• Communications of Mathematical Education
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• v.22 no.4
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• pp.459-469
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• 2008

We give a mathematical approach using Linear Algebra, especially largest eigenvalue and eigenvector on decision making support system. We find a mathematical modeling on decision making problem which could be solved by AHP(Analytic Hierarchy Process) method. Especially, we give a new approach to change evaluation indicator weight on assessing research proposals.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.2
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• pp.927-930
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• 2005

ACSR is a timed process algebra for the specification and analysis of real-time systems, which supports synchronous timed actions and asynchronous instantaneous events. PACSR is an extended ACSR with the notion of probabilities in selection operation. Using PACSR, this paper represents a system fault occurrence and recovery from the fault in the general resource alteration system. The result shows that system fault occurrence can be analyzed from the fault occurrence probability and the recovery probability.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.37 no.4
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• pp.226-231
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• 1988

A program is developed for generating the dynamic equations for the robotic manipulators using the symbolic language muSIMP/ MATH. The muSIMP/ MATH is a LISP-based computer. algebra package, devoted to the manipulation of algebraic expressions including numbers, variables, functions, and matrices. The muSIMP-MATH can operate on personal computer such as IBM-PC. The program is developed, based on the Lagrange-Euler formulation. This program is applicable to the manipulators with any number of degrees of freedom, and maximum number of degrees of freedom is set to be six in this program.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.65-70
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• 1993

In this paper we will extend some notions of bounded linear operators to some unbounded linear operators. Let H be a complex separable Hilbert space and let B(H) denote the algebra of bounded linear operators. A closed densely defind linear operator S in H, with domain domS, is called subnormal if there is a Hilbert space K containing H and a normal operator N in K(i.e., $N^{*}$N=N $N^*/)such that domS .subeq. domN and Sf=Nf for f .mem. domS. we will show that the Radjavi and Rosenthal theorem holds for some unbounded subnormal operators; if $S_{1}$ and $S_{2}$ are unbounded subnormal operators on H with dom $S_{1}$= dom $S^{*}$$_{1}$ and dom $S_{2}$=dom $S^{*}$$_{2}$ and A .mem. B(H) is injective, has dense range and $S_{1}$A .coneq. A $S^{*}$$_{2}$, then $S_{1}$ and $S_{2}$ are normal and $S_{1}$.iden. $S^{*}$$_{2}$.2}$.X>.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.43-46
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• 1989

In this paper, we are concerned with the pointwise-hypoellipticity (see Definition 2.1) of an m-dimensional Frobenious Lie algebra L of analytic complex vector fields in somel open subset .ohm. of $R^{m+1}$. That is, L is a set of complex vector fields in .ohm. with (real-) analytic coefficients satisfying: (A) each point of .ohm. has an open neighborhood in which L is generated by m linearly independent elements of L; (B) L is closed under the commutation bracket [A, B]. The pointwise-analytic hypoellipticity of L is completely characterized by M.S. Baouendi and F. Treves in [1]. Here, we shall prove that if L is hypoelliptic at a point then it must be analytic hypoelliptic in a full neighborhood of the same point. When the coefficients are $C^{\infty}$, hypoellipticity of L was discussed in [2].2].

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.855-865
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• 2012

Recently, we have introduced a group invariant, which is related to the number of elements $x$ and $y$ of a finite group $G$ such that $x{\wedge}y=1_{G{\wedge}G}$ in the exterior square $G{\wedge}G$ of $G$. This number gives restrictions on the Schur multiplier of $G$ and, consequently, large classes of groups can be described. In the present paper we generalize the previous investigations on the topic, focusing on the number of elements of the form $h^m{\wedge}k$ of $H{\wedge}K$ such that $h^m{\wedge}k=1_{H{\wedge}K}$, where $m{\geq}1$ and $H$ and $K$ are arbitrary subgroups of $G$.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.517-528
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• 2011

Cameron and Storvick introduced change of scale formulas for Wiener integrals of bounded functions in the Banach algebra $\mathcal{S}$ of analytic Feynman integrable functions on classical Wiener space. Yoo and Skoug extended this result to an abstract Wiener space. Also Yoo, Song, Kim and Chang established a change of scale formula for Wiener integrals of functions on abstract Wiener space which need not be bounded or continuous. In this paper, we investigate a change of scale formula for generalized Wiener integrals of various functions on classical Wiener space.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.743-755
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• 2019

For every inverse semigroup S with subsemigroup E of idempotents, necessary and sufficient conditions are obtained for the weighted semigroup algebra $l^1(S,{\omega})$ and its second dual to be $l^1(E)$-module amenble. Some results for the module Arens regularity of $l^1(S,{\omega})$ (as an $l^1(E)$-module) are found. If S is either of the bicyclic inverse semigroup or the Brandt inverse semigroup, it is shown that $l^1(S,{\omega})$ is module amenable but not amenable for any weight ${\omega}$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.451-459
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• 2019

Let ${\mathcal{A}}$ and ${\mathcal{B}}$ be two operator ${\ast}$-rings such that ${\mathcal{A}}$ is prime. In this paper, we show that if the map ${\Phi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is bijective and preserves Jordan or ${\ast}$-Jordan triple product, then it is additive. Moreover, if ${\Phi}$ preserves Jordan triple product, we prove the multiplicativity or anti-multiplicativity of ${\Phi}$. Finally, we show that if ${\mathcal{A}}$ and ${\mathcal{B}}$ are two prime operator ${\ast}$-algebras, ${\Psi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is bijective and preserves ${\ast}$-Jordan triple product, then ${\Psi}$ is a ${\mathbb{C}}$-linear or conjugate ${\mathbb{C}}$-linear ${\ast}$-isomorphism.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.375-415
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• 2019

We study spaces of continuous-function-valued functions that have the property that composition with evaluation functionals induce $weak^*$ to norm continuous maps to ${\ell}^p$ space ($p{\in}(1,\;{\infty})$). Versions of $H{\ddot{o}}lder^{\prime}s$ inequality and Riesz representation theorem are proved to hold on these spaces. We prove a version of Dixmier's theorem for spaces of function-valued matrix operators on these spaces, and an analogue of the trace formula for operators on Hilbert spaces. When the function space is taken to be the complex field, the spaces are just the ${\ell}^p$ spaces and the well-known classical theorems follow from our results.