• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.477-492
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• 1994

For the eigenvalue problem of $Au = \lambda u$ where A is considered as a semi-bounded self-adjoint operator on a Hilbert space, we are used to apply two complentary methods finding upper bounds and lower bounds to the eigenvalues. The most popular method for finding upper bounds may be the Rayleigh-Ritz method which was developed in the 19th century while a method for computing lower bounds may be the method of intermediate eigenvalue problems which has been developed since 1950's. In the method of intermediate eigenvalue problems (IEP), we consider the original operator eigenvalue problem as a perturbation of a simpler, resolvable, self-adjoint eigenvalue problem, called a base problem, that gives rough lower bounds.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.22 no.51
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• pp.21-28
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• 1999

The TSP(Traveling Salesman Problem) is one of the most widely studied problems in combinatorial optimization. The most common interpretation of TSP is finding a shortest Hamiltonian tour of all cities. The objective of this paper proposes a new heuristic algorithm MCH(Multi-Convex hulls Heuristic). MCH is a algorithm for finding good approximate solutions to practical TSP. The MCH algorithm is using the characteristics of the optimal tour. The performance results of MCH algorithm are superior to others algorithms (NNH, CCA) in CPU time.

• Advances in Computational Design
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• v.2 no.1
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• pp.71-87
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• 2017

This study focuses on the efficiency and applicability of dynamic relaxation methods in form-finding of membrane structures. Membrane structures have large deformations that require complex nonlinear analysis. The first step of analysis of these structures is the form-finding process including a geometrically nonlinear analysis. Several numerical methods for form-finding have been introduced such as the dynamic relaxation, force density method, particle spring systems and the updated reference strategy. In the present study, dynamic relaxation method (DRM) is investigated. The dynamic relaxation method is an iterative process that is used for the static equilibrium analysis of geometrically nonlinear problems. Five different examples are used in this paper. To achieve the grading of the different dynamic relaxation methods in form-finding of membrane structures, a performance index is introduced. The results indicate that viscous damping methods show better performance than kinetic damping in finding the shapes of membrane structures.

• Communications for Statistical Applications and Methods
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• v.22 no.5
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• pp.401-413
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• 2015

In this article, we review the statistical methods and theory for dose finding in early phase clinical trials, where the primary objective is to identify an acceptable dose for further clinical investigation. The dose finding literature is initially motivated by applications in phase I clinical trials, in which dose finding is often formulated as a percentile estimation problem. We will present some important phase I methods and give an update on new theoretical developments since a recent review by Cheung (2010), with an aim to cover a broader class of dose finding problems and to illustrate how the general dose finding theory may be applied to evaluate and improve a method. Specifically, we will illustrate theoretical techniques with some numerical results in the context of a phase I/II study that uses trinary toxicity/efficacy outcomes as basis of dose finding.

• IEIE Transactions on Smart Processing and Computing
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• v.6 no.1
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• pp.18-20
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• 2017

In this paper, we propose a new classification method to complement a $na{\ddot{i}}ve$ Bayesian classifier. This classifier assumes data distribution to be Gaussian, finds the discriminant function, and derives the decision curve. However, this method does not investigate finding the decision curve in much detail, and there are some minor problems that arise in finding an accurate discriminant function. Our findings also show that this method could produce errors when finding the decision curve. The aim of this study has therefore been to investigate existing problems and suggest a more reliable classification method. To do this, we utilize the gradient to find the decision curve. We then compare/analyze our algorithm with the $na{\ddot{i}}ve$ Bayesian method. Performance evaluation indicates that the average accuracy of our classification method is about 10% higher than $na{\ddot{i}}ve$ Bayes.

• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.559-567
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• 2006

We are interested in the distance problem between two objects in three dimensional Euclidean space. There are many distance problems for various types of objects including line segments, boxes, polygons, circles, disks, etc. In this paper we present an iterative algorithm for finding the distance between two given ellipses. Numerical examples are given.

• Industrial Engineering and Management Systems
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• v.12 no.2
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• pp.151-160
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• 2013

In the past decades, several algorithms based on evolutionary approaches have been proposed for solving job shop scheduling problems (JSP), which is well-known as one of the most difficult combinatorial optimization problems. Most of them have concentrated on finding optimal solutions of a single objective, i.e., makespan, or total weighted tardiness. However, real-world scheduling problems generally involve multiple objectives which must be considered simultaneously. This paper proposes an efficient particle swarm optimization based approach to find a Pareto front for multi-objective JSP. The objective is to simultaneously minimize makespan and total tardiness of jobs. The proposed algorithm employs an Elite group to store the updated non-dominated solutions found by the whole swarm and utilizes those solutions as the guidance for particle movement. A single swarm with a mixture of four groups of particles with different movement strategies is adopted to search for Pareto solutions. The performance of the proposed method is evaluated on a set of benchmark problems and compared with the results from the existing algorithms. The experimental results demonstrate that the proposed algorithm is capable of providing a set of diverse and high-quality non-dominated solutions.

• Journal of The Korean Association For Science Education
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• v.38 no.6
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• pp.865-874
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• 2018

The purpose of this study is to explore the process of inquiry problem finding in high school students' small group free-inquiry. For this purpose, 91 second grade high school students took part in small group free-inquiry. We conducted interviews with students (48 students in 15 groups) who were relatively successful in the inquiry performed for one semester (about 4 months). Based on the results of the interviews, we analyzed the characteristics of the inquiry problem finding through the steps and strategies in the inquiry problem finding process. The main results are as follows: First, in the inquiry problem finding process, steps such as selecting keyword, presenting an inconvenience, presenting a question, and finding an inquiry problem were found, and in particular, the process of selecting the keyword that correspond to the subject of inquiry, such as the material and situation of inquiry, is very important step in inquiry problem finding. Second, the strategies that students used in the process of finding inquiry problem included searching information, review of prior research, sharing of knowledge and experience, linking and extension of knowledge and experience, environmental awareness, expert consultation, discussion of suitability, elaboration, etc. Third, finding an inquiry problem was relatively easy in the inquiry for finding out problems (i.e. inconvenience) in everyday life and investigating ways to solve them. Fourth, the review of prior researches through the internet was useful in the process of selecting keyword and elaboration. Fifth, the factors that students consider when selecting one of several candidate inquiry problems are feasibility, real-life applicability, and economic condition. Sixth, the current affairs had a positive impact on the inquiry problem finding. Based on the above results, we discussed some ways to increase students' inquiry problem finding ability.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.523-558
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• 2021

In this paper, we study some fixed point properties of n-generalized Bregman nonspreading mappings in reflexive Banach space. We introduce a hybrid iterative scheme for finding a common solution for a countable family of equilibrium problems and fixed point problems in reflexive Banach space. Further, we give some applications and numerical example to show the importance and demonstrate the performance of our algorithm. The results in this paper extend and generalize many related results in the literature.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.375-388
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• 2013

In this paper, we introduce an iterative sequence for finding solution of a system of mixed equilibrium problems and the set of fixed points of a nonexpansive mapping in Hilbert spaces. Then, the weak and strong convergence theorems are proved under some parameters controlling conditions. Moreover, we apply our result to fixed point problems, system of equilibrium problems, general system of variational inequalities, mixed equilibrium problem, equilibrium problem and variational inequality.