Showing papers in "Journal of The Korean Mathematical Society in 2012"
TL;DR: It is proven that if the basic reproduction number R0 is less than R0, the global asymptotic stability of the uninfected and infected steady states of the HIV infection models can be established.
Abstract: In this paper, we study the global stability of two mathemat- ical models for human immunodeciency virus (HIV) infection with intra- cellular delays. Therst model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, CD4 + T cells and macrophages taking into account the saturation infec- tion rate. The second model generalizes therst one by assuming that the infection rate is given by Beddington-DeAng functional response. Two time delays are used to describe the time periods between viral entry the two classes of target cells and the production of new virus particles. Lyapunov functionals are constructed and LaSalle-type theorem for delay differential equation is used to establish the global asymptotic stability of the uninfected and infected steady states of the HIV infection models. We have proven that if the basic reproduction number R0 is less than
104 citations
TL;DR: In this article, a mild solution of the Navier-Stokes equations in half spaces for non-decaying initial velocities is presented, and the uni-form bound of the velocityeld and its derivatives is obtained.
Abstract: We construct a mild solutions of the Navier-Stokes equations in half spaces for nondecaying initial velocities. We also obtain the uni- form bound of the velocityeld and its derivatives.
46 citations
TL;DR: The bounds of these topological entropy and measure-theoretic entropy for nonautonomous dynamical systems, such as affine transformations on metrizable groups and smooth maps on Riemannian manifolds, are obtained.
Abstract: In this paper, the topological entropy and measure-theoreti entropy for nonautonomous dynamical systems are studied. Some prop- erties of these entropies are given and the relation between them is dis- cussed. Moreover, the bounds of them for several particular nonau- tonomous systems, such as affine transformations on metrizable groups (especially on the torus) and smooth maps on Riemannian manifolds, are obtained.
45 citations
TL;DR: In this article, the convergence properties of extended negatively depen-dent sequences under some conditions of uniform integrability were studied, and sufficient conditions of the weak law of large numbers, the p-mean convergence and the complete convergence were obtained.
Abstract: The convergence properties of extended negatively depen- dent sequences under some conditions of uniform integrability are studied. Some sufficient conditions of the weak law of large numbers, the p-mean convergence and the complete convergence for extended negatively depen- dent sequences are obtained, which extend and enrich the known results in the literature.
41 citations
TL;DR: In this article, a new extended extragradient iteration algorithm was proposed for finding a common element of the set of xed points of a nonexpansive mapping and a set of solutions of equilibrium prob-lem for a monotone and Lipschitz-type continuous mapping.
Abstract: In this paper, we introduced a new extended extragradient iteration algorithm for nding a common element of the set of xed points of a nonexpansive mapping and the set of solutions of equilibrium prob- lems for a monotone and Lipschitz-type continuous mapping. And we show that the iterative sequences generated by this algorithm converge strongly to the common element in a real Hilbert space.
39 citations
TL;DR: In this article, the Hilbert function and minimal free resolution of a star configuration in the Artinian k-algebra has been shown to have weak Lefschetz properties.
Abstract: We find the Hilbert function and the minimal free resolution of a star-configuration in . The conditions are provided under which the Hilbert function of a star-configuration in is generic or non-generic We also prove that if and are linear star-configurations in of types t and s, respectively, with , then the Artinian k-algebra has the weak Lefschetz property.
36 citations
TL;DR: In this article, the total graph of a commutative ring R with respect to its proper ideal I was studied, which is the graph where the vertices are all elements of R and where there is an undirected edge between two distinct vertices x and y if and only if x + y Z(R).
Abstract: Let R be a commutative ring and I its proper ideal, let S(I) be the set of all elements of R that are not prime to I. Here we introduce and study the total graph of a commutative ring R with respect to proper ideal I, denoted by T(). It is the (undirected) graph with all elements of R as vertices, and for distinct x, y R, the vertices x and y are adjacent if and only if x + y S(I). The total graph of a commutative ring, that denoted by T(), is the graph where the vertices are all elements of R and where there is an undirected edge between two distinct vertices x and y if and only if x + y Z(R) which is due to Anderson and Badawi [2]. In the case I = {0}, ; this is an important result on the definition.
