600.pdf plain text: cubo-2600.txt item: #425 of 481 id: cubo-2601 author: Argyros, Ioannis K.; George, Santhosh title: Extended domain for fifth convergence order schemes date: 2021-04-14 words: 3685 flesch: 82 summary: The numerical experiments appear in Section 4. CUBO 23, 1 (2021) Extended domain for fifth convergence order schemes 99 2 Local convergence It is easier for the local convergence of method (1.2), if we develop some real functions. CUBO 23, 1 (2021) Extended domain for fifth convergence order schemes 101 Theorem 2.1. keywords: analysis; argyros; banach; comput; conditions; continuous; convergence; cubo; domain; equation; example; extended; fifth; functions; george; iterative; local; math; mathematical; method; new; newton; numerical; order; para; radius; schemes; semi; set; solution; space; theorem; u(x∗,r; vol; way; ω((1; −x∗‖; −x∗‖)‖x0 cache: cubo-2601.pdf plain text: cubo-2601.txt item: #426 of 481 id: cubo-2603 author: Yankson, Ernest title: Inequalities and sufficient conditions for exponential stability and instability for nonlinear Volterra difference equations with variable delay date: 2021-04-14 words: 2748 flesch: 89 summary: (2.6) Considering the third term on the right hand side of (2.6) we obtain ∆n −1∑ s=−g0 n−1∑ z=n+s A2(n,z)h2(x(z)) = −1∑ s=−g0 n∑ z=n+s+1 A2(n + 1,z)h2(x(z)) Also, we note that   n−1∑ z=n−g(n) A(n,z)h(x(z))  2 ≤ keywords: a(n; a2(n; cubo; difference; equations; exponential; inequalities; n−1∑; n−1∑ s; n−g(n; n−g(n−1)−1; q(n; s)h(x(s; solution; stability; x(n; z)h2(x(z cache: cubo-2603.pdf plain text: cubo-2603.txt item: #427 of 481 id: cubo-2605 author: Fagnola, Franco; Poletti, Damiano; Sasso, Emanuela title: Energy transfer in open quantum systems weakly coupled with two reservoirs date: 2021-04-14 words: 8444 flesch: 79 summary: = ∑ ω∈B ω ∑ (εn,εm)∈Bω ( Γ+j,ωρm − Γ − j,ωρn ) tr ( PεnD ∗ jPεmDj ) . = n−1∑ k=0 ( Γ+j,1ρk − Γ − j,1ρk+1 ) . keywords: average; chain; coupling; cubo; current; dependence; difference; dimensional; doi; eigenvalues; energy; entropy; explicit; eβ1ω; eβ2ω; e−β2; fagnola; flow; following; formula; fourier; function; generator; gksl; hamiltonian; inequality; interaction; invariant; inverse; j+1; law; lemma; limit; log; markov; math; non; n≥0; open; operators; phys; poletti; proof; pεnd; qj+1,j; quantum; remark; reservoirs; sasso; section; semigroups; small; state; stationary; supj; system; temperature; theorem; transfer; vol; way; weakly; γ+1; γ−j; εk≤b; εm)∈bω; ρl2(hs; ρβj; ωdj; ω∈b cache: cubo-2605.pdf plain text: cubo-2605.txt item: #428 of 481 id: cubo-2606 author: Si bachir, Fatima; Abbas, Saïd ; Benbachir, Maamar; Benchohra, Mouffak; N’Guérékata, Gaston M. title: Existence and attractivity results for \(\psi\)-Hilfer hybrid fractional differential equations date: 2021-04-14 words: 4875 flesch: 85 summary: t ∈ t ∈ keywords: abbas; attractivity; bcς; benchohra; continuous; cubo; derivative; differential; equations; existence; fractional; function; hilfer; hybrid; math; problem; results; solutions; theorem; theory; u(s))ds; u(t; u0v(0,u(0; v(t; vol; γ(λ; λ;ψ; σ;ψ; φ(t; ψ(t; ψ(t1; ψ(t2; ψ′(s)(ψ(t; −ψ(0))1−ς; −ψ(0))1−ςγ(λ; −ψ(s))λ−1w(s; −ψ(s))λ−1|w(s; ∣∣∣∣ cache: cubo-2606.pdf plain text: cubo-2606.txt item: #429 of 481 id: cubo-2607 author: Escassut, Alain title: Idempotents in an ultrametric Banach algebra date: 2021-04-14 words: 4059 flesch: 83 summary: alain.escassut@uca.fr ABSTRACT Let IK be a complete ultrametric field and let A be a unital commu- tative ultrametric Banach IK-algebra. ,Xn} by one of its ideals equipped with its quotient norm of Banach IK-algebra. keywords: affinoid; algebra; banach; closed; commutative; compact; cubo; denote; escassut; finite; ideal; idempotents; maximal; mult(a,‖; norm; open; partition; proof; proposition; subsets; theorem; ultrametric; unique; unital; vol; φ(u; φ(v cache: cubo-2607.pdf plain text: cubo-2607.txt item: #430 of 481 id: cubo-2608 author: Choudhury, Binayak S.; Metiya, Nikhilesh; Kundu, Sunirmal title: Existence, well-posedness of coupled fixed points and application to nonlinear integral equations date: 2021-04-14 words: 7967 flesch: 89 summary: The relation R is said to be directed if for given x,y ∈ X, there exists z ∈ X such that (x, z) ∈ R and (y, z) ∈ R. The relation R is said to be a partial order relation on X if it is reflexive, anti-symmetric and transitive. 179 x, y ∈ X such that lim n→∞ xn = x and lim n→∞ yn = y. (3.22) keywords: application; choudhury; contraction; cubo; d(x; d(xn; d(y; d(yn; existence; f(x; f(xn; f(y; f(yn; fixed; graph; kundu; lim; limit; m(x; mapping; max; metiya; metric; nonlinear; n→∞; point; posedness; problem; property; relation; results; rn+1; set; space; theorem; vol; xn+1 cache: cubo-2608.pdf plain text: cubo-2608.txt item: #431 of 481 id: cubo-2710 author: Prakasha, D. G.; Harish, H.; Veeresha, P.; Venkatesha title: The Zamkovoy canonical paracontact connection on a para-Kenmotsu manifold date: 2021-08-01 words: 5392 flesch: 77 summary: Taking inner product on both sides of (3.3) with X and then for U = Y , we have R∇Z (X, Y, Y, X) = R(X, Y, Y, X) + g(Y, Y )g(X, X) − g(X, Y )g(X, Y ). X − g(X, Y )ξ, (2.10) S(X, ξ) = −(n − 1)η(X), (2.11) S(φX, φY ) keywords: canonical; canonical paracontact; civita; concircular; connection; cubo; curvature; c∇z; fields; g(x; g(y; kenmotsu; kenmotsu manifold; levi; manifold; math; para; paracontact; paracontact connection; prakasha; proof; r(x; respect; ricci; r∇z; symmetric; tensor; u)ξ; vector; vol; zamkovoy; ∇zw cache: cubo-2710.pdf plain text: cubo-2710.txt item: #432 of 481 id: cubo-2711 author: Kalyani, K.; Seshagiri Rao, N. title: Coincidence point results of nonlinear contractive mappings in partially ordered metric spaces date: 2021-08-01 words: 6937 flesch: 86 summary: The existence of fixed point results for self-mappings in partially ordered sets have been considered first by Ran and Reurings [36] and presented some applications to matrix equations therein. The aim of this paper is to prove the coincidence point and common fixed point results for f- nondecreasing self-mapping satisfying generalized contractive conditions of rational type in the context of partially ordered metric spaces. keywords: