• Korean Journal of Mathematics
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• 제16권3호
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• pp.413-424
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• 2008

In [21], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\parallel}\frac{1}{n}\sum\limits_{i=1}^{n}x_i{\parallel}^2+\sum\limits_{i=1}^{n}{\parallel}x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j{\parallel}^2=\sum\limits_{i=1}^{n}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\dots},x_n{\in}V$. We consider the functional equation $$nf(\frac{1}{n}\sum\limits^n_{i=1}x_i)+\sum\limits_{i=1}^{n}f(x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j)=\sum\limits_{i=1}^nf(x_i)$$ Using fixed point methods, we prove the generalized Hyers-Ulam stability of the functional equation $$(1)\;2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})=f(x)+f(y)$$.

• 대한수학회논문집
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• 제36권3호
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• pp.401-411
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• 2021

A Diophantine m-tuple is a set {a₁, a₂, …, a_m} of positive integers such that a_ia_j+1 is a perfect square for all 1 ≤ i < j ≤ m. Let E_k be the elliptic curve induced by Diophantine triple {F_2k, 5F_2k+2, 3F_2k + 7F_2k+2}. In this paper, we find the structure of a torsion group of E_k, and find all integer points on E_k under assumption that rank(E_k(ℚ)) = 1 and some further conditions.

• 한국염색가공학회지
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• 제27권1호
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• pp.1-10
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• 2015

The aim of the current study is to identify the dimerization and decomposition kinetics of the F-$D_M$ type. The regeneration of F-VS from $F_iF_j-D_M$ or the reversibility of the dimerizations were investigated. The order of real rate constants of the dimerization('$K_D{^{ij}}$) would seem to be similar to that of rate constants of a dimerization($K_D{^{ij}}$) for VS dyes at a given pH because of the constancy of the equilibrium constants($K_a{^j}$-value). The reverse reactions of the $D_M$ types are appeared to occur in two steps, the deprotonation of ${\alpha}$-carbon of the $D_M$ types and disproportionation. The ratio of the decomposition of the $D_M$ type to F-Hy and F-VS appears to be related with the ratio of $K_i/K_j$. Similarities were also found among various other reactions, including homo- and mixed dimerization. VS dyes undergoing fast hydrolysis have difficulty in forming a dimer. The higher the reactivity with cellulose or hydroxide ion, the smaller the dimerization. The easiness of the dimerization was thus found to be inversely proportional to the rate of hydrolysis.

• 호남수학학술지
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• 제34권2호
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• pp.279-287
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• 2012

Let $k$ be a field containing the field $\mathbb{Q}$ of rational numbers and let $R=k[x_{ij}{\mid}1{\leq}i{\leq}m,\;1{\leq}j{\leq}n]$ be the polynomial ring over a field $k$ with indeterminates $x_{ij}$. Let $I_t(X)$ be the determinantal ideal generated by the $t$-minors of an $m{\times}n$ matrix $X=(x_{ij})$. Eagon and Hochster proved that $I_t(X)$ is a perfect ideal of grade $(m-t+1)(n-t+1)$. We give a structure theorem for a class of determinantal ideals of grade 3. This gives us a characterization that $I_t(X)$ has grade 3 if and only if $n=m+2$ and $I_t(X)$ has the minimal free resolution $\mathbb{F}$ such that the second dierential map of $\mathbb{F}$ is a matrix defined by complete matrices of grade $n+2$.

• 호남수학학술지
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• 제29권4호
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• pp.653-666
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• 2007

Let R be a commutative Noetherian ring (with a nonzero identity) and let M be an R-module. Further let I be an ideal of R. In this paper, by putting a suitable condition on $Ass_R$(M), we obtain some results concerning $I^{*(M)}$ and prove that the sequence of sets $Ass_R(R/(I^n)^{*(M)})$, $n\;\in\;N$, is increasing and ultimately constant. (Here $(I^n)^{*(M)}$ denotes the integral closure of $I^n$ relative to M.)

• 대한수학회보
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• 제36권4호
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• pp.671-682
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• 1999

Using a base-point free version of the infinite symmetric product we define a fibrewise infinite symmetric product for any fibration $E\;\longrightarrow\;B$. The construction works for any commutative ring R with unit and is denoted by $R_f(E)\;l\ongrightarrow\;B$. For any pointed space B let $G_I(B)\;\longrightarrow\;B$ be the i-th Ganea fibration. Defining $M_R-cat(B):= inf{i\midR_f(G_i(B))\longrihghtarrow\;B$ admits a section} we obtain an approximation to the Lusternik-Schnirelmann category of B which satisfies .g.a product formula. In particular, if B is a 1-connected rational space of finite rational type, then $M_Q$-cat(B) coincides with the well-known (purely algebraically defined) M-category of B which in fact is equal to cat (B) by a result of K.Hess. All the constructions more generally apply to the Ganea category of maps.

