• 한국재료학회:학술대회논문집
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• 한국재료학회 1996년도 재료학회 춘계학술발표회
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• pp.78-78
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• 1996

• 대한수학회보
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• 제49권4호
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• pp.799-813
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• 2012

In this paper, we first show that the iteration {$x_n$} defined by $x_{n+1}=P((1-{\alpha}_n)x_n +{\alpha}_nTP[{\beta}_nTx_n+(1-{\beta}_n)x_n])$ converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {$x_n$} defined by $x_{n+1}={\alpha}_nSx_n+{\beta}_nT[{\alpha}^{\prime}_nSx_n+{\beta}^{\prime}_nTx_n+{\gamma}^{\prime}_n{\upsilon}_n]+{\gamma}_nu_n$ converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].

• 대한수학회보
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• 제57권3호
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• pp.649-660
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• 2020

This paper proves a new regularity criterion for solutions to the Cauchy problem of the 3D Boussinesq equations via one directional derivative of the horizontal component of the velocity field (i.e., (∂_iu₁; ∂_ju₂; 0) where i, j ∈ {1, 2, 3}) in the framework of the anisotropic Lebesgue spaces. More precisely, for 0 < T < ∞, if $$\large{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_o}^T}({\HUGE\left\|{\small{\parallel}{\partial}_iu_1(t){\parallel}_{L^{\alpha}_{x_i}}}\right\|}{\small^{\gamma}_{L^{\beta}_{x_{\hat{i}}x_{\bar{i}}}}+}{\HUGE\left\|{\small{\parallel}{\partial}_iu_2(t){\parallel}_{L^{\alpha}_{x_j}}}\right\|}{\small^{\gamma}_{L^{\beta}_{x_{\hat{i}}x_{\bar{i}}}}})dt<{{\infty}},$$ where ${\frac{2}{{\gamma}}}+{\frac{1}{{\alpha}}}+{\frac{2}{{\beta}}}=m{\in}[1,{\frac{3}{2}})$ and ${\frac{3}{m}}{\leq}{\alpha}{\leq}{\beta}<{\frac{1}{m-1}}$, then the corresponding solution (u, θ) to the 3D Boussinesq equations is regular on [0, T]. Here, (i, ${\hat{i}}$, ${\tilde{i}}$) and (j, ${\hat{j}}$, ${\tilde{j}}$) belong to the permutation group on the set 𝕊₃ := {1, 2, 3}. This result reveals that the horizontal component of the velocity field plays a dominant role in regularity theory of the Boussinesq equations.

• 대한수학회지
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• 제47권5호
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• pp.985-1000
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• 2010

Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type -x"(t) = f(t, y(t)), t $\in$ (0, 1), -y"(t) = g(t, x(t)), t $\in$ (0, 1), x(0) = y(0) = 0, x(1) = ${\alpha}x(\eta)$, y(1) = ${\alpha}y(\eta)$, are obtained. The nonlinearities f, g : (0,1) $\times$ (0, $\infty$ ) $\rightarrow$ (0, $\infty$) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. The parameters $\eta$, $\alpha$, satisfy ${\eta}\;{\in}\;$ (0,1), 0 < $\alpha$ < $1/{\eta}$. An example is provided to illustrate the results.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.535-539
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• 2007

Given operators X and Y acting on a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that AX=Y. In this article, we show the following: Let $Alg\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let $X=(x_{ij})\;and\;Y=(y_{ij})$ be operators in $\mathcal{H}$. Then the following are equivalent: (1) There exists a normal operator $A=(a_{ij})\;in\;Alg\mathcal{L}$ such that AX=Y. (2) There is a bounded sequence $\{\alpha_n\}\;in\;\mathbb{C}$ such that $y_{ij}=\alpha_jx_{ij}\;for\;i,\;j\;{\in}\;\mathbb{N}$. Given vectors x and y in a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that Ax=y. We show the following: Let $Alg\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let $x=(x_i)\;and\;y=(y_i)$ be vectors in $\mathcal{H}$. Then the following are equivalent: (1) There exists a normal operator $A=(a_{ij})\;in\;Alg\mathcal{L}$ such that Ax=y. (2) There is a bounded sequence $\{\alpha_n\}$ in $\mathbb{C}$ such that $y_i=\alpha_ix_i\;for\;i{\in}\mathbb{N}$.

• E2M - 전기 전자와 첨단 소재
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• 제4권3호
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• pp.249-258
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• 1991

