• Journal of applied mathematics & informatics
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• 제23권1_2호
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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.

• 대한수학회지
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• 제56권6호
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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.

• 호남수학학술지
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• 제36권2호
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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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• 제6권3호
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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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• 제19권1호
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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 $1/p_2{\geq}1/p_1-1/2n$.

• 대한전기학회논문지
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• 제38권2호
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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.

• 한국정보처리학회논문지
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• 제1권2호
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• pp.184-193
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• 1994

본 논문은 최소목(Minimum-weight Spanning Tree, MST)에 있어서 네트워크의 랭크 중 몇개가 삭제(또는 파괴) 또는 추가(또는 회복) 되었을 때, MST를 재구성하는 분산 알고리즘을 제안한다. 본 논문에서 제안한 알고리즘의 메세지 복잡도는 Ο(m＋n log(t＋f))이고, 이상시간 복잡도는 Ο(n＋n log(t＋f))가 되며, 여기서 n은 네트워크의 프로세서의 수이고 t(resp. f)는 추가되는 링크의 수(resp. 이전 MST의 삭제된 링크의 수)이다. 그래서 네트워크의 형태가 변형이 된 다음에 f=O이고 m=e일 경우에는 m=t＋n이 된다. 또한 본 논문의 마지막 부분에서는 링크의추가, 삭제와 마찬가지로 프로세서의 추가, 삭제되었을 경우의 알고리즘도 제안한다.

• 한국인터넷방송통신학회논문지
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• 제21권4호
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• pp.177-182
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• 2021

다양한 원재료를 혼합하여 원하는 성분 함유량을 가진 제품을 최소의 비용으로 생산하는 혼합 최적화 문제에 대해 일반적으로 O(n⁴)의 수행 복잡도의 선형계획법을 적용하고 있다. 본 논문에서는 이 문제에 대해 O(n log n)복잡도로 해를 얻을 수 있는 휴리스틱 알고리즘을 제안한다. 제안된 알고리즘은 합금 강판에서 요구하는 성분들의 함유량 범위를 충족시키면서 최소의 원자재비용을 얻기 위해, 원재료 단가 오름차순으로 성분별 함유량을 충족시키도록 원재료 양을 결정하였다. 3가지 사례에 대해 적용한 결과 제안된 알고리즘은 O(n log n)복잡도로 단순한 결정기법을 적용하였음에도 불구하고, LP의 최적화 기법과 동일하거나 보다 좋은 해를 얻을 수 있었다.

• 한국경영과학회지
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• 제25권3호
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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.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 1996년도 추계학술대회발표논문집; 고려대학교, 서울; 26 Oct. 1996
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• pp.295-298
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• 1996

We consider a nonpreemptive single-machine scheduling problem to minimize the mean squared deviation(MSD) of job completion times about a common due date d with a maximum tardiness constraint, i.e., maximum tardiness is less than or equal to the given allowable amount, .DELTA.(MSD/T$_{max}$ problem). We classify the .DELTA.-unconstrained cases in the MSD/T$_{max}$ problem. We provide bounds to discern each case for the problem. It is also shown that the .DELTA.-unconstrained MSD/T$_{max}$ problem is equivalent to the unconstrained MSD problem and the tightly .DELTA.-constrained MSD/T$_{max}$ problem with n jobs and a maximum allowable tardiness .DELTA. can be converted into the constrained MSD problem with a common due date .DELTA. and n-1 jobs. Finally, the solution procedure for MSD/T$_{max}$ problem is provided. provided.