anal; coincidence; common; compatible; complete; continuous; contractive; cubo; d(fx; d(fy; d,≤; f(x; fixed; following; kalyani; mappings; math; metric; monotone; nondecreasing; nonlinear; point; rao; results; self; sequence; seshagiri; spaces; t x; t y; theorem; tx0; txn; vol; ϕ(t)dt cache: cubo-2711.pdf plain text: cubo-2711.txt item: #433 of 481 id: cubo-2712 author: Ahmad, Bashir; Albideewi, Amjad F.; Ntouyas, Sotiris K.; Alsaedi, Ahmed title: Existence results for a multipoint boundary value problem of nonlinear sequential Hadamard fractional differential equations date: 2021-08-01 words: 4654 flesch: 81 summary: In this paper, motivated by aforementioned work on Hadamard fractional differential equations, we introduce and study a nonlocal multipoint boundary value problem involving a nonlinear sequential Hadamard fractional differential equation to enrich the related literature. Consider the boundary value problem for Hadamard fractional differential equations        ( HD7/4 + 2 HD3/4 ) x(t) = f(t, x(t)), keywords: ahmad; alsaedi; boundary; c([1; conditions; continuous; cubo; differential; equations; existence; fractional; hadamard; integral; j=1; log; log t; nonlinear; ntouyas; point; problem; r dr; s r; s)α−2ds; sequential; solution; sλ−1; t −λ; theorem; type; value; vol; x(t; α−2; γ(α; ∣ ∣ cache: cubo-2712.pdf plain text: cubo-2712.txt item: #434 of 481 id: cubo-2714 author: Aguiló Vidal, Bruno title: Free dihedral actions on abelian varieties date: 2021-08-01 words: 1630 flesch: 71 summary: Keywords and Phrases: Abelian varieties, dihedral group, free action. CUBO 23, 2 (2021) Free dihedral actions on Abelian varieties 241 Proof. keywords: abelian; action; catanese; construction; demleitner; dihedral; dimension; free; group; hyperelliptic; manifolds; order; translations; varieties; variety cache: cubo-2714.pdf plain text: cubo-2714.txt item: #435 of 481 id: cubo-2715 author: Mouley, Jyotirmoy; Panja, M. M.; Mandal, B. N. title: Approximate solution of Abel integral equation in Daubechies wavelet basis date: 2021-08-01 words: 6341 flesch: 81 summary: 245–264, August 2021 DOI: 10.4067/S0719-06462021000200245 Approximate solution of Abel integral equation in Daubechies wavelet basis Jyotirmoy Mouley 1 M. M. Panja 2 B. N. Mandal 3 1 Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata-700 009, India. Keywords and Phrases: Abel integral equation, Daubechies scale function, Daubechies wavelet, Gauss-Daubechies quadrature rule. keywords: 2k−1; abel; abel integral; appl; approximate; cubo; daubechies; dyadic; equation; error; exact; example; function; integral; integral equation; k=0; kind; lµ(k; m. m.; mandal; math; method; mouley; numerical; panja; relation; scale; second; solution; space; support; t)µ; table; unknown; values; vol; wavelet; y(x; φ(x; ‖e(x)‖l2[0,1; ‖δyj‖2l2[0,1 cache: cubo-2715.pdf plain text: cubo-2715.txt item: #436 of 481 id: cubo-2716 author: Tung, Chia-chi; Lamberti, Pier Domenico title: On Rellich’s Lemma, the Poincaré inequality, and Friedrichs extension of an operator on complex spaces date: 2021-08-01 words: 9046 flesch: 75 summary: Then: (a) there exists a non-decreasing, unbounded sequence {λ j } of positive real numbers such that the operator equation [u, v] D,h′ = λ(u, v̄)D ∀v ∈ C ∞,c(D), u|dD = 0, (6.1) admits a nontrivial solution u ∈ H1 1,h′ −→ ,c (D) precisely when λ is a member of the countable set {λ j }; 18 That is, each component hj of h ′ is bounded on D; similarly define “C ∞-allowable weight on D”. Define D µ,h := {ψ ∈ C 2,c(D)| S µ,h ψ ∈ L2(D)}, and H(D,S µ,h ) : keywords: allowable; assume; c(d; chi; chia; compact; complex; constant; covering; cubo; denote; dirichlet; domain; domenico; dυ̃; element; embedding; equation; euclidean; exists; extension; finite; following; form; friedrichs; g µ,h; h1µ,h; inequality; j→∞; l2(d; lamberti; lemma; lim; mapping; new; norm; open; operator; pier; poincaré; problem; product; proof; property; r d; relative; rellich; respect; riemann; schrödinger; sequence; sheets; sobolev; solution; space; subdomain; subset; theorem; tung; type; vol; weak; weight; york; µ,h cache: cubo-2716.pdf plain text: cubo-2716.txt item: #437 of 481 id: cubo-2717 author: Kumar, Gaurav; Tyagi, Brij K. title: Weakly strongly star-Menger spaces date: 2021-08-01 words: 4940 flesch: 83 summary: In Section 3 we investigate the relationship of WSSM spaces with other related spaces. Section 4 contains the information on subspaces and product spaces of WSSM and in the last Section 5 we study the image and preimage of WSSM spaces under continuous maps. keywords: closed; compact; countable; covering; covers; cubo; dense; example; finite; kočinac; menger; n∈ω; open; paracompact; product; proof; properties; property; sequence; space; st(fn; st(∪vn; star; subset; topology; vol; weakly; wssm; wssm space cache: cubo-2717.pdf plain text: cubo-2717.txt item: #438 of 481 id: cubo-2718 author: Güney, H. Özlem; Murugusundaramoorthy, G.; Vijaya, K. title: Subclasses of \(\lambda\)-bi-pseudo-starlike functions with respect to symmetric points based on shell-like curves date: 2021-08-01 words: 4833 flesch: 91 summary: [5] S. Joshi, S. Joshi and H. Pawar, “On some subclasses of bi-univalent functions associated with pseudo-starlike function”, J. Egyptian Math. For example, the functions z, z 1−z , − log(1 − z) and 1 2 log 1+z 1−z are members of Σ. However, the Koebe function is not a member of Σ. keywords: 1)(3; 2)2; 4(3λ−; analytic; c21; class; corollary; cubo; f(z; fekete; fibonacci; following; functions; g(w; math; pseudo; pslλs; p̃(z; respect; starlike; subclasses; szegö; univalent; vol; |a2|; |a3|; |h(µ)|; |τ|; σ(p̃(z; σ(α cache: cubo-2718.pdf plain text: cubo-2718.txt item: #439 of 481 id: cubo-2729 author: Haviar, M.; Kurtulík, S. title: A new class of graceful graphs: \(k\)-enriched fan graphs and their characterisations date: 2021-08-01 words: 7587 flesch: 77 summary: A new class of graceful graphs: k-enriched fan graphs 315 characterized in the manner presented here. 2 Preliminaries In this section we recall the necessary basic terms concerning graph labellings as well as the concepts of labelling sequences, labelling relations and simple chessboards, which we use as our tools to describe new classes of graceful graphs. In this text we will denote