• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.735-742
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• 2010

In this paper, we define and study the concept of $\wedge^s_{\delta}$-closure operator and the associated topology $\tau^{\wedge}^s_{\delta}$ on a topological space (X, $\tau$) in terms of g.$\wedge^s_{\delta}$-sets.

• East Asian mathematical journal
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• v.24 no.1
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• pp.35-43
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• 2008

Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let ${\{T_i\}}^N_{i=1}$ be N nonexpansive self-mappings of K with $F\;=\;{\cap}^N_{i=1}F(T_i)\;{\neq}\;{\theta}$ (here $F(T_i)$ denotes the set of fixed points of $T_i$). Suppose that one of the mappings in ${\{T_i\}}^N_{i=1}$ is semi-compact. Let $\{{\alpha}_n\}\;{\subset}\;[{\delta},\;1-{\delta}]$ for some ${\delta}\;{\in}\;(0,\;1)$ and $\{{\beta}_n\}\;{\subset}\;[\tau,\;1]$ for some ${\tau}\;{\in}\;(0,\;1]$. For arbitrary $x_0\;{\in}\;K$, let the sequence {$x_n$} be defined iteratively by $\{{x_n\;=\;{\alpha}_nx_{n-1}\;+\;(1-{\alpha}_n)T_ny_n,\;\;\;\;\;\;\;\;\; \atop {y_n\;=\;{\beta}nx_{n-1}\;+\;(1-{\beta}_n)T_nx_n},\;{\forall}_n{\geq}1,}$, where $T_n\;=\;T_{n(modN)}$. Then {$x_n$} convergence strongly to a common fixed point of the mappings family ${\{T_i\}}^N_{i=1}$. The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of ${\beta}_n\;{\equiv}\;1$ or N=1 are also new.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.17-22
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• 1985

B.M. Munshi and D.S. Bassan defined and developed the concept of super continuity in [5]. The concept has been investigated further by I. L. Reilly and M. K. Vamanamurthy in [6] where super continuity is characterized in terms of the semi-regularization topology. Super continuity is related to the concepts of .delta.-continuity and strong .theta.-continuity developed by T. Noiri in [7]. The purpose of this note is to derive relationships between super continuity and other strong continuity conditions and to develop additional properties of super continuous functions. Super continuity implies continuity, but the converse implication is false [5]. Super continuity is strictly between strong .theta.-continuity and .delta.-continuity and strictly between complete continuity and .delta.-continuity. The symbols X and Y will denote topological spaces with no separation axioms assumed unless explicity stated. The closure and interior of a subset U of a space X will be denoted by Cl(U) and Int(U) respectively and U is said to be regular open (resp. regular closed) if U=Int[Cl(U) (resp. U=Cl(Int(U)]. If necessary, a subscript will be added to denote the space in which the closure or interior is taken.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.6-6
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• 2003

In this work we consider the mathematical formulation and numerical resolution of the linear feedback control problem for Boussinesq equations. The controlled Boussinesq equations is given by $$\frac{{\partial}u}{{\partial}t}-{\nu}{\Delta}u+(u{\cdot}{\nabla}u+{\nabla}p={\beta}{\theta}g+f+F\;\;in\;(0,\;T){\times}\;{\Omega}$$, $${\nabla}{\cdot}u=0\;\;in\;(0,\;T){\times}{\Omega}$$, $$u|_{{\partial}{\Omega}=0,\;u(0,x)=\;u_0(x)$$ $$\frac{{\partial}{\theta}}{{\partial}t}-k{\Delta}{\theta}+(u{\cdot}){\theta}={\tau}+T,\;\;in(0,\;T){\times}{\Omega}$$ $${\theta}|_{{\partial}{\Omega}=0,\;\;{\theta}(0,X)={\theta}_0(X)$$, where $\Omega$ is a bounded open set in $R^{n}$, n=2 or 3 with a $C^{\infty}$ boundary ${\partial}{\Omega}$. The control is achieved by means of a linear feedback law relating the body forces to the velocity and temperature field, i.e., $$f=-{\gamma}_1(u-U),\;\;{\tau}=-{\gamma}_2({\theta}-{\Theta}}$$ where (U,$\Theta$) are target velocity and temperature. We show that the unsteady solutions to Boussinesq equations are stabilizable by internal controllers with exponential decaying property. In order to compute (approximations to) solution, semi discrete-in-time and full space-time discrete approximations are also studied. We prove that the difference between the solution of the discrete problem and the target solution decay to zero exponentially for sufficiently small time step.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.41.1-41.1
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• 2016

