• 대한수학회지
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• 제31권3호
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• pp.401-416
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• 1994

We study the existence of an intermediate solution of nonlinear elliptic boundary value problems (BVP) of the form $$ (BVP) {\Delta u = f(x,u,\Delta u), in \Omega {Bu(x) = \phi(x), on \partial\Omega, $$ where $\Omega$ is a smooth bounded domain in $R^n, n \geq 1, and \partial\Omega \in C^{2,\alpha}, (0 < \alpha < 1), \Delta$ is the Laplacian operator, $\nabla u = (D_1u, D_2u, \cdots, D_nu)$ denotes the gradient of u and $$ Bu(x) = p(x)u(x) + q(x)\frac{d\nu}{du} (x), $$ where $\frac{d\nu}{du} denotes the outward normal derivative of u on $\partial\Omega$.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.753-762
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• 2010

Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K $\rightarrow$ K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K $\rightarrow$ K be a contraction mapping. Let {$\alpha_n$} and {$\beta_n$} be sequences in (0, 1) such that $\lim_{x{\rightarrow}0}{\alpha}_n=0$, (0.1) $\sum_{n=0}^{\infty}\;{\alpha}_n=+{\infty}$, (0.2) 0 < a ${\leq}\;{\beta}_n\;{\leq}$ b < 1 for all $n\;{\geq}\;0$. (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {$x_n$} given by {$x_0\;{\in}\;K$, $y_n\;=\;{\alpha}_{n}f(x_n)+(1-\alpha_n)x_n$, $n\;{\geq}\;0$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, $n\;{\geq}\;0$, (0.4) converges strongly to a point p $\in$ Fix(T} which satisfies the variational inequality

$\leq$ 0, z $\in$ Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.

• Bulletin of the Korean Chemical Society
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• 제7권4호
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• pp.257-262
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• 1986

Thixotropy is a time-dependent shear-thinning phenomenon. We derived a new thixotropic formula which is based on the generalized viscosity formula of Ree and Eyring, $f={\Sigma}\frac{X_i}{{\alpha}_i}sinh^{-1}$ () (Refer to the text concerning the notation.) The following is postulated: (1) thixotropy occurs when small flow units attached to a large flow unit separate from the latter under stress (2) elastic energy(${\omega}$) is stored on the large flow unit during the flow process, and (3) the stored energy contributes to decrease the activation energy for flow. A new thixotropic formula was derived by using these postulations, $f={\frac}{X_0{\beta}_0}{\alpha_0}{\dot{s}}+{\frac}{X_1{\beta}_1}{{\alpha}_1}{\dot{s}}+{\frac}{X_2}{{\alpha_x}}sinh^{-1}$[$({\beta}_0)_2$ exp $(-C_2{\dot{s}}^2/RT){\cdot}{\dot{s}}$] f is the shear stress, and s is the rate of shear. In case of concentrated solutions where the Newtonian flow units have little contribution to the viscosity of the system, the above equation becomes, $f=\frac{X_2}{\alpha_2}sinh^{-1}$[$({\beta}_0)_2$ exp $(-C_2{\dot{s}}^2/RT){\cdot}{\dot{s}}$]. In order to confirm these formulas, we applied to TiO2(anatase and rutile)-water, printing ink and mayonnaise systems. Good agreements between the experiment and theory were observed.

• 대한수학회보
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• 제37권3호
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• pp.461-475
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• 2000

In the present paper, we first give some examples of self-mappings which are asymptoticaly nonexpansive in the intermediate, not strictly hemicontractive, but satisfy the property (H). It is then shown that the modified Mann and Ishikawa iteration processes defined by $x_{n+1}=(1-\alpha_n)x_n+\alpha_nT^nx_n\ and\ x_{n+1}=(1-\alpha_n)x_n+\alpha_nT^n[(1-\beta_n)x_n+\beta_nT^nx_n]$,respectively, converges strongly to the unique fixed point of such a self-mapping in general Banach spaces.

• 대한수학회지
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• 제36권6호
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• pp.1061-1073
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• 1999

Let X be a real normed linear space. Let T : D(T) ⊂ X \longrightarrow X be a uniformly continuous and ∮-strongly quasi-accretive mapping. Let {${\alpha}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} , {${\beta}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} be two real sequences in [0, 1] satisfying the following conditions: (ⅰ) ${\alpha}$n \longrightarrow0, ${\beta}$n \longrightarrow0, as n \longrightarrow$\infty$ (ⅱ) {{{{ SUM from { { n}=0} to inf }}}} ${\alpha}$=$\infty$. Set Sx=x-Tx for all x $\in$D(T). Assume that {u}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} and {v}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} are two sequences in D(T) satisfying {{{{ SUM from { { n}=0} to inf }}}}∥un∥<$\infty$ and vn\longrightarrow0 as n\longrightarrow$\infty$. Suppose that, for any given x0$\in$X, the Ishikawa type iteration sequence {xn}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} with errors defined by (IS)1 xn+1=(1-${\alpha}$n)xn+${\alpha}$nSyn+un, yn=(1-${\beta}$n)x+${\beta}$nSxn+vn for all n=0, 1, 2 … is well-defined. we prove that {xn}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} converges strongly to the unique zero of T if and only if {Syn}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} is bounded. Several related results deal with iterative approximations of fixed points of ∮-hemicontractions by the ishikawa iteration with errors in a normed linear space. Certain conditions on the iterative parameters {${\alpha}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} , {${\beta}$n}{{{{ { }`_{n=0 } ^{$\infty$ } }}}} and t are also given which guarantee the strong convergence of the iteration processes.

