• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1253-1268
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• 2015

It is well known that an integral domain D is a UFD if and only if every nonzero prime ideal of D contains a nonzero principal prime. This is the so-called Kaplansky's theorem. In this paper, we give this type of characterizations of a graded PvMD (resp., G-GCD domain, GCD domain, $B{\acute{e}}zout$ domain, valuation domain, Krull domain, ${\pi}$-domain).

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.109-114
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• 1989

This paper deals with the classifying spaces of finite groups. To any finite group G we associate a space BG with the property that .pi.$_{1}$(BG)=G, .pi.$_{i}$ (BG)=0 for i>1. BG is called the classifying space of G. Consider the problem of finding a stable splitting BG= $X_{1}$$^{V}$ $X_{1}$$^{V}$..$^{V}$ $X_{n}$ localized at pp. Ideally the $X_{i}$ 's are indecomposable, thus displaying the homotopy type of BG in the simplest terms. Such a decomposition naturally splits $H^{*}$(BG). The main purpose of this paper is to give the classification theorem in stable homotopy theory for groups with periodic cohomology i.e. cyclic Sylow p-subgroups for p an odd prime and to calculate some universal stable element. In this paper, all cohomology groups are with Z/p-coefficients and p is an odd prime.prime.

• Journal of the Korean Society for Heat Treatment
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• v.7 no.1
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• pp.17-24
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• 1994

The evaluation and analysis of diffusivity of lithium for coarsening and coarsening kinetics of ${\delta}^{\prime}$ precipitate in Al-Li-Cu-Mg-Zr alloy aged at $170^{\circ}C$ have been investigated by transmission electron microscopy. With ageing time, ${\delta}^{\prime}$ precipitate coaesened to followed $\bar{\gamma}{\propto}t^{1/3}$ and coarsening kinetics was found to be obeyed to the Lifshitz-Slyozov-Wagner(LSW) theory and diffusivity of lithium for coarsening of ${\delta}^{\prime}$ precipitate in Al-Li-Cu-Mg-Zr alloy was obtained to be $5.85{\times}10^{-17}{\sim}1.53{\times}10^{-16}$ by experimental coarsening rate constant and various coarsening kinetic theory. Diffusivity of lithium measured by using various model but MLSW and Tsumuraya (VI) et al. model in Al-Li-Cu-Mg-Zr alloy is similar to that calculated by the Costas's diffusivity equation. It was, therefore, suggested that additing to the Cu, Mg and Zr element in Al-Li system have no great effect on diiffusivity of lithium for coarsening of ${\delta}^{\prime}$ This suggest that in matrix.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.6
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• pp.396-402
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• 1987

A Composite method of finite element and boundary integral methods is introduced to solve the magnetostatic field problems with open boundary. Only the region of prime interest is taken as the compution region where the finite element method is applied. The boundary conditions of the region are dealt with using boundary integral method. The boundary integration in the boundary integral method is done by numerical and analytical techniques repectively. The proposed method is applied to a simple linear problem, and the results are compared with those of the finite element method and the analytic solutions. It is concluded that the proposed method gives more accurate results than the finite element method under the same computing efforts.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.791-795
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• 2010

We study the consequences of Gross's conjecture for cyclic extensions of degree $l^2$ where l is prime, and deduce that the L-values at s = 0 satisfy certain congruence relations.

• Korean Journal of Metals and Materials
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• v.50 no.2
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• pp.164-170
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• 2012

Nanotubular structure formation on the Ti-6Al-4V and Ti-Ta alloy surfaces by electrochemical methods has been studied using the anodizing method. A nanotube layer was formed on Ti alloys in 1.0 M $H_3PO_4$ electrolyte with small additions of $F^-$ ions. The nanotube nucleation and growth of the ${\alpha}$-phase and ${\beta}$-phase appeared differently, and showed different morphology for Cp-Ti, Ti-6Al-4V and Ti-Ta alloys. In the ${\alpha}$-phase of Cp-Ti and martensite ${\alpha}^{\prime}$ and in the ${\alpha}^{{\prime}{\prime}}$ and ${\beta}$-phase of the Ti-Ta alloy, the nanotube showed a clearly highly ordered $TiO_2$ layer. In the case of the Ti-Ta alloy, the pore size of the nanotube was smaller than that of the Cp-Ti due to the ${\beta}$-stabilizing Ta element. In the case of the Ti-6Al-4V alloy, the ${\alpha}$-phase showed a stable porous structure; the ${\beta}$-phase was dissolved entirely. The nanotube with two-size scale and high order showed itself on Ti-Ta alloys with increasing Ta content.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.721-734
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• 2014

Let M be a module over a commutative ring R, and let T(M) be its set of torsion elements. The total torsion element graph of M over R is the graph $T({\Gamma}(M))$ with vertices all elements of M, and two distinct vertices m and n are adjacent if and only if $m+n{\in}T(M)$. In this paper, we study the basic properties and possible structures of two (induced) subgraphs $Tor_0({\Gamma}(M))$ and $T_0({\Gamma}(M))$ of $T({\Gamma}(M))$, with vertices $T(M){\backslash}\{0\}$ and $M{\backslash}\{0\}$, respectively. The main purpose of this paper is to extend the definitions and some results given in [6] to a more general total torsion element graph case.

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.79-85
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• 2013

The structure of a poset P with smallest element 0 is looked at from two view points. Firstly, with respect to the Zariski topology, it is shown that Spec(P), the set of all prime semi-ideals of P, is a compact space and Max(P), the set of all maximal semi-ideals of P, is a compact $T_1$ subspace. Various other topological properties are derived. Secondly, we study the semi-ideal-based zero-divisor graph structure of poset P, denoted by $G_I$ (P), and characterize its diameter.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.549-562
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• 2015

In this paper we introduce the pointfree version of rough sets. For this we consider a lattice L instead of the power set P(X) of a set X. We study the properties of lower and upper pointfree approximation, precise elements, and their relation with prime elements. Also, we study lower and upper pointfree approximation as a Galois connection, and discuss the relations between partitions and Galois connections.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.27-39
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• 2021

We discuss the condition that every nonzero right annihilator of an element contains a nonzero ideal, as a generalization of the insertion-of-factors-property. A ring with such condition is called right AP. We prove that a ring R is right AP if and only if Dn(R) is right AP for every n ≥ 2, where Dn(R) is the ring of n by n upper triangular matrices over R whose diagonals are equal. Properties of right AP rings are investigated in relation to nilradicals, prime factor rings and minimal order.