We present the physical properties of KIC 6220497 exhibiting multiperiodic pulsations from the Kepler photometry. The light curve synthesis represents that the eclipsing system is a semi-detached Algol with a mass ratio of q=0.243, an orbital inclination of i=77.3 deg, and a temperature difference of ${\Delta}T=3,372K$, in which the detached primary component fills its Roche lobe by ~87% and is about 1.6 times larger than the lobe-filling secondary. To detect reliable pulsation frequencies, we analyzed separately the Kepler light curve at the interval of an orbital period. Multiple frequency analyses of the eclipse-subtracted light residuals reveal 32 frequencies in the range of $0.75-20.22d^{-1}$ with semi-amplitudes between 0.27 and 4.55 mmag. Among these, four frequencies ($f_1$, $f_2$, $f_5$, $f_7$) may be attributed to pulsation modes, while the other frequencies can be harmonic and combination terms. The pulsation constants of 0.16-0.33 d and the period ratios of $P_{pul}/P_{orb}=0.042-0.089$ indicate that the primary component is a ${\delta}$ Sct pulsating star in p modes and, thus, KIC 6220497 is an oscillating eclipsing Algol (oEA) star. The dominant pulsation period of about 0.1174 d is considerably longer than the values given by the empirical relations between the pulsational and orbital periods. The surface gravity of log $g_1=3.78$ is significantly smaller than those of the other oEA stars with similar orbital periods. The pulsation period and the surface gravity of the pulsating primary demonstrate that KIC 6220497 would be the more evolved EB, compared with normal oEA stars.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.86-86
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• 2019

We present BV photometric observations and high-resolution spectra of AO Ser, which were obtained at the Mt. Lemmon Optical Astronomy Observatory (LOAO) and the Bohyunsan Optical Astronomy Observatory (BOAO), respectively, in 2017. The radial velocities (RVs) for both components were measured, and the effective temperature of the primary star was found to be $T_{eff,1}=8,820{\pm}62K$ by a comparison of the observed spectra and the Kurucz models. A unique set of fundamental parameters of AO Ser were derived for the first time by a simultaneous analysis of the light and RV curves. The results indicate that our program target is a semi-detached eclipsing system with values of $M_1=2.06{\pm}0.11M_{\odot}$ and $M_2=0.41{\pm}0.03M_{\odot}$, $R_1=1.54{\pm}0.03R_{\odot}$ and $R_2=1.30{\pm}0.02R_{\odot}$, and $L_1=12.9{\pm}0.2L_{\odot}$ and $L_2=0.9{\pm}0.3L_{\odot}$. We applied multiple frequency analyses to the eclipse-subtracted light residuals. As a result, two frequencies of $f_1=21.85151days^{-1}$ and $f_2=23.48405days^{-1}$ were detected and their pulsation constants were calculated to $Q_1=0.0344days$ and $Q_2=0.0320days$. The pulsational characteristics and the position in the HR diagram demonstrate that the primary star is a ${\delta}$ Sct pulsator.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.41.3-42
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• 2016

New CCD photometric observations of GX Aur have been made between 2004 and 2015. Our light curves are the first ever compiled and display the variable O'Connell effect. The light variations are satisfactorily modeled by including time-varying cool-spots on the component stars. Our light curve synthesis indicates that the eclipsing pair is an A-type contact binary with parameters of i = 81.1 deg, ${\Delta}T=36K$, q = 0.950 and f = 46%. Including our 25 timing measurements, a total of 83 times of minimum light spanning about 66 yr were used for a period study. It was found that the orbital period of GX Aur has varied due to two periodic oscillations superposed on an upward-opening parabolic variation. The long-term period increase rate is deduced as $+9.636{\times}10^{-10}d\;yr^{-1}$, which can be produced as a mass transfer from the secondary star to the primary at a rate of $3.136{\times}10^{-6}M_{\odot}\;yr^{-1}$, among the largest rates for contact systems. The periods and semi-amplitudes of the two periodic variations are about $P_3=8.7yr$ and $P_4=21.2yr$, and $K_3=0.011d$ and $K_4=0.017d$, respectively. The most reasonable explanation for both cycles is a pair of light-travel-time effects driven by the possible existence of an unseen third and fourth components with projected masses of $M_3=0.91M_{\odot}$ and $M_4=1.09M_{\odot}$ in eccentric orbits of $e_3=0.13$ and $e_4=0.73$. Because no third light was detected in the light curve synthesis, each circumbinary object could be a compact star or a binary itself.