by f(VG) the set of all vertex labels and by f(EG) the set of all edge labels in the labelling f of a graph G. Several types of graph labellings are known, e.g. α,β,σ,ρ, which have become very well-known since the publication of Rosa’s paper [10] in 1967, and further γ,δ,p,q introduced by Rosa in his dissertation thesis [9] in 1965. keywords: a(l; chessboard; corresponding; cubo; dots; double; edges; fan; fan graphs; figure; following; form; graceful; graceful graphs; grafos; graph; haviar; head; integers; kfn; labelling; main; middle; new; n−i; pairs; path; relation; sequence; simple; size; stars; swan; table; triple; upper; vertex; vertices cache: cubo-2729.pdf plain text: cubo-2729.txt item: #440 of 481 id: cubo-2730 author: Kawamura, Masaya title: On the conformally \(k\)-th Gauduchon condition and the conformally semi-Kähler condition on almost complex manifolds date: 2021-08-01 words: 3496 flesch: 79 summary: − k − 1) 6n(n − 1)(n − 2) ∫ M ekf Tr(T ′B ∧ T̄ ′B)ωnB = − k(n − k − 1) 6n(n − 1)(n − 2) ∫ M e kf (6|wB|2 − 3|T ′B|2)ωnB, (3.7) 340 Masaya Kawamura CUBO 23, 2 (2021) which gives that 2 ∫ M ekf |wB|2ωnB = ∫ M ekf |T ′B|2ωnB, where we used ω n−k−1 B ∧ ∂̄(ωkB) − ∂(ekf ) ∧ ωn−k−1B ∧ ∂̄(ω k B) − ekf∂(ωn−k−1B ) ∧ ∂̄(ω k B) = ∫ M d(ekfωn−k−1 B ∧ ∂̄(ωkB)) keywords: associated; chern; complex; condition; connection; cubo; definition; equivalent; gauduchon; hermitian; kawamura; kähler; lemma; m2n; manifold; metric; n−k−1; quasi; real; semi; structure; th gauduchon; theorem; torsion; vol; ωn−1 cache: cubo-2730.pdf plain text: cubo-2730.txt item: #441 of 481 id: cubo-2847 author: Díaz-Marín, Homero G.; Osuna, Osvaldo title: Non-algebraic limit cycles in Holling type III zooplankton-phytoplankton models date: 2021-12-01 words: 4079 flesch: 73 summary: There can not exist algebraic limit cycles of the dynamical system (2.1) as a real vector field in R2, whenever conditions (2.4) hold true. Along this work we consider only integer values n ≥ 2. Existence of non-algebraic limit cycles for the Lotka-Volterra model were first exhibited by [12]. keywords: algebraic; branches; conditions; corresponding; cubo; curve; cycles; equation; f(x; fig; following; functional; good; iii; invariant; laurent; limit; maŕın; models; newton; non; number; polygon; predator; prey; puiseux; rational; response; series; solution; system; theorem; type; unique; vol; yields cache: cubo-2847.pdf plain text: cubo-2847.txt item: #442 of 481 id: cubo-2848 author: Lampret, Vito title: Basic asymptotic estimates for powers of Wallis’ ratios date: 2021-12-01 words: 3965 flesch: 86 summary: − exp( − as̃1(n))︸ ︷︷ [5] V. G. Cristea, “A direct approach for proving Wallis ratio estimates and an improvement of Zhang-Xu-Situ inequality”, Studia Univ. keywords: appl; approximation; asymptotic; corollary; cubo; error; estimates; exp; formula; functions; inequalities; lampret; math; ratio; relative; sequence; theorem; vol; wallis; wan; |a|; π n; πn)−a/2 cache: cubo-2848.pdf plain text: cubo-2848.txt item: #443 of 481 id: cubo-2849 author: Hidalgo, Rubén A. title: The structure of extended function groups date: 2021-12-01 words: 7816 flesch: 60 summary: The structure of extended function groups 371 by other authors in the sense that they refer it to Kleinian groups whose limit set is a Jordan curve and contains elements permuting the two discs bounded by it. Basic examples of function groups are provided by elementary groups (Kleinian groups with finite limit set), quasi- fuchsian groups (function groups whose limit set is a Jordan curve) and totally degenerate groups (non-elementary finitely generated Kleinian groups whose region of discontinuity is both connected and simply-connected). keywords: accidental; amalgamated; boundary; case; collection; combination; component; conformal; connected; cubo; cyclic; cyclic group; decomposition; discontinuity; discs; element; elementary; equivariant; extended; extended function; finite; finite group; free; function; function group; group; invariant; kleinian; kleinian group; lemma; loops; maskit; math; möbius; non; parabolic; points; proof; quasifuchsian; region; riemann; set; stabilizer; structure; subgroup; theorem; transformations; trivial; vol cache: cubo-2849.pdf plain text: cubo-2849.txt item: #444 of 481 id: cubo-2850 author: Traoré, U. title: Entropy solution for a nonlinear parabolic problem with homogeneous Neumann boundary condition involving variable exponents date: 2021-12-01 words: 7382 flesch: 89 summary: We rewrite (3.1) in the forms ∫ t 0 〈 ∂uN ∂s ,Tk(u N − φ) 〉 ds + ∫ t 0 ∫ Ω a(x,∇uN).∇Tk(uN − φ)dxds + ∫ t 0 ∫ Ω b(uN)Tk(u N − φ)dxds ≤ ∫ t 0 ∫ Ω fNTk(u N − φ)dxds (5.21) and ∫ t 0 〈 ∂uM ∂s ,Tk(u M − φ) 〉 ds + ∫ t 0 ∫ Ω a(x,∇uM).∇Tk(uM − φ)dxds + ∫ t 0 ∫ Ω b(uM)Tk(u M − φ)dxds ≤ ∫ t 0 ∫ Ω fMTk(u M − φ)dxds (5.22) CUBO 23, 3 (2021) Entropy solutions for nonlinear parabolic problems with... 401 where fN(t,x) = fn(x) ∀t Similarly, we show that lim h→∞ lim N,M→∞ (∫ t 0 〈 ∂uN ∂s ,T1(u N − Th(uM)) 〉 + 〈 ∂uM ∂s ,T1(u M − Th(uN)) 〉 ds ) = 0 lim h→∞ lim N,M→∞ ∫ t 0 ∫ Ω [fNT1(u N − Th(uM)) keywords: = ∫; a(x,∇tk(u; a.e; boundary; c(t; converges; cubo; data; entropy; equations; existence; exponents; following; function; i=1; inequality; l1(qt; l1(ω; lemma; lim; lim n; measurable; measure; m→∞; n(t; n=1; neumann; nonlinear; p(x; parabolic; problem; proof; result; solutions; space; stability; study; tk(u; traoré; uniqueness; variable; vol; w1,p; |ui|≤k; |um|; φ)dxds; ∥∥b(ui)∥∥; ≤ ∫ cache: cubo-2850.pdf plain text: cubo-2850.txt item: #445 of 481 id: cubo-2851 author: Philo Nithya, L.; Kureethara, Joseph Varghese title: Independent partial domination date: 2021-12-01 words: 3831 flesch: 69 summary: In Section 3, we define independent partial domination number and study some of their properties. 