• Journal of the Korean Electrochemical Society
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• v.10 no.3
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• pp.219-228
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• 2007

The phase-shift method and correlation constants, i.e., the electrochemical impedance spectroscopy (EIS) techniques for studying linear relationships between the behaviors (${\varphi}\;vs.\;E$) of the phase shift ($0^{\circ}{\leq}-{\varphi}{\leq}90^{\circ}$) for the optimum intermediate frequency and those (${\theta}\;vs.\;E$) of the fractional surface coverage ($1{\geq}{\theta}{\geq}0$), have been proposed and verified to determine the Langmuir, Frumkin, and Temkin adsorption isotherms (${\theta}\;vs.\;E$) of H for the cathodic $H_2$ evolution reaction (HER) at noble and transition-metal/aqueous solution interfaces. At the Pt/0.1 MKOH aqueous solution interface, the Langmuir, Frumkin, and Temkin adsorption isotherms (${\theta}\;vs.\;E$), equilibrium constants ($K=5.6{\times}10^{-10}\;mol^{-1}\;at\;0{\leq}{\theta}<0.81$, $K=5.6{\times}10^{-9}{\exp}(-4.6{\theta})\;mol^{-1}\;at\;0.2<{\theta}<0.8$, and $K=5.6{\times}10^{-10}{\exp}(-12{\theta})\;mol^{-1}\;at\;0.919<{\theta}{\leq}1$, interaction parameters (g = 4.6 for the Temkin and g = 12 for the Frumkin adsorption isotherm), rates of change of the standard free energy ($r=11.4\;kJ\;mol^{-1}$ for g=4.6 and $r=29.8\;kJ\;mol^{-1}$ for g=12), and standard free energies (${\Delta}G_{ads}^0=52.8\;kJ\;mol^{-1}\;at\;0{\leq}{\theta}<0.81,\;49.4<{\Delta}G_{\theta}^0<56.2\;kJ\;mol^{-1}\;at\;0.2<{\theta}<0.8$ and $80.1<{\Delta}_{\theta}^0{\leq}82.5\;kJ\;mol^{-1}\;at\;0.919<{\theta}{\leq}1$) of OH for the anodic $O_2$ evolution reaction (OER) are also determined using the phase-shift method and correlation constants. The adsorption of OH transits from the Langmuir to the Frumkin adsorption isotherm (${\theta}\;vs.E$), and vice versa, depending on the electrode potential (E) or the fractional surface coverage (${\theta}$). At the intermediate values of ${\theta}$, i.e., $0.2<{\theta}<0.8$, the Temkin adsorption isotherm (${\theta}\;vs.\;E$) correlating with the Langmuir or the Frumkin adsorption isotherm (${\theta}\;vs.\;E$), and vice versa, is readily determined using the correlation constants. The phase-shift method and correlation constants are accurate and reliable techniques to determine the adsorption isotherms and related electrode kinetic and thermodynamic parameters. They are useful and effective ways to study the adsorptions of intermediates (H, OH) for the sequential reactions (HER, OER) at the interfaces.

• Korean Journal of Soil Science and Fertilizer
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• v.28 no.3
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• pp.227-232
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• 1995

The model equations including scaling factors to estimate the soil water characteristics curve(SWCC) without direct measurement of soil water tension were developed. Scaling were applied to a data set of soil water content, soil water tension, particle size distribution, and OM contents of the 134 soil samples with the 10 soil textural classes. The capability of the model equations was tested on another 205 soil samples. The parameter, ${\theta}^*$, of soil water contents was used by scale transformation as follows : ${\theta}^*=[{\theta}i-{\theta}(1.5MPa)]$/$[{\theta}(10KPa)-{\theta}(1.5MPa)]$ Using ${\theta}^*$ a model equation to estimate SWCC, which was applicable to all textural classes, was developed as follows: $H(0.1MPa)=0.13{\cdot}({\theta}^*)^{-2.04}$. Other model equations to estimate the water content at the soil water tension of 10KPa [${\theta}(10KPa)$] and 1.5MPa [${\theta}(1.5MPa)$], which are required to ${\theta}^*$ were developed by using scale factors of sand(S) and silt(Si) content and organic matter content(OM) as foilows : ${\theta}(10KPa)=26.80-3.99ln[S]+2.36{\sqrt{[Si]}}+2.88[OM]$ ($R=0.81^{**}$) ${\theta}(1.5KPa)=15.75-2.86ln[S]+0.55{\sqrt{[Si]}}+0.70[OM]$ ($R=0.76^{**}$) The measured and estimated values of ${\theta}(1/30MPa)$ on the 205 soil samples were highly correlated on 1 : 1 corresponding line with $R=0.85^{**}$.

• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.847-853
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• 1998

Suppose we want to compare following non-hierarchical log-linear models, $H_0:f(x, heta inTheta_a)$ vs H_1:g(x, heta inTheta_eta); for; Theta_a,;Theta_etasubsetTheta;such;that;Theta_$\alpha$/ Theta_eta$. The goodness of fit test using the likelihood ratio test statistic for comparing these models could not be acceptable. By using the polyhedrons plots of Choi and Hong (1995), we propose a method to decide a better model between two non-hierarchical log-linear models $f(x: heta inTheta_a) and g(x: heta inTheta_eta)$.

• Journal of the Korean Statistical Society
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• v.19 no.2
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• pp.113-121
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• 1990

Let ${X_n : n=1,2,\cdots}$ be iid random variables with distribution $P_{\theta}, \theta \in H$ where $H$ is some abstract parameter space. We consider a sequential confidence interval I for the mean $\mu = \mu(\theta)$ of $P_{\theta}$ satisfying $P_{\theta}(\mu \in I) \geq 1-\alpha$ and $P_{\theta}(\mu-\delta(\mu) \in I) \leq \beta$ for all $\theta \in H$ for any given an imprecision real valued function $\delta(\mu) > 0$ and error probabilities $0 < \alpha, \beta < 1$. A one-sided sequential confidence interval is constructed under some restriction of the family {P_{\theta} : \theta \in H}$ and the imprecision function $\delta$. This is extended to the two-sided cases.

• Korean Journal of Soil Science and Fertilizer
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• v.48 no.6
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• pp.712-723
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• 2015

This study was conducted to develop the SWCC estimation equation using scaling technique, and to investigate relative sensitivity of the SWCC according to the soil water tension, for the four kinds of soil texture such as Sand [S], Sandy Loam [SL], Loam [L] and Clay Loam [CL]. The SWCC estimation equation of scale factor [${\Theta}sc$] (Eq. 1) was developed based on the log function (Eq. 2) and exponential function (Eq. 3). ${\Theta}sc=[({\Theta}-{\Theta}r)/({\Theta}s-{\Theta}r)]$ (Eq. 1) ${\Theta}sc=-0.196ln(H)+0.4888$ (Eq. 2) ${\Theta}sc=0.3804(H)^{(-0.448)}$ (Eq. 3) where, ${\Theta}$: water content (g/g %), ${\Theta}s$: water content at 0.1bar, ${\Theta}r$: water content at 15bar, H: soil water tension (matric potential) (bar) Relative sensitivity of soil water content was decreased as increase soil water tension, those according to soil water tension were 0.952~0.620 compared to 0.1bar case. Relative sensitivity of scale factor was also decreased as increase soil water tension, those according to soil water tension were 0.890~0.577 compared to 0.2bar case.

• Journal of Environmental Science International
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• v.14 no.2
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• pp.241-249
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• 2005

