• Kyungpook Mathematical Journal
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• 제51권3호
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• pp.251-260
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• 2011

The aim of this paper is to obtain a solution of a certain multidimensional convolution integral equation of Fredholm type whose kernel involves a generalized polynomial set. A number of results follow as special cases from the main theorem by specifying the parameters of the generalized polynomial set.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.101-113
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• 2000

In this paper, we introduce and study a new class of variational inclusions, called the set-valued quasi variational inclusions. The resolvent operator technique is used to establish the equivalence between the set-valued variational inclusions and the fixed point problem. This equivalence is used to study the existence of a solution and to suggest a number of iterative algorithms for solving the set-valued variational inclusions. We also study the convergence criteria of these algorithms.

• Korean Journal of Mathematics
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• 제30권4호
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• pp.571-592
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• 2022

By established a Banach space with the Hausdorff distance, we introduce the alternative fixed-point theorem to explore the existence and uniqueness of a fixed subset of Y and investigate the stability of set-valued Euler-Lagrange functional equations in this space. Some properties of the Hausdorff distance are furthermore explored by a short and simple way.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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• pp.255-275
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• 2022

In this paper, we introduce a new system of set-valued variational inclusion problems in semi-inner product spaces. We use resolvent operator technique to propose an iterative algorithm for computing the approximate solution of the system of set-valued variational inclusion problems. The results presented in this paper generalize, improve and unify many previously known results in the literature.

• 한국인터넷방송통신학회논문지
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• 제23권4호
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• pp.165-170
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• 2023

본 논문은 지금까지 NP-완전 문제로 다항시간 알고리즘이 존재하지 않는 집합피복 문제에 대해 선형시간으로 해를 구할 수 있는 알고리즘을 제안하였다. 지금까지는 최대로 피복할 수 있는 집합을 선택하는 휴이스틱 탐욕 알고리즘만이 알려져 있다. 반면에 제안된 알고리즘은 최대 원소 수 2순위 또는 3순위까지의 노드들 k개를 대상으로 포함-배제 원리 규칙을 적용하여 N개의 노드 모두를 피복하는 피복집합을 구하고, 이들 중 최소 피복집합을 선택하는 경쟁 알고리즘이다. 제안된 알고리즘은 욕심쟁이 알고리즘이 최적 해를 얻지 못하는 단점을 보완하였다. 제안된 알고리즘을 다양한 응용 사례들에 적용한 결과 O(kn²)의 다항시간으로 최적 해를 얻었다.

• 품질경영학회지
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• 제47권4호
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• pp.701-711
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• 2019

Purpose: The problem of optimizing redundancy allocation in multi-level systems is considered when each item in a multi-level system has alternative items with the same function. The number of redundancy of multi-level system is allocated to maximize the reliability of the system under path set and cost limitation constraints. Methods: Based on cost limitation and path set constraints, a mathematical model is established to maximize system reliability. Particle swarm optimization is employed for redundant allocation and verified by numerical experiments. Results: Comparing the particle swarm optimization method and the memetic algorithm for the 3 and 4 level systems, the particle swarm optimization method showed better performance for solution quality and search time. Particularly, the particle swarm optimization showed much less than the memetic algorithm for variation of results. Conclusion: The proposed particle swarm optimization considerably shortens the time to search for a feasible solution in MRAP with path set constraints. PS optimization is expected to reduce search time and propose the better solution for various problems related to MRAP.

• 한국환경과학회지
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• 제29권10호
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• pp.951-959
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• 2020

This study aimed to re-establish the conservation area reflecting landscape ecological value through scenario program, targeting Odaesan National Park. The basic data were mapped in watershed planning units, which were set considering topographical and ecological values. The framework of Marxan with Zones, using an indexation process, was using the mapped indicators. Each best solution according to the scenarios was assessed through sensitivity analysis, and a final solution was selected among the best solutions, considering criteria including area ratio of conservation area and grouping. Lastly, the final solution was verified in the overlap analysis with recent zonation. As a result, through the framework of Marxan with Zones, the best solution of scenario 1, which was set by the highest conservation criteria was selected as the final solution, and the area ratio of conservation area and grouping was excellent. As for the overlap analysis, the suggested conservation area was improved compared to recent zonation in terms of the area ratio (39.4%), biotope grade I (35.6%) and the distribution points (7 places) of legally protected species.

• Structural Engineering and Mechanics
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• 제76권4호
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• pp.451-463
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• 2020

In this paper, a new semi-analytical solution for estimating the pull-in parameters of electrically actuated functionally graded (FG) nanobeams is proposed. All the bulk and surface material properties of the FG nanoactuator vary continuously in thickness direction according to power law distribution. Here, the modified couple stress theory (MCST) and Gurtin-Murdoch surface elasticity theory (SET) are jointly employed to capture the size effects of the nanoscale beam in the context of Euler-Bernoulli beam theory. According to the MCST and SET and accounting for the mid-plane stretching, axial residual stress, electrostatic actuation, fringing field, and dispersion (Casimir or/and van der Waals) forces, the nonlinear nonclassical equation of motion and boundary conditions are obtained derived using Hamilton principle. The proposed semi-analytical solution is derived by employing Galerkin method in conjunction with the Particle Swarm Optimization (PSO) method. The proposed solution approach is validated with the available literature. The freestanding behavior of nanoactuators is also investigated. A parametric study is conducted to illustrate the effects of different material and geometrical parameters on the pull-in response of cantilever and doubly-clamped FG nanoactuators. This model and proposed solution are helpful especially in mechanical design of micro/nanoactuators made of FGMs.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.217-229
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• 2007

In this paper, Genetic Algorithm (GA) is used to find the Maximum Weight Independent Set (MWIS) of a graph. First, MWIS problem is formulated as a 0-1 integer programming optimization problem with linear objective function and a single quadratic constraint. Then GA is implemented with the help of this formulation. Since GA is a heuristic search method, exact solution is not reached in every run. Though the suboptimal solution obtained is very near to the exact one. Computational result comprising an average performance is also presented here.

• 경영과학
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• 제10권2호
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• pp.11-26
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• 1993

This paper presents a new interactive procedure for multiple objective linear programming problem (MOLP). In practical multiple objective linear programming applications, there is usually no need for the decision maker to consider solutions which are not efficient. Therefore, the interactive procedure presented here searches only among efficient solutions and terminates with a solution that is guaranteed to be efficient. It also can converge to nonextreme efficient final solutions rather than being restricted to only extreme efficient points of the feasible set. The procedure does not require sophisticated judgements or inputs from the decision maker. One of the most attractive features of the procedure however, is that the method allows the DM to examine the efficient faces it finds. As iteration goes, the DM can explore a wide variety of efficient faces rather than efficient faces confined to only certain subregion of the feasible set of problem MOLP since the efficient faces that the procedure finds need not be adjacent. This helps the DM explore the nature of the efficient set of problem MOLP and also helps the DM have confidence with a final solution. For these reasons, I feel that the procedure offer significant promise in solving multiple objective linear programs rapidly and in a satisfying manner to the DM.