• 대한원격탐사학회지
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• 제23권4호
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• pp.311-321
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• 2007

해수 속으로 입수된 하향 태양에너지 (down-welling irradiance)가 수심이 깊어짐에 따라 확산 소산되는 정도를 나타내는 하향 확산 감쇠계수 (Diffuse attenuation coefficient of down-welling irradiance, $K_d({\lambda})$)와 해수 속에서의 가시거리를 나타내는 수중시계는 수중에서의 광학적 성격을 나타내는 중요한 지수이다. 이러한 $K_d({\lambda})$ 및 수중시계에 대한 많은 연구가 세계적으로 여러 해역에 대해 수행되어 왔지만 우리나라 연안 해역을 대상으로 하는 연구는 매우 적은 실정이다. 따라서 본 연구에서는 우리나라의 황해 중부해역을 대상으로 $K_d({\lambda})$ 및 수중시계를 관측하였고, 해색위성용 $K_d({\lambda})$ 및 수중시계 알고리즘을 개발하였다. $K_d({\lambda})$ 및 수중시계 관측을 위하여 2006년 9월 $19{\sim}22$일, 4일 동안 황해 중부해역에서 현장관측을 실시하였으며, 총 39개 정점에서 해양 광학적 자료와 해양 환경적 자료를 획득하였다. 획득된 자료를 이용하여 경험적 방법으로 $K_d({\lambda})$와 수중시계 알고리즘을 개발하였으며, 개발된 알고리즘들은 각각 기존의 대양의 자료를 이용하여 개발된 SeaWiFS 해색 센서용 $K_d({\lambda})$ 알고리즘과 NRL (Naval Research Laboratory)에서 개발된 SeaWiFS 센서용 수중시계 알고리즘과 비교하여 보았다. $K_d({\lambda})$ 알고리즘의 경우는 탁도가 높은 해역 값에서 약간의 차이를 보였으며, 수중시계 알고리즘의 경우 NRL의 알고리즘에 비해 약간 높은 계수 값을 얻었다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.494-494
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• 2000

This paper demonstrates that the largest Lyapunov exponent $\lambda$ of recurrent neural networks can be controlled by a gradient method. The method minimizes a square error $e_{\lambda}=(\lambda-\lambda^{obj})^2$ where $\lambda^{obj}$ is desired exponent. The $\lambda$ can be given as a function of the network parameters P such as connection weights and thresholds of neurons' activation. Then changes of parameters to minimize the error are given by calculating their gradients $\partial\lambda/\partialP$. In a previous paper, we derived a control method of $\lambda$via a direct calculation of $\partial\lambda/\partialP$ with a gradient collection through time. This method however is computationally expensive for large-scale recurrent networks and the control is unstable for recurrent networks with chaotic dynamics. Our new method proposed in this paper is based on a stochastic relation between the complexity $\lambda$ and parameters P of the networks configuration under a restriction. Then the new method allows us to approximate the gradient collection in a fashion without time evolution. This approximation requires only $O(N^2)$ run time while our previous method needs $O(N^{5}T)$ run time for networks with N neurons and T evolution. Simulation results show that the new method can realize a "stable" control for larege-scale networks with chaotic dynamics.

• 천문학회보
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• 제44권1호
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• pp.36.1-36.1
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• 2019

We present the observed relationship between Eddington ratio (${\lambda}Edd$) and optical narrow-emission-line ratio ([NII] ${\lambda}6583/H{\alpha}$) of X-ray-selected unobscured active galactic nuclei (AGN) at 0.6 < z < 1.7 using 27 near-infrared spectra from the Fiber Multi-Object Spectrograph mounted on the Subaru telescope along with 26 additional sources from the literature. We show that the ${\lambda}Edd$ and [NII] ${\lambda}6583/H{\alpha}$ ratio at 0.6 < z < 1.7 exhibits a similar distribution of ${\lambda}Edd$-[NII] ${\lambda}6583/H{\alpha}$ anti-correlation that has been found for local ( = 0.036), hard X-ray selected AGN. The observed anti-correlation suggests that [N II] ${\lambda}6583/H{\alpha}$ optical narrow-line ratio in the AGN host galaxy may carry important information about the accretion state of the central supermassive black hole, suggesting the observational hint of consistent relationship from local to z ~ 1.7. Further study is necessary to determine whether the ${\lambda}Edd$-[N II] ${\lambda}6583/H{\alpha}$ correlation in high-redshift still holds at ${\log}{\lambda}Edd$ < -2 compared to local AGN.

• 충청수학회지
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• 제28권2호
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• pp.207-215
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• 2015

The main goal in the present paper is to obtain a particular solution $g_{{\lambda}{\mu}}$, ${\Gamma}^{\nu}_{{\lambda}{\mu}}$ and an algebraic solution $\bar{g}_{{\lambda}{\mu}}$, $\bar{\Gamma}^{\nu}_{{\lambda}{\mu}}$ by means of $g_{{\lambda}{\mu}}$, ${\Gamma}^{\nu}_{{\lambda}{\mu}}$ in UFT $X_4$.