32 citations
TL;DR: In this paper, the unique solvability of backward stochastic Volterra integral equations (BSVIEs) was studied in terms of both the adapted M-solutions introduced in (19) and the adapted solutions via a new method.
Abstract: In this paper we study the unique solvability of backward stochastic Volterra integral equations (BSVIEs in short), in terms of both the adapted M-solutions introduced in (19) and the adapted solutions via a new method. A general existence and uniqueness of adapted M- solutions is proved under non-Lipschitz conditions by virtue of a briefer argument than the ones in (13) and (19), which modifies and extends the results in (13) and (19) respectively. For the adapted solutions, the unique solvability of BSVIEs under more general stochastic non-Lipschitz conditions is shown, which improves and generalizes the results in (7), (14) and (15).
30 citations
TL;DR: In this article, it was shown that under certain conditions every Lie higher derivation and Lie triple derivation on a triangular algebra are proper, respectively, and the main results are then applied to (block) upper triangular matrix algebras and nest algesbras.
Abstract: In this paper, we show that under certain conditions every Lie higher derivation and Lie triple derivation on a triangular algebra are proper, respectively. The main results are then applied to (block) upper triangular matrix algebras and nest algebras.
27 citations
TL;DR: In this paper, the authors investigate the classes of Ding projective, Ding injective and Gorenstein at modules and show that some homological properties of modules over Ding-Chen rings can be generalized to the modules over GAs.
Abstract: The so-called Ding-Chen ring is an n-FC ring which is both left and right coherent, and has both left and right self FP-injective di- mensions at most n for some non-negative integer n. In this paper, we investigate the classes of the so-called Ding projective, Ding injective and Gorenstein at modules and show that some homological properties of modules over Gorenstein rings can be generalized to the modules over Ding-Chen rings. We rst consider Gorenstein at and Ding injective dimensions of modules together with Ding injective precovers. We then discuss balance of functors Hom and tensor.
22 citations
TL;DR: The convex cone V1 generated by separable states is contained in the cone T of all positive semi-definite block matrices whose block transposes are also positive semi -definite.
Abstract: The convex cone V1 generated by separable states is contained in the cone T of all positive semi-definite block matrices whose block transposes are also positive semi-definite. We characterize faces of the cone V1 induced by faces of the cone T which are determined by pairs of subspaces of matrices.
TL;DR: Bouwer et al. as discussed by the authors showed that every generalized Petersengraph admits a unit-distance representation in the Euclidean plane with a n-fold rotational symmetry, with the exception of the families I(n;j;j) and I(12m,m;m;5m).
Abstract: . In 1950 a class of generalized Petersen graphs was introducedby Coxeter and around 1970 popularized by Frucht, Graver and Watkins.The family of I-graphs mentioned in 1988 by Bouwer et al. representsa slight further albeit important generalization of the renowned Petersengraph. We show that each I-graph I(n;j;k) admits a unit-distance rep-resentation in the Euclidean plane. This implies that each generalizedPetersen graph admits a unit-distance representation in the Euclideanplane. In particular, we show that every I-graph I(n;j;k) has an isomor-phic I-graph that admits a unit-distance representation in the Euclideanplane with a n-fold rotational symmetry, with the exception of the fam-ilies I(n;j;j) and I(12m;m;5m), m 1. We also provide unit-distancerepresentations for these graphs. 1. IntroductionI-graphs were introduced in the Foster census [5] and form a natural gen-eralization of the generalized Petersen graphs introduced by Coxeter [8] andnamed by Watkins [26]. This well-known family of graphs has been extensivelystudied [1, 10, 18, 20, 22, 25].Let n3 and j;kbe such that 1 j, k
TL;DR: In this paper, the authors generalize the previous investigations on the topic, focusing on the number of elements of the form h m ^ k of H m k of K such that h m k = 1 H k, where m 1 and H and K are arbitrary subgroups of G. This number gives re- strictions on the Schur multiplier of G and therefore large classes of groups can be described.
