Showing papers in "Kyungpook Mathematical Journal in 2013"

On the Variational Approach for Analyzing the Stability of Solutions of Evolution Equations

Abstract: The eigenvalue problems arise in the analysis of stability of traveling waves or rest state solutions are currently dealt with, using the Evans function method. In the literature, it had been shown that, use of this method is not straightforward even in very simple examples. Here an extended \variational" method to solve the eigenvalue problem for the higher order dierential equations is suggested. The extended method is matched to the well known variational iteration method. The criteria for validity of the eigenfunc- tions and eigenvalues obtained is presented. Attention is focused to nd eigenvalue and eigenfunction solutions of the Kuramoto-Slivashinsky and (K(p,q)) equation.

The Spectrum of the Opertator D(r, 0, 0, s) over the Sequence Spaces c0and c

Abstract: In this paper we have examined the spectra of the operator D(r,0,0, s) on sequence spaces c0 and c.

On φ-pseudo Symmetries of (LCS) n -Manifolds

Abstract: The present paper deals with a study of ϕ-pseudo symmetric and ϕ-pseudo Ricci symmetric (LCS)n-manifolds. It is shown that every ϕ-pseudo symmetric (LCS)n- manifold and ϕ-pseudo Ricci symmetric (LCS)n-manifold are η-Einstein manifold.

Differential Subordination Properties of Sokół-Stankiewicz Starlike Functions

Abstract: Let be an analytic function defined on the open unit disk D and . Condition in terms of complex numbers D and real E with -1 is determined such that implies . Furthermore, the expression and are considered in obtaining similar results.

Some Characterizations of Parabolas

Abstract: We study some properties of tangent lines of parabolas. As a result, we establish some characterizations of parabolas.

On Semiprime Rings with Generalized Derivations

Abstract: . In this paper, we investigate the commutativity of a semiprime ring R ad-mitting a generalized derivation F with associated derivation D satisfying any one of theproperties: (i) F ( x ) ◦D ( y ) = [ x;y ], (ii) D ( x ) ◦F ( y ) = F [ x;y ], (iii) D ( x ) ◦F ( y ) = xy , (iv) F ( x ◦ y ) = [ F ( x ) ;y ] + [ D ( y ) ;x ], and (v) F [ x;y ] = F ( x ) ◦ y − D ( y ) ◦ x for all x;y in someappropriate subsets of R . 1. IntroductionThe commutativity of prime rings with derivation was initiated by Posner in[13]. Thereafter, several authors have proved commutativity theorems for primeor semiprime rings admitting automorphisms or derivations which are centralizingor commuting on some appropriate subsets of R (see [1-7,9,10,12,14] where furtherreferences can be found).Throughout this paper, R will represent an associative ring with center Z ( R ).For any x;y ∈ R , the symbol [ x;y ] and ( x ◦ y ) stand for the commutator xy − yx and the anti-commutator xy + yx respectively. A ring R is called a 2-torsion freeif whenever 2

The Unit Ball of $\mathcal{L}_s(^2d_*(1,w)^2)$

Abstract: First we present the explicit formula for the norm of a symmetric bilinear form on the 2-dimensional real predual of the Lorentz sequence space . Using this formula, we classify the extreme points of the unit ball of .

Extreme Bilinear Forms of $\mathcal{L}(^2d_*(1,w)^2)$

Abstract: First we present the explicit formula for the norm of a bilinear form on the 2-dimensional real predual of the Lorentz sequence space . Using this formula, we classify the extreme points of the unit ball of .

