• 대한수학회지
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• 제46권2호
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• pp.313-325
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• 2009

We consider zero-divisor graphs with respect to primal, nonprimal, weakly prime and weakly primal ideals of a commutative ring R with non-zero identity. We investigate the interplay between the ringtheoretic properties of R and the graph-theoretic properties of ${\Gamma}_I(R)$ for some ideal I of R. Also we show that the zero-divisor graph with respect to primal ideals commutes by localization.

• 호남수학학술지
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• 제29권4호
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• pp.555-567
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• 2007

We first find strongly 2-primal rings whose sub direct product is not (strongly) 2-primal. Moreover we observe some kinds of ring extensions of (strongly) 2-primal rings. As an example we show that if R is a ring and M is a multiplicative monoid in R consisting of central regular elements, then R is strongly 2-primal if and only if so is $RM^{-1}$. Various properties of (strongly) 2-primal rings are also studied.

• 대한수학회논문집
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• 제20권3호
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• pp.457-466
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• 2005

We study in this note rings whose prime radicals are completely prime. We obtain equivalent conditions to the complete 2-primal-ness and observe properties of completely 2-primal rings, finding examples and counterexamples to the situations that occur naturally in the process.

• 대한산업공학회지
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• 제37권2호
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• pp.124-131
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• 2011

In this research report, we propose a heuristic algorithm with some primal recovery strategies for capacitated facility location problems (CFLP), which is a well-known combinatorial optimization problem with applications in distribution, transportation and production planning. Many algorithms employ the branch-and-bound technique in order to solve the CFLP. There are also some different approaches which can recover primal solutions while exploiting the primal and dual structure simultaneously. One of them is a MVCD (Mean Value Cross Decomposition) ensuring convergence without solving a master problem. The MVCD was designed to handle LP-problems, but it was applied in mixed integer problems. However the MVCD has been applied to only uncapacitated facility location problems (UFLP), because it was very difficult to obtain "Integrality" property of Lagrangian dual subproblems sustaining the feasibility to primal problems. We present some heuristic strategies to recover primal feasible integer solutions, handling the accumulated primal solutions of the dual subproblem, which are used as input to the primal subproblem in the mean value cross decomposition technique, without requiring solutions to a master problem. Computational results for a set of various problem instances are reported.

• 대한수학회보
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• 제30권1호
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• pp.71-77
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• 1993

Every ring considered in the paper will be assumed to be commutative and have a unit element. An ideal A of a ring R will be called primal if the elements of R which are zero divisors modulo A, form an ideal of R, say pp. If A is a primal ideal of R, P is called the adjoint ideal of A. The adjoint ideal of a primal ideal is prime [2]. The definition of primal ideals may also be formulated as follows: An ideal A of a ring R is primal if in the residue class ring R/A the zero divisors form an ideal of R/A. If Q is a primary idel of a ring R then every zero divisor of R/Q is nilpotent; therefore, Q is a primal ideal of R. That a primal ideal need not be primary, is shown by an example in [2]. Let R[X], and R[[X]] denote the polynomial ring and formal power series ring in an indeterminate X over a ring R, respectively. Let S be a multiplicative system in a ring R and S$^{-1}$ R the quotient ring of R. Let Q be a P-primary ideal of a ring R. Then Q[X] is a P[X]-primary ideal of R[X], and S$^{-1}$ Q is a S$^{-1}$ P-primary ideal of a ring S$^{-1}$ R if S.cap.P=.phi., and Q[[X]] is a P[[X]]-primary ideal of R[[X]] if R is Noetherian [1]. We search for analogous results when primary ideals are replaced with primal ideals. To show an ideal A of a ring R to be primal, it sufficies to show that a-b is a zero divisor modulo A whenever a and b are zero divisors modulo A.

• 한국통신학회논문지
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• 제10권2호
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• pp.61-68
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• 1985

本 論文에서는 Network flow理論의 한 方法으로 Primal法을 利用하여 流量, 壓力配分의 最適化를 提案하였다. 이 配分制御의 目的은 正常壓力과 最小費用流이며 流量과 壓力問題의 解法은 Primal法을 使用하여 求했다.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.567-579
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• 2009

Recently, Peng et al. proposed a primal-dual interior-point method with new search direction and self-regular proximity for LP. This new large-update method has the currently best theoretical performance with polynomial complexity of O($n^{\frac{q+1}{2q}}\;{\log}\;{\frac{n}{\varepsilon}}$). In this paper we use this search direction to propose a primal-dual interior-point method for convex quadratic programming (QP). We overcome the difficulty in analyzing the complexity of the primal-dual interior-point methods for convex quadratic programming, and obtain the same polynomial complexity of O($n^{\frac{q+1}{2q}}\;{\log}\;{\frac{n}{\varepsilon}}$) for convex quadratic programming.

• 대한수학회논문집
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• 제25권4호
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• pp.655-669
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• 2010

In this paper we propose new primal-dual interior point methods (IPMs) for $P_*(\kappa)$ linear complementarity problems (LCPs) and analyze the iteration complexity of the algorithm. New search directions and proximity measures are defined based on a class of kernel functions, $\psi(t)=\frac{t^2-1}{2}-{\int}^t_1e{^{q(\frac{1}{\xi}-1)}d{\xi}$, $q\;{\geq}\;1$. If a strictly feasible starting point is available and the parameter $q\;=\;\log\;\(1+a{\sqrt{\frac{2{\tau}+2{\sqrt{2n{\tau}}+{\theta}n}}{1-{\theta}}\)$, where $a\;=\;1\;+\;\frac{1}{\sqrt{1+2{\kappa}}}$, then new large-update primal-dual interior point algorithms have $O((1\;+\;2{\kappa})\sqrt{n}log\;n\;log\;{\frac{n}{\varepsilon}})$ iteration complexity which is the best known result for this method. For small-update methods, we have $O((1\;+\;2{\kappa})q{\sqrt{qn}}log\;{\frac{n}{\varepsilon}})$ iteration complexity.

• 대한수학회보
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• 제36권3호
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• pp.579-588
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• 1999

In this paper we study the connections between right quasi-duo rings and 2-primal rings, including several counterexamples for answers to some questions that occur naturally in the process. Actually we concern following three questions and modified ones: (1) Are right quasi-duo rings 2-primal$\ulcorner$, (2) Are formal power series rings over weakly right duo rings also weakly right duo\ulcorner and (3) Are 2-primal rings right quasi-duo\ulcorner Moreover we consider some conditions under which the answers of them may be affirmative, obtaining several results which are related to the questions.

• 대한수학회논문집
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• 제25권3호
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• pp.343-347
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• 2010

In this paper we study the connection between 2-primal rings, (S,1)-rings and related conditions. And we investigate some condition which is the special case of pseudo symmetric. We also study the condition (KJ) which is given by J. Y. Kim and H. L. Jin. We introduce some condition and we prove that our condition is equivalent to the condition (KJ) when it is an (S,1)-ring.