• 대한수학회지
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• 제37권6호
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• pp.915-927
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• 2000

This paper is concerned with degenerate Volterra equations Mu(t) + ∫(sub)0(sup)t k(t-s) Lu(s)ds = f(t) in Banach spaces both in the hyperbolic case, and the parabolic one. The key assumption is played by the representation of the underlying space X as a direct sum X = N(T) + R(T), where T is the bounded linear operator T = ML(sup)-1. Hyperbolicity means that the part T of T in R(T) is an abstract potential operator, i.e., -T(sup)-1 generates a C(sub)0-semigroup, and parabolicity means that -T(sup)-1 generates an analytic semigroup. A maximal regularity result is obtained for parabolic equations. We will also investigate the cases where the kernel k($.$) is degenerated or singular at t=0 using the results of Pruss[8] on analytic resolvents. Finally, we consider the case where $\lambda$ is a pole for ($\lambda$L + M)(sup)-1.

• 대한수학회지
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• 제48권2호
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• pp.267-288
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• 2011

In this paper, we construct eight infinite families of ternary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the special orthogonal group $SO^-$(2n, q). Here q is a power of three. Then we obtain four infinite families of recursive formulas for power moments of Kloosterman sums with square arguments and four infinite families of recursive formulas for even power moments of those in terms of the frequencies of weights in the codes. This is done via Pless power moment identity and by utilizing the explicit expressions of exponential sums over those double cosets related to the evaluations of "Gauss sums" for the orthogonal groups $O^-$(2n, q).

• 대한수학회지
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• 제57권3호
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• pp.585-602
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• 2020

In this paper, we construct four infinite families of binary linear codes associated with double cosets with respect to a certain maximal parabolic subgroup of the orthogonal group O⁺(2n, 2^r). And we obtain two infinite families of recursive formulas for the power moments of Kloosterman sums and those of 2-dimensional Kloosterman sums in terms of the frequencies of weights in the codes. This is done via Pless' power moment identity and by utilizing the explicit expressions of exponential sums over those double cosets related to the evaluations of "Gauss sums" for the orthogonal groups O⁺(2n, 2^r).

• 대한수학회지
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• 제46권6호
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• pp.1193-1206
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• 2009

C. Guenther studied the stability of DeTurck flows by using maximal regularity theory and center manifolds, but these arguments can not solve the stability of Ricci flows because the Ricci flow equation is not strictly parabolic. Recognizing this deficiency, the present paper considers and obtains the stability of Ricci flows, and of quasi-Ricci flows in view of some Killing conditions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권1호
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• pp.75-90
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• 2015

In this paper the existence of global solutions of the parabolic cross-diffusion systems with cooperative reactions is obtained under certain conditions. The uniform boundedness of $W_{1,2}$ norms of the local maximal solution is obtained by using interpolation inequalities and comparison results on differential inequalities.

• 대한수학회지
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• 제34권4호
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• pp.871-894
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• 1997

For a lifted nontrivial additive character $\lambda'$ and a multiplicative character $\chi$ of the finite field with $q^2$ elements, the 'Gauss' sums $\Sigma\lambda'$(tr $\omega$) over $\omega$ $\in$ SU(2n + 1, $q^2$) and $\Sigma\chi$(det $\omega$)$\lambda'$(tr $\omega$) over $\omega$ $\in$ U(2n + 1, $q^2$) are considered. We show that the first sum is a polynomial in q with coefficients involving certain new exponential sums and that the second one is a polynomial in q with coefficients involving powers of the usual twisted Kloosterman sums and the average (over all multiplicative characters of order dividing q-1) of the usual Gauss sums. As a consequence we can determine certain 'generalized Kloosterman sum over nonsingular Hermitian matrices' which were previously determined by J. H. Hodges only in the case that one of the two arguments is zero.

