• 대한수학회논문집
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• 제27권1호
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• pp.47-56
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• 2012

In this article, we continue the study of tense symmetric Heyting algebras (or TSH-algebras). These algebras constitute a generalization of tense algebras. In particular, we describe a discrete duality for TSH-algebras bearing in mind the results indicated by Or lowska and Rewitzky in [E. Orlowska and I. Rewitzky, Discrete Dualities for Heyting Algebras with Operators, Fund. Inform. 81 (2007), no. 1-3, 275-295] for Heyting algebras. In addition, we introduce a propositional calculus and prove this calculus has TSH-algebras as algebraic counterpart. Finally, the duality mentioned above allowed us to show the completeness theorem for this calculus.

• 대한수학회지
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• 제47권1호
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• pp.17-28
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• 2010

In this paper we deal with linear chance-constrained optimization problems, a class of problems which naturally arise in practical applications in finance, engineering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving the deterministic equivalent formulation of a linear chance-constrained optimization problem we construct a conjugate dual problem to it. Then we provide for this primal-dual pair weak sufficient conditions which ensure strong duality. In this way we generalize some results recently given in the literature. We also apply the general duality scheme to a portfolio optimization problem, a fact that allows us to derive necessary and sufficient optimality conditions for it.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.123-137
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• 2009

A multiobjective variational problem involving higher order derivatives is considered and Fritz-John and Karush-Kuhn-Tucker type optimality conditions for this problem are derived. As an application of Karush-Kuhn-Tucker optimality conditions, Wolfe type dual to this variational problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the already existing results in nonlinear programming.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권2호
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• pp.179-192
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• 2012

We find the solution minimizing the shortfall risk by using the Lagrange-multiplier method. The conventional duality method in the expected utility maximization problem is used and we get the same results as in the paper [21].

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.83-99
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• 2002

Optimality conditions are derived for a nonlinear program in which a support function appears in the objective as well as in each constraint function. Wolfe and Mond-Weir type duals to this program are presented and various duality results are established under suitable convexity and generalized convexity assumptions. Special cases that often occur in the literature are those in which a support function is the square root of a positive semi- definite quadratic form or an Lp norm. It is pointed out that these special cases can easily be generated from our results.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.361-376
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• 2005

Optimality conditions are derived for a nonlinear fractional program in which a support function appears in the numerator and denominator of the objective function as well as in each constraint function. As an application of these optimality conditions, a dual to this program is formulated and various duality results are established under generalized convexity. Several known results are deduced as special cases.

• 벤처창업연구
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• 제10권3호
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• pp.85-97
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• 2015

본 연구에서는 자원의존이론을 이용하여 사외이사 비중과 최고경영자의 이사회 의장직 겸임 효과가 하이테크 산업에 속해 있는 국내 상장기업의 인수합병 성과에 미치는 영향을 2004년부터 2012년까지 수행된 인수합병거래 246개를 대상으로 실증 분석하였다. 분석결과에 따르면, 사외이사 비중은 인수합병 성과에 정(+)의 영향을 미치는 것으로 나타났다. 그러나 최고경영자가 이사회 의장직을 겸임하는 경우 인수합병 성과에 부(-)의 영향을 미치는 것으로 나타났다. 사외이사의 비중과 최고경영자의 이사회 의장직 겸임이 지닌 상호작용의 효과를 살펴본 결과, 최고경영자가 이사회 의장직을 겸임하는 경우 사외이사의 비중이 인수합병 성과에 정(+)의 영향을 미치는 것으로 나타났다. 그러나 이사회 의장이 독립적인 지위를 가지는 경우 사외이사의 비중이 인수합병 성과에 부(-)의 영향을 미치는 것으로 나타났다. 아울러 연구결과의 타당성을 확보하기 위해 상호작용항을 통한 회귀분석 및 다양한 사건기간을 대상으로 실증분석을 수행하여 동일한 결과를 얻을 수 있었다. 최고경영자가 이사회 의장직을 겸임하는 경우 리더십 강화 및 조직 내 지휘체계 확립으로 인해 기업 외부의 이해관계자로부터 정당성을 확보하게 된다. 이를 통해 이사회의 자원의존 기능이 강화되며 인수합병 성과에 긍정적인 영향을 미치는 것으로 해석된다. 반대로 이사회 의장이 독립적인 지위를 가지는 경우 최고경영자의 최고책임자로서의 외부 정당성이 약화된다. 따라서 이사회의 자원의존 기능이 감소되고 인수합병 성과에 부정적인 영향을 미치는 것으로 해석할 수 있다. 기존의 선행연구에서는 최고경영자의 이사회 의장직 분리의 긍정적인 효과에 대해서 주목하였다면, 본 연구에서는 최고경영자의 이사회 의장직 겸임의 긍정적인 효과를 실증적으로 보여주었다는 점에서 그 의의가 있다고 생각한다.

• 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.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.111-125
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• 2012

In this paper, we introduce new classes of generalized convex n-set functions called $d$-weak strictly pseudo-quasi type-I univex, $d$-strong pseudo-quasi type-I univex and $d$-weak strictly pseudo type-I univex functions and focus our study on multiobjective subset programming problem. Sufficient optimality conditions are obtained under the assumptions of aforesaid functions. Duality results are also established for Mond-Weir and general Mond-Weir type dual problems in which the involved functions satisfy appropriate generalized $d$-type-I univexity conditions.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.359-375
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• 2014

In this paper, a multiobjective nondifferentiable fractional programming problem (MFP) is considered where the objective function contains a term involving the support function of a compact convex set. A vector valued (generalized) ${\alpha}$-univex function is defined to extend the concept of a real valued (generalized) ${\alpha}$-univex function. Using these functions, sufficient optimality criteria are obtained for a feasible solution of (MFP) to be an efficient or weakly efficient solution of (MFP). Duality results are obtained for a Mond-Weir type dual under (generalized) ${\alpha}$-univexity assumptions.