• 충청수학회지
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• 제9권1호
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• pp.107-113
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• 1996

For continuous maps f of the circle to itself, we show that (1) the set of ${\omega}$-limit points is contained in the set of nonwandering points of $f^n$ for all $n{\geq}1$. (2) if the set of turning points of f is finite, then the set of accumulation points of non wandering set is contained in the set of non wandering points of $f^n$ for all $n{\geq}1$.

• 한국마린엔지니어링학회:학술대회논문집
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• 한국마린엔지니어링학회 2001년도 춘계학술대회 논문집
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• pp.207-212
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• 2001

In this paper, a method to be able to decide the possible maximum gain of P, PI control for the retarded processes under stable condition is proposed. At first, adjustable parameter set causing stability limit are obtained based on the frequency domain condition which makes the roots of transfer function locate on the $j\omega$ axis. And the cut-in frequency $\omega{_p}$ to bring the parameter set to P control from PI control is derived by an equation with 2 parameters L and $T_m$ given, then $\omega{_p}$ is used to compute the maximum gain with stable condition. For the calculation, the controlled process of first order system with time delay element is introduced and all parameters are presumed to be time invariant.

• 대한화학회지
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• 제40권5호
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• pp.317-326
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• 1996

Linear polyenes, ($C_4H_6\;to\;C_{30}H_{32}$)의 frequency dependent longitudinal polarizablilty, ${\alpha}zz(\omega)$ 와 second hyperpolarizabilities, ${\gamma}zzzz(\omega)$를 6-31G basis set에서 ab initio TDHF 이론을 사용하여 계산하였다. 폴리 아세틸렌의 frequency dispersion effect를 보기 위하여 외부 전기장의 주파수 영역에 광학성질을 구한후 무한 사슬을 갖는 고분자에 대하여 extrapolate하였다. 이때걸어준 외부 전기장에서의 광학적 성질에 대한 static field 에서의 광학성질의 비를 사용하여 비공면 영역에서의 dispersion effect를 고찰하였다. 또한 광학성질에 대한 주변 사슬의 효과를 조사하였으며 공명이 일어나는 영역에서의 광학 성질을 계산하기 위한 이론적 방법을 제안하였다.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.521-535
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• 2023

In this work, some various types of Dissipativity in random dynamical systems are introduced and studied: point, compact, local, bounded and weak. Moreover, the notion of random Levinson center for compactly dissipative random dynamical systems presented and prove some essential results related with this notion.

• 충청수학회지
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• 제26권2호
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• pp.351-356
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• 2013

In this article, we discuss the notions of chain prolongation functions on locally compact spaces and get some results for the concepts. We show that chain prolongation function is a cluster map.

• Journal of Advanced Marine Engineering and Technology
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• 제25권5호
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• pp.1086-1090
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• 2001

In this paper, a method deciding the permissible gains of the P and PT controllers for a retarded process under stable condition is proposed. For analysis, the controlled process is assumed to be first-order system with time delay. At first, the adjustable parameter sets causing stability limit are obtained based on the frequency domain condition which makes the roots of the characteristic equation locate on the imaginary axis. And the cut-in frequency ${\omega}_p$ to bring the parameter set to P control from PI control is derived is derived in terms of L and $T_m$ then ${\omega}_p$ is used to compute the maximum gain with stable condition. The results indicate that the permissible controller gains can be described by a unique if parameters L and $T_m$ are know.

• Coupled systems mechanics
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• 제6권3호
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• pp.369-376
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• 2017

Intermolecular interaction energies and conformer geometries of the hydrogen bonded acrylamide dimers have been studied by using the second-order Møller-Plesset (MP2) perturbation theory and the density functional theory (DFT) with 17 density functionals. Dunning's correlation consistent basis sets (up to aug-cc-pVTZ) have been used to study the basis set effects. The DFT calculated interaction energies are compared to the reference energy data calculated by the MP2 method and the coupled cluster method at the complete basis set (CCSD(T)/CBS) limit in order to determine the relative performance of the studied density functionals. Overall, dispersion-energy-corrected density functionals outperform uncorrected ones. The ${\omega}B97XD$ density functional is particularly effective in terms of both accuracy and computational cost in estimating the reference energy values using small basis sets and is highly recommended for similar calculations for larger systems.

• 충청수학회지
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• 제25권1호
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• pp.65-72
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• 2012

Let T > 0 be given. Let $(C[0,T],m_{\varphi})$ be the analogue of Wiener measure space, associated with the Borel proba-bility measure ${\varphi}$ on ${\mathbb{R}}$, let $(L_{2}[0,T],\tilde{\omega})$ be the centered Gaussian measure space with the correlation operator $(-\frac{d^{2}}{dx^{2}})^{-1}$ and ${\el}_2,\;\tilde{m}$ be the abstract Wiener measure space. Let U be the space of all sequence $<c_{n}>$ in ${\el}_{2}$ such that the limit $lim_{{m}{\rightarrow}\infty}\;\frac{1}{m+1}\;\sum{^{m}}{_{n=0}}\;\sum_{k=0}^{n}\;c_{k}\;cos\;\frac{k{\pi}t}{T}$ converges uniformly on [0,T] and give a set function m such that for any Borel subset G of $\el_2$, $m(\mathcal{U}\cap\;P_{0}^{-1}\;o\;P_{0}(G))\;=\tilde{m}(P_{0}^{-1}\;o\;P_{0}(G))$. The goal of this note is to study the relationship among the measures $m_{\varphi},\;\tilde{\omega},\;\tilde{m}$ and $m$.

• Korean Journal of Mathematics
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• 제8권2호
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• pp.121-126
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• 2000

B.Djafari Rouhani and W.A.Kirk [3] proved the following theorem: Let Xbe a reflexive Banach space and $(x_n)_{n{\geq}0}$ be a nonexpansive (resp., firmly nonexpansive )sequence in X. Then the set of weak ${\omega}$-limit points of the sequence $(\frac{x_n}{n})_{n{\geq}1}$(resp., $(x_{n+1}-x_n)_{n{\geq}0$) always lies on a convex subset of a sphere centered at the origin of radius $d={\lim}_{n{\rightarrow}{\infty}}\frac{{\parallel}x_n{\parallel}}{n}$. In this paper we show that the above theorem for nonexpansive(resp., firmly nonexpansive) sequences holds in a general Banach space(resp., a strictly convex dual $X^*$).

• 천문학논총
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• 제30권2호
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• pp.309-313
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• 2015

If the present universe is slightly open then pre-inflation curvature would appear as a cosmic dark-flow component of the CMB dipole moment. We summarize current cosmological constraints on this cosmic dark flow and analyze the possible constraints on parameters characterizing the pre-inflating universe in an inflation model with a present-day very slightly open ${\Lambda}CDM$ cosmology. We employ an analytic model to show that for a broad class of inflation-generating effective potentials, the simple requirement that the observed dipole moment represents the pre-inflation curvature as it enters the horizon allows one to set upper and lower limits on the magnitude and wavelength scale of pre-inflation fluctuations in the inflaton field and the curvature parameter of the pre-inflation universe, as a function of the fraction of the total initial energy density in the inflaton field. We estimate that if the current CMB dipole is a universal dark flow (or if it is near the upper limit set by the Planck Collaboration) then the present constraints on ${\Lambda}CDM$ cosmological parameters imply rather small curvature ${\Omega}_k{\sim}0.1$ for the pre-inflating universe for a broad range of the fraction of the total energy in the inflaton field at the onset of inflation. Such small pre-inflation curvature might be indicative of open-inflation models in which there are two epochs of inflation.