• 대한수학회보
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• 제29권1호
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• pp.117-123
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• 1992

The dimension problem has been one of central themes in the theory of ordered sets. In this paper we focus on amalgamated ordered sets. Although some results can be obviously applied to infinite cases, we assume throughout that all ordered set are finite. If A and B are ordered sets whose orders agree on A.cap.B, then the amalgam of A and B is defined to the the set A.cup.B in which the order is the transitive closure of the union of the two orders, i.e., the smallest order containing the two orders, and is denoted by A .or. B .leq. dim A + dim B for any ordered sets A and B. But it is quite surprising that the dimension of the amalgam of certain 2-dimensional ordered sets can be arbitrarily large.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제12권1호
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• pp.86-93
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• 2012

This paper presents a new approach to solve the pursuit problem based on a univector field method. In our proposed method, a set of eight agents works together instantaneously to find suitable moving directions and follow the univector field to pursue and capture a prey agent by surrounding it from eight directions in an infinite grid-world. In addition, a set of strategies is proposed to make the pursuit problem more realistic in the real world environment. This is a general approach, and it can be extended for an environment that contains static or moving obstacles. Experimental results show that our proposed algorithm is effective for the pursuit problem.

• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.13-31
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• 2015

In this paper, we introduce a general iterative algorithm for finding a common element of the common fixed point set of an infinite family of ${\lambda}_i$-strict pseudo-contractions and the solution set of a general system of variational inclusions for two inverse strongly accretive operators in q-uniformly smooth Banach spaces. Then, we analyze the strong convergence of the iterative sequence generated by the proposed iterative algorithm under mild conditions.

• 한국수학사학회지
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• 제12권1호
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• pp.32-44
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• 1999

This paper is a sequel to [8]. Development of modern logic was initiated by Boole and Morgan. Boolean logic is one of their completed works. Cantor created the set theory along with cardinal and ordinal numbers. His theory on infinite sets brought about a remarkable development on modern mathematical theory, but generated many paradoxes (e.g. Russell Paradox) that in turn motivated mathematicians to solve them. Further, mathematicians attempted to construct sound foundations for Mathematics. As a result three important schools of thought were formed in relation to fundamentals of mathematics for the resolution of paradoxes of set theory, namely logicism developed by Russell and Whitehead, intuitionism lead by Brouwer and formalism contended by Hilbert and Bernays. In this paper, we examine the logic for intuitionism which is originated by Brouwer in 1908 and study Heyting algebra.

• 대한수학회보
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• 제52권6호
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• pp.1777-1795
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• 2015

In this paper, we establish sufficient conditions for the solution set of parametric generalized vector mixed quasivariational inequality problem to have the semicontinuities such as the inner-openness, lower semicontinuity and Hausdorff lower semicontinuity. Moreover, a key assumption is introduced by virtue of a parametric gap function by using a nonlinear scalarization function. Then, by using the key assumption, we establish condition ($H_h$(${\gamma}_0$, ${\lambda}_0$, ${\mu}_0$)) is a sufficient and necessary condition for the Hausdorff lower semicontinuity, continuity and Hausdorff continuity of the solution set for this problem in Hausdorff topological vector spaces with the objective space being infinite dimensional. The results presented in this paper are different and extend from some main results in the literature.

• 한국언어정보학회지:언어와정보
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• 제5권2호
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• pp.1-8
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• 2001

Natural language string sets are known to require a grammar with a generative capacity slightly beyond that of Context Free Grammars. Proofs regarding complexity of natural language have involved particular properties of languages like English, Swiss German and Bambara. While it is not very difficult to prove that Korean is more complex than the simplest of the many infinite sets, no proof has been given of this in the literature. I identify two types of center embedding in Korean and use them in proving that Korean is not a regular set, i.e. that no FSA's can recognize its string set. The regular language i salam i (i salam ul$)^j$ michi (key ha)^k$ essta is intersected with Korean, to give {i salam i (i salam ul$)^j$ michi (key ha$)^k$ essta i $$\mid$$ j, k $\geq$ 0 and j $\leq$ k}. This latter language is proved to be nonregular. As the class of regular sets is closed under intersection, Korean cannot be regular.