New Subclasses of Harmonic Starlike and Convex Functions

Abstract: . The purpose of the present paper is to establish some interesting results in-volving coefficient conditions, extreme points, distortion bounds and covering theoremsfor the classes V H (β) and U H (β). Further, various inclusion relations are also obtainedfor these classes. We also discuss a class preserving integral operator and show that theseclasses are closed under convolution and convex combinations. 1. IntroductionA continuous complex-valued function f = u + iv is said to be harmonic ina simply connected domain D if both u and v are real harmonic in D. In anysimply connected domain we can write f = h + g , where h and g are analytic inD. We call h the analytic part and g the co-analytic part of f. A necessary andsufficient condition for f to be locally univalent and sense-preserving in D is that h 0 (z) ,z> g 0 ∈ D. See Clunie and Sheil-Small [3], for more basic results onharmonic functions one may refer to the following standard introductory text bookby Duren [7], see also Ahuja [1] and Ponnusamy and Rasila ([9], [10]).Let S

On BN-algebras

Abstract: In this paper, we introduce a BN-algebra, and we prove that a BN-algebra is 0-commutative, and an algebra X is a BN-algebra if and only if it is a 0-commutative BF-algebra. And we introduce a quotient BN-algebra, and we investigate some relations between BN-algebras and several algebras.

Simple ECEM Algorithms Using Function Values Only

Abstract: In this paper, we improve the error corrected Euler method(ECEM) intro- duced in (11) by evaluating function values only at local nodes in each time interval. As a result, one can avoid computations of Jacobian matrices on each time interval so that the algorithms become simpler to implement in solving various class of time dependent differ- ential equations numerically. The proposed ECEM formula resembles to the Runge-Kutta method in its representations but both methods have different characteristic properties.

A Note on Maass-Jacobi Forms II

Abstract: This article is a continuation of the paper (21). In this paper we deal with Maass-Jacobi forms on the Siegel-Jacobi space H C m , where H denotes the Poincar e upper half plane and m is any positive integer.

Some Siegel threefolds with a Calabi-Yau model II

Abstract: In a previous paper, we described some Siegel modular threefolds which ad- mit a Calabi-Yau model. Using a different method we give in this paper an enlarged list of such varieties. Basic for this method is a paper of van Geemen and Nygaard. They study a variety X that is the complete intersection of four quadrics in P 7 (C). This is biholomorphic equivalent to the Satake compactification of H2=Γ ' for a certain subgroup Γ ' Sp(2;Z) and it will be the starting point of our investigation. It has been pointed out that a (projective) small resolution of this variety is a rigid Calabi-Yau manifold ˜ X. Then we will consider the action of quotients of modular groups on X and study possible resolutions that admits a Calabi-Yau model in the category of complex spaces.

Supra b-irresolutness and Supra b-connectedness on Topolog- ical Space

Abstract: In this paper, the concept of supra b-irresolute maps is introduced and several properties of it is investigated. Furthermore, the notion of supra b-connectedness is defined and researched by means of supra b-separated sets.

Module-theoretic Characterizations of Strongly t-linked Ex- tensions

Abstract: In this paper, we introduce and study the concept of \strongly t-linked ex- tensions", which is a stronger version of t-linked extensions of integral domains. We show that for an extension of Prufer v-multiplication domains, this concept is equivalent to that of \w-faithfully at".

On SF-rings and Regular Rings

Abstract: . A ring R is called a left (right) SF-ring if simple left (right) R-modules areflat. It is still unknown whether a left (right) SF-ring is von Neumann regular. In thispaper, we give some conditions for a left (right) SF-ring to be (a) von Neumann regular;(b) strongly regular; (c) division ring. It is proved that: (1) a right SF-ring R is regularif maximal essential right (left) ideals of R are weakly left (right) ideals of R (this resultgives an affirmative answer to the question raised by Zhang in 1994); (2) a left SF-ring Ris strongly regular if every non-zero left (right) ideal of R contains a non-zero left (right)ideal of R which is a W-ideal; (3) if R is a left SF-ring such that l(x) (r(x)) is an essentialleft (right) ideal for every right (left) zero divisor x of R, then R is a division ring. 1. IntroductionThroughout this paper, R denotes an associative ring with identity and all ourmodules are unitary. The symbols J(R), Z( R R)(Z(R R )), soc( R R)(soc(R R )) re-spectively stand for the Jacobson radical, left (right) singular ideal and left (right)socle of R. R is semiprimitive if J(R) = 0. R is left non-singular if Z(

Some Identities Involving Euler Polynomials Arising from a Non-linear Differential Equation

Abstract: We derive a family of non-linear differential equations from the generating functions of the Euler polynomials and study the solutions of these differential equations. Then we give some new and interesting identities and formulas for the Euler polynomials of higher order by using our non-linear differential equations.

