• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.475-484
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• 2005

Let W(t) be a Wiener path, let $\xi\;:\;[0,\;{\infty})\;\to\;\mathbb{R}$ be a continuous and increasing function satisfying $\xi$(0) > 0, let $$T_{/xi}=inf\{t{\geq}0\;:\;W(t){\geq}\xi(t)\}$$ be the first-passage time of W over $\xi$, and let F denote the distribution function of $T_{\xi}$. Then the first passage problem has a unique continuous solution as following $$F(t)=u(t)+{\sum_{n=1}^\infty}\int_0^t\;H_n(t,s)u(s)ds$$, where $$u(t)=2\Psi(\xi(t)/\sqrt{t})\;and\;H_1(t,s)=d\Phi\;(\{\xi(t)-\xi(s)\}/\sqrt{t-s})/ds\;for\;0\;{\leq}\;s.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.153-165
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• 2007

This paper deals with the empirical Bayes two-action problem of testing $H_0\;:\;{\theta}{\leq}{\theta}_0$: versus $H_1\;:\;{\theta}>{\theta}_0$ using a linear error loss for some discrete nonexponential families having probability function either $$f_1(x{\mid}{\theta})=(x{\alpha}+1-{\theta}){\theta}^x\prod\limits_{j=0}^x\;(j{\alpha}+1)$$ or $$f_2(x{\mid}{\theta})=[{\theta}\prod\limits_{j=0}^{x-1}(j{\alpha}+1-{\theta})]/[\prod\limits_{j=0}^x\;(j{\alpha}+1)]$$. Two empirical Bayes tests ${\delta}_n^*\;and\;{\delta}_n^{**}$ are constructed. We have shown that both ${\delta}_n^*\;and\;{\delta}_n^{**}$ are asymptotically optimal, and their regrets converge to zero at an exponential decay rate O(exp(-cn)) for some c>0, where n is the number of historical data available when the present decision problem is considered.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1599-1611
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• 2019

Let $m,n{\in}{\mathbb{N}}$. We represent the additive subgroups of the ring ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$, which are also (unital) subrings, and deduce explicit formulas for $N^{(s)}(m,n)$ and $N^{(us)}(m,n)$, denoting the number of subrings of the ring ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$ and its unital subrings, respectively. We show that the functions $(m,n){\mapsto}N^{u,s}(m,n)$ and $(m,n){\mapsto}N^{(us)}(m,n)$ are multiplicative, viewed as functions of two variables, and their Dirichlet series can be expressed in terms of the Riemann zeta function. We also establish an asymptotic formula for the sum $\sum_{m,n{\leq}x}N^{(s)}(m,n)$, the error term of which is closely related to the Dirichlet divisor problem.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.263-273
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• 2014

Ever since Euler solved the so-called Basler problem of ${\zeta}(2)=\sum_{n=1}^{\infty}1/n^2$, numerous evaluations of ${\zeta}(2n)$ ($n{\in}\mathbb{N}$) as well as ${\zeta}(2)$ have been presented. Very recently, Ritelli [61] used a double integral to evaluate ${\zeta}(2)$. Modifying mainly Ritelli's double integral, here, we aim at evaluating certain interesting alternating series.

• 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.

• East Asian mathematical journal
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• v.19 no.1
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• pp.73-80
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• 2003

Let D be a bounded domain in $\mathbb{C}^n$ with $C^2$ boundary. In this paper, we prove the following inequality $${\parallel}u{\parallel}_{p_2,{\alpha}_2}{\lesssim}{\parallel}u{\parallel}_{p_1,{\alpha}_1}+{\parallel}\bar{\partial}u{\parallel}_{p_1,{\alpha}_1+p_1}/2$$, where $1{\leq}p_1{\leq}p_2<\infty,\;{\alpha}_j>0,(n+{\alpha}_1)/p_1=(n+{\alpha}_1)/p_1=(n+{\alpha}_2)/p_2$, and $1/p_2{\geq}1/p_1-1/2n$.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.2
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• pp.144-150
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• 1989

The competitive power extraction problem in a linear n-port network consisting of resistances and independent sources with the same frequency is solved. For solving the problem, the definition of the two-port image impedances is extended to the n-port image impedances. In a competitive power extraction from an n-port network, the load resistances eventually approach the image resistances been found to be between the reciprocal of the short circuit conductance and the open circuit resistance.

• The Transactions of the Korea Information Processing Society
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• v.1 no.2
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• pp.184-193
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• 1994

This paper considers the Updating Minimum-weight Spanning Tree Problem(UMP), that is, the problem to update the Minimum-weight Spanning Tree(MST) in response to topology change of the network. This paper proposes the algorithm which reconstructs the MST after several links deleted and added. Its message complexity and its ideal-time complexity are Ο(m＋n log(t＋f)) and Ο(n＋n log(t＋f)) respectively, where n is the number of processors in the network, t(resp.f) is the number of added links (resp. the number of deleted links of the old MST), And m=t＋n if f=Ο, m=e (i.e. the number of links in the network after the topology change) otherwise. Moreover the last part of this paper touches in the algorithm which deals with deletion and addition of processors as well as links.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.21 no.4
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• pp.177-182
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• 2021

Generally, the linear programming (LP) with O(n⁴) time complexity is applied to mixture optimization problem that can be produce the given ingredients grade product with minimum cost from mixture of various raw materials. This paper suggests heuristic algorithm with O(n log n) time complexity to obtain the solution of this problem. The proposed algorithm meets the content range of the components required by the alloy steel plate while obtaining the minimum raw material cost, decides the quantity of raw material that is satisfied with ingredients grade for ascending order of unit cost. Although the proposed algorithm applies simple decision technique with O(n log n) time complexity, it can be obtains same solution as or more than optimization technique of linear programing.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.3
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• pp.1-15
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• 2000

In this paper, we propose a practical cut generation method based on the Chvatal-Gomory procedure for the (0, 1)-Knapsack problem with a variable capacity. For a given set N of n items each of which has a positive integral weight and a facility of positive integral capacity, a feasible solution of the problem is defined as a subset S of N along with the number of facilities that can satisfy the sum of weights of all the items in S. We first derive a class of valid inequalities for the problem using Chvatal-Gomory procedure, then analyze the associated separation problem. Based on the results, we develop an affective cut generation method. We then analyze the theoretical strength of the inequalities which can be generated by the proposed cut generation method. Preliminary computational results are also presented which show the effectiveness of the proposed cut generation method.