• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.251-264
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• 1995

Applications of the classical Knaster-Kuratowski-Mazurkiewicz (si-mply, KKM) theorem and the fixed point theory of multifunctions defined on convex subsets of topological vector spaces have been greatly improved by adopting the concept of convex spaces due to Lassonde [L1]. In this direction, the first author [P5] found that certain coincidence theorems on a large class of composites of upper semicontinuous multifunctions imply many fundamental results in the KKM theory.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.573-580
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• 2012

A (1, ${\lambda}$)-embedded graph is a graph that can be embedded on a surface with Euler characteristic ${\lambda}$ so that each edge is crossed by at most one other edge. A graph $G$ is called ${\alpha}$-linear if there exists an integral constant ${\beta}$ such that $e(G^{\prime}){\leq}{\alpha}v(G^{\prime})+{\beta}$ for each $G^{\prime}{\subseteq}G$. In this paper, it is shown that every (1, ${\lambda}$)-embedded graph $G$ is 4-linear for all possible ${\lambda}$, and is acyclicly edge-($3{\Delta}(G)+70$)-choosable for ${\lambda}$ = 1, 2.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.10
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• pp.4007-4024
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• 2020

It is tremendously important to construct decision trees to use as a tool for knowledge representation from a given decision table. However, the usual algorithms may split the decision table based on each value, which is not efficient for numerical attributes. The methodology of this paper is to split the given decision table into binary groups as like the CART algorithm, that uses binary split to work for both categorical and numerical attributes. The difference is that it uses split for each attribute established by the directed acyclic graph in a dynamic programming fashion whereas, the CART uses binary split among all considered attributes in a greedy fashion. The aim of this paper is to study the effect of binary splits in comparison with each value splits when building the decision trees. Such effect can be studied by comparing the number of nodes, local and global misclassification rate among the constructed decision trees based on three proposed algorithms.

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.1
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• pp.1-12
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• 1991

This paper studies an optimal algorithm for the Maximum Origin-Destination Flor Path (MODFP) in an acyclic transportation network. We define a Pseudo-Flow each are so that it can give an upper bound to the total flow of a given path. And using the K-th Shortest Path algorithm we obtain upper bound of MODF which is decreasing as the number of searched path grows. Computational Complexity of optimal algorithm is O(K + m) $n_{2}$), K being the total number of searched path. We proved that the problem complexity of finding MODFP in an acyclic network is NP-hard, showing that the-satisfiability problem can be polynomialy reduced to this problem. And we estimated the average of the number K as being (m/n)$^{1,08}$ Exp (0.00689gm) from the computational experiments.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.3
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• pp.31-41
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• 1995

The maximum Origin-Destination Flow Path Problem (MODFP) in an Acyclic Network has known as NP-hard. K. S. Sung has suggested on Optimal Algorithm for MODFP based on the Pseudo flo or arc and the K-th shortest path algorithm. When we try to solve MODFP problem by general Branch and Bound Method (BBM), the upper and lower bounds of subproblems are so weak that the BBM become very inefficient. Here we utilized the Pseudo flow of arc' for the tight bounds of subproblems so that it can produce an efficient BBM for MODFP problem.

• YAKHAK HOEJI
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• v.49 no.1
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• pp.56-59
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• 2005

We synthesized new N-substituted 3-amino-6-chloropyridazine derivatives which were expected to retain biological activity. All synthetic process from pyridazine to 3-aminopyridazines could be carried out conveniently in high yield. N-Substituted 3-amino-6-chloropyridazine derivatives were prepared through amination and acylation from 3,6-dichloropyridazine. 3-Amino-6-chloropyridazine was prepared from the reaction of 3,6-dichloropyridazine with liquid ammonia under autoclave for 6 hrs. The refluxing of 3-amino-6-chloropyridazine and the corresponding acid anhydride for $1{\sim}2$ hrs afforded the N-substituted 3-amino-6-chloropyridazines. Alkyl chain of N-substituent was prolonged to six carbon (hexanoic acid).

• 한국약용작물학회:학술대회논문집
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• 2008.05a
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• pp.266-266
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• 2008

• Journal of Korean Institute of Industrial Engineers
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• v.24 no.4
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• pp.591-600
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• 1998

The scheduling of parallel computing systems consists of two procedures, the assignment of tasks to each available processor and the ordering of tasks in each processor. The assignment procedure is same with a clustering. The clustering is classified into linear or nonlinear according to the precedence relationship of the tasks in each cluster. The parallel computing system can be modeled with a Directed Acyclic Graph(DAG). By the granularity theory, DAG is categorized into Coarse Grain Type(CDAG) and Fine Grain Type(FDAG). We suggest the linear clustering method for the scheduling of CDAG using the genetic algorithm. The method utilizes a properly that the optimal schedule of a CDAG is one of linear clustering. We present the computational comparisons between the suggested method for CDAG and an existing method for the general DAG including CDAG and FDAG.

• Journal of Korean Institute of Industrial Engineers
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• v.16 no.1
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• pp.17-25
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• 1990

Most of the least cost transportation network design problems are frequently formulated as the minimum spanning arborescence problems in directed networks with bitype are costs. These costs are classified whether the arc is included in the path from the root to a specified node over a given spanning arborescence. We prove that this problem is NP-hard, and develop a polynomial time algorithm for acyclic networks. The probelm in acyclic networks is initially formulated as 0-1 integer programming. Next, we prove that the 0-1 relaxed linear programming has an integral optimum solution by complementary slackness conditions. In this paper, we present an $O(n^2)$ algorithm based on a shortest path algorithm.

• Journal of Korean Society for Quality Management
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• v.10 no.2
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• pp.18-24
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• 1982

This paper estimates the reliability & mean time to failure (MTIF) of a cyclic or acyclic network system by the Monte-Carlo simulation method. Estimates of MTTF and Reliability become difficult as the complexity of a system increases. The method in this paper finds all simple paths from the given network, and then simulates the reliability of the required time and MTFF by using these paths. Life-times of the components in a network follow some probability distributions (Exponential, Weibull, Normal, Lognormal, etc.). The method, written in Level II. Basic Language, is validated for some simple examples and then estimates the reliability and MTFF of some cyclic network system.