Showing papers in "Bulletin of The Korean Mathematical Society in 2011"

Global stability of the viral dynamics with crowley-martin functional response

Abstract: It is well known that the mathematical models provide very important information for the research of human immunodeciency virus type. However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T-cells and the viral particles. In this paper, a differential equation model of HIV infection of CD4 + T-cells with Crowley-Martin function response is studied. We prove that if the basic reproduction number R0 1, the HIV infection persists in the host. Wend that the chronic disease steady state is globally asymptotically stable if R0 > 1. Numerical simulations are presented to illustrate the results.

Some notes on ishikawa iteration for multi-valued mappings

Abstract: In Shahzad and Zegeye (Nonlinear Anal. 71 (2009), no. 3-4, 838{844), the authors introduced several Ishikawa iterative schemes for xed points of multi-valued mappings in Banach spaces, and proved some strong convergence theorems by using their iterations. In their proofs of the main results, it seems reasonable and simpler to prove for the iteration fxng to be a Cauchy sequence. In this paper, we modify and improve the proofs of the main results given by Shahzad and Zegeye. Two concrete examples also are given.

Existence and asymptotic stability of solutions of a perturbed fractional functional-integral equation with linear modification of the argument

Abstract: We study the solvability of a perturbed quadratic functional- integral equation of fractional order with linear modication of the argu- ment. This equation is considered in the Banach space of real functions dened, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions.

Generalized weighted composition operators from area Nevanlinna spaces to weighted-type spaces

Abstract: Let denote the class of all analytic functions on the open unit disk of the complex plane . Let n be a nonnegative integer, be an analytic self-map of and . The generalized weighted composition operator is defined by . The boundedness and compactness of the generalized weighted composition operator from area Nevanlinna spaces to weighted-type spaces and little weighted-type spaces are characterized in this paper.

Generalized derivations on semiprime rings

Abstract: Let R be a prime ring, I a nonzero ideal of R and n a fixed positive integer. If R admits a generalized derivation F associated with a derivation d such that c for all x, . Then either R is commutative or n = 1, d = 0 and F is the identity map on R. Moreover in case R is a semiprime ring and for all x, , then either R is commutative or n = 1, , R contains a non-zero central ideal and for all .

Extensions of euler type ii transformation and saalschütz's theorem

Abstract: In this research paper, motivated by the extension of the Euler type I transformation obtained very recently by Rathie and Paris, the authors aim at presenting the extensions of Euler type II transformation. In addition to this, a natural extension of the classical Saalschtz's summation theorem for the series has been investigated. Two interesting applications of the newly obtained extension of classical Saalschtz's summation theorem are given.

Relations among the first variation, the convolutions and the generalized fourier-gauss transforms

Abstract: We first study the generalized Fourier-Gauss transforms of functionals defined on the complexification of an abstract Wiener space (, , ). Secondly, we introduce a new class of convolution products of functionals defined on and study several properties of the convolutions. Then we study various relations among the first variation the convolutions, and the generalized Fourier-Gauss transforms.

Tensor product surfaces with pointwise 1-type gauss map

Abstract: Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle c1 centered at origin with an Euclidean planar curve c2 has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle c1 centered at origin with an Euclidean planar curve c2 to have pointwise 1-type Gauss map.

Competition indices of strongly connected digraphs

Abstract: Cho and Kim (4) and Kim (6) introduced the concept of the competition index of a digraph. Cho and Kim (4) and Akelbek and Kirk- land (1) also studied the upper bound of competition indices of primitive digraphs. In this paper, we study the upper bound of competition in- dices of strongly connected digraphs. We also study the relation between competition index and ordinary index for a symmetric strongly connected digraph.

New bounds for the ostrowski-like type inequalities

Abstract: We improve some inequalities of Ostrowski-like type and further generalize them.Key words: Inequality, Error, Integral, Taylor, Ostrowski2000 MSC: 26D10, 41A55, 65D301. IntroductionIn 1938, Ostrowski [8] proved the following interesting integral inequality which has received con-siderable attention from many researchers.Theorem 1 (See [8]). Let f : [a,b] → R be continuous on [a,b] and differentiable on (a,b) whosederivative function f 0 : (a,b) → R is bounded on (a,b), i.e., kf 0 k ∞ = sup t∈(a,b) |f 0 (t)| < ∞. ThenZb f(x)−1b−a af(t)dt ∞5 14+x− a+b22 (b−a) 2 !(b−a)kf 0 k (1)for all x ∈ [a,b].This inequality gives an upper bound for the approximation of the integral average 1b−a R ba f(t)dtby the value f(x) at point x ∈ [a,b]. The first generalization of Ostrowskis inequality was given byG.V. Milovanovi´c and J.E. Peˇcari´c in [7]. However, note that estimate (1) can be applied only if f 0 is bounded. In the first part of this paper, we will improve (1) by assuming f 0 ∈ L p

