• 대한수학회보
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• 제46권6호
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• pp.1051-1060
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• 2009

In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact $T_1$-subspace. We also study the zero-divisor graph $\Gamma_I$(R) with respect to the completely semiprime ideal I of N. We show that ${\Gamma}_{\mathbb{P}}$ (R), where $\mathbb{P}$ is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph ${\Gamma}_{\mathbb{P}}$ (R).

• 대한수학회보
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• 제54권4호
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• pp.1281-1291
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• 2017

Let R be a strongly 2-primal ring and I a proper ideal of R. Then there are only finitely many prime ideals minimal over I if and only if for every prime ideal P minimal over I, the ideal $P/{\sqrt{I}}$ of $R/{\sqrt{I}}$ is finitely generated if and only if the ring $R/{\sqrt{I}}$ satisfies the ACC on right annihilators. This result extends "D. D. Anderson, A note on minimal prime ideals, Proc. Amer. Math. Soc. 122 (1994), no. 1, 13-14." to large classes of noncommutative rings. It is also shown that, a 2-primal ring R only has finitely many minimal prime ideals if each minimal prime ideal of R is finitely generated. Examples are provided to illustrate our results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권2호
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• pp.93-111
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• 2010

The purpose of this paper is to obtain new complexity results for a second-order cone optimization (SOCO) problem. We define a proximity function for the SOCO by a kernel function. Furthermore we formulate an algorithm for a large-update primal-dual interior-point method (IPM) for the SOCO by using the proximity function and give its complexity analysis, and then we show that the new worst-case iteration bound for the IPM is $O(q\sqrt{N}(logN)^{\frac{q+1}{q}}log{\frac{N}{\epsilon})$, where $q{\geqq}1$.

• East Asian mathematical journal
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• 제29권3호
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• pp.279-292
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• 2013

It is well known that each kernel function defines a primal-dual interior-point method(IPM). Most of polynomial-time interior-point algorithms for linear optimization(LO) are based on the logarithmic kernel function([2, 11]). In this paper we define a new eligible kernel function and propose a new search direction and proximity function based on this function for LO problems. We show that the new algorithm has ${\mathcal{O}}((log\;p){\sqrt{n}}\;log\;n\;log\;{\frac{n}{\epsilon}})$ and ${\mathcal{O}}((q\;log\;p)^{\frac{3}{2}}{\sqrt{n}}\;log\;{\frac{n}{\epsilon}})$ iteration bound for large- and small-update methods, respectively. These are currently the best known complexity results.

• 대한수학회보
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• 제44권1호
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• pp.151-156
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• 2007

A connection between weak ${\pi}-regularity$ and the condition every prime ideal is maximal will be investigated. We prove that a certain 2-primal ring R is weakly ${\pi}-regular$ if and only if every prime ideal is maximal. This result extends several known results nontrivially. Moreover a characterization of minimal prime ideals is also considered.

• 대한수학회보
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• 제44권4호
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• pp.641-649
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• 2007

We in this note introduce a concept, so called ${\pi}-Armendariz$ ring, that is a generalization of both Armendariz rings and 2-primal rings. We first observe the basic properties of ${\pi}-Armendariz$ rings, constructing typical examples. We next extend the class of ${\pi}-Armendariz$ rings, through various ring extensions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권1호
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• pp.41-53
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• 2009

A primal-dual interior point method(IPM) not only is the most efficient method for a computational point of view but also has polynomial complexity. Most of polynomialtime interior point methods(IPMs) are based on the logarithmic barrier functions. Peng et al.([14, 15]) and Roos et al.([3]-[9]) proposed new variants of IPMs based on kernel functions which are called self-regular and eligible functions, respectively. In this paper we define a new kernel function and propose a new IPM based on this kernel function which has $O(n^{\frac{2}{3}}log\frac{n}{\epsilon})$ and $O(\sqrt{n}log\frac{n}{\epsilon})$ iteration bounds for large-update and small-update methods, respectively.