• 대한수학회논문집
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• 제11권1호
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• pp.139-145
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• 1996

We show how some interesting results involving series summation and the digamma function are established by means of Riemann-Liouville operator of fractional calculus. We derive the relation $$ \frac{\Gamma(\lambda)}{\Gamma(\nu)} \sum^{\infty}_{n=1}{\frac{\Gamma(\nu+n)}{n\Gamma(\lambda+n)}_{p+2}F_{p+1}(a_1, \cdots, a_{p+1},\lambda + n; x/a)} = \sum^{\infty}_{k=0}{\frac{(a_1)_k \cdots (a_{(p+1)}{(b_1)_k \cdots (b_p)_k K!} (\frac{x}{a})^k [\psi(\lambda + k) - \psi(\lambda - \nu + k)]}, Re(\lambda) > Re(\nu) \geq 0 $$ and explain some special cases.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.525-534
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• 2019

Let $P(G,{\lambda})$ denote the number of proper vertex colorings of G with ${\lambda}$ colors. The chromatic polynomial $P(C_n,{\lambda})$ for the cycle graph $C_n$ is well-known as $$P(C_n,{\lambda})=({\lambda}-1)^n+(-1)^n({\lambda}-1)$$ for all positive integers $n{\geq}1$. Also its inductive proof is widely well-known by the deletion-contraction recurrence. In this paper, we give this inductive proof again and three other proofs of this formula of the chromatic polynomial for the cycle graph $C_n$.

• 대한수학회보
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• 제50권2호
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• pp.431-440
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• 2013

Let ($M^3$, $g$) be a 3-dimensional closed Sasakian spin manifold. Let $S_{min}$ denote the minimum of the scalar curvature of ($M^3$, $g$). Let ${\lambda}^+_1$ > 0 be the first positive eigenvalue of the Dirac operator of ($M^3$, $g$). We proved in [13] that if ${\lambda}^+_1$ belongs to the interval ${\lambda}^+_1{\in}({\frac{1}{2}},\;{\frac{5}{2}})$, then ${\lambda}^+_1$ satisfies ${\lambda}^+_1{\geq}{\frac{S_{min}+6}{8}}$. In this paper, we remove the restriction "if ${\lambda}^+_1$ belongs to the interval ${\lambda}^+_1{\in}({\frac{1}{2}},\;{\frac{5}{2}})$" and prove $${\lambda}^+_1{\geq}\;\{\frac{S_{min}+6}{8}\;for\;-\frac{3}{2}&lt;S_{min}{\leq}30, \\{\frac{1+\sqrt{2S_{min}}+4}{2}}\;for\;S_{min}{\geq}30$$.

• 대한수학회보
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• 제49권4호
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• pp.705-714
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• 2012

In this paper, we study nonlinear equation arising in MEMS modeling electrostatic actuation. We will prove the local and global existence of solutions of the generalized parabolic MEMS equation. We present that there exists a constant ${\lambda}^*$ such that the associated stationary problem has a solution for any ${\lambda}$ < ${\lambda}^*$ and no solution for any ${\lambda}$ > ${\lambda}^*$. We show that when ${\lambda}$ < ${\lambda}^*$ the global solution converges to its unique maximal steady-state as $t{\rightarrow}{\infty}$. We also obtain the condition for the existence of a touchdown time $T{\leq}{\infty}$ for the dynamical solution. Furthermore, there exists $p_0$ > 1, as a function of $p$, the pull-in voltage ${\lambda}^*(p)$ is strictly decreasing with respect to 1 < $p$ < $p_0$, and increasing with respect to $p$ > $p_0$.

• 대한수학회보
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• 제51권2호
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• pp.357-371
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• 2014

We shall show that the Riesz idempotent $E_{\lambda}$ of every *-paranormal operator T on a complex Hilbert space H with respect to each isolated point ${\lambda}$ of its spectrum ${\sigma}(T)$ is self-adjoint and satisfies $E_{\lambda}\mathcal{H}=ker(T-{\lambda})= ker(T-{\lambda})^*$. Moreover, Weyl's theorem holds for *-paranormal operators and more general for operators T satisfying the norm condition $||Tx||^n{\leq}||T^nx||\,||x||^{n-1}$ for all $x{\in}\mathcal{H}$. Finally, for this more general class of operators we find a sufficient condition such that $E_{\lambda}\mathcal{H}=ker(T-{\lambda})= ker(T-{\lambda})^*$ holds.

• 대한수학회보
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• 제33권1호
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• pp.107-110
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• 1996

Usng the Pochhammer symbol $(\lambda)_n$ given by $$ (1.1) (\lambda)_n = {1, if n = 0 {\lambda(\lambda + 1) \cdots (\lambda + n - 1), if n \in N = {1, 2, 3, \ldots}, $$ we define a general double hypergeometric series by [3, pp.27] $$ (1.2) F_{q:s;\upsilon}^{p:r;u} [\alpha_1, \ldots, \alpha_p : \gamma_1, \ldots, \gamma_r; \lambda_1, \ldots, \lambda_u;_{x,y}][\beta_1, \ldots, \beta_q : \delta_1, \ldots, \delta_s; \mu_1, \ldots, \mu_v; ] = \sum_{l,m = 0}^{\infty} \frac {\prod_{j=1}^{q} (\beta_j)_{l+m} \prod_{j=1}^{s} (\delta_j)_l \prod_{j=1}^{v} (\mu_j)_m)}{\prod_{j=1}^{p} (\alpha_j)_{l+m} \prod_{j=1}^{r} (\gamma_j)_l \prod_{j=1}^{u} (\lambda_j)_m} \frac{l!}{x^l} \frac{m!}{y^m} $$ provided that the double series converges.