• JSTS:Journal of Semiconductor Technology and Science
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• v.13 no.3
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• pp.224-236
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• 2013

This work presents a comparative study of four Double Gate tunnel FET (DG-TFET) architectures: conventional p-i-n DG-TFET, p-n-p-n DG-TFET, a gate dielectric engineered Heterogate (HG) p-i-n DG-TFET and a new device architecture with the merits of both Hetero Gate and p-n-p-n, i.e. HG p-n-p-n DG-TFET. It has been shown that, the problem of high gate capacitance along with low ON current for a p-i-n TFET, which severely hampers the circuit performance of TFET can be overcome by using a p-n-p-n TFET with a dielectric engineered Hetero-gate architecture (i.e. HG p-n-p-n). P-n-p-n architecture improves the ON current and the heterogeneous dielectric helps in reducing the gate capacitance and suppressing the ambipolar behavior. Moreover, the HG architecture does not degrade the output characteristics, unlike the gate drain underlap architecture, and effectively reduces the gate capacitance.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.549-560
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• 1997

For positive integers $n_i \geq 2, i = 1, 2, 3, 4$, such that $\Sigma \frac{n_i}{1} < 2$, there exists a quadrilateral $P = P_1 P_2 P_3 P_4$ in the hyperbolic plane $H^2$ with the interior angle $\frac{n_i}{\pi}$ at $P_i$. Let $\Gamma \subset Isom(H^2)$ be the (discrete) group generated by reflections in each side of $P$. Then the quotient space $H^2/\gamma$ is a differentiable orbifold of type $(^* n_1 n_2 n_3 n_4)$. It will be shown that the deformation space of $Rp^2$-structures on this orbifold can be mapped continuously and bijectively onto the cell of dimension 4 - \left$\mid$ {i$\mid$n_i = 2} \right$\mid$$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.1007-1025
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• 2015

Let $\mathbb{N}_0$ be the set of non-negative integers, and let P(n, l) denote the set of all weak compositions of n with l parts, i.e., $P(n,l)=\{(x_1,x_2,{\cdots},x_l){\in}\mathbb{N}^l_0\;:\;x_1+x_2+{\cdots}+x_l=n\}$. For any element $u=(u_1,u_2,{\cdots},u_l){\in}P(n,l)$, denote its ith-coordinate by u(i), i.e., $u(i)=u_i$. A family $A{\subseteq}P(n,l)$ is said to be t-intersecting if ${\mid}\{i:u(i)=v(i)\}{\mid}{\geq}t$ for all $u,v{\epsilon}A$. A family $A{\subseteq}P(n,l)$ is said to be trivially t-intersecting if there is a t-set T of $[l]=\{1,2,{\cdots},l\}$ and elements $y_s{\in}\mathbb{N}_0(s{\in}T)$ such that $A=\{u{\in}P(n,l):u(j)=yj\;for\;all\;j{\in}T\}$. We prove that given any positive integers l, t with $l{\geq}2t+3$, there exists a constant $n_0(l,t)$ depending only on l and t, such that for all $n{\geq}n_0(l,t)$, if $A{\subseteq}P(n,l)$ is non-trivially t-intersecting, then $${\mid}A{\mid}{\leq}(^{n+l-t-l}_{l-t-1})-(^{n-1}_{l-t-1})+t$$. Moreover, equality holds if and only if there is a t-set T of [l] such that $$A=\bigcup_{s{\in}[l]{\backslash}T}\;A_s{\cup}\{q_i:i{\in}T\}$$, where $$A_s=\{u{\in}P(n,l):u(j)=0\;for\;all\;j{\in}T\;and\;u(s)=0\}$$ and $$q_i{\in}P(n,l)\;with\;q_i(j)=0\;fo\;all\;j{\in}[l]{\backslash}\{i\}\;and\;q_i(i)=n$$.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.513-519
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• 2008

Let (R, m) be a Noetherian local ring with maximal ideal m, E := $E_R$(R/m) and let I be an ideal of R. Let M and N be finitely generated R-modules. It is shown that $H^n_I(M,(H^n_I(N)^{\vee})){\cong}(M{\otimes}_RN)^{\vee}$ where grade(I, N) = n = $cd_i$(I, N). We also show that for n = grade(I, R), one has $End_R(H^n_I(P,R)^{\vee}){\cong}Ext^n_R(H^n_I(P,R),P^*)^{\vee}$.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.573-580
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• 2006

In this paper, we obtain sufficient conditions for the oscillation of every solution of the difference equation $$x_{n+1}-x_n+\sum_{i=1}^{m}p_ix_{n-k_i}+qx_{n-z}=0,\;n=0,1,2,{\cdots},$$ where $p_i{\in}\mathbb{R}$, $k_i{\in}\mathbb{Z}$ for $i=1,2,{\cdots},m$ and $z{\in}\{-1,0\}$. Furthermore, we obtain sufficient conditions for the oscillation of all solutions of the equation $${\Delta}^rx_n+\sum_{i=1}^{m}p_ix_{n-k_i}=0,\;n=0,1,2,{\cdots},$$ where $p_i{\in}\mathbb{R}$, $k_i{\in}\mathbb{Z}$ for $i=1,2,{\cdots},m$. The results are given terms of the $p_i$ and the $k_i$ for each $i=1,2,{\cdots},m$.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.977-986
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• 2010