• 한국안광학회지
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• 제1권2호
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• pp.7-11
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• 1996

동공반사에 의한 동공크기 변화는 luminance 량에 의해 결정되며, 동공크기에 따른 외부 광량의 투과량인 망막조도비 분포함수와 luminance 량에 따른 추체, 간체의 수용체 분포함수에 의존한다. Luminance 에 대한 동공크기 변화는 다음과 같은 수식적 모델로 표현 할 수 있다. $$y(x)={\alpha}+{\beta}\frac{1}{1+{e}{x}{p}(x-x_0)/{\theta}}$$ 여기서 ${\alpha}$는 luminance의 최대값에서 동공직경 크기이고, ${\beta}$는 동공직경 최대, 최소 편차, ${\theta}$는 개인차의 민감도를 나타내는 parameter이다. P.Moon등의 실험값과 비교해 보면 이모델식이 잘 일시함을 알 수 있다.

• 충청수학회지
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• 제26권2호
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• pp.269-273
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• 2013

We prove a characterization of the power function distribution by lower record values. We prove that $F(x)=(\frac{x}{a})^{\alpha}$ for all $x$, 0 < $x$ < $a$, ${\alpha}$ > 0 and $a$ > 0 if and only if $\frac{X_{L(n)}}{X_{L(m)}}$ and $X_{L(m)}$ are independent for $1{\leq}m$ < $n$.

• 대한수학회보
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• 제21권2호
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• pp.87-89
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• 1984

Let X be a Banach space, and let B(X) (resp. CB(X), K(X), CV(X)) denote the family of all nonvoid (resp. closed bounded, compact, convex) subsets of X. The Kuratowski measure of noncompactness is defined by the mapping .alpha.$_{k}$: B(X).rarw. $R_{+}$ with .alpha.$_{k}$(A) = inf {r>0 vertical bar A can be covered by a finite number of sets with diameter less than r}.an r}.

• 한국전기전자재료학회논문지
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• 제15권5호
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• pp.435-440
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• 2002

In this study, we have investigated photo-induced changes of optical energy gap( $E_{OP)}$ and photoluminescence (PL) in amorphous ($\alpha$-) S $e_{100-x}$G $e_{x}$ (x=5, 25 and 33) thin films prepared by conventional thermal evaporation method. In the $\alpha$-S $e_{100-x}$G $e_{x}$ thin film, the $E_{OP}$ is obtained by a linear extrapolation of the ($\alpha$hν)$^{\frac{1}{2}}$ versus hν plot to the energy axis using the optical absorption coefficient ($\alpha$) calculated from the extinction coefficient k measured in the wavelength range of 290~900nm. Although the values of $\Delta$ $E_{OP}$ are very different, all films exhibit photo-induced photo-darkening (PD) effect that is a red shift of $E_{OP}$ . In particular, $\Delta$ $E_{OP}$ in $\alpha$-S $e_{75}$ G $e_{25}$ thin film exhibits the largest value (i, e., $\Delta$ $E^{OP}$ ~40meV for $\alpha$-S $e_{95}$ G $e_{5}$ , $\Delta$ $E_{OP}$ ~200meV for $\alpha$-S $e_{75}$ G $e_{25}$ , $\Delta$ $E_{OP}$ ~130meV for $\alpha$-S $e_{67}$ G $e_{33}$ ). PL spectra in $\alpha$-SeGe by hν$_{HeCd}$ have no-Stokes shift (SS) and show a tendency dependent on both composition and illumination time. We explain the energy-induced phenomena such as the PD and thermal bleaching, the native charged-defect generation and the no-SS PL, etc..the PD and thermal bleaching, the native charged-defect generation and the no-SS PL, etc..tc..

• 한국전기전자재료학회논문지
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• 제15권8호
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• pp.708-712
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• 2002

The crystallization of amorphous $\alpha$-Fe$_2$O$_3$/$\alpha$-AI$_2$O$_3$(0001) thin films during thermal annealing in air has been studied using real-time synchrotron x-ray scattering. The well aligned (0.02$^{\circ}$/ FWHM) $\alpha$-Fe$_2$O$_3$and Fe$_3$O$_4$interfacial crystallites (50- -thick) coexist on the $\alpha$-AI$_2$O$_3$(0001) in the sputter-grown amorphous films at room temperature. The amorphous precursor is crystallized to the epitaxial $\alpha$-Fe$_2$O$_3$grains in three steps with annealing temperature; i ) the growth of the well aligned $\alpha$-Fe$_2$O$_3$interfacial crystallites, together with the transformation of the Fe$_3$O$_4$crystallites to the $\alpha$-Fe$_2$O$_3$ crystallites, ii ) the growth of the less aligned (3.08$^{\circ}$ FWHM)$\alpha$-Fe$_2$O$_3$grains on the well aligned grains (＞40$0^{\circ}C$), and iii) the nucleation of the other less aligned (1.39$^{\circ}$ FWHM) $\alpha$-Fe$_2$O$_3$grains directly on the $\alpha$-AI$_2$O$_3$substrate (＞$600^{\circ}C$). The effective thickness thinner than 230 may be very useful for enhancing the epitaxial quality of $\alpha$-Fe$_2$O$_3$/AI$_2$O$_3$(0001) thin films.