Showing papers in "Kyungpook Mathematical Journal in 2008"

Some Difference Double Sequence Spaces Defined By Orlicz Function

Abstract: In this article we introduce some difference sequence spaces defined by Orlicz function and study different properties of these spaces like completeness, solidity, symmetricity etc. We establish some inclusion results among them.

On Distribution of Order Statistics from Kumaraswamy Distribution

Abstract: . In the present paper we derive the distribution of single order statistics, jointdistribution of two order statistics and the distribution of product and quotient of two or-der statistics when the independent random variables are from continuous Kumaraswamydistribution. In particular the distribution of product and quotient of extreme order statis-tics and consecutive order statistics have also been obtained. The method used is basedon Mellin transform and its inverse. 1. IntroductionIf the random variables X 1 ,X 2 ,···X n are arranged in ascending order of mag-nitudes and then written as X (1) ≤ X (2) ≤ ··· ≤ X (n) Then X (i) is called the i t h order statistics i = 1,··· ,n. The unordered randomvariables X i are usually statistically independent and identically distributed butthe ordered random variables X (i) ,i = 1,2,··· ,n are necessarily dependent. Thedistribution of product and quotient of random variables finds an important placein the literature and much work is done when the random variables are independent.However Subramaniam [9] has derived the distribution of the product and quotientof order statistics from a uniform distribution and negative exponential distributionrespectively. Further Trudel and Malik [6] have derived the distribution of productand ratio of order statistics from Pareto, power and Weibull distributions.Order statistics play an important supporting role in the multiple comparisonsand multiple decision procedures such as the distribution of extreme order statisticsX

Strong Convergence Theorems for Asymptotically Nonexpansive Mappings by Hybrid Methods

Abstract: In this paper, we prove two strong convergence theorems for asymptotically nonexpansive mappings in Hibert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo, Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], Kim, Xu [T. H. Kim, H. K. Xu, Strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140-1152], Martinez-Yanes, Xu [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and some others.

On The Function Rings of Pointfree Topology

Abstract: The purpose of this note is to compare the rings of continuous functions, integer-valued or real-valued, in pointfree topology with those in classical topology. To this end, it first characterizes the Boolean frames (= complete Boolean algebras) whose function rings are isomorphic to a classical one and then employs this to exhibit a large class of frames for which the functions rings are not of this kind. An interesting feature of the considerations involved here is the use made of nonmeasurable cardinals. In addition, the integer-valued function rings for Boolean frames are described in terms of internal lattice-ordered ring properties. As is familiar, pointfree topology - that is, the setting of frames - shares with classical topology the fact that each basic entity (spaces in one case, frames in the other) has associated with it the ring of its real-valued continuous functions, and this in such a way that the correspondence for frames extends that for spaces. To be precise, if RL is the ring associated with a frame L and OX the frame of open sets of a space X then the classical function ring C(X) is naturally isomorphic to R(OX). It may be added here that the correspondence X 7! OX eects a full dual embedding into the category of frames of the category of Tychono spaces - the natural context for considering the rings C(X). Now, given that there is a large supply of non-spatial frames, that is, frames not isomorphic to any OX, the correspondence L 7! RL is certainly a proper extension of the correspondence X 7! C(X), via the intervening X 7! OX. That, however, does not a priori exclude the possibility that every RL might be isomorphic to some C(X) but in fact this is not the case, and one of the purposes of this note is to describe a method of verifying this. There are other ways of doing this, as will be discussed later; the present approach is to provide first a characterization of the Boolean frames L with RL isomorphic to some C(X) and then to show that this excludes all non-atomic L of nonmeasurable cardinal. Actually, it turns out to be convenient to consider these matters first for the

A New Hilbert-type Integral Inequality with Some Parameters and Its Reverse

Abstract: In this paper, by introducing some parameters and estimating the weight function, we give a new Hilbert-type integral inequality with a best constant factor. The equivalent inequality and the reverse forms are considered.

