• Publications of The Korean Astronomical Society
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• v.7 no.1
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• pp.25-30
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• 1992

Recent redshift surveys suggest that most galaxies may be distributed on the surfaces of bubbles surrounding large voids. To investigate the quantitative consistency of this qualitative picture of large-scale structure, we study analytically the clustering properties of galaxies in a universe filled with spherical shells. In this paper, we report the results of the calculations for the spatial and angular two-point correlation functions of galaxies. With ${\sim}20%$ of galaxies in clusters and a power law distribution of shell sizes, $n_{sh}(R){\sim}R^{-{\alpha}}$, ${\alpha}\;{\simeq}\;4$, the observed slope and amplitude of the spatial two-point correlation function ${\xi}_{gg}(r)$ can be reproduced. (It has been shown that the same model parameters reproduce the enhanced cluster two-point correlation function, ${\xi}_{cc}(r)$). The corresponding angular two-point correlation function $w({\theta})$ is calculated using the relativistic form of Limber's equation and the Schecter-type luminosity function. The calculated w(${\theta}$) agrees with the observed one quite well on small separations (${\theta}{\lesssim}2deg$).

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.377-386
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• 2021

In this paper, we use theta-function identities involving parameters 𝑙_5,n, 𝑙'_5,n, and 𝑙'_5,4n to evaluate the Rogers-Ramanujan continued fractions $R(e^{-2{\pi}{\sqrt{n/20}}})$ and $S(e^{-{\pi}{\sqrt{n/5}}})$ for some positive rational numbers n.

• The Pure and Applied Mathematics
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• v.29 no.3
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• pp.245-254
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• 2022

In this paper, we use some theta-function identities involving certain parameters to show how to evaluate Rogers-Ramanujan continued fraction R($e^{-2{\pi}\sqrt{n}}$) and S($e^{-{\pi}\sqrt{n}}$) for $n=\frac{1}{5.4^m}$ and $\frac{1}{4^m}$, where m is any positive integer. We give some explicit evaluations of them.

• Journal of Environmental Science International
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• v.24 no.8
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• pp.981-992
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• 2015

This study is mainly focused on micellar effect of tetradecyltrimethyl ammonium bromide(TTABr) solution including alkylbenzimidazole(R-BI) on dephosphorylation of diphenyl-4-nitrophenylphosphinate(DPNPIN) in carbonate buffer(pH 10.7). Dephosphorylation of DPNPIN is accelerated by $BI^{\Theta}$ ion in $10^2$ M Carbonate buffer(pH 10.7) of $4{\times}10^{-4}$ M TTABr solution up to 80 times as compared with the reaction in Carbonate buffer by no benzimidazole(BI) solution of TTABr. The value of pseudo first order rate constant($k_{\psi}$) of the reaction in TTABr solution reached a maximum rate constant increasing micelle concentration. The reaction mediated by $R-BI^{\Theta}$ in micellar solutions are obviously slower than those by $BI^{\Theta}$, and the reaction rate were decreased with increase of lengths of alkyl groups. It seems due to steric effect of alkyl groups of $R-BI^{\Theta}$ in Stern layer of micellar solution. The surfactant reagent, TTABr, strongly catalyzes the reaction of DPNPIN with R-BI and its anion($R-BI^{\Theta}$) in Carbonate buffer(pH 10.7). For example, $4{\times}10^{-4}$ M TTABr in $1{\times}10^{-4}$ M BI solution increase the rate constant($k_{\psi}=99.7{\times}10^{-4}1/sec$) of the dephosphorylation by a factor ca. 28, when compared with reaction($k_{\psi}=3.5{\times}10^{-4}1/sec$) in BI solution(without TTABr). And no TTABr solution, in BI solution increase the rate constant($k_{\psi}=3.5{\times}10^{-4}1/sec$) of the dephosphorylation by a factor ca. 39, when compared with reaction ($k_{\psi}=1.0{\times}10^{-5}1/sec$) in water solution(without BI).