• 대한수학회논문집
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• 제21권1호
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• pp.37-43
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• 2006

We prove that $M_1\longrightarrow^f\;M_2$ is an injective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ if and only if $M_1\;and\;M_2$ are injective left R-modules, $M_1\longrightarrow^f\;M_2$ is isomorphic to a direct sum of representation of the types $E_l{\rightarrow}0$ and $M_1\longrightarrow^{id}\;M_2$ where $E_l\;and\;E_2$ are injective left R-modules. Then, we generalize the result so that a representation$M_1\longrightarrow^{f_1}\;M_2\; \longrightarrow^{f_2}\;\cdots\;\longrightarrow^{f_{n-1}}\;M_n$ of a quiver $Q={\bullet}{\rightarrow}{\bullet}{\rightarrow}{\cdots}{\rightarrow}{\bullet}$ is an injective representation if and only if each $M_i$ is an injective left R-module and the representation is a direct sum of injective representations.

• Applied Biological Chemistry
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• 제32권2호
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• pp.170-177
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• 1989

2개의 m-methyl group이 치환된 m-xylyl N-methylcarbamates(MXNMC)가 비치환된 phenyl N-methylcarbamates(PNMC)보다 높은 살충작용을 나타내는 이유를 알아보기 위하여 이들 두 유도체들이 확장 $H\ddot{u}ckel$(EHT) 이론에 따른 분자궤도(MO) 이론과 회귀 및 자유에너지 관계(LFER) 분석에 의하여 연구되었다. 가장 안정한 입체구조는 phenyl group이 N-methylcarbamyl group의 면에 대하여 수직(${\theta}=90^{\circ}$)인 형태(Z,Z)이었으며, 회귀분석은 $pI_{50}$ 상수들과 meta-위치 및 m-methyl group의 수소원자 하전과 LUMO에너지의 계산된 MO량을 변수로 취했을 경우가 가장 좋은 상관관계를 나타내었다. Carbamylation 반응에 관한 LFER분석 결과, PNMC에서는 공명(R)-효과(40%)보다 장 (F) 효과(60%)가 약간 컸으나(F>R), MXNMC의 경우에는 R-효과(98.6%)가 F-효과(1.4%)보다 월등히 큰 값($R{\gg}F$)을 보였다. 이와 같은 사실로부터 MXNMC의 살충작용이 증진되는 것은 m-dimethyl group에 의한 hyperconjugation의 결과라고 믿어진다.

• 한국어병학회지
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• 제33권1호
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• pp.83-89
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• 2020

In the study, we investigated the effect of Taurine-F^TM, which is a commercially available fishery nutritional supplements complex, on anti-hepatotoxicity stressed with thioacetamide (TAA) and innate immune responses in olive flounder. To investigate the change in liver toxicity, firstly, TAA (30 ppm/100 g of fish) was intraperitoneally (i.p.) administered 12 hr after the intramuscular (i.m.) injection of Taurine-F^TM (0.02 ml/100 g of fish)(Taurine/TAA). Secondly, Taurine-F^TM was i.m. injected 24 hr after the administration of TAA (TAA/Taurine). Finally, TAA was administered simultaneously with Taurine-F^TM (TAA+Taurine). All blood samples were collected 24 hr after injection. GOT level in group Taurine/TAA appeared similar to the control, whereas group TAA/Taurine and TAA+Taurine showed significantly increased (p<0.05) levels compared to the control. In GPT level, group Taurine/TAA and TAA/Taurine showed elevated levels compared to the control, whereas no significant difference was observed between group TAA+Taurine and the control. Serum ACH₅₀ activity was significantly (p<0.05) augmented 24 hr after Taurine-F^TM injection compared to the control group, whereas no significant increase was observed 48 hr after Taurine-F^TM injection. On the other hand, serum lysozyme activity elevated in an acute stressed condition appeared significantly down-regulated 24 and 48 hr after Taurine-F^TM injection compared to the control. In conclusion, i.m. injected Taurine-F^TM augmented flounder serum complement activity and decreased a possible handling stress resulting in reducing a serum lysozyme activity and recovering hepatotoxicity. Thus, it is assumed that i.m. injection of Taurine-F^TM mixed with antibiotics or available vaccines could be utilized as an anti-hepatotoxic recipe in fish culture industry.

• 전기전자학회논문지
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• 제3권2호
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• pp.236-242
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• 1999

BiCMOS 공정으로 제조된 바이폴라 트랜지스터의 베이스 분산저항 ${\gamma}_{bb}$에서 발생되는 1/f 잡음을 실험 적으로 분석하였다. 공통컬렉터 잡음등가회로의 해석으로부터 $g_m^{-1}-{\gamma}_{bb}-R_B$값이 매우 작을 때는 출력측에서의 1/f 잡음은 순수하게 ${\gamma}_{bb}$에서 발생되는 잡음임을 실험을 통해서 확인할 수 있었다. $S^{1/f}_{Irbb}=K_fI_b{^{A_1}}/f$에서 $A_f=2,\;K_f{\simeq}5{\times}10^{-9}$를 얻었다. 그리고 Hooge상수 ${\alpha}$ 값은 ${\sim}10^{-3}$ 범위로 추출되었다.