Strong Convergence of Modified Iteration Processes for Relatively Nonexpansive Mappings

Abstract: Motivated and inspired by ideas due to Matsushida and Takahashi (J. Approx. Theory 134(2005), 257-266) and Martinez-Yanes and Xu (Nonlinear Anal. 64(2006), 2400- 2411), we prove some strong convergence theorems of modified iteration processes for a pair (or finite family) of relatively nonexpansive mappings in Banach spaces, which improve and extend the corresponding results of Matsushida and Takahashi and Martinez-Yanes and Xu in Banach and Hilbert spaces, repectively.

Growth order of Meromorphic Solutions of Higher-order Linear Differential Equations

Abstract: . In this paper, we investigate higher-order linear differential equations withentire coefficients of iterated order. We improve and extend the result of L. Z. Yangby using the estimates for the logarithmic derivative of a transcendental meromorphicfunction due to Gundersen and the extended Wiman-Valiron theory by Wang and Yi. Wealso consider the nonhomogeneous linear differential equations. 1. Introduction and main resultsIn this paper, we shall assume that the reader is familiar with the fundamentalresults and the standard notation of the Nevanlinna value distribution theory ofmeromorphic functions (see [12], [8]). The term “meromorphic function” will meanmeromorphic in the whole complex plane C.The linear measure of a set E ⊂ [0,+∞) is defined as m(E) =R +∞0 χ E (t)dt.ThelogarithmicmeasureofasetE ⊂ [1,+∞)isdefinedbylm(E) =R +∞1 χ E (t)/tdt,where χ E (t) is the characteristic function of E. The upper and lower densities ofE aredensE = limsup r→+∞ m(E ∩[0,r])r, densE = liminf r→+∞ m(E ∩[0,r])r.For k ≥ 2, we consider a linear differential equation(1.1) A

On the Hyers-Ulam-Rassias Stability of the Bi-Jensen Functional Equation

Abstract: In this paper, we obtain the Hyers–Ulam–Rassias stability of a bi-Pexider functional equation $$f(x + y,z + w) = {f}_{1}(x,z) + {f}_{2}(x,w) + {f}_{3}(y,z) + {f}_{4}(y,w)$$ in the sense of Th.M. Rassias. Also, we establish the superstability of a bi-Jensen functional equation.

Permanence of a Three-species Food Chain System with Impulsive Perturbations

Abstract: We investigate a three-species food chain system with Lotka-Volterra func- tional response and impulsive perturbations. In (23), Zhang and Chen have studied the system. They have given conditions for extinction of lowest-level prey and top predator and considered the local stability of lower-level prey and top predator eradication periodic solution. However, they did not give a condition for permanence, which is one of important facts in population dynamics. In this paper, we establish the condition for permanence of the three-species food chain system with impulsive perturbations. In addition, we give some numerical examples.

Stability for a Holling Type IV Food Chain System With Impulsive Perturbations

Abstract: . We investigate a three species food chain system with a Holling type IVfunctional response and impulsive perturbations. We find conditions for local and globalstabilities of prey(or predator) free periodic solutions by applying the Floquet theory andthe comparison theorems. 1. IntroductionIt is currently very much in vogue to study population models with impulsiveperturbations containing biological and chemical controls. Especially, simple multi-species systems consisting of a three species food chain with impulsive perturbationshave been discussed by a number of researchers [13], [17], [18], [19], [20] and thereare also many literatures on impulsive prey-predator population models [10], [11],[12].A well-known model of such systems is a food chain system with Holling typeIV functional response [7], [14], [20], which can be described the following equation:(1.1)x 0 (t) = x(t)(a−bx(t))−c 1 x(t)y(t)1+e 1 x 2 (t),y 0 (t) = −d 1 y(t)+c 2 x(t)y(t)1+e 1 x 2 (t)−c 3 y(t)z(t)1+e

Uniqueness Theorems For Differential Polynomials Concerning Fixed-Points

Abstract: In this article, we deal with the uniqueness problems on meromorphic functions concerning differential polynomials that share fixed-points. Moreover we extend former results of W. C. Lin and H. X. Yi.

A formula for the colored Jones polynomial of 2-bridge knots

Abstract: We derive a formula for the colored Jones polynomial of 2-bridge knots. For a twist knot, a more explicit formula is given and it leads to a relation between the degree of the colored Jones polynomial and the crossing number.