G-frames as Sums of Some g-orthonormal Bases

Abstract: In this paper we show that a g-frame for a Hilbert space H can be written as a linear combination of two g-orthonormal bases for H if and only if it is a g-Riesz basis for H. Also, we show that every g-frame for a Hilbert space H is a multiple of a sum of three g-orthonormal bases for H.

The Polynomial Numerical Index of Lp(μ)

Abstract: We show that for 1 < p < ∞, k, m ∈ N, n (k) (lp) = inf{n (k) (l m ) : m ∈ N} and that for any positive measure µ, n (k) (Lp(µ)) ≥ n (k) (lp). We also prove that for every Q ∈ P( k lp : lp) (1 < p < ∞), if v(Q) = 0, then ∥Q∥ = 0.

On Nearly Pairwise Compact Spaces

Abstract: In this paper, we introduce the notion of near pairwise compactness which generalizes the notion of pairwise compactness.

Representation Theory of the Lie Group T 3 and Three Index Bessel Functions

Abstract: The theory of generalized Bessel functions is reformulated within the framework of an operational formalism using the multiplier representation of the Lie group as suggested by Miller. This point of view provides more efficient tools which allow the derivation of generating functions of generalized Bessel functions. A few special cases of interest are also discussed.

On the Invariance of Primitive Ideals via φ-derivations on Banach Algebras

Abstract: The noncommutative Singer-Wermer conjecture states that every derivation on a Banach algebra (possibly noncommutative) leaves primitive ideals of the algebra invariant. This conjecture is still an open question for more than thirty years. In this note, we approach this question via some sufficient conditions for the separating ideal of φ-derivations to be nilpotent. Moreover, we show that the spectral boundedness of φderivations implies that they leave each primitive ideal of Banach algebras invariant.

On the Dynamical Behavior of a Two-Prey One-Predator System with Two-Type Functional Responses

Abstract: In the paper, a two-prey one-predator system with defensive ability and Holling type-II functional responses is investigated. First, the stability of equilibrium points of the system is discussed and then conditions for the persistence of the system are established according to the existence of limit cycles. Numerical examples are illustrated to attest to our mathematical results. Finally, via bifurcation diagrams, various dynamic behaviors including chaotic phenomena are demonstrated.

Sequence Space m(M, φ)Fof Fuzzy Real Numbers Defined by Orlicz Functions with Fuzzy Metric

Abstract: . The sequence space m(M,φ) F of fuzzy real numbers is introduced. Someproperties of this sequence space like solidness, symmetricity, convergence-free etc. arestudied. We obtain some inclusion relations involving this sequence space. 1. IntroductionThe concept of fuzzy set theory was introduced by L.A. Zadeh in the year 1965.Later on different classes of sequences of fuzzy numbers have been investigated byEsi [2], Nuray and Savas [6], Syau [9], Tripathy and Baruah ([13], [14], [15]), Tripa-thy and Borgohain [16], Tripathy and Dutta ([17], [18]), Tripathy and Sarma [20]and many others.An Orlicz function is a function M : [0,∞) → [0,∞), which is continuous,non-decreasing and convex with M(0) = 0,M(x) >0,for x>0 and M(x) → ∞, asx→ ∞.If the convexity of the Orlicz function is replaced by M(x+y) ≤ M(x)+M(y),then this function is called as modulus function.Remark. An Orlicz function satisfies the inequality M(λx) ≤ λM(x) for all λwith0 <λ<1.Sargent [8] introduced the crisp set sequence space m(φ) and studied someproperties of this space. Later on it was studied from the sequence space point ofview and some matrix classes were characterized with one member as m(φ) by Rathand Tripathy [7], Tripathy [10] and others. In this article we introduce the spacem(M,φ)

Existence Results for the Nonlinear First Order Fuzzy Neutral Integrodifferential Equations

Abstract: In this paper, we devoted to study the existence and uniqueness of nonlinear fuzzy neutral integrodifferential equations. Moreover we study the fuzzy solution for the normal, convex, upper semicontinuous, and compactly supported interval fuzzy number. The results are obtained by using the Banach fixed-point theorem. An example is provided to illustrate the theory.

