Showing papers in "Kyungpook Mathematical Journal in 1998"

An Inequality of Ostrowski-Grüss Type for Twice Differentiable Mappings and Applications in Numerical Integration

Abstract: In this paper we derive a new integral inequality of Ostrowski-Gruss type and apply it to estimate the error bounds for some numerical quadrature rules.

An inequality of ostrowski's type for cumulative distribution functions

Abstract: The main aim of this paper is to establish an Ostrowski type inequality for the cumulative distribution function of a random variable taking values in a finite interval [a,b]. An application for a Beta random variable is given.

Anti Fuzzy Ideals in BCK-algebras

Abstract: Modifying Biswas' idea, in this paper, we apply the idea to BCK-algebras. We introduce the notion of anti fuzzy ideals of BCK-algebras, lower level cuts of a fuzzy set, lower level ideal, and prove some results on these. We show that a fuzzy subset of a BCK-algebra is a fuzzy ideal if and only if the complement of this fuzzy subset is an anti fuzzy ideal. We also fuzzify lower level cuts and prove that if a fuzzy subset is an anti fuzzy ideal then so is the fuzzifications of its lower level cuts.

Semi-parallel and Semi-symmetric Real Hypersurfaces in Complex Space Forms

Abstract: The nonexistence of semi-parallel, Einstein, and semi-symmetric real hypersurfaces in the complex projective space has been established for . For the Einstein and semi-symmetric conditions, the result also extends to complex hyperbolic space . The known proofs are not valid for n = 2. In this paper, we prove that a real hypersurface cannot be semi-parallel or Einstein. We also show that if is a Hopf hypersurface (one for which the structure vector is principal), it cannot be semisymmetric. However, the general existence problem for semi-symmetric hypersurfaces in is still open.

On the Rate of Pointwise Convergence of Modified Baskakov Type Operators for Functions of Bounded Variation

Abstract: In this paper we study the rate of pointwise convergence of modified Baskakov type operators at those points at which the one sided limits exist.

Fixed Points of Single and Set-valued Mappings

Abstract: In this paper we prove some fixed point theorems for single-valued and set-valued maps in complete metric spaces. The results generalize the corresponding results for single-valued mappings obtained by Skof [12].

Submanifolds of Constant Scalar Curvature in a Space Form

Abstract: Let be a closed submanifold immersed into a space form of constant curvature . Denote by R the normalized scalar curvature and by H the mean curvature of . Suppose that R is constant and . We firstly extend Cheng-Yau's technique to higher co dimension cases. Then we study the rigidity problem for with parallel normalized mean curvature vector field. We show that, if H satisfies a certain inequality, then is totally umbilical or the equaluity holds. We describe all that satisfy this equality. We also prove some rigidity theorems of Yano-Ishihara's type and extend the rigidity theorems of H. Li to higher codimension.

Superstability of Homogeneous Functional Equation

Abstract: The superstability problems of the homogeneous functional equation (1.2) in various settings shall be investigated, and the results shall be applied to the study of an asymptotic behavior of the homogeneous mappings.

Extensions of L-fuzzy Ideals in Semirings

Abstract: We characterize L-fuzzy ideals in semirings and extensions of such ideals with the sup-property.

The Uniform Asymptotic Stability for Functional Differential Equations with Infinite Delay

Abstract: We consider a system of functional differential equations where the phase space is an admissible space which is not a uniform fading memory space and obtain the sufficient conditions to ensure that the zero solution of the functional differential equations with infinite delay is uniformly aymptotically stable.

Limit Cycles in Quadratic Systems with a Weak Focus and a Strong Focus

Abstract: In this paper we study quadratic systems with exactly two finite real singularities, a weak focus and a strong focus, and at least two singularities at infinity. It is proved that if the weak focus is of second or third order then the strong focus is surrounded by at most one limit cycle, and if it exists it is hyperbolic. If the weak focus is of first order while the two foci have opposite stability, then the same conclusion holds.

Finite Element Compensators for Thermoelastic Systems with Boundary Controls and Point Observations

Abstract: Finite dimensional compensators for thermoelastic systems, based on finite elements approximations (not on modal approximations), with high level of unboundedness in control and observation operators are presented.

Expansions of $_4F_3$ When the Upper Parameters Differ by Integers

Abstract: In this article three expansion formulas for a generalized hypergeometric function are derived, when its upper parameters differ by integers. Though the results are special cases of a general continuation formula for , they are sufficiently general and unify a number of known results.