This study deals with micellar effects on dephosphorylation of diphenyl-4- nitrophenylphosphate (DPNPPH), diphenyl-4-nitrophenylphosphinate (DPNPlN) and isopropylphenyl-4-nitrophenyl phosphinate (IPNPlN) mediated by $OH^\Theta$ or o-iodosobenzoate ion $(IB^\Theta)$ in aqueous and CTAX solutions. Dephosphorylation of DPNPPH, DPNPIN and IPNPIN mediated by $OH^\Theta$ or o-iodosobenzoate ion $(IB^\Theta)$ is relatively slow in aqueous solution. The reactions in CTAX micellar solutions are, however, much accelerated because CTAX micelles can accommodate both reactants in their Stem layer in which they can easily react, while hydrophilic $OH^\Theta\;(or\;IB^\Theta)$ and hydrophobic substrates are not mixed in water. Even though the concentrations $(>10^{-3}\;M)\;of\;OH^\Theta\;(or\;IB^\Theta)$ in CTAX solutions are much larger amounts than those $(6\times10^{-6}\;M)$ of substrates, the rate constants of the dephosphorylations are largely influenced by the change of concentration of the ions, which means that the reactions are not followed by the pseudo first order kinetics. In comparison to effect of the counter ions of CTAX in the reactions, CTACI is more effective on the dephosphorylation of substrates than CTABr due to easier expelling of $Cl^\Theta$ ion by $OH^\Theta\;(or\;IB^\Theta)$ ion from the micelle, because of easier solvation of $Cl^\Theta$ ion by water molecules. The reactivity of IPNPlN with $OH^\Theta\;(or\;IB^\Theta)$ is lower than that of DPNPlN. The reason seems that the 'bulky' isopropyl group of IPNPIN hinders the attack of the nucleophiles.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.117-129
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• 2005

We give a generalization of bilateral mock theta functions of order eight and show that they are $F_q$-functions. We also give an integral representation for these functions. We give a relation between mock theta functions of the first set and bilateral mock theta functions of the second set.

• Journal of Environmental Science International
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• v.15 no.5
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• pp.485-491
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• 2006

In the aqueous solutions the dephosphorylations of isopropyl phenyl-4-nitrophenyl phosphinate(IPNPIN) mediated by hydroxide$(OH^{\theta})$ and o-iodosobenzoate$(IB^{\theta})$ ions ate relatively slow, because of hydrophobicity of the substrate, and however it appears that $OH^{\theta}$ is inherently better nucleophile than $IB^{\theta}$, which is more soft ion. On the other hand, in cetyltrimetyiammonium bromide(CTABr) solutions which contain cationic micelles, the dephosphorylations of IPNPIN mediated by $OH^{\theta}$ or $IB^{\theta}$ ate very accelerated to 120 or 100,000 times as compared with those in the aqueous solutions. The values of pseudo first order rate constants reach a maximum with increasing. Such rate maxima are typical of micellar catalysed bimolecular reactions and the rise in rate constant followed by a gradual decrese is characteristic of reactions of hydrophobic substrates. In the cationic micellar solutions of CTABr, $IB^{\theta}$ accelerates the reactions much more than that $OH^{\theta}$ does. The reason seems that $IB^{\theta}$ which is more hydrophobic and soft ion than $OH^{\theta}$ is more easily moved into the Stern layer of the CTABr micelles than $OH^{\theta}$. In the anionic micellar solutions of sodium dodecyl sulfate(SDS), the dephosrhorylations of IPNPIN ate slower than those in aqeous solutions. It means that $OH^{\theta}$ or $IB^{\theta}$ cannot easily move and approach to the Stern layer of the micelle in which almost all the hydrophobic substrate are located and which has a negative circumstance.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.595-611
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• 2001

Let Q(n,1) be the set of even unimodular positive definite integral quadratic forms in n-variables. Then n is divisible by 8. For A[X] in Q(n,1), the theta series $\theta$(sub)A(z) = ∑(sub)X∈Z(sup)n e(sup)$\pi$izA[X] (Z∈h (※Equations, See Full-text) the complex upper half plane) is a modular form of weight n/2 for the congruence group Γ$_1$(8) = {$\delta$∈SL$_2$(Z)│$\delta$≡()mod 8} (※Equation, See Full-text). If n$\geq$24 and A[X], B{X} are tow quadratic forms in Q(n,1), the quotient $\theta$(sub)A(z)/$\theta$(sub)B(z) is a modular function for Γ$_1$(8). Since we identify the field of modular functions for Γ$_1$(8) with the function field K(X$_1$(8)) of the modular curve X$_1$(8) = Γ$_1$(8)＼h(sup)* (h(sup)* the extended plane of h) with genus 0, we can express it as a rational function of j(sub) 1,8 over C which is a field generator of K(X$_1$(8)) and defined by j(sub)1,8(z) = $\theta$$_3$(2z)/$\theta$$_3$(4z). Here, $\theta$$_3$ is the classical Jacobi theta series.

• 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.