• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1155-1161
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• 2014

In this paper, we rederive the identity ${\Gamma}_q(x){\Gamma}_q(1-x)={\frac{{\pi}_q}{sin_q({\pi}_qx)}$. Then, we give q-analogue of Gauss' multiplication formula and study representation of q-oscillator algebra in terms of the q-factorial polynomials.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.249-260
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• 2014

Cameron and Storvick discovered a change of scale formula for Wiener integral of functionals in a Banach algebra $\mathcal{S}$ on classical Wiener space. We express the analytic Feynman integral of cylinder function as a limit of Wiener integrals. Moreover we obtain the same change of scale formula as Cameron and Storvick's result for Wiener integral of cylinder function. Our result cover a restricted version of the change of scale formula by Kim.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.423-432
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• 2010

We describe the asymptotic behavior of functions of the Royden p-algebra in terms of p-extremal length. We also prove that each bounded $\cal{A}$-harmonic function with finite energy on a complete Riemannian manifold is uniquely determined by the behavior of the function along p-almost every curve.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.419-428
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• 2007

In this paper, we will investigate the Hessian geometry of the homogeneous domain over the hypersurface given by a function F : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ with ${\mid}{\det}\;DdF\mid=1$.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.77-90
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• 2000

In this paper, we will establish the existence theorem of the operator valued function space integral over paths in abstract Wiener space under the general conditions rather than the known conditions.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.563-568
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• 2006

We introduce how to construct a non-unimodal level O-sequence which has all different local maxima as many as we desire.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.423-443
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• 2020

Generalizations of essential arity of partial functions, based on essential sets of arguments, are introduced, and their interplay with the minor relation of functions is investigated.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.9 no.4
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• pp.37-48
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• 1999

Current encryption methods have been applied to secure communication using discrete chaotic system whose output is a noise-like signal which differs from the conventional encryption methods that employ algebra and number theory[1-2] We propose an optical encryption method that transforms the primary pattern into the image pattern of discrete chaotic function first a primary pattern is encoded using permutation algorithm, In the proposed system we suggest the permutation algorithm using the output of key steam generator and its security level is analyzed. In this paper we worked out problem of the application about few discrete chaos function through a permutation algorithm and enhanced the security level. Experimental results with image signal demonstrate the proper of the implemented optical encryption system.

• Proceedings of the KIEE Conference
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• 1979.08a
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• pp.69-72
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• 1979

This paper deals with the computer method of finding the minimal sum of products for a switching function by using the MASK method derived from the characteristics of the Boolean algebra. The experiments with the program which is dissimilar to the previous computer programs show that the algorithm presented will be more efficient.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.361-366
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• 2009

In this paper we consider constructive function triples on the real numbers $\mathbb{R}$ and on (not necessarily commutative) integral domains D which permit the construction of a multitude of d-algebras via these constructive function triples. At the same time these constructions permit one to consider various conditions on these d-algebras for subsets of solutions of various equations, thereby producing geometric problems and interesting visualizations of some of these subsets of solutions. In particular, one may consider what notions such as "locally BCK" ought to mean, certainly in the setting provided below.