• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.339-348
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• 2023

It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right R-module is nilpotent-invariant. We prove that R ≅ R₁ × R₂, where R₁, R₂ are rings which satisfy R₁ is a semi-simple Artinian ring and R₂ is square-free as a right R₂-module and all idempotents of R₂ is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right R-modules. Such a module is shown to have isomorphic simple modules eR and fR, where e, f are orthogonal primitive idempotents such that eRf ≠ 0.

• East Asian mathematical journal
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• v.16 no.1
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• pp.111-123
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• 2000

Northcott and McKerrow proved that if R is a left noetherian ring and E is an injective left R-module, then $E[x^{-1}]$ is an injective left R[xl-module. Park generalize Northcott and McKerrow's result so that if R is a left noetherian ring and E is an injective left R-module, then $E[x^{-S}]$ is an injective left $R[x^s]$-module, where S is a submonoid of N(N is the set of all natural numbers). In this paper we show $$Hom_{R[x^S]}(M[x^{-S}],\;N[x^{-S}]){\cong}Hom_R(M,\;N)[[x^S]]$$ and using the above result and this isomorphism, finally we show that $$Ext^i_{R[x^S]}(M[x^{-S}],\;N[x^{-S}]){\cong}Ext^i_R(M,\;N)[[x^S]]$$.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.257-261
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• 2000

Northcott and Mckerrow proved that if R is a left noe-therian ring and E is an injective left R-module, then E[x-1] is an injective left R[x]-module. In this paper we generalize Northcott and McKerrow's result so that if R is a left noetherian ring and E is an in-jective left R-module, then E[x-S] is an injective left R[xS]-module, where S is a submonoid of N (N is the set of all natural numbers).

• Journal of Radiation Protection and Research
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• v.2 no.1
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• pp.24-30
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• 1977

Les eaux de $g\'{e}n\'{e}rateur$ de vapeur d'un $r\'{e}acteur$ P. W. R peuvent $\^{e}tre$ $contamin\'{e}es$ par des $radio-\'{e}lements$. Ces eaux sont habituellement $condition\'{e}es$ 'phosphate' pour limiter leur $agressivit\'{e}$ et la tendence actuelle est de remplacer les phosphate par un conditionment 'Amoniaques'. La $pr\'{e}sente$ $\'{e}tude$ a pour but de definir la $possibilit\'{e}$ $d'{\'{e}}purer$ des eaux $condition\'{e}es$ $\'{a}$ l'ammoniaque $\'{a}$ l'aide $d'{\'{e}}changeurs$ d'ion organiques. Des Facteurs de $D\'{e}contamination$ (F. D) en Cesium 137 et Strontium 90 et la $dur\'{e}e$ du cycle $d'{\'{e}}puration$ ont $d\^{u}$ $\^{e}tre$ bien meilleurs avec une colonne de 10 ml de $r\'{e}sine$ Carborylique Duolite $CC_4$ mise sous forme acide, suivie d'une colonne de 10 ml de $r\'{e}sine$ cationique Amberlite IR 120 mise sous forme acide et suivie d'une colonne de 10 ml de $r\'{e}sine$ anionique Amberlite IRA 400 mise sous forme hydroxyde.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.463-471
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• 2013

Let R be a ring with identity 1, $I(R){\neq}\{0\}$ be the set of all nonunit idempotents in R, and M(R) be the set of all primitive idempotents and 0 of R. We say that I(R) is additive if for all e, $f{\in}I(R)$ ($e{\neq}f$), $e+f{\in}I(R)$. In this paper, the following are shown: (1) I(R) is a finite additive set if and only if $M(R){\backslash}\{0\}$ is a complete set of primitive central idempotents, char(R) = 2 and every nonzero idempotent of R can be expressed as a sum of orthogonal primitive idempotents of R; (2) for a regular ring R such that I(R) is a finite additive set, if the multiplicative group of all units of R is abelian (resp. cyclic), then R is a commutative ring (resp. R is a finite direct product of finite field).

• Journal of The Korean Association For Science Education
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• v.39 no.4
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• pp.511-523
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• 2019

In this age of the $4^{th}$ industrial revolution, we, science educators, are giving more light on students' agentic behavior in the process of educating future scientist. This study, with the analytic lens of epistemic agency, explores the key stages of a student-driven R&E program rather than the scientist-led R&E program. It also examines to understand the emergence of students' epistemic agency in each stage of R&E. Data from participant observation for 18 months and in-depth interviews were collected and analyzed with the constant comparative method of grounded theory. This study identifies and describes five key stages of student-driven R&E: The stage of exploring research theme, designing research, performing lab activity, interpreting results, and communicating research. It also finds that (a) students' epistemic agency emerged with the constant interactions with the R&E structure; (b) students' epistemic agency has deep relations with the epistemic beliefs of the students; (c) students positioned themselves as decision-makers in the R&E practice; (d) the redistributed power and authority of the R&E contributed to the emergence of students' epistemic agency.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1117-1127
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• 2011

In this paper, a class of more general delayed viral infection model with lytic immune response is proposed by Song et al.[1] ([Journal of Mathematical Analysis Application 373 (2011), 345-355). We derive the basic reproduction numbers $R_0$ and $R_0^*$ 0 for the viral infection, and establish that the global dynamics are completely determined by the values of $R_0$ and $R_0^*$. If $R_0{\leq}1$, the viral-free equilibrium $E_0$ is globally asymptotically stable; if $R_0^*{\leq}1$ < $R_0$, the immune-free equilibrium $E_1$ is globally asymptotically stable; if $R_0^*$ > 1, the chronic-infection equilibrium $E_2$ is globally asymptotically stable by using the method of Lyapunov function.