Controllability of second order semi-linear neutral impulsive differential inclusions on unbounded domain with infinite delay in banach spaces

Abstract: In this paper, we prove sufficient conditions for controllability of second order semi-linear neutral impulsive differential inclusions on unbounded domain with innite delay in Banach spaces using the theory of strongly continuous Cosine families. We shall rely on axed point theorem due to Ma for multi-valued maps. The controllability results in innite dimensional space has been proved without compactness on the family of Cosine operators.

DEFORMATIONS OF d=BCK-ALGEBRAS

Abstract: In this paper, we study the effects of a deformation mapping on the resulting deformation d=BCK-algebra obtained via such a defor- mation mapping. Besides providing a method of constructing d-algebras from BCK-algebras, it also highlights the special properties of the stan- dard BCK-algebras of posets as opposed to the properties of the class of divisible d=BCK-algebras which appear to be of interest and which form a new class of d=BCK-algebras insofar as its not having been identied before.

Strong limit theorems for weighted sums of nod sequence and exponential inequalities

Abstract: Some properties for negatively orthant dependent sequence are discussed. Some strong limit results for the weighted sums are ob- tained, which generalize the corresponding results for independent se- quence and negatively associated sequence. At last, exponential inequal- ities for negatively orthant dependent sequence are presented.

The lower autocentral series of abelian groups

Abstract: . In the present paper we introduce the lower autocentral seriesof autocommutator subgroups of a given group. Following our previouswork on the subject in 2009, it is shown that every nite abelian groupis isomorphic with n th -term of the lower autocentral series of some niteabelian group. 1. IntroductionLet A = Aut( G ) denote the group of automorphisms of a given group G . Forany element g 2 G and 2 A the element [ g; ] = g 1 g is an autocommutator of g and : We de ne the autocommutator of higher weight inductively asfollows:[ g; 1 ; 2 ;:::; i ] = [[ g; 1 ; 2 ;:::; i 1 ] ; i ]for all 1 ; 2 ;:::; i 2 A: So the autocommutator subgroup of weight i + 1 is de ned in the followingway: K i ( G ) = [ G;A;:::;A | {z } i -times ] = ⟨ [ g; 1 ; 2 ;:::; i ] j g 2 G; 1 ; 2 ;:::; i 2 A⟩: Clearly K i ( G ) is a characteristic subgroup of G for all i  1. Therefore, oneobtains a descending chain of autocommutator subgroups of G as follows: G  K 1 ( G )  K 2 ( G )   K i ( G )  ; which we may call it the

Controllability of second-order impulsive functional differential equations with state-dependent delay

Abstract: The purpose of this paper is to investigate the controllability of certain types of second order nonlinear impulsive systems with state- dependent delay. Sufficient conditions are formulated and the results are established by using axed point approach and the cosine function theory. Finally examples are presented to illustrate the theory.

Chaotic property of weighted composition operators

Abstract: . In the present paper, we study the chaotic property of wei-ghted composition operators acting on the holomorphic function space H (U). 1. IntroductionA continuous linear operator T acting on a separable Frechet space X iscalled hypercyclic provided there exists a vector x 2 X such that its orbitorb( T;x ) = fT n x : n = 0 ; 1 ;:::g is dense in X . A periodic point for T is avector x2 X such that T n x = x for some n2 N. Finally, T is said to bechaotic if it is hypercyclic and its set of periodic points is dense in X .In 1929, ff [1] showed that the translation operator T a : H (C) ! H (C)de ned by ( T a f )( z ) = f ( z + a ), a= 0, is hypercyclic on the Frechet space H (C)of entire functions. This result was generalized by Godefroy and Shapiro [7]who proved that each operator on H (C N ) which commutes with all translationsand is not a scalar multiple of the identity, is chaotic. Other classical examplesof hypercyclic and chaotic operators are weighted shifts on l p spaces [8, 10] andadjoints of multiplication operators on Hilbert spaces of holomorphic functions[7].Let U stand for the open unit disk in C. Each

VALUE SHARING RESULTS OF A MEROMORPHIC FUNCTION f(z) AND f(qz)

Abstract: In this paper, we investigate sharing value problems related to a meromorphic function f ( z) and f ( qz), where q is a non-zero constant. It is shown, for instance, that if f ( z) is zero-order and shares two valves CM and one value IM with f ( qz), then f ( z) = f ( qz).

