• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.533-555
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• 2022

In this paper, we introduce a new algorithm for finding a solution of an equilibrium problem in a real Hilbert space. Our paper extends the single projection method to pseudomonotone variational inequalities, from a 2018 paper of Shehu et. al., to pseudomonotone equilibrium problems in a real Hilbert space. On the basis of the given algorithm for the equilibrium problem, we develop a new algorithm for finding a common solution of a equilibrium problem and fixed point problem. The strong convergence of the algorithm is established under mild assumptions. Several of fundamental experiments in finite (infinite) spaces are provided to illustrate the numerical behavior of the algorithm for the equilibrium problem and to compare it with other algorithms.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.225-258
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• 2024

In this paper, we study the problem of finding a common solution to a fixed point problem involving a finite family of ρ-demimetric operators and a split monotone inclusion problem with monotone and Lipschitz continuous operator in real Hilbert spaces. Motivated by the inertial technique and the Tseng method, a new and efficient iterative method for solving the aforementioned problem is introduced and studied. Also, we establish a strong convergence result of the proposed method under standard and mild conditions.

• Journal of The Korean Association For Science Education
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• v.26 no.7
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• pp.835-842
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• 2006

The aims of this study are to investigate how Kepler found a scientific problem for the retinal image theory and how abductive reasoning was used in his theory development, and to find implications for teaching creativity in science class from his thinking processes in the scientific discovery. Through the analysis of the related literatures, it was found that Kepler's problem finding in his retinal image theory came from the critical analysis of contemporary theories of vision, based on his relevant knowledge of optics, as he formulated his own hypothesis to build a new theory in eye vision employing optical phenomenon in spherical lens, which is a kind of abductive reasoning. From the results, three suggestions are proposed, that: (a) in the development of creativity teaching material, the situations like Kepler's problem finding need to be included in the programs; (b) it should be taught that relevant scientific knowledge is important for problem finding and hypothesis formulating; and (c) the experience of successful problem solving by themselves could help them find new scientific problem(s).

• Journal of Korean Society of Transportation
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• v.14 no.1
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• pp.51-67
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• 1996

The optimal path-finding problem becomes complicated when multiple variables are simultaneously considered such as physical route length, degree of congestion, traffic capacity of intersections, number of intersections and lanes, and existence of free ways. Therefore, many researchers in various fields (management science, computer science, applied mathematics, production planning, satellite launching) attempted to solve the problem by ignoring many variables for problem simplification, by developing intelligent algorithms, or by developing high-speed hardware. In this research, an integration of expert system technique and case-based reasoning in high level with a conventional algorithms in lower level was attempted to develop an optimal path-finding system. Early application of experienced driver's knowledge and case data accumulated in case base drastically reduces number of possible combinations of optimal paths by generating promising alternatives and by eliminating non-profitable alternatives. Then, employment of a conventional optimization algorithm provides faster search mechanisms than other methods such as bidirectional algorithm and $A^*$ algorithm. The conclusion obtained from repeated laboratory experiments with real traffic data in Seoul metropolitan area shows that the integrated approach to finding optimal paths with consideration of various real world constraints provides reasonable solution in a faster way than others.

• School Mathematics
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• v.1 no.2
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• pp.547-554
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• 1999

This paper gives an example of experimental mathematics education which leads students to understand logically the problem of finding gold from doing some experiments.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.2
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• pp.47-58
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• 2001

The purpose of this study is to present methods for determining the k most vital arcs (k-MVAs) in shortest path problem (SPP) using evolutionary algorithms. The problem of finding the k-MVAs in SPP is to find a set of k arcs whose simultaneous removal from the network causes the greatest increase in the shortest distance between two specified nodes. Generally, the problem of determining the k-MVAs in SPP has been known as NP-hard. Therefore, to deal with problems of the real world, heuristic algorithms are needed. In this study we present three kinds of evolutionary algorithms for finding the k-MVAs in SPP, and then to evaluate the performance of proposed algorithms.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.447-456
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• 2017

The purpose of this paper is to introduce some strong convergence theorems for the problem of finding a common zero of a finite family of monotone operators and the problem of finding a common fixed point of a finite family of nonexpansive in Hilbert spaces by hybrid projection method.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1347-1359
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• 2017

The purpose of this paper is to give some new iterative methods for finding a common zero of a finite family of monotone operators in Hilbert spaces. We also give the applications of the obtained result for the convex feasibility problem and constrained convex optimization problem in Hilbert spaces.

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.727-734
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• 1999

Let G be a connected graph of n vertices. The problem of finding a depth-first spanning tree of G is to find a connected subgraph of G with the n vertices and n-1 edges by depth-first-search. in this paper we propose an O(n) time algorithm to solve this problem on permutation graphs.

• International conference on construction engineering and project management
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• 2007.03a
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• pp.777-786
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• 2007

This paper presents a modified simulated annealing algorithm to optimize linear scheduling projects with multiple resource constraints and its effectiveness is verified with a proposed problem. A two-stage solution-finding procedure is used to model the problem. Then the simulated annealing and the modified simulated annealing are compared in the same condition. The comparison results and the reasons of improvement by the modified simulated annealing are presented at the end.