Abstract: Recently, we have introduced a group invariant, which is re- lated to the number of elements x and y of a nite group G such that x ^ y = 1 G^ G in the exterior square G ^ G of G. This number gives re- strictions on the Schur multiplier of G and, consequently, large classes of groups can be described. In the present paper we generalize the previous investigations on the topic, focusing on the number of elements of the form h m ^ k of H ^ K such that h m ^ k = 1 H^ K , where m 1 and H and K are arbitrary subgroups of G.
TL;DR: In this paper, the boundedness of a large class of multi-sublinear operators on product generalized Morrey spaces with non-doubling measures was established for Calder-on-Zygmund operators, fractional inte-grals and maximal operators.
Abstract: In this paper the boundedness for a large class of multi- sublinear operators is established on product generalized Morrey spaces with non-doubling measures As special cases, the corresponding results for multilinear Calder� on-Zygmund operators, multilinear fractional inte- grals and multi-sublinear maximal operators will be obtained
TL;DR: Based on the regularity estimates for the semigroups, iteration tech-nique and the classical existence theorem of global attractors, this paper proved that the convective Cahn-Hilliard equation possesses a global attractor in Hk (k 0) space, which attracts any bounded subset of Hk(Ω) in the H k -norm.
Abstract: In this paper, we consider the convective Cahn-Hilliard equa- tion. Based on the regularity estimates for the semigroups, iteration tech- nique and the classical existence theorem of global attractors, we prove that the convective Cahn-Hilliard equation possesses a global attractor in Hk ( k 0) space, which attracts any bounded subset of Hk(Ω) in the H k -norm.
TL;DR: In this article, forced second order differential equation with p -Laplacian and nonlinearities given by a Riemann-Stieltje integrals in the form of ( p( t ) ϕ ( x'( t ) ))' + q 0 ( t) ϕ( x ( t )) + ∫ b 0 q ( t; s ) ρ (s) ( x (t )) d� ( s ) = e ( t ), where ϕ u ) := ju j sgn u, ; b 2 (0 ; 1) ;
Abstract: We consider forced second order differential equation with p -Laplacian and nonlinearities given by a Riemann-Stieltje integrals in the form of ( p ( t ) ϕ ( x ' ( t ) ))' + q 0 ( t ) ϕ ( x ( t )) + ∫ b 0 q ( t; s ) ϕ (s) ( x ( t )) d� ( s ) = e ( t ) ; where ϕ ( u ) := ju j sgn u , ; b 2 (0 ; 1) ; � 2 C (0 ; b ) is strictly increasing such that 0 � (0) 0 on ( t 0; 1), q 2 C ((0 ; 1) (0 ; b )), and � : (0 ; b ) ! R is nondecreasing. Interval oscillation criteria of the El-Sayed type and the Kong type are obtained. These criteria are further extended to equations with deviating arguments. As special cases, our work generalizes, unies, and improves many existing results in the literature.
TL;DR: In this paper, the authors studied the relationship between con- tinuous order-representability and the fulllment of the usual covering properties on topological spaces and provided an application of their results to the social choice theory context.
Abstract: In the present paper, we study the relationship between con- tinuous order-representability and the fulllment of the usual covering properties on topological spaces. We also consider the case of some al- gebraic structures providing an application of our results to the social choice theory context.
TL;DR: In this paper, the existence of the gener-alized Fourier-Feynman transform of the functional F given by F ( x) = ^ (( e1;x) � ;:::; ( en;x ) ; where ( e,x) denotes the Paley-Wiener-Zyg stochastic integral with x in a very general function space Ca;b(0 ;T ) and ^ is the Fourier transform of complex measure on B( R n ) withnite total variation.
