Showing papers in "Communications of The Korean Mathematical Society in 2006"
TL;DR: In this paper, it was shown that if a continuous surjective map f on a compact metric space X has the average shadowing property, then every point x is chain recurrent.
Abstract: We prove that if a continuous surjective map f on a compact metric space X has the average shadowing property, then every point x is chain recurrent. We also show that if a homeo- morphism f has more than two flxed points on S 1 , then f does not satisfy the average shadowing property. Moreover, we construct a homeomorphism on a circle which satisfles the shadowing prop- erty but not the average shadowing property. This shows that the converse of the theorem 1.1 in (6) is not true.
23 citations
TL;DR: In this paper, the authors extend the Marcinkiewicz-zygmund strong laws for linear statistics under certain moment condi- tions on both the weights and the distribution.
Abstract: Strong laws are established for linear statistics that are weighted sums of a random sample. We show extensions of the Marcinkiewicz-Zygmund strong laws under certain moment condi- tions on both the weights and the distribution. The result obtained extends and sharpens the result of Sung ((12)).
20 citations
TL;DR: A common fixed point theorem for compatible maps of type on fuzzy metric spaces with arbitrary continuous t-norm is proved.
Abstract: In this paper we prove a common fixed point theorem for compatible maps of type on fuzzy metric spaces with arbitrary continuous t-norm.
17 citations
TL;DR: In this paper, the authors characterize the boundedness and compactness of weighted composition operators acting on Hardy spaces of the unit disk and show that the composition operator C' deflned by C'(f) = fo' and when ''z = z we have the multiplication operator Mdeflated by Mˆ(f)) = ˆf.
Abstract: In this paper, we characterize the boundedness and compactness of weighted composition operatorsC'f = ˆfo' act- ing between Bergman-type spaces. LetD be the open unit disk in the complex planeC: Denote byH(D) the space of holomorphic functions on D: A weighted composition op- eratorC'(f)(z) = ˆ(z)f('(z)); for all z 2 D; where ' andare holomorphic functions deflned in D such that '(D) ‰ D: When ˆ = 1; we just have the composition operator C' deflned by C'(f) = fo' and when '(z) = z we have the multiplication operator Mdeflned by Mˆ(f) = ˆf: During the last century, composition operators have been studied extensively on spaces of analytic functions with the aim to explore the connection between the behavior of C' and function the- oretic properties of ': During the past few decades this subject has undergone explosive growth. As a consequence of the Littlewood Subor- dination principle (10) it is known that every analytic self map ' induces a bounded composition on Hardy and weighted Bergman spaces of the unit disk. However characterizing the compact composition operators acting on Hardy spaces of the disk was a di-cult problem. Commend- able work in this direction was done by Schwartz (14), Shapiro and Taylor (15), MacCluer and Shapiro (11) and Shapiro (16). Many other impor- tant properties of C' have also been studied on these spaces. We refer
17 citations
TL;DR: In this paper, a new bivariate beta distribution based on the Appell function of the third kind is introduced and various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and conditional moments.
Abstract: A new bivariate beta distribution based on the Appell function of the third kind is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and conditional moments. The method of maximum likelihood is used to derive the associated estimation procedure as well as the Fisher information matrix.
15 citations
TL;DR: In this article, the authors used calculus inequalities and embedding theorems in R 1 to establish W 1 2-estimates for the solutions of the predator population model with cross-difiusion and self-disease terms.
Abstract: Using calculus inequalities and embedding theorems in R 1 , we establish W 1 2-estimates for the solutions of prey-predator population model with cross-difiusion and self-difiusion terms. Two cases are considered ; (i) d1 = d2, fi12 = fi21 = 0, and (ii) 0 < fi21 < 8fi11, 0 < fi12 < 8fi22. It is proved that solutions are bounded uni- formly pointwise, and that the uniform bounds remain independent of the growth of the difiusion coe-cient in the system. Also, con- vergence results are obtained when t ! 1 via suitable Liapunov functionals. ut = ¢((d1 + fi11u + fi12v)u) + u(a1 i b1u i c1v) in › £ (0;1); vt = ¢((d2 + fi21u + fi22v)v) + v(a2 + b2u i c2v) in › £ (0;1); @u @" = @v @" = 0 on @› £ (0;1); u(x;0) = u0(x) ‚ 0; v(x;0) = v0(x) ‚ 0 in ›;
14 citations
TL;DR: In this article, the boundedness and the com-pactness of weighted composition operator between and Bergman type space on the unit ball of the unit sphere of the graph is studied.
