• Communications of the Korean Mathematical Society
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• 제26권2호
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• pp.197-205
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• 2011

Explicit sufficient conditions are established for the oscillation of the one order neutral differential equations with impulsive $(x(t)+{\sum\limits^n_{i=1}}c_ix(t-{\sigma}_i))'+px(t-{\tau})=0$, $t{\neq}t_{\kappa}$, ${\Delta}(x(t_{\kappa})+{\sum\limits^n_{i=1}}c_ix(t_{\kappa}-{\sigma}_i))+p_0x(t_{\kappa}-{\tau})=0$, $c_i{\geq}0$, $i=1,2,{\ldots}n$, $p{\tau}$>0, $p_0{\tau}$>0, ${\Delta}(x_{\kappa})=x(t^+_{\kappa})-x(t_{\kappa})$. Explicit sufficient and necessary condition are established when $c_i$ = 0, i = 1, 2, ${\ldots}$, n.

• Journal of the Korean Mathematical Society
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• 제47권6호
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• pp.1147-1165
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• 2010

In this paper we compare a torsion free sheaf F on $P^N$ and the free vector bundle $\oplus^n_{i=1}O_{P^N}(b_i)$ having same rank and splitting type. We show that the first one has always "less" global sections, while it has a higher second Chern class. In both cases bounds for the difference are found in terms of the maximal free subsheaves of F. As a consequence we obtain a direct, easy and more general proof of the "Horrocks' splitting criterion", also holding for torsion free sheaves, and lower bounds for the Chern classes $c_i$(F(t)) of twists of F, only depending on some numerical invariants of F. Especially, we prove for rank n torsion free sheaves on $P^N$, whose splitting type has no gap (i.e., $b_i{\geq}b_{i+1}{\geq}b_i-1$ 1 for every i = 1,$\ldots$,n-1), the following formula for the discriminant: $$\Delta(F):=2_{nc_2}-(n-1)c^2_1\geq-\frac{1}{12}n^2(n^2-1)$$. Finally in the case of rank n reflexive sheaves we obtain polynomial upper bounds for the absolute value of the higher Chern classes $c_3$(F(t)),$\ldots$,$c_n$(F(t)) for the dimension of the cohomology modules $H^iF(t)$ and for the Castelnuovo-Mumford regularity of F; these polynomial bounds only depend only on $c_1(F)$, $c_2(F)$, the splitting type of F and t.

• Honam Mathematical Journal
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• 제33권2호
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• pp.153-161
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• 2011

Greg([Greg]) considered that $$N_k= \sum\limits_{i=1}^k(-1)^{i+1}P_{i,k}(p)N_1^i$$ where the $P_{i,k}$'s were polynomials with positive integer coefficients. In this paper, we will give the equations for $\sum\limits{P_{i,k}$ modulo 3. Using this, if we send a information for elliptic curve to sender, we can make a new checksum method for Manchester coding in IEEE 802.3 or IEEE 802.4.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.1-37
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• 2004

We consider the following system of discrete equations $u_i(\kappa)\;=\;{\Sigma{N}{\ell=0}}g_i({\kappa},\;{\ell})f_i(\ell,\;u_1(\ell),\;u_2(\ell),\;{\cdots}\;,\;u_n(\ell)),\;{\kappa}\;{\in}\;\{0,\;1,\;{\cdots}\;,\;T\},\;1\;{\leq}\;i\;{\leq}\;n\;where\;T\;{\geq}\;N\;>\;0,\;1\;{\leq}i\;{\leq}\;n$. Existence criteria for single, double and multiple constant-sign solutions of the system are established. To illustrate the generality of the results obtained, we include applications to several well known boundary value problems. The above system is also extended to that on $\{0,\;1,\;{\cdots}\;\}\;u_i(\kappa)\;=\;{\Sigma{\infty}{\ell=0}}g_i({\kappa},\;{\ell})f_i(\ell,\;u_1(\ell),\;u_2(\ell),\;\cdots\;,\;u_n(\ell)),\;{\kappa}\;{\in}\;\{0,\;1,\;{\cdots}\;\},\;1\;{\leq}\;i\;{\leq}\;n$ for which the existence of constant-sign solutions is investigated.

