• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.565-575
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• 2013

Let H be a real Hilbert space and let T : H ${\rightarrow}$ H be a Lipschitz pseudocontractive mapping. We introduce a modified Ishikawa iterative algorithm and prove that if $F(T)=\{x{\in}H:Tx=x\}{\neq}{\emptyset}$, then our proposed iterative algorithm converges strongly to a fixed point of T. No compactness assumption is imposed on T and no further requirement is imposed on F(T).

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1165-1176
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• 2009

This paper is concerned with the interval oscillation of the second order nonlinear ordinary differential equation (r(t)|y'(t)|$^{{\alpha}-1}$ y'(t))'+p(t)|y'(t)|$^{{\alpha}-1}$ y'(t)+q(t)f(y(t))g(y'(t))=0. By constructing ageneralized Riccati transformation and using the method of averaging techniques, we establish some interval oscillation criteria when f(y) is not differetiable but satisfies the condition $\frac{f(y)}{|y|^{{\alpha}-1}y}$ ${\geq}{\mu}_0$ > 0 for $y{\neq}0$.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.1003-1008
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• 2010

In allelic model $X\;=\;(x_1,\;x_2,\;\cdots,\;x_d)$, $$M_f(t)\;=\;f(p(t))\;-\;\int_0^t\;Lf(p(t))ds$$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we define $T_tf\;=\;E_{p_0}^{p^*}\;[f((P(t))]$ for $t\;{\geq}\;0$ for using a new diffusion operator $L^*$ and we show the diffusion relations between $T_t$ and diffusion operator $L^*$.

• 한국식품저장유통학회지
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• 제23권6호
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• pp.848-858
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• 2016

국내 삼계탕 제조업체에서의 스팀식 레토르트기내 위치별 $F_0$ 분포를 조사하고 이에 따라 시료를 3가지 $F_0$값(10~20, 20~30, 및 >30) 수준으로 구분하여, 처리구별 품질 차이를 확인하였다. $F_0$값의 수준이 높아질수록 삼계탕 가슴부위육의 육수에서의 무기질 함량, 육의 $L^*$과 $b^*$ 값, 죽과 육에서의 소화율 및 육수의 탁도는 증가하는 경향을 보였고, 육에서의 유리 아미노산 함량과 가슴살과 뼈의 경도는 오히려 유의적으로 낮아지는 경향을 보였다. 전자코로 측정된 육수와 가슴살의 향기 패턴은 시료에 따라 큰 차이를 나타냈다. 관능학적 평가 결과 높은 $F_0$값으로 처리할수록 색, 이취, 조직감 및 향미 등 모든 지표 값이 낮아지는 경향이 확인되었는데, 특히 T3 시료의 색과 조직감은 T1과 T2시료에서보다 확실히 열등하게 평가되었다. 따라서 삼계탕의 품질 열화를 줄이기 위해서는 가능한 한 최소한의 $F_0$값 처리가 요구되며, 이를 위해서는 레토르트기의 우수한 성능과 효율성이 보장되고 이와 관련한 각 공장에 적합한 살균기술의 표준화가 필요할 것으로 사료된다.

• 대한수학회지
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• 제44권4호
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• pp.1025-1050
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• 2007

Let $X_k(x)=({\int}^T_o{\alpha}_1(s)dx(s),...,{\int}^T_o{\alpha}_k(s)dx(s))\;and\;X_{\tau}(x)=(x(t_1),...,x(t_k))$ on the classical Wiener space, where ${{\alpha}_1,...,{\alpha}_k}$ is an orthonormal subset of $L_2$ [0, T] and ${\tau}:0 is a partition of [0, T]. In this paper, we establish a change of scale formula for conditional Wiener integrals $E[G_{\gamma}|X_k]$ of functions on classical Wiener space having the form $$G_{\gamma}(x)=F(x){\Psi}({\int}^T_ov_1(s)dx(s),...,{\int}^T_o\;v_{\gamma}(s)dx(s))$$, for $F{\in}S\;and\;{\Psi}={\psi}+{\phi}({\psi}{\in}L_p(\mathbb{R}^{\gamma}),\;{\phi}{\in}\hat{M}(\mathbb{R}^{\gamma}))$, which need not be bounded or continuous. Here S is a Banach algebra on classical Wiener space and $\hat{M}(\mathbb{R}^{\gamma})$ is the space of Fourier transforms of measures of bounded variation over $\mathbb{R}^{\gamma}$. As results of the formula, we derive a change of scale formula for the conditional Wiener integrals $E[G_{\gamma}|X_{\tau}]\;and\;E[F|X_{\tau}]$. Finally, we show that the analytic Feynman integral of F can be expressed as a limit of a change of scale transformation of the conditional Wiener integral of F using an inversion formula which changes the conditional Wiener integral of F to an ordinary Wiener integral of F, and then we obtain another type of change of scale formula for Wiener integrals of F.