Finite Dimension in Associative Rings

Abstract: The aim of the present paper is to introduce the concept "Finite dimension" in the theory of associative rings R with respect to two sided ideals. We obtain that if R has finite dimension on two sided ideals, then there exist uniform ideals U1,U2,··· ,Un of R whose sum is direct and essential in R. The number n is independent of the choice of the uniform ideals Ui and 'n' is called the dimension of R.

On Observability of Fuzzy Dynamical Matrix Lyapunov Systems

Abstract: . In this paper we generate a fuzzy dynamical matrix Lyapunov system andobtain a sufficient condition for the observability of this system. 1. IntroductionThe importance of control theory in Applied mathematics and its occurrencein several problems such as mechanics, electromagnetic theory, thermodynamics,artificial satellites etc., are well known. The observability condition assures theconstruction of the state from the output. This property is intrensic for systemsand play an important role in the theory of linear systems.The objective of this paper is to provide sufficient condition for observability offirst order matrix Lyapunov system described by(1.1) X 0 (t) = A(t)X(t)+X(t)B(t)+F(t)U(t), X(0) = X 0 , t>0,(1.2) Y(t) = C(t)X(t)+D(t)U(t),where U(t) is a n× nfuzzy input matrix called fuzzy control and Y(t) is a n× nfuzzy output matrix. Here A(t),B(t),F(t),C(t), and D(t) are matrices of ordern×n, whose elements are continuous functions of t on J= [0,T] ⊂ R(T>0).The problem of controllability and observability for systems of ordinary differ-ential equations has been studied by Barnett [2] and for matrix Lyapunov systemsby Murty, Rao and Suresh Kumar [8]. Recently the observability criteria for fuzzydynamical control systems was studied by Ding and Kandel [5].In section 2 we present some basic definitions and results relating to fuzzy setsand also some properties of Kronecker products and obtain general solution of thesystem (1.1), when U(t) is a crisp continuous matrix.In section 3 we generate a fuzzy dynamical matrix Lyapunov system and alsoobtain its solution set.

Some properties of a Certain family of Meromorphically Univalent Functions defined by an Integral Operator

Abstract: . Making use of a linear operator, we introduce certain subclass of meromor-phically univalent functions in the punctured unit disk and study its properties includingsome inclusion results, coefficient and distortion problems. Our result generalize manyresults known in the literature. 1. IntroductionLetPdenote the class of functions f(z) of the form(1.1) f(z) = z −1 +X ∞k=1 a k z k−1 .which are analytic and univalent in the punctured unit diskU ∗ = {z: z∈ C and0 <|z| <1} = U\{0}.The classPis closed under the Hadamard product or convolution(f∗g)(z) = z −1 +X ∞k=1 a k b k z k−1 = (g∗f)(z),where f(z) = z −1 +X ∞k=1 a k z k−1 ,g(z) = z −1 +X ∞k=1 b k z k−1 .In terms of the Pochhammer symbol (or the shifted factorial) (λ) n given by(λ) 0 = 1 and (λ) n = λ(λ+ 1)...(λ+ n+ 1) (n∈ N = {1,2,3,···}),we define the function φ(a,c;z) by(1.2) φ(a,c;z) = z −1 +X ∞k=1 (a) k (b) k z k−1 Received January 4, 2007.2000 Mathematics Subject Classification: 30C45, 30C80.Key words and phrases: Hypergeometric function, differential subordination, convolu-tion, distortion, meromorphic functions.