He-Ne레이저(.lambda.=0.6328[.mu.m])를 광원으로 사용하는 y-cut LiNbO$_{3}$기판의 광 도파로 형성 과정을 빔 전송방식 메카니즘을 이용하여 광 도파로에서 광파의 전계 변화 및 전계 분포에 대하여 시뮬레이션 하였다. 그리고 Xl(55[.mu.m])* Zl(5000[.mu.m])인 LiNbO$_{3}$기판의 광 도파로 폭을 4[.mu.m], 버퍼층을 0.02[.mu.m]로 하였을때 도파로 층의 깊이가 0.2[.mu.m]인 지점에서 인가전압에 대한 x방향의 전계(E$_{x}$)와 y방향의 전계(E$_{y}$ )분포를 관찰하였다. 또한 단일 도파로의 파라미터 조건을 적용하여 X-스위치를 구성하였을때 전계를 인가하지 않은 상태에서 굴절율 변화(dn) 0.002, 도파로 폭(w) 3[.mu.m]로 하여 도파로의 교차각(.alpha.)을 0.4.deg.~0.6.deg.로 변화시킨 경우, .alpha.=0.5.deg.와 0.6.deg.일 때는 광빔이 bar측으로 출력되었고 .alpha.=0.4에서는 광빔이 cross측으로 출력 됨을 확인하였다. 따라서 위에서 확인된 도파로의 교차각 .alpha.=0.4.deg.인 경우, 전극간격(gap)이 2[.mu.m]인 조건에서 스위칭 전압을 인가하였을 때 25[V]에서 전기광학 효과에 의하여 광빔이 cross측에서 bar측으로 변조됨을 확인함으로써 X-스위치 광변조기의 기본적인 설계조건을 구현하였다.

• Animal cells and systems
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• 제2권4호
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• pp.489-493
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• 1998

Various heterodimers of the thyroid hormone receptor (TR) with other nuclear hormone receptors confer a wide range of transcriptional activities on thyroid hormone response elements (TREs) in the presence of the thyroid hormone ($T_3$). The present study analyzed the potential roles of retinoid X receptor (RXR) isoforms $\alpha$ and $\beta$ in $T_3$-mediated transcription on a well characterized TRE, a direct repeat of AGGTCA separated by four nucleo-tides (DR4), using electrophoretic mobility shift assays and transient transfection in CV-1 cells. We demonstrated that RXR$\alpha$ supressed liganded $TR_{\alpha}$-induced transcription while $RXR_{\beta}$ did not although both $TR_{\alpha}/RXR_{\alpha}$ and $TR_{\alpha}/RXR_{\beta}$ heterodimers were the predominant forms bound to the TRE-DR4 in the presence of $T_3$. We further demonstrated using Scatchard analysis that the two heterodimers had similar affinities for the TRE-DR4. All these observations suggest that the TRE-DR4 accomodates different types of TR/RXR heterodimers for a more finely tuned transcriptional response to $T_3$.

• 한국인터넷방송통신학회논문지
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• 제17권3호
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• pp.1-7
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• 2017

본 논문은 ${\alpha}^{\gamma}{\equiv}{\beta}$(mod p)에서 ${\gamma}$를 구하는 Pollard의 Rho와 Brent의 이산대수 알고리즘의 수행횟수를 크게 감소시키는 알고리즘을 제안하였다. 제안된 방법은 Brent 방법으로 충돌을 검출하였다. 차이점은 $x_0=1$ 대신 $x_0={\alpha}{\beta}$을, $y=x_i$, ($i=2^k$) 대신 크기가 10인 Queue에 $y_j{\leftarrow}x_i$, ($i=2^k$, $1{\leq}j{\leq}10$)를 저장하는 방법을, ${\beta}_{\gamma}$ 대신 ${\beta}={\beta}_{\gamma}$, ${\beta}_{{\gamma}^{\prime}}$, ${\beta}_{{\gamma}^{-1}}$의 충돌을 찾는 방법을 적용하였다. 제안된 Queue 적용법은 $x_0=y_0=1$로 ${\beta}_{\gamma}$의 충돌을 검출하는 Pollard의 Rho 알고리즘의 수행횟수를 65.02%, $x_0=1$으로 ${\beta}_{\gamma}$의 충돌을 검출하는 Brent 알고리즘의 수행횟수를 47.80% 감소시켰다.

• 대한수학회지
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• 제32권4호
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• pp.725-737
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• 1995

Let $X_t = (X_t^(1), X_t^(2))', t \geqslant 0$, be a real stationary 2-dimensional Gaussian process with $EX_t^(1) = EX_t^(2) = 0$ and $$ EX_0 X'_t = (_{\rho(t) r(t)}^{r(t) \rho(t)}), $$ where $r(t) \sim $\mid$t$\mid$^-\alpha, 0 < \alpha < 1/2, \rho(t) = o(r(t)) as t \to \infty, r(0) = 1, and \rho(0) = \rho (0 \leqslant \rho < 1)$. For $t > 0, u > 0, and \upsilon > 0, let L_t (u, \upsilon)$ be the time spent by $X_s, 0 \leqslant s \leqslant t$, above the level $(u, \upsilon)$.

• 한국세라믹학회지
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• 제29권1호
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• pp.23-28
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• 1992

Alumina ceramics was reinforced by in-situ formation of La-${\beta}$-aluminate in ${\alpha}$-alumina matrix. The powder mixture of which composition is (100-12x)Al2O3+x(La2O3+11Al2O3) was prepared for the formation of La-${\beta}$-aluminate in ${\alpha}$-alumina matrix. The amount of La-${\beta}$-aluminate in the matrix was controlled by varing x which is number of moles. The dense composite was produced by sintering at 1600$^{\circ}C$ in air or hot-pressing at 1550$^{\circ}C$ under 30 MPa. Bending strength and fracture toughness were increased, resulting from the grain growth inhibition and the crack deflection and crack bridging mechanism when La-${\beta}$-aluminate was produced in ${\alpha}$-alumina matrix.