A Topological Method to Compute Spectral Flow

Abstract: This paper describes a topological method to compute the spectral flow of a family of twisted Dirac operators, it includes two detailed examples. Briefly, a formula of Atiyah, Patodi and Singer expresses the spectral flow in terms of Chern-Simons invariants and rho invariants. The first step is to construct a flat cobordism to a new bigger 3-manifold. The advantage of the new connection is that it is in the path component of a reducible connection. The second step is to calculate the effect of these operations on the invariants. The final step is an application of the G-signature theorem to compute the invariants. The spectral flow of a family of operators is a generalization of the signature of a selfadjoint finite dimensional operator. If At is a family of operators with a real, discrete, spectrum, then the spectral flow of At is the number of eigenvalues that move from negative to positive minus the number which move from positive to negative. Recalling that the number of positive eigenvalues minus the number of negative eigenvalues, we see that SF(At) = Sign A1 − Sign A0 for finite dimensional operators. In this paper, we extend to spectral flow the method that we used to compute Chern– Simons invariants of flatSU2 connections in a previous paper [A]. After outlining the method, we work out two examples in detail. Briefly, a formula of Atiyah, Patodi and Singer expresses the spectral flow in terms of Chern–Simons invariants and rho invariants [APS]. To compute the rho invariant of a flat SU2 connection on one 3-manifold, we construct a flat cobordant connection on a new, bigger 3-manifold. It is straightforward to compute the difference between the rho invariant of a connection and a flat cobordant connection. The advantage � Partially supported by an NSF Postdoctoral Fellowship while the author was visiting MSRI.

m-Entire Admissible Components of Solutions of a type of a System of Algebraic Differential Equations

Abstract: In this paper, for a system of generalized higher order algebraic differential equations in the complex plane, we investigate the system of solutions containing the m-entire admissible components by using the value distribution theory of Nevanlinna and obtain some results which are more precise and more general than the previous ones. It is the further disscussion of [8].

Cauchy Completions of Quasi-uniform Frames

Abstract: We show that the category qUnifFrm of frames endowed with quasi-uniformity and quasi-uniform frame homomorphisms is topological over the category Frm of frames and frame homomorphisms and construct Cauchy completions of quasi uniform frames.

Self-distributive Modular Pogroupoids and Posets

Abstract: In this paper we show that the modular pogroupoid(semigroup) S() is a self-distributive if its associated poset .

Children Ideals and Children Rings

Abstract: Children pairs, children rings and children ideals are defined and studied. In particular, we characterize all the children pairs in the ring Z of integers and all the children ideals in Zn.

Fuzzy Maximal and Complete Fuzzy Normal BCK-filters

Abstract: We state fuzzy maximal BCK-filters and complete fuzzy normal BCK-filters in BCK-algebras, and investigate its properties.

Proximity Frames and H-completness

Abstract: In this paper, we introduce a concept of meet interpolation orders on lattices and then using these we introduce a concept of in lattices with a meet interpolation order and investigate some basic properties of . Secondly, we introduce a concept of proximity orders on frames and show that proximity orders on frames can be characterized by on frames. Finally, we show that if L is a frame with a meet interpolation order (quasi-proximity frame, proximity frame, resp.), then the strict extension is a H-completion (almost compactification, compactification, resp.) of L.

A Local Limit Theorem for Homogeneous Markov Chains

Abstract: In this paper a local limit theorem is proved for a sequence of random variables that are linked in a homogeneous Markov chain with arbitrary set of possible states. The achieved results makes it possible to estimate the rate of convergence without assuming the existence of absolute moments of order not less than the third for the transition probabilities.

Multidimensional Fractional Integral Operators Involving a Generalized Polynomial Set

Abstract: Recently Srivastava et al.[17, 20], and several others have obtained several results for fractional integral operators in one and more dimensions. Motivated by this, we establish here various theorems involving compositions, inversion formulas, and multidimensional Mellin transforms and convolutions of two new families of multidimensional fractional integral operators involving a generalized polynomial set. Each of the results obtained in this paper would unify and extend the corresponding (known or new) results for simpler families of fractional integral operators.

Left-symmetric Structures on Weakly Graded Lie Algebras

Abstract: In this paper we present a new idea for the construction of left-symmetric structures on nilpotent Lie algebras. Although the techniques are quite simple, we rediscover many of the known left-symmetric structures and we obtain a lot of new examples. The first part of this paper is self-contained and gives elementary proofs and constructions of many well known situations. In the second part of this paper, we indicate how these left-symmetric structures can be used to construct an affine structure on a large class of virtually nilpotent groups.