• 대한수학회지
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• 제60권6호
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• pp.1233-1254
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• 2023

We introduce two subclasses of abelian McCoy rings, so-called π-CN-rings and π-duo rings, and systematically study their fundamental characteristic properties accomplished with relationships among certain classical sorts of rings such as 2-primal rings, bounded rings etc. It is shown that a ring R is π-CN whenever every nilpotent element of index 2 in R is central. These rings naturally generalize the long-known class of CN-rings, introduced by Drazin [9]. It is proved that π-CN-rings are abelian, McCoy and 2-primal. We also show that, π-duo rings are strongly McCoy and abelian and also they are strongly right AB. If R is π-duo, then R[x] has property (A). If R is π-duo and it is either right weakly continuous or every prime ideal of R is maximal, then R has property (A). A π-duo ring R is left perfect if and only if R contains no infinite set of orthogonal idempotents and every left R-module has a maximal submodule. Our achieved results substantially improve many existing results.

• 한국국방경영분석학회지
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• 제25권2호
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• pp.97-105
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• 1999

When infeasible interior-point methods are applied to large-scale linear programming problems, they become unstable and cannot solve the problems if convergence rates of primal feasibility, dual feasibility and duality gap are not well-balanced. We can balance convergence rates of primal feasibility, dual feasibility and duality gap by introducing control parameters. As a result, the stability and the efficiency of infeasible interior-point methods can be improved.

• 한국문화재보존과학회:학술대회논문집
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• 한국문화재보존과학회 2004년도 제20회 발표논문집
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• pp.115-130
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• 2004

Plant-based cultural assets using straw and grass as household goods of our people's have been used as indispensable tools for practical living for a very long time. However, only a limited number of artifacts were unearthed so far due to tile fragility of the material. For this reason, research on plant-based cultural properties had close to no progress, and the appropriateness of the PEG method, high-grade alcohol method, alcohol--ether-resin method, and Paraloid B-72 used in preserving plant-based cultural properties has not been sufficiently investigated. Therefore, this study examined the weight change rate by applying the methods of Primal MC-76 and vacuum freeze-drying used mostly as a earth-layer hardening material among PEG and acrylic resin, which are applied widely for preservation of waterlogged archaeological wood, as a means to preserve plant-based cultural properties along with the examination of the subject material, and an experiment was also performed on moisture absorption. The findings as a result were, first, the plant-based material being studied was found to be Typha (Typha orientalis Presl). Secondly, the weight change experiment applying $PEG\#400$ and $PEG\#4000$ confirmed a steady increase of weight if PEG -2Step is used for treatment. Third, in preserving all subject materials with soil, treatment with $PEG\#4000$, Primal MC-76, and vacuum freeze-drying showed that tile vacuum freeze-drying method resulted in the largest or $20\%$ reduction in weight, while Primal MC-76 resulted in $18\%$ and $PEG\#4000$ in $8\%$ of weight reduction. It was concluded that, considering the stability of soil measurement, this came to be because resin permeation was carried out along with tile drying process. Fourth, the weight changes were found to be around $10\%$ in various humidity conditions after the preservation treatment. The greatest weight change rate was seen in the case of $PEG\#4000$, particularly having chemicals gush out in a high humidity (RH $84\%$ or higher) environment. In the case of Primal MC-76 and vacuum freeze-drying methods, $6\~8\%$ weight changes were detected, and the lowest weight change was found in the case of the vacuum freeze-drying method. Fifth, as for color changes after treatment, blackening occurred most strongly with $PEG\#4000$, while Primal MC-76 and vacuum freeze-drying manifested colors closest to dry straw or grass. However, the texture of straw was not very evident in the case of Primal MC-76, due to a glossy surface, but vacuum freeze-drying was found to offer tile best result in terms of texture. Putting together the results of the above experiments, vacuum freeze-drying presented after being treated with PEG2-Step the most stabilized changes in weight, while it offered the smallest change in color as well.