• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.191-207
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• 2000

Let R be a ommutative ring with unity and F a finite free R-module. For a nonnegative integer r, there exists a natural filtration of$S_r(S_2F)$ such that its associated graded module is isomorphic to $\Sigma_{{\lambda}{\epsilon}{\tau}_r}\;L_{\lambda}F$, where ${\Gamma}_{\gamma}$ set of partitions such that $$\mid${\lambda}$\mid$-2r,{{\widetilde}{\lambda}}-{{\widetilde}{\lambda}}_1},...,{{\widetilde}{\lambda}}_k},\;each\;{{\widetilde}{\lambda}}_t}$,is even. We call such filtrations plethysm formulas. We extend the above plethysm formula to the version of chain complexes. By plethysm formula we mean the composition of universally free functors. $Let{\emptyset}:G->F$ be a morphism of finite free R-modules. We construct the natural decomposition of $S_{r}(S_2{\emptyset})$,up to filtrations, whose associated graded complex is isomorphic to ${\Sigma}_{{\lambda}{\varepsilon}{\tau}}_r}\;L_{\lambda}{\emptyset}$.

• Kyungpook Mathematical Journal
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• v.17 no.1
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• pp.47-56
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• 1977

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.153-159
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• 1995

In this paper, we study the inclusion realtion between recursive sets. And we prove that if $\overline{R(f)}{\backslash}R(f)$ is not empty, then it is infinite, and we characterize the necessary and sufficent condition for which $\overline{R(f)}{\backslash}R(f)$ is countable.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.761-768
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• 2021

Let I be a nonzero ideal of a prime ring R and m, n are positive integers. If R admits a generalized derivation F satisfying F(x)ⁿF(y)^m - xⁿy^m = 0 for any y, x ∈ I, then F(x) = ax for any x ∈ R and a^m+n = 1, where a ∈ C, the extended centroid of R.

• Journal of the Korea Safety Management & Science
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• v.11 no.3
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• pp.209-216
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• 2009

A development in method of evaluating the measurement precisions using approximate F tests and variance components from expected mean square (EMS) is investigated. The research proposes three-factor mixed measurement models with the fixed and random factors. Unrestricted and unconstrained design work was rarely studied, while restricted and constrained designs have been significantly discussed. The unrestricted and unconstrained designs assume to be an independence of interaction. The proposed evaluation method about the measurement precisions can be extended to four-factor random measurement model or mixed measurement model. The study also presents the three evaluation indexes of precisions such as R&RTR (Reproducibility & Repeatability-To-Total Precision Ratio), PTR (Precision-To-Tolerance Ratio), and SNR (Signal-To-Noise Ratio). Numerical examples are proposed to evaluate the approximate F tests with Satterthwaite degrees of freedom and three indexes using the measurement precisions from EMS.

• Journal of the Korean Chemical Society
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• v.29 no.3
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• pp.277-282
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• 1985

The effects of linear free energy relationship (LFER) on the imidoyl proton (H${\alpha}$)-substituent chemical shift (SCS) in case of varying para-substituted C-phenyl group in N-benzylideneaniline derivatives were studied. The H${\alpha}$-SCS values and LFER parameters such as ${\sigma}$,${\sigma}^+$, ${\sigma}_I$,${\sigma}_R, F and R were applied to the Hammett, Okamoto-Brown, and Taft, Swain-Lupton's dual substituents parameter (DSP) equations. The results were: (1) the blending coefficient values, ${\lambda}$ = 2.8∼3.2, it's means that the resonance effect (R) was larger than inductive effect (I) and field effect (F), and (2) the values of percent resonance and percent field effects were %R = 66.6 and %F = 33.4, respectively, yielding the ratio of resonance effect (R) to field effect (F) of 2 : 1.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.864-869
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• 2003

KS F 2808 was revised in 2000 and KS F 2862-1 was newly established in 2001. Thus Related Korean Industrial Standard such as KS F 4724, KS F 4735, KS F 4736 should be revised according to KS F 2808 and KS F 28612-1. This study aims to elicit the new rating numbers such as R$\sub$w/, R$\sub$w/＋C, R$\sub$w/＋C$\sub$tr/, L$\sub$m/ defined in KS F 2862-1 instead of exiting rating number; transmission loss of 500Hz.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1759-1776
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• 2015

We determine the general solution of the generalized additive-quartic functional equation f(x + 3y) + f(x - 3y) + f(x + 2y) + f(x - 2y) + 22f(x) - 13 [f(x + y) + f(x - y)] + 24f(y) - 12f(2y) = 0 without assuming any regularity conditions on the unknown function f : ${\mathbb{R}}{\rightarrow}{\mathbb{R}}$ and its stability is investigated.

• Proceedings of the Korea Association of Crystal Growth Conference
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• 2000.06a
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• pp.1-33
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• 2000

Silicon carbide ceramics with sintering additives from the system AlN-Y$_2$O$_3$ can be gas-pressure sintered to theoretical density. While commonly a combination of sesquioxides is used such as Al$_2$O$_3$-Y$_2$O$_3$, the oxynitrid additives offer the advantage that only a nitrogen atmosphere is require instead of a powder. By starting form a mixture of ${\beta}$-SiC and ${\alpha}$-SiC, and by performing dedicated heat treatments after densification, anisotropic grain growth is obtained which leads to a platelet microstructure showing enhance fracture toughness. In the present work, recent improvement of the mechanical behaviour of these materials at ambient and high temperatures is reported. By means of a surface oxidation treatment in air it is possible to obtain four-point bending strengths in excess of 1 GPa, and the strength retention at high temperatures is significantly improved.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.397-408
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• 2015

In this paper, we solve the Hyers-Ulam stability problem for the following cubic type functional equation $$f(rx+sy)+f(rx-sy)=rs^2f(x+y)+rs^2f(x-y)+2r(r^2-s^2)f(x)$$in quasi-Banach space and non-Archimedean space, where $r={\neq}{\pm}1,0$ and s are real numbers.