• 충청수학회지
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• 제24권4호
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• pp.849-862
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• 2011

In this paper, we introduce certain concepts which provide us with a perspective and insight into the generalization of orthogonality with the normalized duality mapping. The material of this paper will be mainly, but not only, used in developing algorithms for the best approximation problem in a Banach space.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.273-281
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• 2003

The purpose of this paper is to study the duality theorems in cone constrained multiobjective nonlinear programming for pseudo-invex objectives and quasi-invex constrains and the constraint cones are arbitrary closed convex ones and not necessarily the nonnegative orthants.

• 한국경영과학회지
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• 제10권2호
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• pp.24-27
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• 1985

This paper presents sufficient conditions for zero duality gap of Lagrangean relaxation in mixed integer programming problems and discusses about an algorithm which updates multipiers using the dual varibles of the linear programming constructed by fixing integer variables.

• 대한수학회논문집
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• 제19권1호
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• pp.179-196
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• 2004

Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.

• 대한수학회논문집
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• 제15권2호
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• pp.275-284
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• 2000

The existence and convergence theorems for fixed points of mappings of asymptotically nonexpansive type are established in Banach spaces with a weakly continuous duality mapping but without uniform convexity.

• 한국초등수학교육학회지
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• 제17권2호
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• pp.351-370
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• 2013

본 연구는 초등학교 6학년 영재학급 학생들이 정다면체 및 삼각다면체의 쌍대 관계를 탐구하면서 입체도형의 구성 요소를 통해 쌍대 관계를 어떻게 인식하고 이미지화하여, 결과적으로는 어떤 시각화 방법을 사용하는지 분석하는데 목적이 있다. 이를 위해 인천과 서울지역에 거주하는 총 4개 학급 60명의 학생들이 대상으로 학습지를 분석하였으며, 이들 중 소속 학급 내 성취 수준이 중상 이상인 12명의 학생들을 대상으로 관찰 및 면담을 통해 사고 과정을 보다 상세히 분석하였다. 다면체의 쌍대 관계를 탐구하는 과정에 필요한 구성요소에는 면, 꼭짓점, 모서리의 개수라는 일차적인 요소가 존재하고 한 면에 모인 꼭짓점의 수, 한 꼭짓점에 모인 면의 수라는 이차적인 요소가 존재한다. 일반적인 학생들은 구성 요소들의 개수에 집중하여 유사점 구별이라는 방법을 주로 사용하는데, 이 경우 정다면체의 쌍대관계는 쉽게 인식하였다. 하지만 삼각다면체의 쌍대관계까지 인식해 낸 학생들의 경우는 한 단계 더 나아가서 입체의 이미지를 떠올리며 유사점이 과연 공간에서 어떤 형태로 나타나는지를 확인해 본 결과 공간으로 전환되는 사고는 (대상 회전), (보조선 그리기), (입체도형 일부 만들기), (입체도형 안에 입체도형 만들기)의 형태로 나타나서 시각화하게 됨을 확인하였다.

• 대한수학회지
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• 제53권1호
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• pp.19-25
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• 2016

In this paper, some omissions in Mishra and Lai [13], have been pointed out and their corrective measures have been discussed briefly.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.413-428
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• 2012

Every contingent claim is unable to be replicated in the incomplete markets. Shortfall risk is considered with some risk exposure. We show how the dynamic optimization problem with the capital constraint can be reduced to the problem to find an optimal modified claim $\tilde{\psi}H$ where$\tilde{\psi}H$ is a randomized test in the static problem. Convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used as risk measure. It can be shown that we have the same results as in [21, 22] even though convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used. In this paper, we use Fenchel duality Theorem in the literature to deduce necessary and sufficient optimality conditions for the static optimization problem using convex duality methods.

• 대한수학회지
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• 제59권6호
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• pp.1203-1227
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• 2022

In this paper we develop the homological properties of the Gorenstein (𝓛, 𝓐)-flat R-modules 𝓖𝓕_{(𝓕(R),𝓐)} proposed by Gillespie, where the class 𝓐 ⊆ Mod(R^op) sometimes corresponds to a duality pair (𝓛, 𝓐). We study the weak global and finitistic dimensions that come with the class 𝓖𝓕_{(𝓕(R),𝓐)} and show that over a (𝓛, 𝓐)-Gorenstein ring, the functor - ⊗_R - is left balanced over Mod(R^op) × Mod(R) by the classes 𝓖𝓕_{(𝓕(R^op),𝓐)} × 𝓖𝓕_{(𝓕(R),𝓐)}. When the duality pair is (𝓕(R), 𝓕𝓟Inj(R^op)) we recover the G. Yang's result over a Ding-Chen ring, and we see that is new for (Lev(R), AC(R^op)) among others.

• 대한수학회지
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• 제42권6호
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• pp.1111-1120
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• 2005

Hong and Nel in [8] obtained a number of spectral dualities between a cartesian closed topological category X and a category of algebras of suitable type in X in accordance with the original formalism of Porst and Wischnewsky[12]. In this paper, there arises a dual adjointness S $\vdash$ C between the category X = Lim of limit spaces and that A of MV-algebras in X. We firstly show that the spectral duality: $S(A)^{op}{\simeq}C(X^{op})$ holds for the dualizing object K = I = [0,1] or K = 2 = {0, 1}. Secondly, we study a duality between the category of Tychonoff spaces and the category of semi-simple MV-algebras. Furthermore, it is shown that for any $X\;\in\;Lim\;(X\;{\neq}\;{\emptyset})\;C(X,\;I)$ is densely embedded into a cube $I^/H/$, where H is a set.