• Journal of the Korean Society of Costume
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• v.1
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• pp.59-65
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• 1977

Les modes des costumes naitonaux de $cor{\acute{e}}e$ est plus simple que celle du Occident. mais les facons, sur les quelles les mesures fondamentalement agissent, ont des $varit{\acute{e}}s$ selon les personnes qui se les habillent: masculines, $f{\acute{e}}m$ nines, jeunes, vieilles. Le but de cette ${\acute{e}}tude$ est, par l'anayse statistique des mesures, $d'{\acute{e}}tablir$ comment sont les $vari{\acute{e}}t{\acute{e}}s$. Les $r{\acute{e}}sultats$ de ce travail peuveut $\hat{e}tre$ $r{\acute{e}}sum{\acute{e}}s$ ainsi: 1. Plus $\grave{a}g{\acute{e}}s$ sont les personnes, plue larges et longues les Cheo-go-ri (vestes). 2. A propos des longeur des vestes, on les $g{\acute{e}}n{\acute{e}}ralement$ $consid{\acute{e}}re$ comme les $donn{\acute{e}}es$ principalement $subondonn{\acute{e}}es$ aux tailles des personnes $habill{\acute{e}}es$. mais a mon travail, le tour do poitrine peut-$\hat{e}tre$ le plus relatis en ce problemes. [parce que le coefficient $conr{\acute{e}}ratif$ ayant rapponts au tour de poitrine (r=0.512) est plus haut que celui qui est relatif a la taille (r=0.436).

• Journal of Life Science
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• v.19 no.3
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• pp.384-389
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• 2009

This study was carried out to elucidate the relation between expression levels of three melanin synthesis genes (Tyrosinase, Tyrosinase-related protein 1 and Dopachrome tautomerase) according to the Melanocortin-1 receptor genotypes with coat color patterns in Hanwoo cattle, Jeju black cattle and Holsteins. Using real-time semiquantitative reverse transcription-PCR assay (RT-PCR), the expression levels of these three genes were analyzed in skin tissues from four representative coat colored areas: yellowish-brown from MC1R e/e Hanwoo, wild type black from $E^+/E^+$ Jeju black cattle (JBC), and dominant black and white pied regions from $E^D/E^D$ Holstein. The TYR, TYRP1 and DCT genes showed higher expression levels of 4.5, 2.3 and 2.5 times higher in the black skin area of Holsteins than those of from JBC, respectively (p<0.001). In addition, the expression levels of these three genes from JBC were significantly higher than those from Hanwoo cattle (p<0.001). These results show that coat color phenotypes in Hanwoo cattle, JBC and Holsteins is directly correlated with TRY, TYRP1 and DCT transcription levels, which probably reflected involvement with MC1R genotypes; e/e in Hanwoo, $E^+/E^+$ in JBC and $E^D/E^D$ in Holsteins. Consequently, this study suggested that the status of MC1R protein may not only induce the transcription activities of a series of TYR and its related genes responsible for melanin synthesis, but also determine the levels of total melanin contents in bovine skin.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.323-334
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• 2008

We define injective and projective representations of quivers with two vertices with n arrows. In the representation of quivers we denote n edges between two vertices as ${\Rightarrow}$ and n maps as $f_1{\sim}f_n$, and $E{\oplus}E{\oplus}{\cdots}{\oplus}E$ (n times) as ${\oplus}_nE$. We show that if E is an injective left R-module, then $${\oplus}_nE{\Longrightarrow[50]^{p_1{\sim}p_n}}E$$ is an injective representation of $Q={\bullet}{\Rightarrow}{\bullet}$ where $p_i(a_1,a_2,{\cdots},a_n)=a_i,\;i{\in}\{1,2,{\cdots},n\}$. Dually we show that if $M_1{\Longrightarrow[50]^{f_1{\sim}f_n}}M_2$ is an injective representation of a quiver $Q={\bullet}{\Rightarrow}{\bullet}$ then $M_1$ and $M_2$ are injective left R-modules. We also show that if P is a projective left R-module, then $$P\Longrightarrow[50]^{i_1{\sim}i_n}{\oplus}_nP$$ is a projective representation of $Q={\bullet}{\Rightarrow}{\bullet}$ where $i_k$ is the kth injection. And if $M_1\Longrightarrow[50]^{f_1{\sim}f_n}M_2$ is an projective representation of a quiver $Q={\bullet}{\Rightarrow}{\bullet}$ then $M_1$ and $M_2$ are projective left R-modules.