• Current Optics and Photonics
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• 제5권3호
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• pp.329-335
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• 2021

The problem of polarized light scattering by a cylinder on or close to a planar substrate is analytically solved. The light is assumed to be normally incident to the axis of the cylinder. Transverse magnetic (TM) and transverse electric (TE) polarizations are treated separately. The solution for each polarization is composed of a coupled set of linear equations which couples the scattering characteristics of the cylinder and the planar substrate. The coupling comes from the scattering by the planar substrate and by the cylinder. The solution of the coupled set of equations obtained by iterative substitution consists of infinite series, where each term represents the contribution of single and multiple scatterings of all orders.

• 한국지리정보학회지
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• 제16권3호
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• pp.193-210
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• 2013

본 연구에서는 기상청에서 제공하는 공간해상도 27km 지역규모의 A1B 시나리오 기반의 RCM 자료와 비집수면적 개념을 도입한 GIS기반의 무한사면안정모형을 이용하여 전라북도 수계를 대상으로 미래 기후변화에 따른 사면안정 변동성을 평가하였다. 우선, 미래의 사면안정성 변동성 평가를 위하여 RCM 자료는 공간적으로 유역단위에서 강우관측소 지점단위로, 시간적으로 월단위에서 일단위 자료로 다운스케일링을 수행하였다. 또한, 무한사면안정모형의 중요 매개변수인 습윤지수 산정을 위하여 비집수면적 개념을 도입하여 격자기반의 습윤지수 정보를 획득하였으며 범용수치지형도, 정밀토양도, 임상도를 이용하여 지형 지질 임상학적 매개변수을 추출하여 GIS기반의 무한사면안정모형을 구축하였다. 이상의 미래 강우입력자료와 무한사면안정모형을 이용하여 현재(1971~2000)대비 미래(2010~2100)에 대한 사면안정 변동성을 평가하였다. 본 논문은 2편으로 구성되어 있으며, 제1편에서는 기후변화 시나리오에 따른 사면안정 변동성 해석을 위한 RCM자료의 가공 및 무한사면안정모형의 구축 등 방법론을 제시한다.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1583-1602
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• 2011

A special system of partial differential equations (PDEs) occur in a natural way while studying a class of irrotational inviscid fluid flow problems involving infinite channels. Certain aspects of solutions of such PDEs are analyzed in the context of flow problems involving multiple layers of fluids of different constant densities in a channel associated with arbitrary bottom topography. The whole analysis is divided into two parts-part A and part B. In part A the linearized theory is employed along with the standard Fourier analysis to understand such flow problems and physical quantities of interest are derived analytically. In part B, the same set of problems handled in part A are examined in the light of a weakly non-linear theory involving perturbation in terms of a small parameter and it is shown that the original problems can be cast into KdV type of nonlinear PDEs involving the bottom topography occurring in one of the coefficients of these equations. Special cases of bottom topography are worked out in detail and expressions for quantities of physical importance are derived.

• 대한기계학회논문집A
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• 제25권1호
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• pp.11-15
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• 2001

We present the design and strength evaluation of an anodically bonded pressurized cavity array, based on the energy release rate measured from the anodically bonded plates of two dissimilar materials. From a theoretical analysis, a simple fracture mechanics model of the pressurized cavity array has been developed. The energy release rate (ERR) of the bonded cavity with an infinite bonding length has been derived in terms of cavity pressure, cavity size, bonding length, plate size and material properties. The ERR with a finite bonding length has been evaluated from the finite element analysis performed for varying cavity and plate sizes. It is found that, for an inter-cavity bonding length greater than the half of the cavity length, the bonding strength of cavity array approaches to that of the infinite plate. For a shorter bonding length, however, the bonding strength of the cavity array is monotonically decreased with the ratio of the bonding length to the cavity length. The critical ERR of 6.21J/㎡ has been measured from anodically bonded silicon-glass plates. A set of critical pressure curves has been generated for varying cavity array sizes, and a design method of the pressurized cavity array has been developed for the failure-free wafer-level packaging of MEMS devices.