Zeros and Uniqueness of Difference Polynomials of Meromorphic Functions

Abstract: This research is a continuation of a recent paper due to the first author in (9). Different from previous results, we investigate the value distribution of difference poly- nomials of moromorphic functions in this paper. In particular, we are interested in the existence of zeros of f (z) n (f (z +c) m +f (z) m ) a, where f is a moromorphic function, n, m are two non-negative integers, and , are non-zero complex numbers. However, the proof here is obviously different to the one in (9). We also study difference polynomials of entire functions sharing a common value, which improves the result in (10, 13).

A Class of Invertible Bilateral Weighted Shifts

Abstract: . In this note we study a class of invertible weighted bilateral shifts on Hilbertspace introduced by Haskell Rosenthal recently. We show that every Rosenthal shift isunitarily equivalent to its inverse, not quasisimilar to its adjoint, and has a nontrivialhyperinvariant subspace. We write, as usual, Z for the set of integers and N(N 0 ) for the set of positive(nonnegative) integers. We also write l 2 (Z) for the separable, infinite dimensional,complex Hilbert space l 2 (Z) := ff n g n2 Z :  n 2 C ; ∑ n2 Z j n j 2 0, then the operator B w 2 L( l 2 (Z)) definedby(1) B w e n = w n e n +1 ; n 2 Z ; is a (invertible, forward) weighted bilateral shift. A trivial calculation gives thedefining equations(2)

Some Further Results on Uniqueness of Entire Functions and Fixed Points

Abstract: . In this paper, we investigate the uniqueness problem on entire functionssharing fixed points (ignoring multiplicities). Our main results improve and generalizesome results due to Zhang [13], Qi-Yang [10] and Dou-Qi-Yang [1]. 1. IntroductionIn this paper, a meromorphic function will mean meromorphic in the wholecomplex plane. We assume that the reader is familiar with standard notations andfundamental results of Nevanlinna Theory as explained in [12].We say that two meromorphic functions f and g share a small function a(z) IM(ignoring multiplicities) when f −a and g−a have the same zeros. If f and g havethe same zeros with the same multiplicities, then we say that f and g share a(z)CM (counting multiplicities).Let p be a positive integer and a ∈ C. We denote by N p (r, 1f−a ) the countingfunction of the zeros of f − a where an m-fold zero is counted m times if m ≤ pand p times if m > p. We denote by N L (r, 1f−1 ) the counting function for 1-pointsof both f(z) and g(z) about which f(z) has a larger multiplicity than g(z), withmultiplicity not being counted. We say that a finite value z

Meromorphic Functions Sharing a Nonzero Polynomial IM

Abstract: . We study the uniqueness of meromorphic functions concerning nonlinear dif-ferential polynomials sharing a nonzero polynomial IM. Though the main concern of thepaper is to improve a recent result of the present author [12], as a consequence of the mainresult we also generalize two recent results of X. M. Li and L. Gao [11]. 1. Introduction, De nitions and ResultsIn this paper, by meromorphic functions we will always mean meromorphicfunctions in the complex plane. We adopt the standard notations in the Nevan-linna theory of meromorphic functions as explained in [7], [15] and [16]. For anonconstant meromorphic function h, we denote by T(r;h) the Nevanlinna charac-teristic of hand by S(r;h) any quantity satisfying S(r;h) = ofT(r;h)gas r!1possibly outside a set of nite linear measure. A meromorphic function a(z)(61)is called a small function with respect to f, provided that T(r;a) = S(r;f).Let f and gbe two nonconstant meromorphic functions, and let abe a nitevalue. We say that fand gshare the value aCM (counting multiplicities), providedthat f aand g ahave the same set of zeros with the same multiplicities. Similarly,we say that fand gshare aIM (ignoring multiplicities), provided that f aandg ahave the same set of zeros ignoring multiplicities.In 1959, W. K. Hayman (see [6], Corollary of Theorem 9) proved the followingtheorem:Theorem A. Let f be a transcendental meromorphic function and n(3) is aninteger. Then f