• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.11-24
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• 2013

Let m and n be fixed positive integers and M a right R-module. Recall that M is said to be ($m$, $n$)-injective if $Ext^1$(P, M) = 0 for any ($m$, $n$)-presented right R-module P; M is said to be ($m$, $n$)-flat if $Tor_1$(N, P) = 0 for any ($m$, $n$)-presented left R-module P. In terms of some derived functors, relative injective or relative flat resolutions and dimensions are investigated. As applications, some new characterizations of von Neumann regular rings and p.p. rings are given.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.511-528
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• 2008

Let (R, m) be a 2-dimensional regular local ring with algebraically closed residue field R/m. Let K be the quotient field of R and $\upsilon$ be a prime divisor of R, i.e., a valuation of K which is birationally dominating R and residually transcendental over R. Zariski showed that there are finitely many simple $\upsilon$-ideals $m\;=\;P_0\;{\supset}\;P_1\;{\supset}\;{\cdots}\;{\supset}\;P_t\;=\;P$ and all the other $\upsilon$-ideals are uniquely factored into a product of those simple ones [17]. Lipman further showed that the predecessor of the smallest simple $\upsilon$-ideal P is either simple or the product of two simple $\upsilon$-ideals. The simple integrally closed ideal P is said to be free for the former and satellite for the later. In this paper we describe the sequence of simple $\upsilon$-ideals when P is satellite of order 3 in terms of the invariant $b_{\upsilon}\;=\;|\upsilon(x)\;-\;\upsilon(y)|$, where $\upsilon$ is the prime divisor associated to P and m = (x, y). Denote $b_{\upsilon}$ by b and let b = 3k + 1 for k = 0, 1, 2. Let $n_i$ be the number of nonmaximal simple $\upsilon$-ideals of order i for i = 1, 2, 3. We show that the numbers $n_{\upsilon}$ = ($n_1$, $n_2$, $n_3$) = (${\lceil}\frac{b+1}{3}{\rceil}$, 1, 1) and that the rank of P is ${\lceil}\frac{b+7}{3}{\rceil}$ = k + 3. We then describe all the $\upsilon$-ideals from m to P as products of those simple $\upsilon$-ideals. In particular, we find the conductor ideal and the $\upsilon$-predecessor of the given ideal P in cases of b = 1, 2 and for b = 3k + 1, 3k + 2, 3k for $k\;{\geq}\;1$. We also find the value semigroup $\upsilon(R)$ of a satellite simple valuation ideal P of order 3 in terms of $b_{\upsilon}$.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.5
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• pp.1066-1073
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• 1993

Using regular finite elements and infinite elements simultaneously, elastic boundary value problems with infinite domain can be analyzed more effectively and accurately. In this paper, two dimensional infinite elements have been formulated by means of applying the derived mapping function to the coordinates and multiplying the regular displacement shape functions by a decay function. Orders(m, n) of the mapping and decay functions are found for the purpose of obtaining the convergent solutions without respect to the various decay lengthes. As a result of numerical tests for an infinite plate with a hole under internal pressure, two sets of function orders are obtained as follows. (a) n=0, m=1.5 (b) n=m=0.65

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1177-1190
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• 2022

Let R be a commutative ring with identity. We call the ring R to be an almost quasi-coherent ring if for any finite set of elements α₁, …, α_p and a of R, there exists a positive integer m such that the ideals $\bigcap{_{i=1}^{p}}\;R{\alpha}^m_i$ and Ann_R(α^m) are finitely generated, and to be almost von Neumann regular rings if for any two elements a and b in R, there exists a positive integer n such that the ideal (αⁿ, bⁿ) is generated by an idempotent element. This paper establishes necessary and sufficient conditions for the Nagata's idealization and the amalgamated algebra to inherit these notions. Our results allow us to construct original examples of rings satisfying the above-mentioned properties.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.1031-1051
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• 2012

In this paper, we will investigate the concept of the torsion-graph of an R-module M, in which the set $T(M)^*$ makes up the vertices of the corresponding torsion graph, ${\Gamma}(M)$, with any two distinct vertices forming an edge if $[x:M][y:M]M=0$. We prove that, if ${\Gamma}(M)$ contains a cycle, then $gr({\Gamma}(M)){\leq}4$ and ${\Gamma}(M)$ has a connected induced subgraph ${\overline{\Gamma}}(M)$ with vertex set $\{m{\in}T(M)^*{\mid}Ann(m)M{\neq}0\}$ and diam$({\overline{\Gamma}}(M)){\leq}3$. Moreover, if M is a multiplication R-module, then ${\overline{\Gamma}}(M)$ is a maximal connected subgraph of ${\Gamma}(M)$. Also ${\overline{\Gamma}}(M)$ and ${\overline{\Gamma}}(S^{-1}M)$ are isomorphic graphs, where $S=R{\backslash}Z(M)$. Furthermore, we show that, if ${\overline{\Gamma}}(M)$ is uniquely complemented, then $S^{-1}M$ is a von Neumann regular module or ${\overline{\Gamma}}(M)$ is a star graph.