A concept unifying the armendariz and ni conditions

Abstract: We study the structure of the set of nilpotent elements in various kinds of ring and introduce the concept of NR ring as a general- ization of Armendariz rings and NI rings. We determine the precise re- lationships between NR rings and related ring-theoretic conditions. The Kothe's conjecture is true for the class of NR rings. We examined whether several kinds of extensions preserve the NR condition. The classical right quotient ring of an NR ring is also studied under some conditions on the subset of nilpotent elements.

Change point test for dispersion parameter based on discretely observed sample from sde models

Abstract: In this paper, we consider the cusum of squares test for the dispersion parameter in stochastic differential equation models. It is shown that the test has a limiting distribution of the sup of a Brownian bridge, unaffected by the drift parameter estimation. A simulation result is provided for illustration.

Minimal noncommutative reversible and reflexive rings

Abstract: The reflexiveness and reversibility were introduced by Mason and Cohn respectively. The structures of minimal reversible rings and minimal reflexive rings are completely determined. The term minimal means having smallest cardinality.

On McCoy modules

Abstract: Extending the notion of McCoy rings, we introduce the class of McCoy modules. Over a given ring R, it contains the class of Ar- mendariz modules (over R). Some properties of this class of modules are established, and equivalent conditions for McCoy modules are given. Moreover, we study the relationship between a module and its polynomial module. Several known results relating to McCoy rings can be obtained as corollaries of our results.

A survey on american options: old approaches and new trends

Abstract: This is a survey on American options. An American option allows its owner the privilege of early exercise, whereas a European op- tion can be exercised only at expiration. Because of this early exercise privilege American option pricing involves an optimal stopping problem; the price of an American option is given as a free boundary value problem associated with a Black-Scholes type partial differential equation. Up un- til now there is no simple closed-form solution to the problem, but there have been a variety of approaches which contribute to the understanding of the properties of the price and the early exercise boundary. These ap- proaches typically provide numerical or approximate analytic methods to �nd the price and the boundary. Topics included in this survey are early approaches(treesnite difference schemes, and quasi-analytic methods), an analytic method of lines and randomization, a homotopy method, an- alytic approximation of early exercise boundaries, Monte Carlo methods, and relatively recent topics such as model uncertainty, backward stochas- tic differential equations, and real options. We also provide open problems whose answers are expected to contribute to American option pricing.

Stability of an additive functional inequality in proper cq -algebras

Abstract: In this paper, we prove the Hyers{Ulam{Rassias stability of the following additive functional inequality: ∥f(2x) + f(2y) + 2f(z)∥ � ∥ 2f(x + y + z)∥: (0.1) We investigate homomorphisms in proper CQ� -algebras and derivations on proper CQ � -algebras associated with the additive functional inequality (0.1).

COMPACT MATRIX OPERATORS BETWEEN THE SPACES m (ϕ), n (ϕ) AND ℓp

Abstract: We give the characterizations of the classes of matrix trans-formations (), () ([5, Theorem 2]), () ([5, Theorem 1]) and () for , establish estimates for the norms of the bounded linear operators defined by those matrix transformations and characterize the corresponding subclasses of compact matrix operators.

Generalized analytic feynman integral via function space integral of bounded cylinder functionals

Abstract: In this paper, we use a generalized Brownian motion to dene a generalized analytic Feynman integral. We then obtain some results for the generalized analytic Feynman integral of bounded cylinder functionals of the form F(x) = ^ ((g1;x) � ;:::;(gn;x) � ) dened on a very general function space Ca;b(0;T). We also present a change of scale formula for function space integrals of such cylinder func- tionals.