Abstract: In this paper werst investigate the existence of the gener- alized Fourier-Feynman transform of the functional F given by F ( x) = ^ (( e1;x) � ;:::; ( en;x) � ) ; where ( e;x) � denotes the Paley-Wiener-Zyg stochastic integral with x in a very general function space Ca;b(0 ;T ) and ^ is the Fourier transform of complex measure on B( R n ) withnite total variation. We then dene two sequential transforms. Finally, we establish that the one is to identify the generalized Fourier-Feynman transform and the another transform acts like an inverse generalized Fourier-Feynman transform.
TL;DR: In this article, it was shown that a proper graded submodule Q of M is semiprime if and only if grad(Q) \ h(M) = Q \ h (M) and if M is nitely generated.
Abstract: Let G be a group. Let R be a G-graded commutative ring with identity and M be a G-graded multiplication module over R. A proper graded submodule Q of M is semiprime if whenever InKQ, where Ih(R), n is a positive integer, and Kh(M), then IKQ. We characterize semiprime submodules of M. For example, we show that a proper graded submodule Q of M is semiprime if and only if grad(Q) \ h(M) = Q \ h(M). Furthermore if M is nitely generated, then we prove that every proper graded submodule of M is contained in a graded semiprime submodule of M. A proper graded submodule Q of M is said to be almost semiprime if (grad(Q) \ h(M))n (grad(0M) \ h(M)) = (Q \ h(M))n (grad(0M) \ Q \ h(M)): Let K; Q be graded submodules of M. If K and Q are almost semiprime in M such that Q + K M and Q \ KMg for all g 2 G, then we prove that Q + K is almost semiprime in M.
TL;DR: It is proved that under some curvature conditions, any transversally harmonic map isTransversally totally geodesic.
Abstract: Let (M; F) and (M ' ; F ' ) be two foliated Riemannian mani- folds with M compact. If the transversal Ricci curvature of F is nonneg- ative and the transversal sectional curvature of Fis nonpositive, then any transversally harmonic map ϕ : (M; F) ! (M ' ; F ' ) is transversally totally geodesic. In addition, if the transversal Ricci curvature is positive at some point, then ϕ is transversally constant.
TL;DR: In this article, the memory type boundary stabilization for an Euler-Bernoulli beam with one end fixed and control at the other end is considered, and the existence of solutions using the Galerkin method and then investigate the exponential stability of solutions by using multiplier technique.
Abstract: In this paper, the memory type boundary stabilization for an Euler-Bernoulli beam with one end fixed and control at the other end is considered. We prove the existence of solutions using the Galerkin method and then investigate the exponential stability of solutions by using multiplier technique.
TL;DR: In this article, the n-th degree Jacobi polynomials are constructed to approximate the control vector and the differentiation matrix is used to approximate derivative term in the state system.
Abstract: This paper attempts to present a numerical method for solving optimal control problems. The method is based upon constructing the n-th degree Jacobi polynomials to approximate the control vector and use differentiation matrix to approximate derivative term in the state system. The system dynamics are then converted into system of algebraic equations and hence the optimal control problem is reduced to constrained optimization problem. Numerical examples illustrate the robustness, accuracy and efficiency of the proposed method.
TL;DR: In this article, the concepts of t-extending and t-Baer for modules are gen- eralized to those of FI-textending, and a characterization of T-Extending modules relative to an annihilator condition is given.
Abstract: The concepts of t-extending and t-Baer for modules are gen- eralized to those of FI-t-extending and FI-t-Baer respectively. These are also generalizations of FI-extending and nonsingular quasi-Baer proper- ties respectively and they are inherited by direct summands. We shall establish a close connection between the properties of FI-t-extending and FI-t-Baer, and give a characterization of FI-t-extending modules relative to an annihilator condition.
TL;DR: In this article, the existence of holomorphic functions for an almost complex structure (, J), defined by setting,,m, to be (1, 0)-forms, was studied.
