• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1320-1325
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• 2008

In the manufacture of automobile suspension modules at a company as parts supplier, the design process includes the detail design and the design modification via structural and fatigue durability analyses considering PoF(physics of failure) of their weldments that are repeated more than four times sequentially. The approval of the design and the release of final drawings follows. For the suspension modules, e.g. control arms and cross member, the man-hours per worker required in the process outlined above can reach as high as 1,414hours. Application of the developed integrated design system can reduce the man-hours of 1,004. In comparison with the conventional design process, this integrated design system reduces the required time by about 40%. If expense is taken into account, a savings of approximately $192,000 is estimated, assuming the design process accounts for 1.5% of total sales for the parts supplier

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.617-630
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• 2011

Let X, Y be vector spaces, and let r be 2 or 4. It is shown that if an odd mapping $f:X{\rightarrow}Y$ satisfies the functional equation $${\hspace{50}}rf(\frac{\sum_{j=1}^{d}\;x_j} {r})+\;{\sum\limits_{\iota(j)=0,1 \atop {\sum_{j=1}^{d}}\;{\iota}(j)=l}}\;rf(\frac{\sum_{j=1}^{d}{(-1)^{\iota(j)}x_j}}{r}) \\({\ddag}){\hspace{160}}=(_{d-1}C_l-_{d-1}C_{l-1}+1)\;{\sum\limits_{j=1}^{d}\;f(x_j)}$$ then the odd mapping $f:X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation in Banach modules over a unital $C^*$-algebra. As an application, we show that every almost linear bijection $h:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ of a unital $C^*$-algebra ${\mathcal{A}}$ onto a unital $C^*$-algebra ${\mathcal{B}}$ is a $C^*$-algebra isomorphism when $h(2^nuy)=h(2^nu)h(y)$ for all unitaries $u{\in}{\mathcal{A}}$, all $y{\in}{\mathcal{A}}$, and $n=0,1,2,{\cdots}$.

• Proceedings of the Korean Society for Bioinformatics Conference
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• 2005.09a
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• pp.431-436
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• 2005

Living cells are sustained not by individual activities but rather by coordinated summative efforts of different biological functional modules. While recent research works have focused largely on finding individual functional modules, this paper attempts to explore the connections or relationships between different cellular functions through cross-function domain interaction maps. Exploring such a domain interaction map can help understand the underlying inter-function communication mechanisms. To construct a cross-function domain interaction map from existing genome-wide protein-protein interaction datasets, we propose a two-step procedure. First, we infer conserved domain-domain interactions from genome-wide protein-protein interactions of yeast, worm and fly. We then build a cross-function domain interaction map that shows the connections of different functions through various conserved domain interactions. The domain interaction maps reveal that conserved domain-domain interactions can be found in most detected cross-functional relationships and a f9w domains play pivotal roles in these relationships. Another important discovery in the paper is that conserved domains correspond to highly connected protein hubs that connect different functional modules together.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.577-587
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• 2002

Let A be a commutative ring and M an Artinian .A-module. Let $\sigma$ be a torsion radical functor and (T, F) it's corresponding partition of Spec(A) In [1] the concept of Cohen-Macauly modules was generalized . In this paper we shall define $\sigma$-co-Cohen-Macaulay (abbr. $\sigma$-co-CM). Indeed this is one of the aims of this paper, we obtain some satisfactory properties of such modules. An-other aim of this paper is to generalize the concept of cograde by using the left derived functor $U^{\alpha}$$_{I}$(-) of the $\alpha$-adic completion functor, where a is contained in Jacobson radical of A.A.

• Honam Mathematical Journal
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• v.20 no.1
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• pp.1-14
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• 1998

In this short note we study the torsion theories over a commutative ring R and discuss a relative dimension related to such theories for R-modules. Let ${\sigma}$ be a torsion functor and (T, F) be its corresponding partition of Spec(R). The concept of ${\sigma}$-Cohen Macaulay (abbr. ${\sigma}$-CM) module is defined and some of the main points concerning the usual Cohen-Macaulay modules are extended. In particular it is shown that if M is a non-zero ${\sigma}$-CM module over R and S is a multiplicatively closed subset of R such that, for all minimal element of T, $S{\cap}p={\emptyset}$, then $S^{-1}M$ is a $S^{-1}{\sigma}$-CM module over $S^{-1}$R, where $S^{-1}{\sigma}$ is the direct image of ${\sigma}$ under the natural ring homomorphism $R{\longrightarrow}S^{-1}R$.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.323-356
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• 2006