Abstract: In this paper, we study the boundedness and the com-pactness of weighted composition operator between and Bergman type space on the unit ball of . Also, the norm of corresponding weighted composition operator is computed.
12 citations
TL;DR: In this article, the authors obtained a new common flxed point theorem by using a new contractive condition in intu- itionistic fuzzy metric spaces, which generalizes and extends many known results in fuzzy metric space and metric spaces.
Abstract: The purpose of this paper is to obtain a new common flxed point theorem by using a new contractive condition in intu- itionistic fuzzy metric spaces. Our result generalizes and extends many known results in fuzzy metric spaces and metric spaces.
11 citations
TL;DR: In this article, the authors express the analytic Feynman integral over as a limit of Wiener integrals over and establish change of scale formulas for Wiener Integrals over for some functionals.
Abstract: Wiener measure and Wiener measurability behave badly under the change of scale transformation. We express the analytic Feynman integral over as a limit of Wiener integrals over and establish change of scale formulas for Wiener integrals over for some functionals.
10 citations
TL;DR: The supra fuzzy topology which generated from a fuzzy bitopological space is used to introduce and study the concepts of continuity (resp. openness, closeness) of mapping, separation axioms and compactness for a fuzzybitopo- logical spaces.
Abstract: In this paper, we used the supra fuzzy topology which generated from a fuzzy bitopological space (1) to introduce and study the concepts of continuity (resp. openness, closeness) of mapping, separation axioms and compactness for a fuzzy bitopo- logical spaces. Our deflnition preserve much of the correspondence between concepts of fuzzy bitopological spaces and the associated fuzzy topological spaces.
9 citations
TL;DR: It is shown how to associate an intuitionistic fuzzy sub(semi)group with an intuitionism fuzzy graph in a natural way.
Abstract: The notion of intuitionistic fuzzy graphs is introduced. We show how to associate an intuitionistic fuzzy sub(semi)group with an intuitionistic fuzzy graph in a natural way.
TL;DR: In this article, a change of scale formula for Wiener integrals of various functions on which need not be bounded or continuous is presented. But this formula is only applicable to the generalized Fresnel class F(B) which corresponds to the Banach algebra S on classical Wiener space.
Abstract: Cameron and Storvick discovered change of scale formulas for Wiener integrals of bounded functions in a Banach algebra S of analytic Feynman integrable functions on classical Wiener space. Yoo and Skoug extended these results to abstract Wiener space for a generalized Fresnel class containing the Fresnel class F(B) which corresponds to the Banach algebra S on classical Wiener space. In this paper, we present a change of scale formula for Wiener integrals of various functions on which need not be bounded or continuous.
TL;DR: An iterative algorithm is presented which is mainly based on computing the distance between a given point and a standard ellipse in the xyiplane to simplify the distance function between the two ellipses.
Abstract: We are interested in the distance problem between two objects in three dimensional Euclidean space. There are many dis- tance problems for various types of objects including line segments, boxes, polygons, circles, disks, etc. In this paper we present an iter- ative algorithm for flnding the distance between two given ellipses. Numerical examples are given. 1. Introduction and preliminaries The distance problem between two given objects in three dimensional space can be found often in computer-aided geometric design systems. Further, it is important to propose an e-cient algorithm for flnding the distance between two objects. There are many distance problems for various types of objects including line segments (5), boxes (6), polygons (8), circles (7), disks (1), etc. In the literature, many problems already have been studied and various numerical techniques to compute the optimal distance have been given. In this paper we consider the problem of flnding the distance between two given ellipses. The representation of an ellipse in three dimensional space can be given by using a geometric transformation of a standard ellipse in the xyiplane. This may simplify the distance function between the two ellipses. Thus, our problem is reduced to the distance problem between one standard ellipse and the other ellipse. We can present an iterative algorithm which is mainly based on computing the distance between a given point and a standard ellipse.
TL;DR: In this article, the generic submanifolds of a Riemannian manifold with a hypercosymplectic 3-structure are studied. Integra-bility conditions for certain distributions on the generic Submanifold are discussed.