Abstract: Given an almost complex structure (, J), , that is defined by setting , ,m, to be (1, 0)-forms, we find conditions on () for the existence of holomorphic functions an classify the almost complex structures by type (,q). Then we determine types for several examples in and including the natural almost complex structure on .
TL;DR: In this paper, the quantum sl() representation category using the web space is studied and a linear expansion with respect to a presentation of the quantum representation category of sl() is presented.
Abstract: In this paper, we study the quantum sl() representation category using the web space. Specially, we extend sl() web space for as generalized Temperley-Lieb algebras. As an application of our study, we find that the HOMFLY polynomial specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of sl(). Moreover, we correct the false conjecture [30] given by Chbili, which addresses the relation between some link polynomials of a periodic link and its factor link such as Alexander polynomial () and Jones polynomial () and prove the corrected conjecture not only for HOMFLY polynomial but also for the colored HOMFLY polynomial specialized to a one variable polynomial.
TL;DR: In this article, the authors study fundamental properties of!-limit sets and discuss the relationship between limit sets and attraction for non-autonomous discrete dynamical systems, and introduce some basic con- cepts such as limit set and attraction.
Abstract: In this paper we study !-limit sets and attraction of non- autonomous discrete dynamical systems. We introduce some basic con- cepts such as !-limit set and attraction for non-autonomous discrete sys- tem. We study fundamental properties of !-limit sets and discuss the relationship between !-limit sets and attraction for non-autonomous dis- crete dynamical systems.
TL;DR: In this article, the tilted Carathodory class by angle (, ), denoted by ) is considered, an element of which maps the unit disc into the tilted right half-plane { : Re > 0}.
Abstract: This paper mainly deals with the tilted Carathodory class by angle (, ), denoted by ) an element of which maps the unit disc into the tilted right half-plane { : Re > 0}. Firstly we will characterize from different aspects, for example by subordination and convolution. Then various estimates of functionals over are deduced by considering these over the extreme points of or the knowledge of functional analysis. Finally some subsets of analytic functions related to including close-to-convex functions with argument , -spirallike functions and analytic functions whose derivative is in are also considered as applications.
TL;DR: In this article, a finite p-group G with for all nonnormal subgroups H is classified up to isomorphism, where H is a fixed positive integer and G is a finite prime power order.
Abstract: Assume G is a finite p-group and i is a fixed positive integer. In this paper, finite p-groups G with for all nonnormal subgroups H are classified up to isomorphism. As a corollary, this answer Problem 116(i) proposed by Y. Berkovich in his book "Groups of Prime Power Order Vol. I" in 2008.
TL;DR: In this paper, an invariant -orbit closure contained in a closed interval with diameter 1/ε is defined, and a function by the supremum of such -orbit with frequency in base is defined.
Abstract: For > 1, let : [0, 1] [0, 1) be the -transformation. We consider an invariant -orbit closure contained in a closed interval with diameter 1/, then define a function by the supremum such -orbit with frequency in base , i.e., the maximum value in -orbit closure. This paper effectively determines the maximal domain of , and explicitly specifies all possible minimal intervals containing -orbits.
TL;DR: In this article, the holonomy displacement along a simple closed curve on a complete geodesic surface S in the base space is given by V ( ) = e A ( )i ; where A( ) is the area of the region on the surface S surrounded by ; = 1=2 or 0 depending on whether S is a complex submanifold or not.
Abstract: For the \Hopf bundle" S 1 ! S 2n;1 ! CH n , horizontal lifts of simple closed curves are studied. Let be a piecewise smooth, simple closed curve on a complete totally geodesic surface S in the base space. Then the holonomy displacement along is given by V ( ) = e A ( )i ; where A( ) is the area of the region on the surface S surrounded by ; = 1=2 or 0 depending on whether S is a complex submanifold or not. We also carry out a similar investigation for the complex Heisenberg group R ! H 2n+1 ! C n .