Let X and Y be vector spaces. It is shown that a mapping $f\;:\;X{\rightarrow}Y$ satisfies the functional equation $$mn_{mn-2}C_{k-2}f(\frac {x_1+...+x_{mn}} {mn})$$ $(\ddagger)\;+mn_{mn-2}C_{k-1}\;\sum\limits_{i=1}^n\;f(\frac {x_{mi-m+1}+...+x_{mi}} {m}) =k\;{\sum\limits_{1{\leq}i_1<... if and only if the mapping $f : X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation $(\ddagger)$ in Banach modules over a unital $C^*-algebra$. Let A and B be unital $C^*-algebra$ or Lie $JC^*-algebra$. As an application, we show that every almost homomorphism h : $A{\rightarrow}B$ of A into B is a homomorphism when $h(2^d{\mu}y) = h(2^d{\mu})h(y)\;or\;h(2^d{\mu}\;o\;y)=h(2^d{\mu})\;o\;h(y)$ for all unitaries ${\mu}{\in}A,\;all\;y{\in}A$, and d = 0,1,2,..., and that every almost linear almost multiplicative mapping $h:\;A{\rightarrow}B$ is a homomorphism when h(2x)=2h(x) for all $x{\in}A$. Moreover, we prove the Cauchy-Rassias stability of homomorphisms in $C^*-algebras$ or in Lie $JC^*-algebras$, and of Lie $JC^*-algebra$ derivations in Lie $JC^*-algebras$.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.693-699
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• 2010

In this paper we show that the flat property of a left R-module does not imply (carry over) to the corresponding inverse polynomial module. Then we define an induced inverse polynomial module as an R[x]-module, i.e., given an R-linear map f : M $\rightarrow$ N of left R-modules, we define $N+x^{-1}M[x^{-1}]$ as a left R[x]-module. Given an exact sequence of left R-modules $$0\;{\rightarrow}\;N\;{\rightarrow}\;E^0\;{\rightarrow}\;E^1\;{\rightarrow}\;0$$, where $E^0$, $E^1$ injective, we show $E^1\;+\;x^{-1}E^0[[x^{-1}]]$ is not an injective left R[x]-module, while $E^0[[x^{-1}]]$ is an injective left R[x]-module. Make a left R-module N as a left R[x]-module by xN = 0. We show inj $dim_R$ N = n implies inj $dim_{R[x]}$ N = n + 1 by using the induced inverse polynomial modules and their properties.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.331-349
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• 2002

Let G be a reductive algebraic group and let B, F be G-modules. We denote by $VEC_{G}$ (B, F) the set of isomorphism classes in algebraic G-vector bundles over B with F as the fiber over the origin of B. Schwarz (or Karft-Schwarz) shows that $VEC_{G}$ (B, F) admits an abelian group structure when dim B∥G = 1. In this paper, we introduce a stable functor $VEC_{G}$ (B, $F^{\chi}$) and prove that it is an abelian group for any G-module B. We also show that this stable functor will have nice properties.

• Mycobiology
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• v.46 no.4
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• pp.349-360
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• 2018

Whole-genome sequencing of Flammulina ononidis, a wood-rotting basidiomycete, was performed to identify genes associated with carbohydrate-active enzymes (CAZymes). A total of 12,586 gene structures with an average length of 2009 bp were predicted by the AUGUSTUS tool from a total 35,524,258 bp length of de novo genome assembly (49.76% GC). Orthologous analysis with other fungal species revealed that 7051 groups contained at least one F. ononidis gene. In addition, 11,252 (89.5%) of 12,586 genes for F. ononidis proteins had orthologs among the Dikarya, and F. ononidis contained 8 species-specific genes, of which 5 genes were paralogous. CAZyme prediction revealed 524 CAZyme genes, including 228 for glycoside hydrolases, 21 for polysaccharide lyases, 87 for glycosyltransferases, 61 for carbohydrate esterases, 87 with auxiliary activities, and 40 for carbohydrate-binding modules in the F. ononidis genome. This genome information including CAZyme repertoire will be useful to understand lignocellulolytic machinery of this white rot fungus F. ononidis.

• Honam Mathematical Journal
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• v.38 no.2
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• pp.231-241
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• 2016

In this paper we will define the tight integral closure of a finite set of ideals of a ring relative to a module and we will study some related results.