• 충청수학회지
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• 제22권3호
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• pp.467-480
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• 2009

In 1859, Bernhard Riemann, in his epoch-making memoir, extended the Euler zeta function $\zeta$(s) (s > 1; $s{\in}\mathbb{R}$) to the Riemann zeta function $\zeta$(s) ($\Re$(s) > 1; $s{\in}\mathbb{C}$) to investigate the pattern of the primes. Sine the time of Euler and then Riemann, the Riemann zeta function $\zeta$(s) has involved and appeared in a variety of mathematical research subjects as well as the function itself has been being broadly and deeply researched. Among those things, we choose to make a further investigation of the following subjects: Evaluation of $\zeta$(2k) ($k {\in}\mathbb{N}$); Approximate functional equations for $\zeta$(s); Series involving the Riemann zeta function.

• 한국정보통신학회논문지
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• 제9권8호
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• pp.1774-1779
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• 2005

본 논문에서는 그래프 이론에 기초를 둔 GFDD를 사용하여 디지털논리시스템을 구성하는 한가지 방법을 제안하였다. 제안한 방법은 먼저 유한체와 그래프 이론의 수학적 성질을 논의하였으며, 단일변수에 대한 동작영역과 함수영역간의 변환을 용이하게 하기 위한 변환행렬 $\psi$GF(P)(1)과 $\xi$GF(P)(1)을 논의하였다. 그리고 디지털스위칭함수를 구하기 위한 Reed-Muller 확장을 논의하였으며, 이를 다변수인 경우로 확장하기 위해 Kronecker Product를 논의하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제26권1호
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• pp.41-45
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• 1987

In this paper, we give several fixed point theorems in a complete metric space for two multi-valued mappings commuting with two single-valued mappings. In fact, our main theorems show the existence of solutions of functional equations f($\chi$)=g($\chi$)$\in$S$\chi$∩T$\chi$ and $\chi$=f($\chi$)=g($\chi$)$\in$S$\chi$∩T$\chi$ under certain conditions. We also answer an open question proposed by Rhoades-Singh-Kulsherestha. Throughout this paper, let (X, d) be a complete metric space. We shall follow the following notations : CL(X) = {A; A is a nonempty closed subset of X}, CB(X)={A; A is a nonempty closed and founded subset of X}, C(X)={A; A is a nonempty compact subset of X}, For each A, B$\in$CL(X) and $\varepsilon$>0, N($\varepsilon$, A) = {$\chi$$\in$X; d($\chi$, ${\alpha}$) < $\varepsilon$ for some ${\alpha}$$\in$A}, E$\sub$A, B/={$\varepsilon$ > 0; A⊂N($\varepsilon$ B) and B⊂N($\varepsilon$, A)}, and (equation omitted). Then H is called the generalized Hausdorff distance function fot CL(X) induced by a metric d and H defined CB(X) is said to be the Hausdorff metric induced by d. D($\chi$, A) will denote the ordinary distance between $\chi$$\in$X and a nonempty subset A of X. Let R$\^$+/ and II$\^$+/ denote the sets of nonnegative real numbers and positive integers, respectively, and G the family of functions ${\Phi}$ from (R$\^$+/)$\^$s/ into R$\^$+/ satisfying the following conditions: (1) ${\Phi}$ is nondecreasing and upper semicontinuous in each coordinate variable, and (2) for each t>0, $\psi$(t)=max{$\psi$(t, 0, 0, t, t), ${\Phi}$(t, t, t, 2t, 0), ${\Phi}$(0, t, 0, 0, t)} $\psi$: R$\^$+/ \longrightarrow R$\^$+/ is a nondecreasing upper semicontinuous function from the right. Before sating and proving our main theorems, we give the following lemmas:

• 호남수학학술지
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• 제33권3호
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• pp.341-346
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• 2011

We deal with a kind of impossible decomposition of some entire functions in terms of a certain form.