• Journal of the Korean Society of Costume
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• v.53 no.6
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• pp.145-159
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• 2003

The purpose of this study was to classify body type for ready-to-wear sizes. The subjects were 300 women ages of 18-24. they were measured direct anthropometry. The body types for sizing system were divided by Rohrer Index. KS drop value and ISO drop value. The results of this study were as follows. 1. By adapting the Rohrer Index. we classify 3 types from anthropometric measurements. The thin type covered 39.3%, the standard type 51.0% and the obesity type 18.7%. The characteristics of clusters were as follows. Thin type was characterized by tall. slender type and slim. The standard type was characterized by middle sized. The obesity type was characterized by short. fat type. and large bust. 2. By adapting the KS system drop value. we classify 3 types from anthropometric measurements. The H type(drop 0) covered 25.6%. the N type(drop 6) 65.2% and the A type(drop 12) 9.2%. Type H was slightly tall large bust. and curved from waist to hip. Type A was slightly thin. large hip and smaller bust than type N. Principal factor components were bust size. The height could be divided into three groups. The Petite(l50cm) covered 5.5%. the Regular(l60cm) 64.7% and the Tall(l70cm) 29.8%. Through the crosstab of height and body type. we extracted regular height by N type 46.2% the largest cell. The body type was the higher order of N type. H type and A type. The tall was the higher order of Regular. Tall and Petite. 3. By adapting the ISO system drop value. we classify 3 types from anthropometric measurements. The H type(drop 0) covered 15.0%. the M type(drop 6) 41.0% and the A type(drop 12) 44.0%. Type H was slightly short. slightly fat and large bust. Type A was slightly tall. slight thin than type M. The height could be divided into three groups. We adjust the height section after allow for height distribution. The Short(152cm) covered 12.8%. the Regular(160cm) 66.9% and the Long(168cm) 20.3%. Through the crosstab of height and body type, we extracted regular height by M type 29.3% the largest cell. The body type was the higher order of M type, A type and H type. The tall was the higher order of Regular, Long and short.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.2
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• pp.41-46
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• 2003

In this paper, we investigate the $SP_{\alpha}$-integral and the $M_{\alpha}$-integral defined on an interval of the n-dimensional Euclidean space $\mathbb{R}^n$. In particular, we show that these two integrals are equivalent.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.351-360
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• 2005

Let T be a regular semigroup and let S be a regular subsemigroup of T. In this paper we study the relationship between the idempotent separating congruence on S and the idempotent separating congruence on T, when T and S are connected by a splitmap ${\theta} : T {\to} S$.

• Journal of Life Science
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• v.21 no.7
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• pp.997-1003
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• 2011

Menopause and obesity are associated with metabolism. The purpose of this study was to examine the changes of PPAR${\gamma}$, PGC-1(${\alpha},\;{\beta}$), NRf-1 and TFAM mRNA and mitochondria biogenesis in adipocytes and investigate the effect of swimming exercise for 6weeks on ovariectomized rats. Rats were randomly assigned to 3 groups: (1) ovariectomized rats fed with a control diet (C, n=4), (2) ovariectomized rats fed with high fat diet (H, n=4), and (3) ovariectomized rats trained to exercise and fed with high fat diet (H+EX, n=4). Exercise was performed by swimming for 5 days/wk, with a progressive increase in exercise over the course of 6 weeks. Results showed that the fat tissue weight in the H group was markedly increased (p<0.01) compared to other groups, however, regular exercise significantly decreased fat weight. The PPAR-${\gamma}$ (p<0.05), PGC-$1{\alpha}$ (p<0.01), -$1{\beta}$ (p<0.05), NRf-1 (p<0.01) and TFAM (p<0.05) mRNA expression in the adipocytes of H+EX were higher than in the H group. These results suggest that regular exercise for 6 weeks might exert positive effects by increasing PPAR-${\gamma}$, PGC-1 (${\alpha},\;{\beta}$), NRf-1 and TFAM mRNA expression and mitochondria in adipocytes. Thus, regular exercise may be helpful in the improvement of mitochondria biogenesis function in obese, ovariectomized rats.

• Journal of Korea Multimedia Society
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• v.3 no.3
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• pp.298-308
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• 2000

We present an efficient algorithm for finding the sequence of extreme vortices of a moving regular convex polyhedron of with respect to a fixed plane H.. The algorithm utilizes the spherical Voronoi diagram that results from the outward unit normal vectors nF$_{i}$ 's of faces of P. It is well-known that the Voronoi diagram of n sites in the plane can be computed in 0(nlogn) time, and this bound is optimal. However. exploiting the convexity of P, we are able to construct the spherical Voronoi diagram of nF$_{i}$ ,'s in O(n) time. Using the spherical Voronoi diagram, we show that an extreme vertex problem can be transformed to a spherical point location problem. The extreme vertex problem can be solved in O(logn) time after O(n) time and space preprocessing. Moreover, the sequence of extreme vertices of a moving regular convex polyhedron with respect to H can be found in (equation omitted) time, where m$^{j}$ $_{k}$ (1$\leq$j$\leq$s) is the number of edges of a spherical Voronoi region sreg(equation omitted) such that (equation omitted) gives one or more extreme vertices.