• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• v.9 no.1
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• pp.189-192
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• 2005

In this paper, we present a Petri Net (PN) model for reliability analysis of a shared database system. The system consists of components; a database, two processors, two memory and a bus. The database should be operational and at least one of the component should be also operational. Otherwise system will be down. Each component can be failed and repaired individually. Stochastic Reward Net (SRN) Model for reliability analysis is developed. SRN is potential to define various reward function and can be easily used to obtain performance measures. The modeling techniques using variable cardinality, enabling function, timed transition priority in SRN are shown.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.123-129
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• 2023

For an ordered set W = {w₁, w₂, . . . , w_k} of vertices and a vertex v in a connected graph G, the k-vector r(v|W) = (d(v, w₁), d(v, w₂), . . . , d(v, w_k)) is called the metric representation of v with respect to W, where d(x, y) is the distance between the vertices x and y. A set W is called a resolving set for G if distinct vertices of G have distinct metric representations with respect to W. The minimum cardinality of a resolving set for G is its metric dimension dim(G), and a resolving set of minimum cardinality is a basis of G. The corona product, G ⊙ H of graphs G and H is obtained by taking one copy of G and n(G) copies of H, and by joining each vertex of the ith copy of H to the ith vertex of G. In this paper, we obtain bounds for dim(G ⊙ K₁), characterize all graphs G with dim(G ⊙ K₁) = dim(G), and prove that dim(G ⊙ K₁) = n - 1 if and only if G is the complete graph K_n or the star graph K_1,n-1.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.10
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• pp.109-117
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• 2014

In navigation route planning systems using A* algorithms, the cardinality of an Open list, which is a list of candidate nodes through which a terminal node can be accessed, increases as the path length increases. In this paper, a method of alternately utilizing the Dijkstra's algorithm and the A* algorithm to reduce the cardinality of the Open list is investigated. In particular, by employing a depth parameter, named Level, the two algorithms are alternately performed depending on the Level's value. Using the hybrid searching approach, the Open list constructed in the Dijkstra's algorithm is transferred into the Open list of the A* algorithm, and consequently, the unconstricted increase of the cardinality of the Open list of the former algorithm can be avoided and controlled appropriately. In addition, an optimal or nearly optimal path similar to the Dijkstra's route, but not available in the A* algorithm, can be found. The experimental results, obtained with synthetic and real-life benchmark data, demonstrate that the computational cost, measured with the number of nodes to be compared, was remarkably reduced compared to the traditional searching algorithms, while maintaining the similar distance to those of the latter algorithms. Here, the values of Level were empirically selected. Thus, a study on finding the optimal Level values, while taking into consideration the actual road conditions remains open.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.391-399
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• 2005

In this paper we present an algorithm based on network flow techniques which provides a solution for a combinatorial problem. Then, in order to provide all the solutions of this problem, we make use of an algorithm that given the bipartite graph $G=(V_1 {\cup}{V_2},\;E,\;{\omega})$ outputs the enumeration of all bipartite matchings of given cardinality v and cost c.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.261-264
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• 2007

퍼지 추론은 애매한 지식을 효과적으로 처리할 수 있는 장점이 있다. 그러나 규칙의 연관속성은 규칙을 과다하게 생성하기 때문에 유용하고 중요한 규칙을 결정하는데 여러 가지 문제점이었다. 본 논문에서는 퍼지 규칙에서 규칙간의 상관성을 고려하여 불필요한 속성을 제거하고, 퍼지규칙의 상대농도를 이용하여 추론결과의 정확성을 유지하면서 규칙의 수를 최소화 하는 방법을 제안한다. 제안한 방법의 타당성을 검증하기 위하여 기존의 규칙 감축 방법에 따른 출론 결과와 비교 검증하였다.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.455-462
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• 2014

Let D be an integral domain with Spec(D) finite, K the quotient field of D, [D,K] the set of rings between D and K, and SFc(D) the set of semistar operations of finite character on D. It is well known that |Spec(D)| ${\leq}$ |SFc(D)|. In this paper, we prove that |Spec(D)| = |SFc(D)| if and only if D is a valuation domain, if and only if |Spec(D)| = |[D,K]|. We also study integral domains D such that |Spec(D)|+1 = |SFc(D)|.

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.169-179
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• 2009

Let P be a (n, n − 1, j)-poset, which is a partially ordered set of cardinality n with n − 1 maximal elements and $j(1{\leq}j{\leq}n-1)$ minimal elements, and $P^*$ the dual poset of P. In this paper, we obtain two types of incidence codes of nonempty proper subset S of P and $P^*$, respectively, by using Bogart's method [1] (see Theorem 3.3).

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.25-29
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• 2001

We present a two dimensional linear programming knapsack problem with the extended GUB constraint. The presented problem is an extension of the cardinality constrained linear programming knapsack problem. We identify some new properties of the problem and derive a solution algorithm based on the parametric analysis for the knapsack right-hand-side. The solution algorithm has a worst case time complexity of order O($n^2logn$). A numerical example is given.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.521-540
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• 2004

In this paper, we give a sharp estimate on the cardinality of the set generating the convex hull containing the image of harmonic maps with polynomial growth rate on a certain class of manifolds into a Cartan-Hadamard manifold with sectional curvature bounded by two negative constants. We also describe the asymptotic behavior of harmonic maps on a complete Riemannian manifold into a regular ball in terms of massive subsets, in the case when the space of bounded harmonic functions on the manifold is finite dimensional.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.705-717
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• 2018

We construct some infinite series of free and nearly free curves using pencils of conics with a base locus of cardinality at most two. These curves have an interesting topology, e.g. a high degree Alexander polynomial that can be explicitly determined, a Milnor fiber homotopy equivalent to a bouquet of circles, or an irreducible translated component in the characteristic variety of their complement. Monodromy eigenspaces in the first cohomology group of the corresponding Milnor fibers are also described in terms of explicit differential forms.