3 Independent partial domination In this section, we define independent partial domination number and present some observations and some of the basic results. keywords: cardinality; chain; cubo; definition; dominating set; domination; graph; i(g; independent; independent partial; independent set; ip(g; ipd; math; maximal; minimal; n[s; nithya; number; partial; partial domination; proof; proposition; section; set; sets; vertices; vol; |n[bi]|; γp(g; ∣∣∣∣∣∣ cache: cubo-2851.pdf plain text: cubo-2851.txt item: #446 of 481 id: cubo-2852 author: Anastassiou, George A. title: Foundations of generalized Prabhakar-Hilfer fractional calculus with applications date: 2021-12-01 words: 5235 flesch: 91 summary: e γ;ψ ρ,µ,ω,a+f ) (x) = ∫ x a ψ′ (t) (ψ (x) − ψ (t))µ−1 Eγρ,µ [ω (ψ (x) − ψ (t)) ρ ]f (t)dt, (1.2) and ( e γ;ψ ρ,µ,ω,b−f ) (x) = ∫ b x ψ′ (t) (ψ (t) − ψ (x))µ−1 Eγρ,µ keywords: a+f; b],ψ; calculus; cubo; fractional; generalized; hilfer; i=1; prabhakar; proof; r1r3; theorem; γ;ψ; ρ,µ,ω cache: cubo-2852.pdf plain text: cubo-2852.txt item: #447 of 481 id: cubo-2853 author: Almuthaybiri, Saleh S.; Jonnalagadda, Jagan Mohan; Tisdell, Christopher C. title: Existence and uniqueness of solutions to discrete, third-order three-point boundary value problems date: 2021-12-01 words: 5569 flesch: 81 summary: In addition, developing a theory of discrete boundary value problems has the po- tential to inform our understanding of continuous boundary value problems. j.jaganmohan@hotmail.com ABSTRACT The purpose of this article is to move towards a more com- plete understanding of the qualitative properties of solutions to discrete boundary value problems. keywords: +2∑; +30; boundary; boundary value; bounds; complete; conditions; continuous; cubo; difference; discrete; equations; existence; fixed; following; function; green; h(t; math; new; order; point; positive; problems; proof; s)(t; s=1; s=2; solutions; t +2∑; t(t; theorem; theory; tisdell; u(t; unique; uniqueness; value; vol; |g(t; η(η cache: cubo-2853.pdf plain text: cubo-2853.txt item: #448 of 481 id: cubo-2854 author: Dragomir, S. S. title: Some integral inequalities related to Wirtinger's result for \(p\)-norms date: 2021-12-01 words: 4432 flesch: 90 summary: 1b − a ∫ b a ( x − a b − a ∫ b a f (s) ds − ∫ x a f (t) dt ) g′ (x) dx ∣∣∣∣∣ ≤ 1 b − a ∫ b a ∣∣∣∣∣x − ab − a ∫ b a f (s) ds − ∫ x a f (t) dt ∣∣∣∣∣ |g′ (x)| dx ≤ 1 b − a (∫ b a ∣∣∣∣∣x − ab − a ∫ b a f (s) ds − ∫ x a f (t) dt ∣∣∣∣∣ p dx )1/p (∫ b a |g′ (x)|q dx )1/q =: I (3.10) Using (2.15) we have I ≤ Using (3.7) we have ∣∣∣∣C ( ℓ − a + b 2 , g′ )∣∣∣∣ ≤ (b − a)1/p (p − 1)1/p πp ( 1 b − a ∫ b a ∣∣∣∣∣t − a + b2 − 1b − a ∫ b a ( s − a + b 2 ) ds ∣∣∣∣∣ p dt )1/p (∫ b a |g′′ (x)|q dx )1/q = (b − a)1/p (p − 1)1/p πp ( 1 b − a ∫ b a ∣∣∣∣t − a + b2 ∣∣∣∣p dt )1/p (∫ b a |g′′ (x)|q dx )1/q = (b − a)1+1/p 2 (p − 1)1/p (p + 1)1/p πp (∫ b a |g′′ (x)|q dx )1/q , which proves the desired inequality (3.12). keywords: a)b −; b −; b)2; cubo; ds −; inequalities; inequality; integral; p dt; t)2 −; vol; wirtinger; − a)1; − g; − ∫; ∣∣∣∣∣ cache: cubo-2854.pdf plain text: cubo-2854.txt item: #449 of 481 id: cubo-2855 author: Elazzouzi, Abdelhai; Ezzinbi, Khalil; Kriche, Mohammed title: On the periodic solutions for some retarded partial differential equations by the use of semi-Fredholm operators date: 2021-12-01 words: 5783 flesch: 81 summary: In [22], the authors proved the periodicity for a nonhomogeneous linear differential equation when the linear part generates a C0-semigroup on E and they obtained the existence and uniqueness of periodic solutions for this class of equations. To achieve this goal, we suppose that Equation (1.1) admits a bounded solution on the positive real line and under suitable estimations on the norm of the operator L, we derive periodic solution of Equation (1.1) from bounded ones on the positive real line by using the perturbation theory of semi-Fredholm operators and the Chow and Hale’s fixed point theorem. keywords: banach; bounded; closed; continuous; cubo; d(a; differential; dim; elazzouzi; equation; existence; ezzinbi; fixed; following; follows; fredholm; functional; im(i; integral; ker(i; kriche; lemma; lim; linear; log; map; mω|s−1; operator; partial; periodic; periodicity; proof; retarded; satisfies; semi; semigroup; solutions; space; sup; t0(ω; theorem; vol; work; x(ω; y(t; |l|; ψ)| cache: cubo-2855.pdf plain text: cubo-2855.txt item: #450 of 481 id: cubo-2856 author: Atash, Ahmed Ali; Kulib, Maisoon Ahmed title: Extension of exton's hypergeometric function \(K_{16}\) date: 2021-12-01 words: 5490 flesch: 85 summary: dt (2.1) K (α,β) 16,p (a, b, c, d; e; x, y, z, u) = 1 B(a, e − a) 1 B(d, e − a − d) ∫ 1 0 ∫ 1 0 ta−1sd−1(1 − t)e−a−1(1 − s)e−a−d−1 × (1 − xt − zs(1 − t))−b(1 − yt − us(1 − t))−c1F1 ( α; β; − p t(1 − t) ) dtds (2.2) K (α,β) 16,p (a, b, c, d; e; x, y, z, u) = 1 B(a, e − a) B(d, e − a − d) × ∫ 1 0 ∫ 1 0 ta−1sd−1(1 − t)e−a−1(1 − s)e−a−d−1(1 − zs)−b(1 − us)−c × ( 1 − ( x − zs 1 − zs ) t )−b ( 1 − ( y − us 1 − us ) t )−c 1F1 ( α; β; − p t(1 − t) ) dtds (2.3) K (α,β) 16,p 1 0 ta−1(1 − t)d−a−1(1 − xt)−b(1 − yt)−cdt. keywords: 1f1; b(a; cubo; e −; extended; exton; following; function; generating; hypergeometric; integral; proof; t(1 −; ta−1(1 −; u(1 −; z(1 −; β)16,p; − a)r+s; − p; − t; − xt; − xt)−b(1; − yt cache: cubo-2856.pdf plain text: cubo-2856.txt item: #451 of 481 id: cubo-2951 author: Prasad, Rajendra; Akyol, Mehmet Akif; Kumar, Sushil; Singh, Punit Kumar title: Quasi bi-slant submersions in contact geometry date: 2022-04-04 words: 6285 flesch: 83 summary: For all W,Z ∈ Γ(D1) and X ∈ Γ(D ⊕ D2), we have gM([W,Z],X) = gM(∇W Z,X) − gM (∇ZW,X). = gM (∇W φZ,φX) − gM(∇ZφW,φX), = gM (∇W ψZ,φX) + gM(∇W ωZ,φX) − gM (∇ZψW,φX) − gM (∇W ωZ,φX), = cos2 θ1gM(∇W Z,X) − cos2 θ1gM(∇ZW,X) − gM(TW ωψZ − TZωψW,X) +gM(H∇W ωZ + TW ωZ,φPX + ψRX + ωRX) −gM(H∇ZωW + TZωW,φPX + ψRX + ωRX). keywords: akyol; contact; cos2; cosymplectic; cubo; distribution; equations; geodesic; geometry; gm(∇w; hermitian; invariant; kumar; lemma; manifold; math; metric; prasad; proof; proper; quasi; quasi bi; riemannian; semi; singh; slant; slant submersion; submersion; totally; vol; γ(d; γ(d1; γ(kerf∗ cache: cubo-2951.pdf plain text: cubo-2951.txt item: #452 of 481 id: cubo-2952 author: Prasad, K. Rajendra; Khuddush, Mahammad; Vidyasagar, K. V. title: Infinitely many positive solutions for an iterative system of singular BVP on time scales date: 2022-04-04 words: 4885 flesch: 88 summary: The point t ∈ T is left-dense, left-scattered, right-dense, right-scattered if ρ(t) = t, ρ(t) < t, σ(t) = t, σ(t) > t, respectively. t ∈ keywords: boundary; continuous; cubo; i=1; iterative; khuddush; point; positive; prasad; problems; proof; scales; solutions; system; t)t; theorem; time; value; vidyasagar; vol; τm)λ(τm)gm(υ1(τm))∆τm; ℵ(t; ℵ(τ1; ℵ(τm−1;   