• Proceedings of the Korean Vacuum Society Conference
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• 한국진공학회 2012년도 제42회 동계 정기 학술대회 초록집
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• pp.426-426
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• 2012

본 연구에서는 GaAs p-i-n 접합 구조에 InAs 양자점을 삽입한 양자점 태양전지(Quantum Dot Solar Cell; QDSC)의 내부 전기장(internal electric field)을 조사하기 위하여 Photoreflectance (PR) 방법을 이용하였다. QDSC 구조는 GaAs p-i-n 구조의 공핍층 내에 8주기의 InAs 양자점 층을 삽입하였으며 각 양자점 층은 40 nm 두께의 i-GaAs로 분리하였다. InAs/GaAs QDSC는 분자선박막 성장장치(molecular beam epitaxy; MBE)를 이용하여 성장하였다. 이 때 양자점의 형성은 InAs 2.0 ML(monolayer)를 기판온도 $470^{\circ}C$에서 증착하였다. QDSC 구조에서 여기광원의 세기에 따른 전기장의 변화를 조사하였다. 아울러 양자점 층 사이의 i-GaAs 층 내에 6.0 nm의 AlGaAs 퍼텐셜 장벽(potential barrier)을 삽입하여 퍼텐셜 장벽 유무에 따른 전기장 변화를 조사하였다. PR 측정에서 여기광원으로는 633 nm의 He-Ne 레이저를 이용하였으며 여기광의 세기는 $2mW/cm^2$에서 $90mW/cm^2$까지 변화를 주어 여기광세기 의존성실험을 수행하였다. 여기광의 세기가 증가할수록 photovoltaic effect에 의한 내부 전기장의 변화를 관측할 수 있었다. PR 결과로부터 p-i-n 구조의 p-i 영역과 i-n 접합 계면의 junction field를 검출하였다. p-i-n의 i-영역에 양자점을 삽입한 경우 PR 신호에서 Franz-Keldysh oscillation (FKO)의 주파수가 p-i-n 구조와 비교하여 변조됨을 관측하였다. 이러한 FKO 주파수성분은 fast Fourier transform (FFT)을 이용하여 검출하였다. FKO의 주파수 성분들은 고전기장하에서 electron-heavyhole (e-hh)과 electron-lighthole (e-lh) 전이에 의해 나타나는 성분으로 확인되었다.

• Journal of the Korean Mathematical Society
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• 제47권1호
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• pp.135-163
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• 2010

Motivated by [Science in China (Ser. A Mathematics) 36 (2006), no. 7, 721?732], this article deals with the following discrete type BVP $\LARGE\left\{{{\;{\Delta}[{\phi}({\Delta}x(n))]\;+\;f(n,\;x(n\;+\;1),{\Delta}x(n),{\Delta}x(n + 1))\;=\;0,\;n\;{\in}\;[0,N],}}\\{\;{x(0)-{\sum}^m_{i=1}{\alpha}_ix(n_i) = A,}}\\{\;{x(N+2)-\;{\sum}^m_{i=1}{\beta}_ix(n_i)\;=\;B.}}\right.$ The sufficient conditions to guarantee the existence of at least three positive solutions of the above multi-point boundary value problem are established by using a new fixed point theorem obtained in [5]. An example is presented to illustrate the main result. It is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multifixed-point theorems can be extended to treat nonhomogeneous BVPs. The emphasis is put on the nonlinear term f involved with the first order delta operator ${\Delta}$x(n).

