• Journal of applied mathematics & informatics
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• v.31 no.3_4
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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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• v.27 no.5_6
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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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• v.28 no.3_4
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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 $L^*$.

• Food Science and Preservation
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• v.23 no.6
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• pp.848-858
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• 2016

This study was conducted to determine the $F_0$-values of a retort machine at different locations and to evaluate the effects of these $F_0$-values on various quality characteristics of retorted Samgyetang samples. Samples were divided into three groups based on $F_0$-values-T1, 10~20; T2, 20~30; T3, >30. Mineral content in Samgyetang broth and breast meat mostly increased with increasing $F_0$-values. In general, the free amino acid values, hardness, and springiness, except for bone springiness, of Samgyetang decreased significantly at higher $F_0$-values. Protein content of meat and broth of the treated samples were significantly lower than that of the control. An increase in the digestion rate of meat and porridge, as well as the turbidity of the broth was observed in most of the treated samples with increasing $F_0$-values. With increasing $F_0$-values, the $L^*$ and $b^*$ values of meat and the $b^*$ values of broth tended to increase, while the $a^*$ value of broth increased significantly. Electronic nose analysis revealed different flavor patterns for samples treated at different $F_0$-values. For sensory traits, samples treated with higher $F_0$-values tended to receive lower evaluations. Particularly, the color and texture of T3 samples were lower than those of T1 and T2 samples. In conclusion, to improve the quality of Samgyetang, the efficiency and optimization of retort machines as well as the standardization of sterilization techniques are needed.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.2
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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.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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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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• v.26 no.1
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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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• v.28 no.2
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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.

• Journal of the Korean Vacuum Society
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• v.4 no.2
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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.