• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.361-372
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• 2006

In this paper, we consider the multi-point boundary value problems for one-dimensional p-Laplacian at resonance: $({\phi}_p(x'(t)))'=f(t,x(t),x'(t))$, subject to the boundary value conditions: ${\phi}_p(x'(0))={\sum}^{n-2}_{i=1}{\alpha}_i{\phi}_p(x'({\epsilon}i)),\;{\phi}_p(x'(1))={\sum}^{m-2}_{i=1}{\beta}_j{\phi}_p(x'({\eta}_j))$ where ${\phi}_p(s)=/s/^{p-2}s,p>1,\;{\alpha}_i(1,{\le}i{\le}n-2){\in}R,{\beta}_j(1{\le}j{\le}m-2){\in}R,0<{\epsilon}_1<{\epsilon}_2<...<{\epsilon}_{n-2}1,\;0<{\eta}1<{\eta}2<...<{\eta}_{m-2}<1$, By applying the extension of Mawhin's continuation theorem, we prove the existence of at least one solution. Our result is new.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1211-1220
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• 2009

In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian $({\phi}_p(u'))'$(t)+q(t)f(t,u(t),u'(t))=0, t $\in$ (0, 1), subject to the boundary conditions: $u(0)=\sum\limits_{i=1}^{n-2}{\alpha}_iu({\xi}_i),\;u(1)=\sum\limits_{i=1}^{n-2}{\beta}_iu({\xi}_i)$ where $\phi_p$(s) = $|s|^{n-2}s$, p > 1, $\xi_i$ $\in$ (0, 1) with 0 < $\xi_1$ < $\xi_2$ < $\cdots$ < $\xi{n-2}$ < 1 and ${\alpha}_i,\beta_i{\in}[0,1)$, 0< $\sum{\array}{{n=2}\\{i=1}}{\alpha}_i,\sum{\array}{{n=2}\\{i=1}}{\beta}_i$<1. Using a fixed point theorem due to Bai and Ge, we study the existence of at least three positive solutions to the above boundary value problem. The important point is that the nonlinear term f explicitly involves a first-order derivative.

• 한국진공학회지
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• 제7권2호
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• pp.112-117
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• 1998

TiN을 Cu의 확산방지막으로 사용하기 위해 많은 연구가 되어왔는데, 이 연구에서는 특히 X-ray photoelectron spectroscopy(XPS)를 이용하여 TiN박막에서의 Cu의 확산현상을 연구하였다. TiN박막은 일반적으로 columnar grain을 형성하면서 성장을 하는데, 녹는점의 1/3에 해당하는 비교적 낮은 온도에서는 grain들의 경계를 따라 Cu가 확산함을 확인하였다. Atomic force microscopy(AFM)를 이용하여 grain의 모양을 관찰하였고, 이 grain boundary 를 통한 확산 현상을 연구하기 위하여, modified surface accumulation method를 이용하였 다. 연구 결과, TiN박막에서의 Cu의 grain boundary diffusion의 활성화 에너지 $Q_b$는 0.23 eV, Diffusivity $D_{bo}$는 $5.5\times10^{-12{\textrm{cm}^2$/sec의 값을 얻었다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권1호
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• pp.35-56
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• 2015

In this paper, we classify all nonconstant smooth CR maps from a sphere $S_{n,1}{\subset}\mathbb{C}^n$ with n > 3 to the Shilov boundary $S_{p,q}{\subset}\mathbb{C}^{p{\times}q}$ of a bounded symmetric domain of Cartan type I under the condition that p - q < 3n - 4. We show that they are either linear maps up to automorphisms of $S_{n,1}$ and $S_{p,q}$ or D'Angelo maps. This is the first classification of CR maps into the Shilov boundary of bounded symmetric domains other than sphere that includes nonlinear maps.

• Bulletin of the Korean Chemical Society
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• 제13권6호
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• pp.665-669
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• 1992

We consider the problem of a random walker on a one-dimensional lattice (N sites) confronting a centrally-located deep trap (trapping probability, T=1) and N-1 adjacent sites at each of which there is a nonzero probability s(0 < s < 1) of the walker being trapped. Exact analytic expressions for < n > and the average number of steps required for trapping for arbitrary s are obtained for two types of finite boundary conditions (confining and reflecting) and for the infinite periodic chain. For the latter case of boundary condition, Montroll's exact result is recovered when s is set to zero.

• 한국초전도학회:학술대회논문집
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• 한국초전도학회 2007년도 High Temperature Superconductivity Vol.XVII
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• pp.39-39
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• 2007

• 대한수학회보
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• 제54권2호
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• pp.543-557
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• 2017

In this paper, we investigate the notion of q-pseudoconvexity to discuss and describe some geometric characterizations of q-pseudoconvex domains ${\Omega}{\subset}{\mathbb{C}}^n$. In particular, we establish that ${\Omega}$ is q-pseudoconvex, if and only if, for every boundary point, the Levi form of the boundary is semipositive on the intersection of the holomorphic tangent space to the boundary with any (n-q+1)-dimensional subspace $E{\subset}{\mathbb{C}}^n$. Furthermore, we prove that the Kiselman's minimum principal holds true for all q-pseudoconvex domains in ${\mathbb{C}}^p{\times}{\mathbb{C}}^n$ such that each slice is a convex tube in ${\mathbb{C}}^n$.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.81-105
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• 2003

This paper deals with the very interesting problem about the influence of piecewise smooth boundary conditions on the distribution of the eigenvalues of the negative Laplacian in R$^3$. The asymptotic expansion of the trace of the wave operator (equation omitted) for small ｜t｜ and i=√-1, where (equation omitted) are the eigenvalues of the negative Laplacian (equation omitted) in the (x$^1$, x$^2$, x$^3$)-space, is studied for an annular vibrating membrane $\Omega$ in R$^3$together with its smooth inner boundary surface S$_1$and its smooth outer boundary surface S$_2$. In the present paper, a finite number of Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components (equation omitted)(i = 1,...,m) of S$_1$and on the piecewise smooth components (equation omitted)(i = m +1,...,n) of S$_2$such that S$_1$= (equation omitted) and S$_2$= (equation omitted) are considered. The basic problem is to extract information on the geometry of the annular vibrating membrane $\Omega$ from complete knowledge of its eigenvalues by analysing the asymptotic expansions of the spectral function (equation omitted) for small ｜t｜.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.167-182
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• 2007

The existence of solutions of the following multi-point boundary value problem $${x^{(n)}(t)=f(t,\;x(t),\;x'(t),{\cdots}, x^{(n-2)}(t))+r(t),\;0 is studied. Sufficient conditions for the existence of at least one solution of BVP(*) are established. It is of interest that the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don't apply the Green's functions of the corresponding problem and the method to obtain a priori bounds of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.

• 호남수학학술지
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• 제19권1호
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• pp.81-86
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• 1997

The aim of this paper is to prove the boundary behavior between the Caratheodory and Kobayashi-Royden metrics in a strongly pseudoconvex bounded domain with $C^2$-boundary in $\mathbb{C}^n$ and to show that the converse does not holds. S. Venturini([Ven]) proved the corresponding result with distances in place of the infinitesimal metrics.