• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.433-444
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• 2024

Our study explores the connection between the Pythagorean theorem and the Fixed-point theorem in metric spaces. Both of which center around the concepts of distance transformations and point relationships. The Pythagorean theorem deals with right triangles in Euclidean space, emphasizing distances between points. In contrast, fixed-point theorems pertain to the points that remain unchanged under specific transformations thereby preserving distances. The article delves into the intrinsic correlation between these concepts and presents a novel study in Euclidean metric spaces, examining the relationship between contraction mapping and Pythagorean Right Triangles. Practical applications are also discussed particularly in the context of image compression. Here, the integration of the Pythagorean right triangle paradigm with contraction mappings results in efficient data representation and the preservation of visual data relation-ships. This illustrates the practical utility of seemingly abstract theories in addressing real-world challenges.

• 대한수학회지
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• 제53권2호
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• pp.347-362
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• 2016

In this paper, we are concerned with abstract random linear operators on probabilistic unitary spaces which are a generalization of generalized random linear operators on a Hilbert space defined in [25]. The representation theorem for abstract random bounded linear operators and some results on the adjoint of abstract random linear operators are given.

• 대한수학회지
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• 제37권6호
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• pp.915-927
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• 2000

This paper is concerned with degenerate Volterra equations Mu(t) + ∫(sub)0(sup)t k(t-s) Lu(s)ds = f(t) in Banach spaces both in the hyperbolic case, and the parabolic one. The key assumption is played by the representation of the underlying space X as a direct sum X = N(T) + R(T), where T is the bounded linear operator T = ML(sup)-1. Hyperbolicity means that the part T of T in R(T) is an abstract potential operator, i.e., -T(sup)-1 generates a C(sub)0-semigroup, and parabolicity means that -T(sup)-1 generates an analytic semigroup. A maximal regularity result is obtained for parabolic equations. We will also investigate the cases where the kernel k($.$) is degenerated or singular at t=0 using the results of Pruss[8] on analytic resolvents. Finally, we consider the case where $\lambda$ is a pole for ($\lambda$L + M)(sup)-1.

• 한국측량학회지
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• 제31권6_2호
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• pp.511-520
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• 2013

Recently, human activities have expanded from outdoor spaces to indoor spaces since a lot of complex buildings were constructed over the world. Especially, visitors in a shopping mall would like to receive specific information of interest regarding various shopping-related activities as well as shopping itself. However, when it comes to providing the information, existing guide services have some drawbacks. Firstly, the existing services cannot provide visitors with the information of other stores simply and promptly on the current location. Secondly, the services have difficulties in representation and share of the shopping-related knowledge, and in providing inferred information. Thus, the purpose of this study is to develop a method that allows topological analysis utilizing ontology technique around the current position in such shopping mall in order to provide shopping-related information. For this, the shopping activity ontology model is designed, and based on the ontology model, inferencing rules are defined in order to extract the information of interest efficiently through semantic queries. Also, a geocoding method in indoor spaces is used regarding the current location, and optimal routing analysis, which is one of topological analysis, is applied with the result from the semantic queries. As a result, an Android application is developed for 3D visualization and user interface.

• 대한수학회논문집
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• 제9권3호
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• pp.607-616
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• 1994

I. M. Gelfand and G. E. Shilov [GS] introduced the Gelfand-Shilov spaces of type S, generalized type S and type W of test functions to investigate the uniqueness of the solutions of the Cauchy problems of partial differential equations. Using the heat kernel method Matsuzawa gave structure theorems for distributions, hyperfunctions and generalized functions in the dual space $(S^s_r)'$ of the Gelfand-Shilov space of type S in [M1, M2 and DM], respectively. Also, we gave structure theorems for ultradistributions, Fourier hyperfunctions in [CK, KCK], respectively.

• 대한수학회지
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• 제35권2호
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• pp.371-386
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• 1998

Let G be a compact Lie group and M a semialgebraic G space in some orthogonal representation space of G. We prove that if G is finite then M has an equivariant semialgebraic triangulation. Moreover this triangulation is unique. When G is not finite we show that M has a semialgebraic G CW complex structure, and this structure is unique. As a consequence compact semialgebraic G space has an equivariant simple homotopy type.

• 대한수학회논문집
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• 제34권2호
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• pp.585-602
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• 2019

We characterize Gelfand-continuous functions from a Tychonoff space X into an Arens-Michael algebra A. Then we define several algebras of such functions, and investigate them as topological algebras. Finally, we provide a class of examples of (metrizable) commutative unital complete Arens-Michael algebras A and locally compact spaces X for which all these algebras differ from each other.

• 대한수학회보
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• 제60권1호
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• pp.237-255
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• 2023

In this article, we find bases for the spaces of modular forms $M_2({\Gamma}_0(88),\;({\frac{d}{\cdot}}))$ for d = 1, 8, 44 and 88. We then derive formulas for the number of representations of a positive integer by the diagonal quaternary quadratic forms with coefficients 1, 2, 11 and 22.

• 한국콘텐츠학회논문지
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• 제13권6호
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• pp.9-19
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• 2013

본 논문에서는 가상 상황속의 사건들에 역사적 맥락을 부여하기 위한 통합적 직관적 정보표현구조로서 시공간 그래프(Spatio-Temporal Graph)를 설계하고 구현하였다. 일반적으로 사건은 공간뿐 아니라 시간을 점유함으로써 역사적 사실이 된다. 따라서 가상 상황을 시뮬레이션하기 위해서는 공간적 측면을 표현하기 위한 삼차원 정보구조에 시간적 측면을 더한 다차원적인 맥락에 사건들을 위치시키는 일이 핵심적 기초가 된다. 이러한 다차원적 맥락은 온톨로지 뷰, 인스턴스 뷰, 시공간 뷰, 실제 뷰 등과 같은 여러 수준에서의 통합적 직관적 지식표현수단들을 통해 구현된다. 이와 같이 구현된 시공간 그래프에 기반한 시뮬레이션 시스템에 예제 시나리오를 적용하여 실용성을 검증한다. 본 기술은 지능형 교육시스템이나 차세대 시뮬레이션 게임 등에 필수적인 다양한 상황들을 제공하는 시뮬레이션 시스템의 중심요소가 된다.

• 한국콘텐츠학회논문지
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• 제12권6호
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• pp.21-31
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• 2012

가상현실은 현실처럼 구성된 가상공간과 그 속에서 살아가는 에이전트들로 구성되어 있다. 여기서 가상공간이란 시각적 표현뿐만 아니라 질량, 중력, 마찰력등과 같은 물리속성들과 법칙들에 의해 규율되는 질서 있는 공간을 의미한다. 이러한 가상공간을 구축하기 위해서는 인간과 유사한 행동을 하는 가상 에이전트와 그를 둘러싼 환경을 설계해야 한다. 정해진 공간이나 기억에 대하여 설계자의 지식에 따라서 그대로 반응하게 만들어진 기존의 반응형 에이전트의 행동방식을 개선하여 능동적 행동이 가능하기 위해서는 에이전트의 활동 공간에 관련된 다양한 지식이 필요하다. 본 연구에서는 이러한 지식중에서 공간적 지식에 관한 표현구조를 설계하고 구현한다. 이와 같은 지식표현은 사실적이고 효율적인 물리적 가상환경을 구축하는 바탕으로 사용됨과 동시에 가상에이전트들의 지식을 표현하는 구조로 이용된다.