Abstract: Generic submanifolds of a Riemannian manifold en- dowed with a hypercosymplectic 3-structure are studied. Integra- bility conditions for certain distributions on the generic submanifold are discussed. Geometry of leaves of certain distributions are also studied.
TL;DR: On the unit disk of the complex plane, a characteriza- tion of Bloch function is expressed in this article, extending the known result on the basis of a characterisation of the Bloch functions.
Abstract: On the unit disk of the complex plane, a characteriza- tion of Bloch function is expressed extending known result.
TL;DR: In this article, a new iterative algorithm for approximating zeros of accretive operators in Banach spaces is proposed, which is based on the algorithm proposed in this paper.
Abstract: In this paper, we introduce and study a new iterative algorithm for approximating zeroes of accretive operators in Banach spaces
TL;DR: A ring R is called (left principally) quasi-Baer if the left annihilator of every (principal) left ideal of R is generated by an idempotent.
Abstract: A ring R is called (left principally) quasi-Baer if the left annihilator of every (principal) left ideal of R is generated by an idempotent. Let R be a ring, G be an ordered monoid acting on R by fl and R be G-compatible. It is shown that R is (left principally) quasi-Baer if and only if skew monoid ring Rfl(G) is (left principally) quasi-Baer. If G is an abelian monoid, then R is (left principally) quasi-Baer if and only if the Cohn-Jordan exten- sion A(R;fl) is (left principally) quasi-Baer if and only if left Ore quotient ring G i1 Rfl(G) is (left principally) quasi-Baer.
TL;DR: In this article, all the derivations of the non-associative algebra WN0;0;s1 and its subalgebra WN 0;s;01 are presented.
Abstract: Several authors flnd all the derivations of an algebra (1), (3), (7). A Weyl type non-associative algebra and its subalgebra are deflned in the paper (2), (3), (10). All the derivations of the non- associative algebra WN0;0;s1 is found in this paper (4). We flnd all the derivations of the non-associative algebra WN0;s;01 in this paper (5).
TL;DR: In this paper, the notion of p-stacks was introduced to characterize S ⁄ -continuous functions, sep- aration axioms, supracompactness and some properties on supra- topological spaces.
Abstract: In (1), we introduced the notion of p-stacks. In this pa- per, by using p-stacks we characterize S ⁄ -continuous functions, sep- aration axioms, supracompactness and some properties on supra- topological spaces. We also introduce the notion of p-supracomp- actness and study some properties.
TL;DR: In this article, the authors show that if the minimal basically disconnected cover ⁄Xi of Xi is given by the space of flxed aeZ(X) # - ultrafllters on Xi (i = 1;2) and the product space of a P-space and a countably locally weakly Lindelof basi-cally disconnected space is basically disconnected, then (x £ X, y £ Y, x £ Y ) is the minimal essentially disconnected cover of X £ Y.
Abstract: In this paper, we show that if the minimal basically disconnected cover ⁄Xi of Xi is given by the space of flxed aeZ(X) # - ultrafllters on Xi (i = 1;2) and ⁄X1 £ ⁄X2 is a basically discon- nected space, then ⁄X1 £ ⁄X2 is the minimal basically discon- nected cover of X1 £ X2 Moreover, observing that the product space of a P-space and a countably locally weakly Lindelof basi- cally disconnected space is basically disconnected, we show that if X is a weakly Lindelof almost P-space and Y is a countably locally weakly Lindelof space, then (⁄X £ ⁄Y , ⁄X £ ⁄Y ) is the minimal basically disconnected cover of X £ Y
TL;DR: In this paper, a generalized vector variational inequality with operator solutions (GOVVI) was proposed, which extends variational inequalities into a multivalued case, and a more general pseudomonotone operator is treated.
Abstract: In a recent paper, Domokos and [2] gave an interesting interpretation of variational inequalities (VI) and vector variational inequalities (VVI) in Banach space settings in terms of variational inequalities with operator solutions (in short, OVVI). Inspired by their work, in a former paper [4], we proposed the scheme of generalized vector variational inequality with operator solutions (in short, GOVVI) which extends (OVVI) into a multivalued case. In this note, we further develop the previous work [4]. A more general pseudomonotone operator is treated. We present a result on the existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [8] within the framework of (GOVVI) by exploiting some techniques on (GOVVI) or (GVVI) in [4].