cache: cubo-2952.pdf plain text: cubo-2952.txt item: #453 of 481 id: cubo-2953 author: Auffarth, Robert; Lucchini Arteche, Giancarlo; Quezada, Pablo title: Smooth quotients of abelian surfaces by finite groups that fix the origin date: 2022-04-04 words: 6753 flesch: 80 summary: Note first that the action is faithful since it comes from the faithful action of G × ∆ on B. Consider then K as a subgroup of PGL3 = Aut(P 2) and let K1 be its preimage in SL3. The case G = G(2, 2) is excluded since G is then a Klein group and thus the representation is not irreducible. keywords: abelian; action; analytic; case; case g; corresponds; cubo; element; example; finite; following; group; invariant; isomorphic; lemma; non; note; order; origin; pair; particular; possible; proof; pseudoreflections; quotient; representation; smooth; stabilizer; surfaces; torsion; trivial cache: cubo-2953.pdf plain text: cubo-2953.txt item: #454 of 481 id: cubo-2954 author: T., Reji; Varughese, Jinitha; R., Ruby title: On graphs that have a unique least common multiple date: 2022-04-04 words: 4306 flesch: 86 summary: Consider the graph H = G◦G∪G, where G◦G is the graph obtained by identifying a least degree vertex in two copies of G. Then (1) e(H) ≡ 0 (mod 3). Applying Theorem 1.5, G ◦ G is P3 ∪ K2- decomposable keywords: adjacent; case; common; common multiple; decomposable; e(g; e(h; edges; graphs; lcm(p3; mod; multiple; subcase; theorem; tk2; unique; vertex; vertices; vol cache: cubo-2954.pdf plain text: cubo-2954.txt item: #455 of 481 id: cubo-2955 author: El Hammar, Hasnae; Allalou, Chakir; Abbassi, Adil; Kassidi, Abderrazak title: The topological degree methods for the fractional \(p(\cdot)\)-Laplacian problems with discontinuous nonlinearities date: 2022-04-04 words: 7022 flesch: 83 summary: +∞, (1.3) p is symmetric i. e. p(x, y) = p(y, x), ∀(x, y) ∈ Ω × Ω; (1.4) CUBO 24, 1 (2022) ∈ Ω and 〈ϕ,v〉 = ∫ Ω hvdx ∀v keywords: abbassi; allalou; anal; appl; banach; boundary; compact; cubo; degree; discontinuous; elliptic; equations; existence; exponent; following; fractional; function; h(x; hammar; kassidi; kim; lemma; lim; math; methods; nonlinear; nonlinearities; open; operator; p(x; p(·)-laplacian; problems; proposition; semicontinuous; set; sobolev; solutions; spaces; theorem; theory; topological; type; u.s.c; upper; variable; vol; weak; y)dxdy; |u(x; ψ(x; ω×ω; ′(x)(ω cache: cubo-2955.pdf plain text: cubo-2955.txt item: #456 of 481 id: cubo-2957 author: Guerfi, Abderrahim; Ardjouni, Abdelouaheb title: Existence, uniqueness, continuous dependence and Ulam stability of mild solutions for an iterative fractional differential equation date: 2022-04-04 words: 4123 flesch: 83 summary: t 0 (t − s) α−1 x(s)ds, provided the right side is pointwise defined on R+, where Γ is the gamma function. ∫ t 0 (t − s) n−α−1 x(n) keywords: continuous; cubo; dependence; differential; equations; existence; fractional; i−1; j=0; lemma; mild; point; problem; proof; solution; stability; t α; theorem; ulam; uniqueness; vol; x(t; α−1; ∣ ∣ cache: cubo-2957.pdf plain text: cubo-2957.txt item: #457 of 481 id: cubo-2958 author: Ballico, Edoardo title: A characterization of \(\mathbb F_q\)-linear subsets of affine spaces \(\mathbb F_{q^2}^n\) date: 2022-04-04 words: 4375 flesch: 87 summary: ∈ Fq \ Eq, and I ′ q := I ′′ q ∪ {0}. We say that C(a, c) is the circle of Fq2 with center a and squared-radius c. Note that C(a, 0) = {a} and #C(a, c) = q + 1 for all c ∈ Fq \ {0}. keywords: affine; ballico; closed; closure; definition; finite; fix; fq2; linear; matrices; mod; non; note; numerical; odd; proposition; range; remark; set; square; subsets; vol cache: cubo-2958.pdf plain text: cubo-2958.txt item: #458 of 481 id: cubo-2959 author: Rahman, Shamsur title: Some results on the geometry of warped product CR-submanifolds in quasi-Sasakian manifold date: 2022-04-04 words: 3144 flesch: 79 summary: Some results on the geometry of warped product ... 111 The remaining case, when ξ ∈ T DT is dealt with the following two theorems. [2] has studied the geometry of warped product submanifolds in Kaehler manifolds and showed that the warped product submanifold of the type D⊥×yDT is trivial where DT and D⊥ are φ-invariant and anti-invariant submanifolds of a Sasakian manifold, respectively. keywords: contact; cubo; d⊥×ydt; field; geometry; invariant; manifold; normal; product; quasi; results; sasakian; submanifolds; tangent; tensor; vector; vol; warped; warped product; γ(t; ∈ t cache: cubo-2959.pdf plain text: cubo-2959.txt item: #459 of 481 id: cubo-2965 author: Gesztesy, Fritz; Michael, Isaac; Pang, Michael M. H. title: Optimality of constants in power-weighted Birman–Hardy–Rellich-Type inequalities with logarithmic refinements date: 2022-04-12 words: 16809 flesch: 93 summary: ((0, ρ)), m, N ∈ N, α ∈ R, ρ, γ ∈ (0, ∞), γ > eN ρ. ∣ ∣ 2 > A(m, α) ˆ ρ 0 dx x α−2m ∣ ∣f(x) ∣ ∣ 2 + B(m, α) N ∑ k=1 ˆ ρ 0 dx x α−2m k ∏ p=1 [lnp(γ/x)] −2 ∣ ∣f(x) ∣ ∣ 2 , f ∈ C ∞ 0 ((0, ρ)), m, N ∈ N, keywords: 0,ρ/20; 0,∞; 16j6k6n; 1−εk; = −; a(m; amer; assume; b(m; birman; c20; case; constants; convergence; corollary; cubo; c∞0; differential; dimensional; dxxα; dxxα−2; dxx−1; dxx−1+ε0; equations; function; gesztesy; h1,ε; hardy; independent; inequalities; inequality; j(ε; j=1; k(0; k(ε; k6n; k=1; lemma; lim; ln(1; lnj(γ; lnj+1(γ; lnp(t; logarithmic; math; michael; n(0; note; n−1∑; n−2∏; n−3∏; operators; optimality; p=1; pang; paper; particular; pm(σ0(0))p; power; proc; proof; rellich; results; sect; sequence; sharp; sharpness; sobolev; soc; spaces; terms; theorem; theory; type; vol; weighted; x)/θ)f; x+θ; yα−2m|g(y)|2; ˆ ρ; γj−1(ε; δ),ε; ε(x; ε0,ε1; εk)γj; ψ(x)]2; ′m(σ0(0; ℓ=1; −1−εj; −σj; ∣∣2; ∣∣∣∣ cache: cubo-2965.pdf plain text: cubo-2965.txt item: #460 of 481 id: cubo-2966 author: Haldar, Goutam title: Uniqueness of entire functions whose difference polynomials share a polynomial with finite weight date: 2022-04-12 words: 8514 flesch: 91 summary: Let F and G be non-constant meromorphic functions such that G is a Mobius transformation of F. Suppose that there exists a subset I ⊂ R+ with linear measure mesI = Using these theories, some mathematicians in the