• 대한수학회보
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• 제49권4호
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• pp.705-714
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• 2012

In this paper, we study nonlinear equation arising in MEMS modeling electrostatic actuation. We will prove the local and global existence of solutions of the generalized parabolic MEMS equation. We present that there exists a constant ${\lambda}^*$ such that the associated stationary problem has a solution for any ${\lambda}$ < ${\lambda}^*$ and no solution for any ${\lambda}$ > ${\lambda}^*$. We show that when ${\lambda}$ < ${\lambda}^*$ the global solution converges to its unique maximal steady-state as $t{\rightarrow}{\infty}$. We also obtain the condition for the existence of a touchdown time $T{\leq}{\infty}$ for the dynamical solution. Furthermore, there exists $p_0$ > 1, as a function of $p$, the pull-in voltage ${\lambda}^*(p)$ is strictly decreasing with respect to 1 < $p$ < $p_0$, and increasing with respect to $p$ > $p_0$.

• Structural Engineering and Mechanics
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• 제63권1호
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• pp.55-64
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• 2017

The paper concerns concrete carbonation, the phenomena that occurs in every type of climate, especially in urban-industrial areas. In European Standards, including Eurocode (EC) for concrete structures the demanded durability of construction located in the conditions of the carbonation threat is mainly assured by the selection of suitable thickness of reinforcement cover. According to EC0 and EC2, the thickness of the cover in the particular class of exposure depends on the structural class/category and concrete compressive strength class which is determined by cement content and water-cement ratio (thus the quantitative composition) but it is not differentiated for various cements, nor additives (i.e., qualitative composition), nor technological types of concrete. As a consequence the selected thickness of concrete cover is in fact a far estimation - sometimes too exaggerated (too safe or too risky). The paper presents the elaborated "self-terminated carbonation model" that includes abovementioned factors and enables to indicate the maximal possible depth of carbonation. This is possible because presented model is a hyperbolic function of carbonation depth in time (the other models published in the literature use the parabolic function that theoretically assume the infinite increase of carbonation depth value). The paper discusses the presented model in comparison to other models published in the literature, moreover it contains the algorithm of concrete cover design with use of the model as well as an example of calculation of the cover thickness.

• 한국의학물리학회지:의학물리
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• 제18권2호
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• pp.73-80
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• 2007

제주 해안에서 잡은 60여 개의 군소를 대상으로 한 실험 데이터 중에서 5개의 세포에 대한 실험 결과를 분석해 보니 주목할 만한 결과들이 나왔다. 이들 5개의 세포들 중에 3개의 세포에서는 $32^{\circ}C$에서 $10^{\circ}C$까지 온도를 내리는 동안에 이완된 진동 상태, 연속발화상태 사이의 과분극 기간이 짧은 버스팅, 혼돈 양상의 버스팅, 주기 배가 양상, 연속발화 기간은 길고 휴지 기간은 짧은 버스팅, 일정하게 반복되는 비팅 상태이거나 타원형 버스팅, 휴지상태가 차례차례로 나타났으며, $10^{\circ}C$에서 $32^{\circ}C$까지 온도를 올리는 동안에는 그 반대 순서로 발화 형태가 변화하였다. 같은 온도 범위에서 80분 정도의 주기로 계속해서 열변화 자극을 줄 때마다 이러한 발화 형태 변화는 일정하게 나타났다. 그러나 나머지 두 세포의 경우에는 이와는 다른 발화 형태의 온도에 따른 변화를 보였다. 이들 경우에 이러한 열변화 자극을 24시간 이상 지속하였으나 발화 진폭은 크게 줄어들지 않았다. 그리고 평균발화 진동수, 버스팅 신호 사이의 평균 과분극상태 지속시간, 활동전위 진폭과 활동전위의 최저값 등을 $C^{++}$로 짠 프로그램을 실행시켜서 비교 분석 가능하였다. 온도에 따른 발화 진동수의 분포는 저온과 고온에서는 낮으나 중간 영역에서는 높은 종 모양의 형태를 보였는데, 온도를 내리는 동안에는 온도를 올리는 동안 보다 발화 진동수가 높았다.