Lévy Khinchin Formula on Commutative Hypercomplex System

Abstract: . A commutative hypercomplex system L 1 (Q,m) is, roughly speaking, a spacewhich is defined by a structure measure (c(A,B,r),(A,B ∈ β(Q)). Such space has beenstudied by Berezanskii and Krein. Our main purpose is to establish a generalization ofconvolution semigroups and to discuss the role of the L´evy measure in the L´evy-Khinchinrepresentation in terms of continuous negative definite functions on the dual hypercomplexsystem. 1. IntroductionThe integral representation of negative definite functions is known in the liter-ature as the L´evy-Khinchin formula. This was established for G= Rin the late1930’s by L´evy and Khinchin. It had been extended to Lie groups by Hunt [9] andby Parthasarathy et al [13] to locally compact abelian groups with a countable case.In 1969 Harzallah [7] gave a representation formula for an arbitrary locally compactabelian group. Hazod [8] obtained a L´evy-Khinchin formula for an arbitrary locallycompact group. The general L´evy-Khinchin formula and the special case, where theinvolution is identical are due to Berg [4]. Lasser [12] deduced the L´evy-Khinchinformula for commutative hypergroups. Now these contribution may be viewed asa L´evy-Khinchin formula for negative definite functions defined on commutativehypercomplex systems.Let Q be a complete separable locally compact metric space of pointsp,q,r··· ,β(Q) be the σ-algebra of Borel subsets, and β

On the Ideal Extensions in Γ-Semigroups

Abstract: In 1981, Sen [4] have introduced the concept of -semigroups. We have known that -semigroups are a generalization of semigroups. In this paper, we introduce the concepts of the extensions of s-prime ideals, prime ideals, s-semiprime ideals and semiprime ideals in -semigroups and characterize the relationship between the extensions of ideals and some congruences in -semigroups.

Norm and Numerical Radius of 2-homogeneous Polynomials on the Real Space lp2, (1 ∞)

Abstract: . In this note, we present some inequalities for the norm and numerical radiusof 2-homogeneous polynomials from the 2-dimensional real space l 2p , (1 < p < ∞) to itselfin terms of their coefficients. We also give an upper bound for n (k) (l 2p ),(k = 2,3,···). 1. IntroductionIn this paper, we consider only real Banach spaces. Given a Banach space Ewe write B E for its unit ball and S E for its unit sphere. The dual space of E isdenoted by E ∗ and letΠ(E) = {(x,x ∗ ) : x ∈ S E , x ∗ ∈ S E ∗ ,x ∗ (x) = 1}.A mapping P : E → E is called a (continuous) k-homogeneous polynomialif there is a (continuous) k-linear mapping A : E × ··· × E → E such thatP(x) = A(x,··· ,x) for every x ∈ E. Let P( k E : E) denote the Banach spaceof all k-homogeneous polynomials from E to itself, endowed with the polynomialnorm kPk = sup x∈B E kP(x)k. We refer to the book [5] by Dineen for backgroundon polynomials. It is natural to generalize the concepts of numerical range andnumerical radius of linear operators to homogeneous polynomials. The numericalrange of P ∈ P(

A Chemotherapy-Diffusion Model for the Cancer Treatment and Initial Dose Control

Abstract: A one site chemotherapy agent-difiusion model is proposed which accounts for difiusion of chemotherapy agent, normal and cancer cells. It is shown that, by controlling the initial conditions, consequently an initial dose of the chemotherapy agent, the system is guaranteed to evolute towards a target equilibrium state. Or, growth of the normal cells occurs against decay of the cancer cells. Efiects of difiusion of chemotherapy-agent and cells are investigated through numerical computations of the concentrations in square and triangular cancer sites.

Weakly Complementary Cycles in 3-Connected Multipartite Tournaments

Abstract: The vertex set of a digraph D is denoted by V (D). A c-partite tournament is an orientation of a complete c-partite graph. A digraph D is called cycle complementary if there exist two vertex disjoint cycles C1 and C2 such that V (D) = V (C1) ( V (C2), and a multipartite tournament D is called weakly cycle complementary if there exist two vertex disjoint cycles C1 and C2 such that V (C1) ( V (C2) contains vertices of all partite sets of D. The problem of complementary cycles in 2-connected tournaments was completely solved by Reid (4) in 1985 and Z. Song (5) in 1993. They proved that every 2-connected tournament T on at least 8 vertices has complementary cycles of length t and jV (T)j i t for all 3 • tjV (T)j=2. Recently, Volkmann (8) proved that each regular multipartite tournament D of order jV (D)j ‚ 8 is cycle complementary. In this article, we analyze multipartite tournaments that are weakly cycle complementary. Especially, we will characterize all 3-connected c-partite tournaments with c ‚ 3 that are weakly cycle complementary. 1. Terminology In this paper all digraphs are flnite without loops and multiple arcs. The vertex set and the arc set of a digraph D are denoted by V (D) and E(D), respectively. If xy is an arc of a digraph D, then we write x ! y and say x dominates y, and if X and Y are two disjoint vertex sets or subdigraphs of D such that every vertex of X dominates every vertex of Y , then we say that X dominates Y , denoted by X ! Y. Furthermore, X ; Y denotes the fact that there is no arc leading from Y to X. If D is a digraph, then the out-neighborhood N + D (x) = N + (x) of a vertex x is the set of vertices dominated by x and the in-neighborhood N i D (x) = N i (x) is the set of vertices dominating x. Therefore, if the arc xy 2 E(D) exists, then y is an outer neighbor of x and x is an inner neighbor of y. The numbers d + (x) = d + (x) = jN + (x)j and d i (x) = d i (x) = jN i (x)j are called the outdegree and the indegree of x, respectively. Furthermore, the numbers - + D = - + = minfd + (x)jx 2 V (D)g and - i D = - i = minfd i (x)jx 2 V (D)g are the minimum outdegree and the minimum