world began to study the uniqueness questions of meromorphic functions sharing values with their shifts, and study the value distribution of the nonlinear difference polynomials, and produced many fine works, for example, see [1, 5, 6, 7, 11, 15, 16, 23, 27, 29, 30, 31, 40, 44]. keywords: + s(r; complex; constant; cubo; difference; entire; f(z; finite; following; functions; g(z; lc(f; lc(g; lemma; m(r; math; meromorphic; n +; n(r; n0(r; nevanlinna; nl(r; non; order; p(z; polynomial; results; share; sharing; theorem; tn+1; transcendental; uniqueness; value; vol; zero cache: cubo-2966.pdf plain text: cubo-2966.txt item: #461 of 481 id: cubo-3094 author: Ouaro, Stanislas; Rabo, Noufou; Traoré, Urbain title: Numerical analysis of nonlinear parabolic problems with variable exponent and \(L^1\) data date: 2022-08-22 words: 8333 flesch: 84 summary: − ∇v − − ∇v − keywords: a(x; analysis; approximation; condition; convergence; cubo; entropy; equations; example; existence; exponent; following; function; k n+1; l1(ω; lemma; lp(.)(ω; method; mild; n+1; nonlinear; note; numerical; operator; ouaro; p(x; paper; parabolic; problem; proof; scheme; solution; space; study; thanks; theorem; traoré; u ε; uniqueness; uεn+1; variable; vol; weak; ε n+1; ε,0; ε,1; λku;  ;  ;  ;  ;   cache: cubo-3094.pdf plain text: cubo-3094.txt item: #462 of 481 id: cubo-3095 author: He, Cong; Chen, Jingchun title: Vlasov-Poisson equation in weighted Sobolev space \(W^{m, p}(w)\) date: 2022-08-22 words: 5638 flesch: 89 summary: − φg) · ∂ α x ∂ β v ∇vg, |∂ α x ∂ β v (f − g)| p−2 · ∂αx ∂ β v (f − g)w 〉 . (4.20) Multiplying |∂αx ∂ β v (f −g)| p−2·∂αx ∂ β v (f −g)w on both sides of (4.20), and then integrating over Rnx × R n v yields that 1 p d dt ‖∂αx ∂ β v (f − g)‖ p L p x,v(w) + ∑ β1<β C β1 β 〈 ∂β−β1v v · ∂ β1 v ∇x∂ α x (f − g), |∂ α x ∂ β v (f − g)| p−2 · ∂αx ∂ β v (f − g)w 〉 ︸ ︷︷ ︸ J̃1 = 〈 ∇xφf · |∂ α x ∂ β v (f − g)| p, ∇vw 〉 ︸ ︷︷ ︸ J̃2 − ∑ 06=α1≤α Cα1α 〈 ∂α1x ∇xφf · ∂ α−α1 x ∂ β v ∇v(f − g), |∂ α x ∂ β v (f − g)| p−2 · ∂αx ∂ β v (f − g)w 〉 ︸ ︷︷ ︸ J̃3 − ∑ 0≤α1≤α C α1 α 〈 ∂ α1 x (∇xφf − ∇xφg) · ∂ α−α1 x ∂ β v ∇vg, |∂ α x ∂ β v (f − g)| p−2 · ∂αx ∂ β v (f − g)w 〉 ︸ ︷︷ ︸ J̃4 . (4.21) We could repeat the estimates in the proof of the existence except for some special term. keywords: cubo; derivative; equation; estimates; existence; g)‖lpx; global; k+1‖; l p; order; p x; p(w; poisson; proof; p−1; sobolev; solutions; space; sup; term; theorem; v(w; vlasov; vol; weighted; β v; ‖∂i+α1x; ‖∂αx; ∂ β; ∇vf; ∇xφ; ∇xφf;   cache: cubo-3095.pdf plain text: cubo-3095.txt item: #463 of 481 id: cubo-3096 author: Djibaoui, Meriem; Moussaoui, Toufik title: Variational methods to second-order Dirichlet boundary value problems with impulses on the half-line date: 2022-08-22 words: 3718 flesch: 87 summary: Since u ∈ H10 (0, ∞), it is evident that u(0) = u(∞) = 0. For j ∈ {1, 2, . . . with ∞ ∑ j=1 ajg(tj), ∞ ∑ j=1 ajg(tj) p(tj) , ∞ ∑ j=1 bjg(tj) pδ(tj) , ∞ ∑ j=1 bjg(tj) pδ+1(tj) are convergent series, such that the impulsive functions Ij have sublinear growths i.e., |Ij(u)| ≤ aj + bj|u| δ for every u ∈ R, j ∈ {1, 2, . . .}. keywords: boundary; critical; cubo; dirichlet; f(t; h10; impulsive; j=1; order; p(tj; point; problem; solution; theorem; tj+1; u(0; value; variational; weak; α‖u‖2; ∞ ∑; ∥ ∥ cache: cubo-3096.pdf plain text: cubo-3096.txt item: #464 of 481 id: cubo-3099 author: Kawamura, Masaya title: On an \(a\) \(priori\) \(L^\infty\) estimate for a class of Monge-Ampère type equations on compact almost Hermitian manifolds date: 2022-08-22 words: 9209 flesch: 91 summary: − 1)ψχn−α−1tu ∧ ωα−2 ∧ ∂ω ∧ ∂̄ω −α(n − α)ψχn−α−1tu ∧ ωα−1 ∧ ∂∂̄ω } (4.8) On the other hand, we have that by Stokes’ theorem, I = ∫ 1 0 ∫ M e −pu d dt (χntu − ψχn−αtu ∧ ωα)dt = ∫ 1 0 ∫ M e −pu √ −1∂∂̄u ∧ (nχn−1tu − (n − α)ψχn−α−1tu ∧ ωα)dt = ∫ 1 0 ∫ M d(e−pu √ −1∂̄u ∧ (nχn−1tu − (n − α)ψχn−α−1tu ∧ ωα))dt − ∫ 1 0 ∫ M √ −1∂e−pu ∧ ∂̄u ∧ (nχn−1tu − (n − α)ψχn−α−1tu ∧ ωα)dt + ∫ 1 0 ∫ M √ −1e−pu∂̄u ∧ ∂(nχn−1tu − (n − α)ψχn−α−1tu ∧ ωα)dt = p ∫ 1 0 ∫ M e −pu √ −1∂u ∧ ∂̄u ∧ (nχn−1tu − (n − α)ψχn−α−1tu ∧ ωα)dt −1 p ∫ 1 0 ∫ M √ −1∂̄e−pu ∧ ∂(nχn−1tu − (n − α)ψχn−α−1tu ∧ ωα)dt = p ∫ keywords: ampère; chern; class; compact; complex; connection; cubo; equation; estimate; e−pu; e−puχn−1 ∧; following; function; hermitian; ij̄; ik̄; inequality; īj̄; kawamura; k̄j̄; large; lemma; local; m e; manifold; metric; monge; nχn−1tu; n−1; p2 ∫; priori; proof; real; respect; satisfies; smooth; sn(χu; solution; structure; su ∧; theorem; torsion; tu −; type; uniform; unitary; vol; zi)∂ϕ(zs; α)ψχn−α−1tu ∧; ωn−lds; ωα)dt; ϕs̄; ∂̄u ∧; ∂̄χ; − α; −1∂̄∂∂̄u; −pu; ∧ ω; ∧ ωdsdt; ∧ ωdt; ∧ ωn−1; ∧ ωα−1; ∫ m; ∫ t cache: cubo-3099.pdf plain text: cubo-3099.txt item: #465 of 481 id: cubo-3101 author: Bochi, Jairo; Iommi, Godofredo; Ponce, Mario title: Perfect matchings in inhomogeneous random bipartite graphs in random environment date: 2022-08-22 words: 3369 flesch: 77 summary: Given an environment ω ∈ Ω, we construct a sequence of random bipartite graphs Gn,ω considering the sets of vertices Wn,ω = (w1(ω), . . . Let (Gn,ω)n≥1 be a sequence of random bipartite graphs on a random environment ω keywords: a(ij)(ω; bipartite; bochi; cubo; denote; edge; entries; environment; erdős; following; graphs; inhomogeneous; iommi; large; law; matchings; matrix; mean; measure; number; perfect; ponce; probability; random; result; rényi; scaling; space; theorem; vol cache: cubo-3101.pdf plain text: cubo-3101.txt item: #466 of 481 id: cubo-3102 author: Fredj, Fouad; Hammouche, Hadda title: On existence results for hybrid \(\psi-\)Caputo multi-fractional differential equations with hybrid conditions date: 2022-08-22 words: 5962 flesch: 83 summary: [23] Y. Zhao, S. Sun, Z. Han and Q. Li, “Theory of fractional hybrid differential equations”, Comput. − h(t,v(t))| ≤ L(t)|u(t) − v(t)|, and |f(t,u(t),v(t)) keywords: banach; c(j; cdq;ψu(t; conditions; continuous; cubo; derivative; differential; equations; existence; fixed; fractional; fredj; functions; h(t; hammouche; hybrid; iq;ψ; lemma; operator; order; point; problem; results; solution; theorem; u(t; uniqueness; vol; γ(p; γ(q; γ(ηi; ψ−caputo; ∣ ∣;  ;  ;  ;  ;  ;   cache: cubo-3102.pdf plain text: cubo-3102.txt item: #467 of 481 id: cubo-3103 author: Tekir, Ünsal; Koç, Suat; Abu-Dawwas, Rashid; Yıldız, Eda title: Graded weakly 1-absorbing prime ideals date: 2022-08-22 words: 7840 flesch: 93 summary: In [15], Refai et al. defined and studied graded prime ideals. A proper graded ideal P of a graded ring R is called graded prime ideal if whenever xy ∈ P for some x, y ∈ h(R) then either x ∈ P or y ∈ P . keywords: absorbing; case; contradiction; cubo; divides; elements; g ∈; graded; graded ideal; graded prime; graded ring; graded weakly; g∈g; h(r; ideal; ideal p; nonunits; pg2; prime; prime ideal; proof; proper; ring; theorem; vol; weakly; weakly prime; xg1; xyz; y ∈; yg2; zg3; ∈ p cache: cubo-3103.pdf plain text: cubo-3103.txt item: #468 of 481 id: cubo-3105 author: Van Maldeghem, Hendrik; Victoor, Magali title: On Severi varieties as intersections of a minimum number of quadrics date: 2022-08-22 words: 12139 flesch: 76 summary: = φ(p+q) for points p, q ∈ E6(K). = ∑ {p,q}⊆P a{p,q}XpXq, with a{p,q} ∈ K. Since all points corresponding to the standard basis vectors belong to E6(K), we have a{p} = 0, for all p ∈ P. Now let p, q ∈ P be distinct but non-collinear in Γ. Then one easily checks that 〈ep + eq〉 ∈ E6(K). keywords: black; c(v; cartan; case; collinear; conic; contradiction; coordinates; corresponding; cubic; cubo; dimensional; disjoint; e6(k; equation; example; extension; field; fixed; flat; following; follows; form; g2,6(k; generalized; gq(2; grey; host; image; intersection; k27; lemma; lines; maldeghem; map; minimum; number; observation; order; paper; plane; point; projective; proof; quadratic; quadrics; regular; s2,2(k; segre; set; severi; short; singular; space; spread; subspace; unique; v2(k; varieties; variety; vector; veronese; victoor; white; φ(u; φ(v; φ(w cache: cubo-3105.pdf plain text: cubo-3105.txt item: #469 of 481 id: cubo-3106 author: Jinnah, M. I.; Mathew, Shine C. title: Ideal based graph structures for commutative rings date: 2022-08-22 words: 3889 flesch: 88 summary: Clearly max R is a dominating set for Γ ∗∗ 2 (R). Now, if R is local with maximal ideal m, since Γ∗ 2 (R) is complete, m must be principal with index of nilpotency 2. (⇐): If R is a direct sum of two fields, Γ∗2(R) ∼= K2 and if R is local with principal maximal ideal having index of nilpotency 2, Γ∗ 2 (R) ∼= K1. keywords: adjacent; commutative; fields; graph; ideal; local; maximal; non; proof; ring; set; split; subgraph; theorem; γ∗2(r cache: cubo-3106.pdf plain text: cubo-3106.txt item: #470 of 481 id: cubo-3107 author: Seshagiri Rao, N.; Kalyani, K. title: Fixed point results of \((\phi,\psi)\)-weak contractions in ordered \(b\)-metric spaces date: 2022-08-22 words: 8944 flesch: 87 summary: In addition to Theorem 3.8, if for all (υ,ξ),(r,s) ∈ P × P, there exists (c∗,d∗) ∈ P × P such that (h(c∗,d∗),h(d∗,c∗)) is comparable to (h(υ,ξ),h(ξ,υ)) and to (h(r,s),h(s,r)), then h and f have a unique coupled common fixed point in P × [24] E. Graily, S. M. Vaezpour, R. Saadati and Y. J. Cho, “Generalization of fixed point theorems in ordered metric spaces concerning generalized distance”, Fixed Point Theory Appl., 30, 8 pages, 2011. keywords: coincidence; common; complete; condition; continuous; contractions; cubo; d(fυ; d(υ; d(υn; decreasing; fixed; following; fυn; generalized; gυn; h(υ; kalyani; lim; mappings; math; max; metric; metric spaces; monotone; non; n→+∞; pages; point; proof; radenović; rao; results; sequence; seshagiri; set; spaces; theorem; theory; vol; ξn+1; υn+1 cache: cubo-3107.pdf plain text: cubo-3107.txt item: #471 of 481 id: cubo-3154 author: Carpintero, C.; Rosas, E.; Rajesh, N.; Saranyasri, S. title: On upper and lower ω-irresolute multifunctions date: 2014-10-01 words: 4841 flesch: 87 summary: A point x ∈ X is called a condensation point of A if for each U ∈ τ with x ∈ U, the set U ∩ A is uncountable. ∈ U ⊂ F+(V) keywords: closed; f(x; f(x0; f+(v; l.ω; lower; multifunction; neighborhood; open; point; proof; set; space; subset; theorem; u.ω; upper; ωo(x; ωo(y cache: cubo-3154.pdf plain text: cubo-3154.txt item: #472 of 481 id: cubo-3205 author: Craig, Andrew; Haviar, Miroslav; São João, José title: Dual digraphs of finite semidistributive lattices date: 2022-12-21 words: 10671 flesch: 79 summary: = vE if and only if u 61 v and v 61 u. We can finally summarise the previous results in the following characterisations of join-semidistribu- tivity, meet-semidistributivity and semidistributivity of finite lattices via the properties of their dual digraphs: CUBO 24, 3 (2022) Dual digraphs of finite semidistributive lattices 381 Corollary 3.9. This open access article is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. http://cubo.ufro.cl/ https://doi.org/10.56754/0719-0646.2403.0369 CUBO 24, 3 (2022) Dual digraphs of finite semidistributive lattices 371 1 Introduction Semidistributivity was first described by Jónsson keywords: closed; closure; craig; cubo; definition; digraph; disjoint; dominating; dual; dual digraph; element; filter; finite; finite lattice; finite semidistributive; form; haviar; ideal; join; lattice; lemma; maximal; mdfips; meet; minimal; order; pair; ploščica; prime; proof; proposition; relation; representation; semidistributive; set; theorem; tirs; transitive; urquhart; vertex; vertices; vol; ↑x,↓y; ∈ v cache: cubo-3205.pdf plain text: cubo-3205.txt item: #473 of 481 id: cubo-3206 author: Georgiev, Svetlin; Majdoub, Mohamed title: Two nonnegative solutions for two-dimensional nonlinear wave equations date: 2022-12-21 words: 6033 flesch: 91 summary: x2 0 sign(x1)sign(x2)(x1 − s1)2(x2 − s2)2g(t1, s1, s2) × − log |x − ξ| ) dξ = (h1 + h2t) p 2π (∫ |x−ξ|≤t log(t keywords: cubo; dimensional; equations; existence; g(t1; georgiev; ivp; j=1; lemma; log; l∑ j=1; majdoub; mebarki; nonlinear; nonnegative; positive; proof; r))pj; s1)2(x2; sign(x1)sign(x2)(x1; solutions; t1)2; vol; wave; ∣∣∣∣ cache: cubo-3206.pdf plain text: cubo-3206.txt item: #474 of 481 id: cubo-3207 author: Panigrahi, Saroj; Rout, Sandip title: Existence of positive solutions for a nonlinear semipositone boundary value problems on a time scale date: 2022-12-21 words: 7041 flesch: 94 summary: = 1, M = 1, α, β, γ, δ ≥ 0, g(t, y) = y ln(1+y) and h(t, y) = √ y sin y 6 . First we show that Tλ(K) ⊂ K. Let y ∈ K and t keywords: boundary; c[ρ(c; conditions; cubo; existence; g(s; g(t; h(t; h1)–(h3; lemma; max; min; nonlinear; positive; problem; proof; semipositone; small; solutions; t ∈; theorem; time; t∈[t1; value; x(s; y(s; y(t; λ2h(s; ρ(c; ρ(c)≤t≤σ(d; σ(d)]t cache: cubo-3207.pdf plain text: cubo-3207.txt item: #475 of 481 id: cubo-3208 author: Bouaouid, Mohamed; Kajouni, Ahmed; Hilal, Khalid; Melliani, Said title: A class of nonlocal impulsive differential equations with conformable fractional derivative date: 2022-12-21 words: 6561 flesch: 82 summary: [10] M. Bouaouid, “Mild solutions of a class of conformable fractional differential equations with nonlocal conditions”, Acta Math. [11] M. Bouaouid, M. Atraoui, K. Hilal and S. Melliani, “Fractional differential equations with nonlocal-delay condition”, J. Adv. keywords: appl; bouaouid; cauchy; conformable; cubo; derivative; differential; equations; existence; f(s; following; fractional; function; g(x; hi(x(ti; hilal; i=1; impulsive; math; melliani; mild; nonlocal; problem; solutions; sup; sα α; sα−1 t; t t; tα α; tα −; tα1; tα2; vol; x(s))ds; x(t; ∣ =; ∣ t; ∣ |; ∣ ∣; ∣ ∫ cache: cubo-3208.pdf plain text: cubo-3208.txt item: #476 of 481 id: cubo-3209 author: Saavedra, Manuel; Villavicencio, Helmuth title: On the minimum ergodic average and minimal systems date: 2022-12-21 words: 3555 flesch: 80 summary: Recall that a point x ∈ X is periodic for T : X → X if T n(x) = x for some n ∈ N and the minimal such n is called the period of T . Given x ∈ X, if X = O(p), then there is nothing to prove. keywords: average; c(x; compact; continuous; cubo; e(x; ergodic; i(x; i=0; lemma; lim; measure; metric; minimal; minimum; non; open; point; proof; set; space; systems; transformation; ̺(a; α(f cache: cubo-3209.pdf plain text: cubo-3209.txt item: #477 of 481 id: cubo-3210 author: Gopal, N. S.; Jonnalagadda, J. M. title: Positive solutions of nabla fractional boundary value problem date: 2022-12-21 words: 6271 flesch: 86 summary: ≤ ∇Eλ,ν,ν−1(t, ρ(a)) for t ∈ Na+1; (4) ∇Eλ,ν,ν−1(t, ρ(a)) is a decreasing function with respect to t for t ∈ Na+1 On the other hand, define the set Ω2 = {u ∈ K : ∥u∥ < r2}. keywords: a+2; appl; boundary; b∑ s; calculus; conditions; continuous; cubo; decreasing; definition; difference; discrete; f(t; fractional; function; g(s; g(t; gopal; jonnalagadda; lemma; max; min; nabla; nba+2; point; positive; problem; proof; s)f(s; solutions; theorem; t∈nba; t∈ndc; u(s; u(t; value; vol; ν−1(b; ρ(a; ρ(s; ∈ r; ∥tu∥ cache: cubo-3210.pdf plain text: cubo-3210.txt item: #478 of 481 id: cubo-3211 author: Pal, Buddhadev; Kumar, Santosh; Kumar, Pankaj title: Einstein warped product spaces on Lie groups date: 2022-12-21 words: 5621 flesch: 84 summary: In our paper, from Corollary 3.5, we can say that bi-invariant metric generated by the Killing form on semi-simple compact Lie group G1 is one in which we cannot construct non trivial Einstein warped product with base G1. Let G1 and G2 be semi-simple compact Lie groups of dimensions m1, m2 > 2 and bi-invariant metric tensors coming from their respective Killing forms. keywords: = −; compact; compact lie; constant; cubo; curvature; einstein; equation; fiber; form; function; geom; geometry; grad; group; hf1; invariant; invariant metric; killing; kumar; left; lie; lie group; manifold; math; metric; non; pal; product; ric2; riemannian; scalar; semi; simple; space; vol; warped; warped product cache: cubo-3211.pdf plain text: cubo-3211.txt item: #479 of 481 id: cubo-3212 author: Cammaroto, Filippo title: Infinitely many solutions for a nonlinear Navier problem involving the \(p\)-biharmonic operator date: 2022-12-21 words: 7030 flesch: 80 summary: Then the following facts hold: (r1) if p1 < p < p2, for all λ ∈ R and for all µ > 0, the problem (Pλ,µ) admits a sequence of non-zero weak solutions; (r2) if p1 < p = p2, there exists µ1 > 0 + V (x)|u|p−2u = λh(x)|u|m−2u + µr(x)s(u) in Ω u = ∆u = 0 on Ω (P λ,µ) the following facts hold: (r1) if p1 < p < p2, for all λ ∈ R and for all µ > 0, the problem (P λ,µ) admits a sequence of non-zero weak solutions; (r2) if p1 < p = p2, there exists µ1 > 0 keywords: = +; b(x0; biharmonic; boundary; cammaroto; case; choice; class; cubo; differential; equations; existence; f(x; following; fourth; functions; g(x; global; lim; math; max; minimum; navier; nonlinear; operator; order; p k; pages; paper; particular; problem; proof; pλ,µ; sequence; similar; solutions; theorem; vol; w(x))dx; weak cache: cubo-3212.pdf plain text: cubo-3212.txt item: #480 of 481 id: cubo-3213 author: Castillo, René Erlín; Sultan, Babar title: A derivative-type operator and its application to the solvability of a nonlinear three point boundary value problem date: 2022-12-21 words: 6042 flesch: 79 summary: = n∑ j=0 D(φ,j)ω (f)(a) I (φ,j) ω (1)(x) + Rn(x), (4.1) with Rn(x) = g(x) − g(a) D (φ,n) ω g(ξ) ( D(φ,n)ω (f)(ξ) − D (φ,n) ω (f)(a) ) , (4.2) where x ̸= a and ξ is between a and x. Proof. − D (φ,1) ω (Rn)(a) D (φ,1) ω (g)(θ1) keywords: application; boundary; c2[0; castillo; conformable; continuous; cubo; derivative; differential; equation; existence; e−λ; f(x; formula; fractional; function; g(s; integral; k(s; new; nonlinear; operator; order; point; problem; proof; solution; solvability; sultan; sup; theorem; type; value; variable; vol; x(s; |f(s; βe−λη; φ(s; ω′(s; ∣∣∣∣∆ cache: cubo-3213.pdf plain text: cubo-3213.txt item: #481 of 481 id: cubo-3214 author: Milovanović, Gradimir V.; Mir, Abdullah; Hussain, Adil title: Estimates for the polar derivative of a constrained polynomial on a disk date: 2022-12-21 words: 5203 flesch: 80 summary: |P(z)| + ( |β| + 1 kn−1 ) mk } + ( |β| − k 1 + kn ){ s + √ kn−s|an−s| − mk − √ |a0|√ kn−s|an−s| − mk }( max |z|=1 |P(z)| − mk kn ) , (2.1) where mk = min|z|=k |P(z)|. + ( |β| + 1 kn−1 ) mk } + ( |β| − k 1 + kn ){ s + √ kn−s|an−s| − mk − √ |a0|√ kn−s|an−s| − mk }( max |z|=1 |P(z)| − mk kn ) , which is exactly (2.1). keywords: aνz; complex; constrained; cubo; degree; degree n; derivative; govil; inequalities; inequality; k k; kn max; kn−s|an−s|; lemma; math; max; max |z|=1; milovanović; mir; number; polar; polynomial; theorem; vol; zeros; |a0|; |dβp(z)|; |p(z)|; |q′(z)|; |z|=1; |z|=1 |p(z)|; |β|; ν=0; ′(z)|; − mk; − √; ≥ n cache: cubo-3214.pdf plain text: cubo-3214.txt