L 2 -error analysis of fully discrete discontinuous galerkin approximations for nonlinear sobolev equations

Abstract: In this paper, we develop a symmetric Galerkin method with interior penalty terms to construct fully discrete approximations of the solution for nonlinear Sobolev equations. To analyze the convergence of discontinuous Galerkin approximations, we introduce an appropriate projection and derive the optimal error estimates.

ON THE 2k-TH POWER MEAN VALUE OF THE GENERALIZED QUADRATIC GAUSS SUMS

Abstract: . The main purpose of this paper is using the elementary andanalytic methods to study the properties of the 2 k -th power mean valueof the generalized quadratic Gauss sums, and give two exact mean valueformulae for k = 3 and 4. 1. IntroductionLet q  2 be an integer, ˜ denotes a Dirichlet character modulo q . For anyinteger n , we de ne the generalized quadratic Gauss sums G ( n;˜ ; q ) as follows: G ( n;˜ ; q ) =∑ qa =1 ˜ ( a ) e ( na 2 q ) ; where e ( y ) = e 2 ˇiy . This sum is important, because it is a generalization ofthe classical quadratic Gauss sums G ( n;q ), which is de ned by G ( n ; q ) =∑ qa =1 e ( na 2 q ) : About the properties of G ( n;˜ ; q ), some authors had studied it, and obtainedmany interesting results. For example, for any integer n with ( n;q ) = 1, fromthe general result of Cochrane and Zheng [2] we can deduce that jG ( n;˜ ; q ) j  2 ! ( q ) q 12 ; where ! ( q ) denotes the number of all distinct prime divisors of q . The casewhere q is a prime is due to Weil [4]. Zhang [5] proved that for any odd prime

Finite non-nilpotent generalizations of hamiltonian groups

Abstract: G, we dene the subgroup A(G) to be intersection of the normalizers of all non-cyclic subgroups of G. Set A0 = 1. Dene Ai+1(G)=Ai(G) = A(G=Ai(G)) for i 1. By A1 (G) denote the terminal term of the ascending series. It is proved that if G.

Duality of co-poisson hopf algebras

Abstract: . Let A be a co-Poisson Hopf algebra with Poisson co-bracket  . Here it is shown that the Hopf dual A ◦ is a Poisson Hopf algebra withPoisson bracket ff;gg ( x ) = ⟨ ( x ) ;f g⟩ for any f;g 2 A ◦ and x 2 A if A is an almost normalizing extension over the ground eld. Moreover weget, as a corollary, the fact that the Hopf dual of the universal envelopingalgebra U (g) for a nite dimensional Lie bialgebra g is a Poisson Hopfalgebra. Let G be a Lie group with Lie algebra g. Then its coordinate ring O ( G ) isa Hopf algebra and can be replaced by the Hopf dual U (g) ◦ of the universalenveloping algebra U (g). In fact, it is well-known that U (g) ◦ is equal to O ( G )if G is connected and simply connected. Moreover it is convenient to work on U (g) ◦ instead of O ( G ) since U (g) ◦ has a natural grading. For instance, see [3,Chapter 2] and [2].Recall that a Lie group G is said to be a Poisson Lie group if its coordinatering O ( G ) is a Poisson Hopf algebra. If G is a Poisson Lie group, then its Liealgebra g becomes a nite dimensional Lie bialgebra with a co-bracket

On the local cohomology of minimax modules

Abstract: . Let R be a commutative Noetherian ring, a an ideal of R , and M a minimax R -module. We prove that the local cohomology modules H j a ( M ) are a-cominimax; that is, Ext iR ( R= a ;H j a ( M )) is minimax for all i and j in the following cases: (a) dim R= a = 1; (b) cd(a) = 1, where cd isthe cohomological dimension of a in R ; (c) dim R  2. In these cases wealso prove that the Bass numbers and the Betti numbers of H j a ( M ) are nite. 1. IntroductionThroughout this paper, let R denote a commutative Noetherian ring withnon-zero identity and a an ideal of R . For an R -module M , the j -th localcohomology module of M with respect to a is de ned as H j a ( M ) = lim ! n Ext jR ( R= a n ;M ) : We refer the reader to [6] or [9] for more details about local cohomology.Hartshorne [10] de ned an R -module M to be a -co nite if Supp( M )  V (a)and Ext iR ( R= a ;M ) is nitely generated for all i and asked: For which rings R and ideals a are the modules H a j ( M ) a -co nite for all jand all nitely generated modules M?