• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.195-201
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• 1992

Let G(A) denote a generalized Kac Moody Lie algebra associated to a symmetrizable generalized Cartan matrix A. In this paper, we study on representations of G(A). Highest weight modules and the category O are described. In the main theorem we show that some G(A) modules from the category O are completely reducible. Also a criterion for irreducibility of highest weight modules is obtained. This was proved in [3] for the case of Kac Moody Lie algebras.

• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.103-110
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• 1995

In their recent paper[2], they show that the existence theory for the analytic operator-valued Feynman path integral can be extended by making use of recent developments in the theory of Dirichlet forms and Markov process. In this field, there is the necessity of studying certain generalized functionals of the process (of Feynman-Kac type). Their study have been concerned with Feynman-Kac type functionals related with smooth measures associated with the classical Dirichlet form (associated with the Laplacian).(omitted)

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.107-113
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• 2010

In this paper, we study the root system of rank 2 symmetric hyperbolic Kac-Moody algebras. We give the sufficient conditions for existence of imaginary roots of square length -2k ($k\;{\in}\;\mathbb{Z}$>0). We also give several relations between the roots on g(A).

• Journal of the Korean Society for Aviation and Aeronautics
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• v.15 no.4
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• pp.83-93
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• 2007

The aviation industry is expected to grow faster and the role of it is expected to be bigger as time goes by. Airport operating company is a major part of the aviation industry. For an airport operating company to be successful, strong relationship with customers is essential. One of the methods to acquire the customer loyalty is establishing a brand. For KAC, 'Skycity' should be chosen as the main brand. And along with it, harmonious modeling of a of KAC and BI of Skycity should be devised. By doing this, KAC can gain customers' affection and loyalty.

• Journal of Information Science Theory and Practice
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• v.8 no.4
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• pp.40-54
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• 2020

This proposed work aims to understand the Korean Academic Circle (KAC)'s research trend on the "One Belt One Road" (OBOR) by employing a quantitative analysis of the recent research articles published by the KAC. To do so, this proposed research has used the well-known network analysis software, Ucinet 6, by which the papers on related topics are collected and filtered from Korea Citation Index. To perform the analytical selection, the proposed work has chosen 'keywords' as the core research object and performed analysis from transverse to longitudinal aspects, and from holistic to individual aspects, respectively; and from this, the KAC's research trend on OBOR is derived. The present work has established that the KAC's attention is continuously increasing on OBOR and has sustainability. Centered on the OBOR, Korean researchers have spread their studies in various dimensions ranging from the issues like China's political economy to Sino-Korea economic and trade exchanges, and so on. The KAC has even combined OBOR with Korea's international development initiatives, which can help Korea benefit from active and sustainable cooperation with China. Moreover, the proposed work has found that Korean researchers have also actively expressed their growing attention, highlighted Korea's interest, and showed concern about China hegemony and Sinocentrism in their recent documented research works.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.763-775
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• 1996

For $Q = [0,S] \times [0,T]$ let C(Q) denote Yeh-Wiener space, i.e., the space of all real-valued continuous functions x(s,t) on Q such that x(0,t) = x(s,0) = 0 for every (s,t) in Q. Yeh [10] defined a Gaussian measure $m_y$ on C(Q) (later modified in [13]) such that as a stochastic process ${x(s,t), (s,t) \epsilon Q}$ has mean $E[x(s,t)] = \smallint_{C(Q)} x(s,t)m_y(dx) = 0$ and covariance $E[x(s,t)x(u,\upsilon)] = min{s,u} min{t,\upsilon}$. Let $C_\omega \equiv C[0,T]$ denote the standard Wiener space on [0,T] with Wiener measure $m_\omega$. Yeh [12] introduced the concept of the conditional Wiener integral of F given X, E(F$\mid$X), and for case X(x) = x(T) obtained some very useful results including a Kac-Feynman integral equation.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.239-268
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• 2015

Let Q be a finite quiver and $G{\subseteq}Aut(\mathbb{k}Q)$ a finite abelian group. Assume that $\hat{Q}$ and ${\Gamma}$ are the generalized Mckay quiver and the valued graph corresponding to (Q, G) respectively. In this paper we discuss the relationship between indecomposable $\hat{Q}$-representations and the root system of Kac-Moody algebra $g({\Gamma})$. Moreover, we may lift G to $\bar{G}{\subseteq}Aut(g(\hat{Q}))$ such that $g({\Gamma})$ embeds into the fixed point algebra $g(\hat{Q})^{\bar{G}}$ and $g(\hat{Q})^{\bar{G}}$ as a $g({\Gamma})$-module is integrable.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.227-274
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• 2001

In this paper we intended to discuss the following topics: (1) Notation, generalities, Markov processes. The close relationship between (generators of) Markov processes and the martingale problem is exhibited. A link between the Korovkin property and generators of Feller semigroups is established. (2) Feynman-Kac semigroups: 0-order regular perturbations, pinned Markov measures. A basic representation via distributions of Markov processes is depicted. (3) Dirichlet semigroups: 0-order singular perturbations, harmonic functions, multiplicative functionals. Here a representation theorem of solutions to the heat equation is depicted in terms of the distributions of the underlying Markov process and a suitable stopping time. (4) Sets of finite capacity, wave operators, and related results. In this section a number of results are presented concerning the completeness of scattering systems (and its spectral consequences). (5) Some (abstract) problems related to Neumann semigroups: 1st order perturbations. In this section some rather abstract problems are presented, which lie on the borderline between first order perturbations together with their boundary limits (Neumann type boundary conditions and) and reflected Markov processes.

• Journal of Agricultural Extension & Community Development
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• v.5 no.2
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• pp.177-186
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• 1998

It is nearing the establishment of KAC(Korean Agricultural Chamber) as an institution for intensive reflection of farmer's public opinions in agricultural administration. In this study, researchers examined the management of Agricultural Chambers in France and Japan, which have experienced the action of Agricultural Chamber in advance of Korea. And discussed the anticipated change in agricultural extension taking advantage of departure of KAC. Discourses and movements to establish KAC is putting pressure the existing agricultural extension system into innovation. Taking a side view that there were little contribution of agents belonging to the existing agricultural extension agencies, the problem of restructuring agricultural extension system has assumed very serious dimensions. Therefore, agents in agricultural extension agencies should lay their own view before the probable reorganization of agricultural extension system.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1243-1259
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• 2013

In this paper, we study the root system of rank 2 hyperbolic Kac-Moody algebras. We give some sufficient conditions for the existence of imaginary roots of square length $-2k(k{\in}\mathbb{Z}_{>0}$. We also give several relations between the integral points on the hyperbola $\mathfrak{h}$ to show that the value of the symmetric bilinear form of any two integral points depends only on the number of integral points between them. We also give some generalizations of Binet formula and Catalan's identity.