Modules Which Are Lifting Relative To Module Classes

Abstract: In this paper, we study a module which is lifting and supplemented relative to a module class. Let R be a ring, and let X be a class of R-modules. We will define X-lifting modules and X-supplemented modules. Several properties of these modules are proved. We also obtain results for the case of specific classes of modules.

Enumeration of Algebraic Tangles with Applications to Theta-curves and Handcuff Graphs

Abstract: We enumerate all algebraic tangles of seven crossings or less up to equivalence. These tangles are mutually distinguished by the corresponding links and their double. The result will be used for enumerating µ-curves and handcufi graphs in a forthcoming paper.

Crosscap Numbers of Two-component Links

Abstract: We deflne the crosscap number of a 2-component link as the minimum of the flrst Betti numbers of connected, non-orientable surfaces bounding the link. We discuss some properties of the crosscap numbers of 2-component links.

Polynomial Equation in Radicals

Abstract: Necessary and sucient conditions for a radical class of rings to satisfy the polynomial equation (R(x)) = ( (R))(x) have been investigated. The interrelationship of polynomial equation, Amitsur property and polynomial extensibility is given. It has been shown that complete analogy of R.E. Propes result for radicals of matrix rings is not possible for polynomial rings.

Another Look at Average Formulas of Nevanlinna Counting Functions of Holomorphic Self-maps of the Unit Disk

Abstract: This is an extended version of the paper (K) of the author. The average formulas on the circles and disks around arbitrary points of Nevanlinna counting functions of holomorphic self-maps of the unit disk, given in terms of the boundary values of the self- maps, are shown to give another characterization of the whole class or a special subclass of inner functions in terms of Nevanlinna counting function in addition to the previous applications to Rudin's orthogonal functions. It plays a very important role in the holomorphic change of variables by w = '(z) in the integral representations and in the study of the composition operator C'(f) = f ' (Sh). The average formulas of N' on the circles and disks around the origin are given and exploited to the explicit representation of the Nevanlinna counting functions of Rudin's orthogonal functions in (K). In this paper, we compute the averages of N' on the circles and disks around arbitrary points in the unit disk in terms of the boundary values of ' and add another application of the average formulas for the characterization of the inner functions as well as a special class of inner functions. See Theorems 2.3 and 2.4. We also clarify the results in (K) on the Nevanlinna counting function of an orthogonal function ' and the essential norm of the corresponding composition operator C'. See Theorem 4.1.

$\bar{WT}$ -Classes of Differential Forms on Riemannian Manifolds

Abstract: . The purpose of this paper is to study the relations between quasilinear ellipticequations on Riemannian manifolds and differential forms. Two classes of differential formsare introduced and it is shown that some differential expressions are connected in a naturalway to quasilinear elliptic equations. 1. IntroductionThe theory of A-harmonic forms plays a crucial role in many fields, such aspotential theory, partial differential equations and quasiconformal analysis. At thesame time, they are extensions of harmonic functions and p-harmonic functions,p>1. In recent years, there have been remarkable advances made in the field ofA-harmonic forms. Many interesting results about them and their applications infields such as potential theory, quasiregular analysis and the theory of elasticityhave been found; see [4], [5] and [1]. There are also some other interesting results,such as the relations between quasiregular mappings on Riemannian manifolds anddifferential forms, see [3], [10] and [11]. In this paper, we introduce two classes ofdifferential forms and show that some differential expressions are connected in anatural way to quasilinear elliptic equations.We next introduce some notations and symbols used in this paper. Most of