TL;DR: In this paper, the authors considered a type of large deviation principle using Freidlin-Wentzell exponential estimates for the solutions to perturbed stochastic differential equations (SDEs) driven by the Martingale measure (Gaussian noise).
Abstract: We consider a type of large deviation Principle(LDP) using Freidlin-Wentzell exponential estimates for the solutions to perturbed stochastic differential equations(SDEs) driven by Martingale measure(Gaussian noise). We are using exponential tail estimates and exit probability of a diffusion process. Referring to Freidlin-Wentzell inequality, we want to show another approach to get LDP for the solutions to SDEs.
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TL;DR: In this paper, the positive coexistence of a simple food chain model with ratio-dependent functional response and cross-difiusion is dis-cussed and the extinction conditions for all three interacting species and for one or two of three species are studied.
Abstract: The positive coexistence of a simple food chain model with ratio-dependent functional response and cross-difiusion is dis- cussed. Especially, when a cross-difiusion is small enough, the exis- tence of positive solutions of the system concerned can be expected. The extinction conditions for all three interacting species and for one or two of three species are studied. Moreover, when a cross- difiusion is su-ciently large, the extinction of prey species with cross-difiusion interaction to predator occurs. The method em- ployed is the comparison argument for elliptic problem and flxed point theory in a positive cone on a Banach space.
TL;DR: The exponential fuzzy probability for quadratic fuzzy number and trigonometric fuzzy number defined by quadratics function and trig onometric function are studied and the exponential fuzzy probabilities for fuzzy numbers driven by operations are calculated.
Abstract: We study the exponential fuzzy probability for quadratic fuzzy number and trigonometric fuzzy number defined by quadratic function and trigonometric function, respectively. And we calculate the exponential fuzzy probabilities for fuzzy numbers driven by operations.
TL;DR: As a generalization of ideals in subtraction algebras, the notion of rough ideals is discussed in this paper, where rough ideals are defined as a generalisation of the ideals of subtraction.
Abstract: As a generalization of ideals in subtraction algebras, the notion of rough ideals is discussed.
TL;DR: In this article, the Bergman projection type operator Pr is defined and conditions on which the operator is bounded on L p (B;d) are given, and it is shown that if f 2 L p(b;d), then (1i k w k 2 )rf(w) ¢ z 2 lp(b) p(B,d).
Abstract: In this paper, we will deflne the Bergman projection type operator Pr and flnd conditions on which the operator Pr is bound-ed on L p (B;d"). By using the properties of the Bergman projection type operator Pr, we will show that if f 2 L p(B;d"), then (1i k w k 2 )rf(w) ¢ z 2 L p (B;d"). We will also show that if (1i k w k 2 ) rf(w)¢z hz;wi 2 L p (B;d"), then f 2 L p(B;d").
TL;DR: In this article, it was shown that for a linear dynamical system f(x) = Ax of C n, f has the Th-inverse(Th-orbital inverse or Th- weak inverse) shadowing property if and only if the matrix A is hyperbolic.
Abstract: In this paper, we give a characterization of hyperbolic linear dynamical systems via the notions of various inverse shadow- ing. More precisely it is proved that for a linear dynamical system f(x) = Ax of C n , f has the Th-inverse(Th-orbital inverse or Th- weak inverse) shadowing property if and only if the matrix A is hyperbolic.
TL;DR: In this article, it was shown that a representation of a quiver is an injective representation if and only if it is isomorphic to a direct sum of representation of the types and where are injective left R-modules.
Abstract: We prove that is an injective representation of a quiver if and only if are injective left R-modules, is isomorphic to a direct sum of representation of the types and where are injective left R-modules. Then, we generalize the result so that a representation of a quiver is an injective representation if and only if each is an injective left R-module and the representation is a direct sum of injective representations.
TL;DR: In this paper, the authors give conditions that P(ns) t = 1 Xt (properly normalized) converges weakly to Wiener measure if the corresponding result for P(n) t=1 Xt is true.
Abstract: Let Xt be an m-dimensional linear process deflned by Xt = P 1=0 Aj Ztij; t = 1;2;:::, where fZtg is a sequence of m-dimensional random vectors with mean 0 : m £ 1 and positive deflnite covariance matrix i : m £ m and fAjg is a sequence of coe-cient matrices. In this paper we give su-cient conditions so that P(ns) t=1 Xt (properly normalized) converges weakly to Wiener measure if the corresponding result for P (ns) t=1 Zt is true.