• 전자공학회논문지A
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• 제32A권2호
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• pp.57-65
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• 1995

The effects of device geometry and layout on high speed performance such as current gain outoff frequency(f$_{T}$) and maximum oscillation frequency(f$_{max}$) are of very improtant for the scaling-down of geterojunction bipolar transistors(HBT$_{s}$). In this paper AlGaAs/GaAs HBTs are fabricated by MBE epitaxial growth and conventional mesa process, and the experimental data of emitter-base geometru dependency of HBT performance are presented in order to provide the quantitative information for optimum device structure design. It is shown that f$_{T}$ and f$_{max}$ are inversely proportional to the emiter stripe width, while the low emitter perimeter/area ratio is better to f$_{T}$ and worse ot f$_{max}$. It is also demonstrated the f$_{T}$ and f$_{max}$ are highly improved by the emitter-base spacing reduction resulting in less parsitic effects. As the result f$_{T}$ of 42GHz and f$_{max}$ of 23GHz are obtained for fabricated HBT with emitter area of 3${\times}20^{\mu}m^{2}$ and E-B spacing of 0.2$\mu$m.m.m.

• 대한수학회논문집
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• 제34권1호
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• pp.185-202
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• 2019

In this paper, we investigate many types of stability, like (uniform stability, exponential stability and h-stability) of the first order dynamic equations of the form $$\{u^{\Delta}(t)=Au(t)+f(t),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ and $$\{u^{\Delta}(t)=Au(t)+f(t,u),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ in terms of the stability of the homogeneous equation $$\{u^{\Delta}(t)=Au(t),\;\;t{\in}{\mathbb{T}},\;t>t_0\\u(t_0)=x{\in}D(A),$$ where f is rd-continuous in $t{\in}{\mathbb{T}}$ and with values in a Banach space X, with f(t, 0) = 0, and A is the generator of a $C_0$-semigroup $\{T(t):t{\in}{\mathbb{T}}\}{\subset}L(X)$, the space of all bounded linear operators from X into itself. Here D(A) is the domain of A and ${\mathbb{T}}{\subseteq}{\mathbb{R}}^{{\geq}0}$ is a time scale which is an additive semigroup with property that $a-b{\in}{\mathbb{T}}$ for any $a,b{\in}{\mathbb{T}}$ such that a > b. Finally, we give illustrative examples.

• Korean Journal of Mathematics
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• 제26권1호
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• pp.75-85
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• 2018

In this paper, we study nonconstant warping functions on an Einstein warped product manifold $M=B{\times}_{f^2}F$ with a warped product metric $g=g_B+f(t)^2g_F$. And we consider a 2-dimensional base manifold B with a metric $g_B=dt^2+(f^{\prime}(t))^2du^2$. As a result, we prove the following: if M is an Einstein warped product manifold with a 2-dimensional base, then there exist generally nonconstant warping functions f(t).

• Kyungpook Mathematical Journal
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• 제28권2호
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• pp.129-139
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• 1988

Let $T^{\alpha}_{\lambda}$(p, A, B) denote the class of functions $$f(z)=z^p-{\sum\limits^{\infty}_{k=1}}{\mid}a_{p+k}{\mid}z^{p+k}$$ which are regular and p valent in the unit disc U = {z: |z| <1} and satisfying the condition $\left|{\frac{{e^{ia}}\{{\frac{f^{\prime}(z)}{z^{p-1}}-p}\}}{(A-B){\lambda}p{\cos}{\alpha}-Be^{i{\alpha}}\{\frac{f^{\prime}(z)}{z^{p-1}}-p\}}}\right|$<1, $z{\in}U$, where 0<${\lambda}{\leq}1$, $-\frac{\pi}{2}$<${\alpha}$<$\frac{\pi}{2}$, $-1{\leq}A$<$B{\leq}1$, 0<$B{\leq}1$ and $p{\in}N=\{1,2,3,{\cdots}\}$. In this paper, we obtain sharp results concerning coefficient estimates, distortion theorem and radius of convexity for the class $T^{\alpha}_{\lambda}$(p, A, B). It is further shown that the class $T^{\alpha}_{\lambda}$(p, A, B) is closed under "arithmetic mean" and "convex linear combinations". We also obtain class preserving integral operators of the form $F(z)=\frac{p+c}{z^c}{\int^z_0t^{c-1}}f(t)dt$, c>-p, for the class $T^{\alpha}_{\lambda}$(p, A, B). Conversely when $F(z){\in}T^{\alpha}_{\lambda}$(p, A, B), radius of p valence of f(z) has also determined.

• 한국진공학회지
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• 제4권2호
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• pp.119-123
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• 1995

Bridgman 방법으로 성장한 InSe: Co 단결정의 근적외 영역에서의 광흡수 특성을 상온에서 조사하였다. 1350, 1530, 1710nm 파장영역에서 Td 대칭을 갖는 Co2+ 이온의 4A2(4F)$\longrightarrow$4T1(4F)전이에 대응되는 3개의 흡수 peak를 관측하였다. 이 미세구조는 스핀-궤도 결합효과에 의하여 분리된 Co2+ 이온의 4T1(4F) 준위의 $\Gamma$6, $\Gamma$8, $\Gamma$7+$\Gamma$8 준위와 바닥상태 4A2(4F)의 $\Gamma$8 준위 사이의 전자전이에 기인하며, 결정장이론에 의하여 잘 설명되었다.