Let $X_1$, $X_2$, $\cdots$ be identically distributed negatively associated random variables with $EX_1\;=\;0$ and $E|X_1|^3$ < $\infty$. In this paper we prove $lim_{{\epsilon\downarrow}0}\;\frac{1}{-\log\;\epsilon}\sum\limits_{n=1}^\infty\frac{1}{n^2}ES_n^2I\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;2$ and $lim_{\epsilon\downarrow0}\;\epsilon^{2-p}\sum\limits_{n=1}^\infty\frac{1}{n^p}$ $E|S_n|^pI\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;\frac{2}{2-p}$ for 0 < p < 2, where $S_n\;=\;\sum\limits_{i=1}^{n}X_i$ and 0 < $\sigma^2\;=\;EX_1^2\;+\;\sum\limits_{i=2}^{\infty}Cov(X_1,\;X_i)$ < $\infty$. We consider some results of i.i.d. random variables obtained by Liu and Lin(2006) under negative association assumption.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2009.11a
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• pp.37-37
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• 2009

박막태양전지는 p-i-n substrate형과 n-i-p substrate형 두가지구조로 제조된다. 각 layer에서 activation energy와 band gap energy를 ASA simulator를 통해 조절해보았다. Simulation결과 p-i-n substrate형에서 p-layer와 n-i-p substrate형 n-layer에서 동일하게 activation energy 0.2eV, band gap energy 1.80eV에 최고효율 나왔고 각각 10.07%, 10.17%의 최고효율을 구할 수 있었다. 최적화 과정을 통하여 같은 조건에서 p-i-n substrate형 보다 n-i-p substrate형이 보다 높은 효율을 낸다는 것을 알 수 있었으며 본 연구를 통해 각 구조의 차이를 알 수 있었고 이는 높은 효율의 박막태양전지 설계에 도움이 될 것 이다.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.507-513
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• 2010

Let {$X_i,-{\infty}$ < 1 < $\infty$} be a doubly infinite sequence of identically distributed and negatively associated random variables with mean zero and finite variance and {$a_i,\;-{\infty}$ < i < ${\infty}$} be an absolutely summable sequence of real numbers. Define a moving average process as $Y_n={\sum}_{i=-\infty}^{\infty}a_{i+n}X_i$, n $\geq$ 1 and $S_n=Y_1+{\cdots}+Y_n$. In this paper we prove that E|$X_1$|$^rh$($|X_1|^p$) < $\infty$ implies ${\sum}_{n=1}^{\infty}n^{r/p-2-q/p}h(n)E{max_{1{\leq}k{\leq}n}|S_k|-{\epsilon}n^{1/p}}{_+^q}<{\infty}$ and ${\sum}_{n=1}^{\infty}n^{r/p-2}h(n)E{sup_{k{\leq}n}|k^{-1/p}S_k|-{\epsilon}}{_+^q}<{\infty}$ for all ${\epsilon}$ > 0 and all q > 0, where h(x) > 0 (x > 0) is a slowly varying function, 1 ${\leq}$ p < 2 and r > 1 + p/2.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.245-250
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• 2002

Consider the Convex Polygon Pm={Al , A2, ‥‥, Am} With Vertex points A$\_$i/ = (a$\_$i/, b$\_$i/),i : 1,‥‥, m, interior P$\^$0/$\_$m/, and length of perimeter denoted by L(P$\_$m/). Let R$\_$n/ = {B$_1$,B$_2$,‥‥,B$\_$n/), where B$\_$i/=(x$\_$i/,y$\_$I/), i =1,‥‥, n, denote a regular polygon with n sides of equal length and equal interior angle. Kaiser[4] used the regular polygon R$\_$n/ to approximate P$\_$m/, and the problem examined in his work is to position R$\_$n/ with respect to P$\_$m/ to minimize the area of the symmetric difference between the two figures. In this paper we give the quality of a approximating regular polygon R$\_$n/ to approximate P$\_$m/.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.157-163
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• 1997

Based on a n-regular polygon $P_n$, we show that $r_n = 1/(2 \sum^{[(n-4)/4]+1}_{j=0}{cos 2j\pi/n)}$ is the ratio of contractions $f_i(1 \leq i \leq n)$ at each vertex of $P_n$ yielding a symmetric gasket $G_n$ associated with the just-touching I.F.S. $g_n = {f_i $\mid$ 1 \leq i \leq n}$. Moreover we see that for any odd n, the ratio $r_n$ is still valid for just-touching I.F.S $H_n = {f_i \circ R $\mid$ 1 \leq i \leq n}$ yielding another symmetric gasket $H_n$ where R is the $\pi/n$-rotation with respect to the center of $P_n$.