• Journal of electromagnetic engineering and science
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• v.13 no.1
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• pp.16-21
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• 2013

This study presents the angular effects of virtual vertices inserted for effective treatment of the boundary edge laid on an infinite conducting surface in a half-space scattering problem. We investigated the angular effects of virtual vertices by first computing the radar cross section (RCS) of a specific scatterer; i.e., a tilted conducting plate in contact with the ground surface, by inserting the virtual vertex in half-space. Here, the electric field integral equation is used to solve this problem with various virtual vertex angles (${\theta}_{\nu}$) and conducting plate inclination angles (${\theta}_r$) ranging from $0^{\circ}$ to $180^{\circ}$. The effects of the angles ${\theta}_{\nu}$ and ${\theta}_r$ on the RCS computation are clearly shown with numerical results with and without the virtual vertices in free- and half-spaces.

• Proceedings of the Optical Society of Korea Conference
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• 1989.02a
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• pp.81-84
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• 1989

EHZP is a kind of holographic optical element, which is generated by the interference of two divergent spherical waves from point sources on the same axis. It has the spherical aberration that the focal power increases as the radial distance r increases. By using this property, optimal design of EHZP was performed for f-$\theta$ lens. As the result of optimization, the f-$\theta$ condition and the field flattening condition were well satisfied when EHZP has f0=0.803f, faR=4.076f, 1=0.406f. It was assumed for calculation of field flattening condition that the incident wave was a plane wave with the diameter of 1mm.

• 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.

• Korean Chemical Engineering Research
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• v.54 no.6
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• pp.734-745
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• 2016

This review article described the electrochemical Frumkin, Langmuir, and Temkin adsorption isotherms of over-potentially deposited hydrogen (OPD H) and deuterium (OPD D) for the cathodic $H_2$ and $D_2$ evolution reactions (HER, DER) at Pt, Ir, Pt-Ir alloy, Pd, Au, and Re/normal ($H_2O$) and heavy water ($D_2O$) solution interfaces. The Frumkin, Langmuir, and Temkin adsorption isotherms of intermediates (OPD H, OPD D, etc.) for sequential reactions (HER, DER, etc.) at electrode/solution interfaces are determined using the phase-shift method and correlation constants, which have been suggested and developed by Chun et al. The basic procedure of the phase-shift method, the Frumkin, Langmuir, and Temkin adsorption isotherms of OPD H and OPD D and related electrode kinetic and thermodynamic parameters, i.e., the fractional surface coverage ($0{\leq}{\theta}{\leq}1$) vs. potential (E) behavior (${\theta}$ vs. E), equilibrium constant (K), interaction parameter (g), standard Gibbs energy (${\Delta}G_{\theta}{^{\circ}}$) of adsorption, and rate (r) of change of ${\Delta}G_{\theta}{^{\circ}}$ with ${\theta}$ ($0{\leq}{\theta}{\leq}1$), at the interfaces are briefly interpreted and summarized. The phase-shift method and correlation constants are useful and effective techniques to determine the Frumkin, Langmuir, and Temkin adsorption isotherms and related electrode kinetic and thermodynamic parameters (${\theta}$ vs. E, K, g, ${\Delta}G_{\theta}{^{\circ}}$, r) at electrode/solution interfaces.

• Journal of the Korean Society for Precision Engineering
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• v.11 no.6
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• pp.117-126
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• 1994

This paper describes an application step of a $R^{-{\theta}}$ method which measures circular movements in machining centers. The detection of composite errors of circular movements and a high precision cutting method in machining centers were investigated by the analysis of data measured by $R^{\theta }$method which can detect the rotating angle and is applicable to variable measuring radius. When the error by squareness error and unbalance of position-loop-gain were mixed, the detection method of each error was proposed. Although the errors by squarenss error and backlash compensation were mixed, the errors by squareness error be detected. If the errors by unbalance of position-loop-gain and backlash compensation were mixed, the errors by unbalance of position-loop-gain could not detected. A high precision cutting mehod, which uses the NC program compensated by using feed-back data from error measured by the $R^{\theta }$method, was proposed.

• Journal of Integrative Natural Science
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• v.11 no.3
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• pp.154-160
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• 2018

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p-r{\geq}3)$, r = rank(K) with a projection matrix K under the quadratic loss, based on a sample $Y_1$, $Y_2$, ${\cdots}$, $Y_n$. In this paper a James-Stein type estimator with shrinkage form is given when it's variance distribution is specified and when the norm ${\parallel}{\theta}-K{\theta}{\parallel}$ is constrain, where K is an idempotent and symmetric matrix and rank(K) = r. It is characterized a minimal complete class of James-Stein type estimators in this case. And the subclass of James-Stein type estimators that dominate the sample mean is derived.