• Honam Mathematical Journal
• /
• v.20 no.1
• /
• pp.135-145
• /
• 1998

In this paper, we focus on the convex-valued selection theorem out of four main selection theorems; zero-dimensional, convex-valued, compact-valued, finite-dimensional theorems based on Michael's papers. We prove some theorems about lower semi-continuous set-valued mappings, and derive some applications to closed continuous set-valued mappings and to functional analysis. We also give a partial solution to the open problem posed by Engelking, Heath, and Michael.

• Honam Mathematical Journal
• /
• v.15 no.1
• /
• pp.1-4
• /
• 1993

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.257-267
• /
• 2005

The aim of this paper is to give three equilibrium existence theorems for generalized games with lower semi continuous constraint and preference multimaps by using Michael's continuous selection theorem.

• Journal of the Korean Statistical Society
• /
• v.30 no.1
• /
• pp.21-30
• /
• 2001

Suppose we observe a set of data (X$_1$,Y$_1$(, …, (X$_{n}$,Y$_{n}$) and use the Nadaraya-Watson regression estimator to estimate m(x)=E(Y│X=x). in this article bandwidth selection problem for the Nadaraya-Watson regression estimator is investigated. In particular cross validation method based on average square error(ASE) is considered. Theoretical results here include a central limit theorem that quantifies convergence rates of the bandwidth selector.tor.

• Communications for Statistical Applications and Methods
• /
• v.15 no.3
• /
• pp.333-342
• /
• 2008

Variable selection theorem in the linear regression model is extended to the analysis of covariance model. When some of regression variables are omitted from the model, it reduces the variance of the estimators but introduces bias. Thus an appropriate balance between a biased model and one with large variances is recommended.

• Kyungpook Mathematical Journal
• /
• v.48 no.1
• /
• pp.1-14
• /
• 2008

In this paper, we investigate the existence of solutions of second order impulsive neutral functional differential inclusions which the nonlinearity F admits convex and non-convex values. Some results under weaker conditions are presented. Our results extend previous ones. The methods rely on a fixed point theorem for condensing multivalued maps and Schaefer's fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values.

• Proceedings of the IEEK Conference
• /
• 1999.06a
• /
• pp.1013-1016
• /
• 1999

Simple Genetic Algorithm(SGA) proposed by J. H. Holland is a population-based optimization method based on the principle of the Darwinian natural selection. The theoretical foundations of GA are the Schema Theorem and the Building Block Hypothesis. Although GA does well in many applications as an optimization method, still it does not guarantee the convergence to a global optimum in GA-hard problems and deceptive problems. Therefore as an alternative scheme, there is a growing interest in a co-evolutionary system, where two populations constantly interact and co-evolve. In this paper we propose an extended schema theorem associated with a schema co-evolutionary algorithm(SCEA), which explains why the co-evolutionary algorithm works better than SGA. The experimental results show that the SCEA works well in optimization problems including deceptive functions.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.6 no.2
• /
• pp.35-49
• /
• 1981

This paper is concerned with developing a Multi-period Behavioral Model for the portfolio selection problem. The unique feature of the model is that it treats a number of factors and decision variables considered germane in decision making on an interrelated basis. The formulated problem has the structure of a Chance Constrained programming Model. Then empoloying arguments of Central Limit Theorem and normality assumption the stochastic model is reduced to that of a Non-Linear Programming Model. Finally, a number of interesting properties for the reduced model are established.

• Journal of applied mathematics & informatics
• /
• v.33 no.5_6
• /
• pp.517-530
• /
• 2015

In this paper, we establish a class of strong limit theorems, represented by inequalities, for the arbitrary random field with respect to the product binomial distributions indexed by the infinite tree on the generalized random selection system by constructing the consistent distri-bution and a nonnegative martingale with pure analytical methods. As corollaries, some limit properties for the Markov chain field with respect to the binomial distributions indexed by the infinite tree on the generalized random selection system are studied.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.4 no.1
• /
• pp.39-48
• /
• 2000

In this paper we define T-fuzzy integrals of set-valued mappings, which are extensions of fuzzy integrals of the single-valued functions defined by Sugeno. And we discuss their properties.