• 대한수학회논문집
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• 제27권2호
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• pp.257-264
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• 2012

Exton introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ${\ldots}$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function ${\Psi}_1$, and a Humbert function ${\Phi}_2$. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function $X_8$, whose kernels include the Exton functions ($X_2$, $X_8$) itself, the Horn's function $H_4$, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권1호
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• pp.5-12
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• 1998

We evaluate the sum of certain class of generalized hypergeometric series of unit argument. Summation formulas, contiguous to Watson's, Whipple's, Lavoie's and Choi's theorems in the theory of the generalized hypergeometric series, are obtained. Certain limiting cases of these results are given.

• 한국안광학회지
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• 제12권1호
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• pp.85-90
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• 2007

안경렌즈의 무반사 코팅물질로 사용되는 황화아연(Zinc Sulphide : ZnS)의 단일박막을 실리콘과 슬라이드 유리 기판위에 스핀코팅방법으로 증착하였다. 박막 증착 후 변입사각분광타원계(VASE : Variable Angle Spectroscopic Ellipsometer)를 사용하여 1.5~5.0 eV 광 에너지 영역에서 타원 각(ellipsometry angle) ${\Delta}$, ${\Psi}$를 측정하였다. 이 측정결과들을 Jellison Modine 분산관계식을 사용하여 최적맞춤하고, 매개변수들을 구하여 박막의 광학상수인 굴절계수 $n({\lambda})$와 소광계수 $k({\lambda})$를 결정하였다.

• Korean Journal of Mathematics
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• 제24권3호
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• pp.545-565
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• 2016

In this paper, we present some general results on the pointwise convergence of the non-convolution type nonlinear singular integral operators in the following form: $$T_{\lambda}(f;x)={\large\int_{\Omega}}K_{\lambda}(t,x,f(t))dt,\;x{\in}{\Psi},\;{\lambda}{\in}{\Lambda}$$, where ${\Psi}$ = and ${\Omega}$ = stand for arbitrary closed, semi-closed or open bounded intervals in ${\mathbb{R}}$ or these set notations denote $\mathbb{R}$, and ${\Lambda}$ is a set of non-negative numbers, to the function $f{\in}L_{p,{\omega}}({\Omega})$, where $L_{p,{\omega}}({\Omega})$ denotes the space of all measurable functions f for which $\|{\frac{f}{\omega}}\|^p$ (1 ${\leq}$ p < ${\infty}$) is integrable on ${\Omega}$, and ${\omega}:{\mathbb{R}}{\rightarrow}\mathbb{R}^+$ is a weight function satisfying some conditions.

• Biomolecules & Therapeutics
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• 제19권4호
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• pp.445-450
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• 2011

Preciously, we demonstrated that a novel NHE-1 inhibitor, KR-33028 attenuated cortical neuronal apoptosis induced by glutamate. In the present study, we investigated the signaling mechanism of neuroprotective effect of KR-33028 against glutamate-induced neuronal apoptosis, especially focusing on mitochondrial death pathway. Our data showed that glutamate induces a biphasic rise in mitochondrial $Ca^{2+}$ and that KR-33028 significantly prevents the second phase increase, but not the first phase increase in mitochondrial $Ca^{2+}$. Furthermore, KR-33028 restored the ${\Delta}{\Psi}_m$ dissipation and cytochrome c release into cytoplasm induced by glutamate in a concentration-dependent manner. The inhibition of mitochondrial $Ca^{2+}$ overload by ruthenium red also inhibited glutamate-induced apoptotic cell death, mitochondrial membrane potential, ${\Delta}{\Psi}_m$ dissipation and cytochrome c release. These data suggest that inhibition of mitochondrial $Ca^{2+}$ overload is likely to be attributable to anti-apoptotic effect of KR-33028. Taken together, our results suggest that anti-apoptotic effects of NHE-1 inhibitor, KR-33028 may be mediated through maintenance of mitochondrial function.

• 충청수학회지
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• 제26권4호
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• pp.769-780
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• 2013

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the log-sine and log-cosine integrals have been evaluated, in the existing literature on the subject, in many different ways. Very recently, Choi [6] presented explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta function. In the present sequel to the investigation [6], we evaluate the log-sine and log-cosine integrals involved in more complicated integrands than those in [6], by also using the Beta function.