• Kyungpook Mathematical Journal
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• 제43권4호
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• pp.499-502
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• 2003

The aim of the present paper is to establish for commutativity of rings with unity 1 satisfying one of the properties $(xy)^{k+1}=x^ky^{k+1}x$ and $(xy)^{k+1}=yx^{k+1}y^k$, for all x, y in R, and the mapping $x{\rightarrow}x^k$ is an anti-homomorphism where $k{\geq}1$ is a fixed positive integer.

• Communications for Statistical Applications and Methods
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• 제17권4호
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• pp.483-491
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• 2010

This study provides the explicit computation of the ruin probability of a Le￠vy process on finite time horizon in Theorem 1 with the help of a fluctuation identity. This paper also gives the numerical results of the ruin probability in Variance Gamma(VG) and Normal Inverse Gaussian(NIG) models as illustrations. Besides, the paths of VG and NIG processes are simulated using the same parameter values as in Madan et al. (1998).

• 대한수학회보
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• 제32권2호
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• pp.321-328
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• 1995

In this note all are commutative rings with identity and all modules are unital. Let R be a ring. An R-module M is called a multiplication module if for every submodule N of M there esists an ideal I of R such that N = IM. Clearly the ring R is a multiplication module as a module over itself. Also, it is well known that invertible and more generally profective ideals of R are multiplication R-modules (see [11, Theorem 1]).

• Korean Journal of Mathematics
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• 제19권4호
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• pp.381-390
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• 2011

This paper is a direct continuation of [1]. In this paper we derive tensorial representations of contracted ES curvature tensors of $g-ESX_n$ and prove several generalized identities involving them. In particular, a variation of the generalized Bianchi's identity in $g-ESX_n$, which has a great deal of useful physical applications, is proved in Theorem (2.9).

• 한국정보통신학회논문지
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• 제10권10호
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• pp.1773-1778
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• 2006

본 논문에서는 개선된 자동정리증명 기법에 기초하여 유한체상의 디지털논리 시스템을 구성하는 방법을 제안하였다. 제안한 방법은 먼저 유한체상의 중요한 학적 성질을 논의하였고 자동정리증명기법의 개념과 기본 성질을 서술하였다. 그리고 개선된 자동정리증명기법을 적용하기 위해 몇 가지 정의를 하였으며 이를 근간으로 디지털논리 시스템의 Building Block을 제안하였다. 또한, 디지털논리 시스템을 구성하기 위한 중요한 관계를 정의하였으며 최종 유한체상의 디지털논리시스템을 개선된 자동정리 증명 기법에 의해 구성하였다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.1623-1628
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• 2004

In the 3-dimensional cyclic Lotka-Volterra equations, we show the solution on the invariant hyperplane. In addition, we show the existence of the invariant hyperplane by the center manifold theorem under the some conditions. With this result, we can lead the hyperplane of the n-dimensional cyclic Lotka-Volterra equaions. In other section, we study the 3- or 4-dimensional Hamiltonian Lotka-Volterra equations which satisfy the Jacobi identity. We analyze the solution of the Hamiltonian Lotka- Volterra equations with the functions called the split Liapunov functions by [4], [5] since they provide the Liapunov functions for each region separated by the invariant hyperplane. In the cyclic Lotka-Volterra equations, the role of the Liapunov functions is the same in the odd and even dimension. However, in the Hamiltonian Lotka-Volterra equations, we can show the difference of the role of the Liapunov function between the odd and the even dimension by the numerical calculation. In this paper, we regard the invariant hyperplane as the important item to analyze the motion of Lotka-Volterra equations and occur the chaotic orbit. Furtheremore, an example of the asymptoticaly stable and stable solution of the 3-dimensional cyclic Lotka-Volterra equations, 3- and 4-dimensional Hamiltonian equations are shown.

• Structural Engineering and Mechanics
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• 제32권3호
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• pp.407-427
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• 2009

A fundamental solution for the transient, quasi-static, plane problems of linear viscoelasticity is introduced for a specific material. An integral equation has been found for any problem as a result of dynamic reciprocal identity which is written between this fundamental solution and the problem to be solved. The formulation is valid for the first, second and mixed boundary-value problems. This integral equation has been solved by BEM and algorithm of the BEM solution is explained on a sample, mixed boundary-value problem. The forms of time-displacement curves coincide with literature while time-surface traction curves being quite different in the results. The formulation does not have any singularity. Generalized functions and the integrals of them are used in a different form.

• 대한수학회보
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• 제42권4호
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• pp.679-690
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• 2005

Let K be a commutative ring with unity, R a prime K-algebra of characteristic different from 2, d a non-zero derivation of R, I a non-zero right ideal of R, f($x_1,{\cdots},\;x_n$) a multilinear polynomial in n non-commuting variables over K, a $\in$ R. Supppose that, for any $x_1,{\cdots},\;x_n\;\in\;I,\;a[d(f(x_1,{\cdots},\;x_n)),\;f(x_1,{\cdots},\;x_n)]$ = 0. If $[f(x_1,{\cdots},\;x_n),\;x_{n+1}]x_{n+2}$ is not an identity for I and $$S_4(I,\;I,\;I,\;I)\;I\;\neq\;0$$, then aI = ad(I) = 0.

• Kyungpook Mathematical Journal
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• 제52권4호
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• pp.433-441
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• 2012

We adapt the concept of shrinking projection method of Takahashi et al. [J. Math. Anal. Appl. 341(2008), 276-286] to the iteration scheme studied by Kim and Lee [Kyungpook Math. J. 48(2008), 685-703] for two relatively weak nonexpansive mappings. By letting one of the two mappings be the identity mapping, we also obtain strong convergence theorems for a single mapping with two types of computational errors. Finally, we improve Kim and Lee's convergence theorem in the sense that the same conclusion still holds without the uniform continuity of mappings as was the case in their result.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.113-126
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• 2007

Let A and E be $m{\times}n$ matrices and W an $n{\times}m$ matrix, and let $A_{d,w}$ denote the W-weighted Drazin inverse of A. In this paper, a new representation of the W-weighted Drazin inverse of A is given. Some new properties for the W-weighted Drazin inverse $A_{d,w}\;and\;B_{d,w}$ are investigated, where B=A+E. In addition, the Banach-type perturbation theorem for the W-weighted Drazin inverse of A and B are established, and the perturbation bounds for ${\parallel}B_{d,w}{\parallel}\;and\;{\parallel}B_{d,w}-A_{d,w}{\parallel}/{\parallel}A_{d,w}{\parallel}$ are also presented. When A and B are square matrices and W is identity matrix, some known results in the literature related to the Drazin inverse and the group inverse are directly reduced by the results in this paper as special cases.