Global Attractivity and Oscillations in a Nonlinear Impulsive Parabolic Equation with Delay

Abstract: Global attractivity and oscillatory behavior of the following nonlinear impul- sive parabolic dierential equation which is a general form of many population models ( @u(t,x) @t = 4u(t,x) u (t,x) + f(u(t ,x )),t 6 t k, u(t + ,x) u(tk,x) = gk(u(tk,x)),k 2 I1, ( ) the solutions of ( ) with Neumann boundary condition are established. These results not only are true but also improve and complement existing results for ( ) without diusion or impulses. Moreover, when these results are applied to the Nicholson's blowflies model and the model of Hematopoiesis, some new results are obtained.

Second Order Impulsive Neutral Functional Differential Inclusions

Abstract: . In this paper, we investigate the existence of solutions of second order im-pulsive neutral functional differential inclusions which the nonlinearity F admits convexand non-convex values. Some results under weaker conditions are presented. Our resultsextend previous ones. The methods rely on a fixed point theorem for condensing mul-tivalued maps and Schaefer’s fixed point theorem combined with lower semi-continuousmultivalued operators with decomposable values. 1. IntroductionIn this paper, we consider the existence results of solutions for the followingsecond-order neutral functional differential inclusions with the form(1.1)p(t)u 0 (t)−Z tt−τ q(s)u(s)ds 0 ∈ F(t,u t ), a.e.t∈ [0,T]\{t 1 ,t 2 ,··· ,t m },(1.2) ∆u| t=t k = I k (u(t −k )), ∆u 0 | t=t k = J k (u(t −k )), k= 1,2,··· ,m,(1.3) u(t) = a(t),t∈ [−τ,0],u 0 (0) = η,where F: [0,T] × C→ P(R n ) is a multi-valued map, C= {ϕ : [−τ,0] → R ; ϕis continuous everywhere except for a finite number of points ˜tat which ϕ(˜t − ) andϕ(˜t

The Basis Number of the Lexicographic Product of Different Ladders with Paths and Cycles

Abstract: In (8) M. Y. Alzoubi and M. M. Jaradat studied the basis number of the com- position of paths and cycles with Ladders, Circular ladders and Mobius ladders. Namely, they proved that the basis number of these graphs is 4 except possibly for some cases in each of them. Since the lexicographic product is noncommutative, in this paper we inves- tigate the basis number of the lexicographic product of the dierent kinds of ladders with paths and cycles. In fact, we prove that the basis number of almost all of these graphs is 4.

On the Trajectory Null Scrolls in 3-Dimensional Minkowski Space-Time E13

Abstract: . In this paper, the trajectory null scroll in 3-dimensional Minkowski space-timeE 31 is given by a firmly connected null oriented line moving with Cartan frame along nullcurve. Some theorems and results between curvatures of base curve and distribution pa-rameter of this surface are obtained. Moreover, some theorems and results related to beingdevelopable and minimal of this surface are given. And also, some relationships amonggeodesic curvature, geodesic torsion and the curvatures of null base curve of trajectorynull scroll are found. 1. IntroductionIn literature there are many studies related to ruled surfaces and their invari-ants (distribution parameters, Blaschke invariants, sectional curvature, apex angles,etc) in 3-dimensional Euclidean space E 3 , [1], [2]. In a spatial motion, the trajec-tories of oriented lines embedded in a moving space (or in a moving rigid body)are generally trajectory ruled surfaces (or ruled surfaces). Therefore the geometryof trajectory ruled surfaces is important in the study of space kinematics or spa-tial mechanisms. And also, the developable of the trajectory ruled surfaces havea number of applications in geometric modeling and model-based manufacturingof mechanical products, [3], [4], [5]. Lorentz metric in 3-dimensional Minkowskispace-time E