• Korean Journal of Mathematics
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• 제21권4호
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• pp.429-437
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• 2013

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be independent and identically distributed random variables having common exponential density with unknown mean ${\mu}$. In the sequential confidence interval estimation for the exponential hazard rate ${\theta}=1/{\mu}$, when the loss function is strictly convex, the following stopping rule is proposed with the half length d of prescribed confidence interval $I_n$ for the parameter ${\theta}$; ${\tau}$ = smallest integer n such that $n{\geq}z^2_{{\alpha}/2}\hat{\theta}^2/d^2+2$, where $\hat{\theta}=(n-1)\bar{X}{_n}^{-1}/n$ is the minimum risk estimator for ${\theta}$ and $z_{{\alpha}/2}$ is defined by $P({\mid}Z{\mid}{\leq}{\alpha}/2)=1-{\alpha}({\alpha}{\in}(0,1))$ Z ~ N(0, 1). For the confidence intervals $I_n$ which is required to satisfy $P({\theta}{\in}I_n){\geq}1-{\alpha}$. These estimated intervals $I_{\tau}$ have the asymptotic consistency of the sequential procedure; $$\lim_{d{\rightarrow}0}P({\theta}{\in}I_{\tau})=1-{\alpha}$$, where ${\alpha}{\in}(0,1)$ is given.

• Korean Journal of Materials Research
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• 제9권12호
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• pp.1155-1159
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• 1999

Thin film solar cells on a glass/$SnO_2$ substrate with p-SiC/i-Si/n-Si heterojunction structures were fabricated using a plasma-enhanced chemical-vapor deposition system. The photovoltaic properties of the solar cells were examined with varying the gas phase composition, x=$CH_4/\;(SiH_4+CH_4)$, during the deposition of the p-SiC layer. In the range of x=0~0.4, the efficiency of solar cell increased because of the increased band gap of the p-SiC window layer. Further increase in the gas phase composition, however, led to a decrease in the cell efficiency probably due to in the increased composition mismatch at the p-SiC/i-Si layers. As a result, the efficiency of a glass/$SnO_2$/p-SiC/i-SiC/i-Si/n-Si/Ag thin film solar cell with $1cm^2$ area was 8.6% ($V_{oc}$=0.85V, $J_{sc}$=16.42mA/$cm^2$, FF=0.615) under 100mW/$cm^2$ light intensity.

• Journal of Sensor Science and Technology
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• 제1권1호
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• pp.5-12
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• 1992

We have fabricated a-Si:H multilayer for contact-type linear image sensor by means of RF glow discharge decomposition method. The ITO/i-a-Si:H/Al structure has relatively high dark current due to indium diffusion and carrier injection from both electrodes, resulting in low photocurrent to dark current. To suppress the dark current and to enhance interface electric field between ITO and i-a-Si:H film we have fabricated ITO/insulator/i-a-S:H/p-a-S:H/Al multilayer film with blocking structure. The photocurrent of ITO/$SiO_{2}(300{\AA})$/i-a-Si:H/p-a-Si:H($1500{\AA}$)/Al multilayer sensor with 5V bias voltage became saturated at about 20nA under $20{\mu}W/cm^{2}$ light intensity, while the dark current was less than 0.1nA. To increase the light generation efficiency we have adopted ITO/$SiO_{x}N_{y}(300{\AA})$/i-a-Si:H/p-a-Si:H($1500{\AA}$)/Al structure, showing photocurrent of 30nA and dark current of 0.08nA with 5V bias voltage. Also the spectral photosensitivity of the multilayer was enhanced for short wavelength visible region of 560nm, compared with that of the a-Si:H monolayer of 630nm. And its photoresponse time was about 0.3msec with the film homogeneity of 5% deviation.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.55-60
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• 2014

In this paper, we will obtain Marcinkiewicz's type limit laws for fuzzy random sets as follows : Let {$X_n{\mid}n{\geq}1$} be a sequence of independent identically distributed fuzzy random sets and $E{\parallel}X_i{\parallel}^r_{{\rho_p}}$ < ${\infty}$ with $1{\leq}r{\leq}2$. Then the following are equivalent: $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ a.s. in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in probability in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_1$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_r$ where $S_n={\Sigma}^n_{i=1}\;X_i$.