• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.403-414
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• 2019

Theta functions are the sections of line bundles on a complex torus. Noncommutative versions of theta functions have appeared as theta vectors and quantum theta operators. In this paper we describe a super version of theta vectors and quantum theta operators. This is the natural unification of Manin's result on bosonic operators, and the author's previous result on fermionic operators.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.249-256
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• 2016

There are many concepts around classical theta functions, theta vectors and quantum theta functions. Manin clarified the relation among these concepts with the symmetry of functional equations. We extend his results to the super torus.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.503-517
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• 2016

For positive integers d and n, let $[n]^d$ be the set of all vectors ($a_1,a_2,{\cdots},a_d$), where ai is an integer with $0{\leq}a_i{\leq}n-1$. A subset S of $[n]^d$ is called a Sidon set if all sums of two (not necessarily distinct) vectors in S are distinct. In this paper, we estimate two numbers related to the maximum size of Sidon sets in $[n]^d$. First, let $\mathcal{Z}_{n,d}$ be the number of all Sidon sets in $[n]^d$. We show that ${\log}(\mathcal{Z}_{n,d})={\Theta}(n^{d/2})$, where the constants of ${\Theta}$ depend only on d. Next, we estimate the maximum size of Sidon sets contained in a random set $[n]^d_p$, where $[n]^d_p$ denotes a random set obtained from $[n]^d$ by choosing each element independently with probability p.

• Communications for Statistical Applications and Methods
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• v.20 no.4
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• pp.329-337
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• 2013

Consider a p-variate($p{\geq}3$) normal distribution with mean ${\theta}$ and covariance matrix ${\sum}={\sigma}^2{\mathbf{I}}_p$ for any unknown scalar ${\sigma}^2$. In this paper we improve the James-Stein estimator of ${\theta}$ in cases of shrinking toward some vectors using the Stein variance estimator. It is also shown that this domination does not hold for the positive part versions of these estimators.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.435-442
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• 2017

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}$ (p ${\geq}$ 3) under the quadratic loss from multi-variate normal population. We find a James-Stein type estimator which shrinks towards the projection vectors when the underlying distribution is that of a variance mixture of normals. In this case, the norm ${\parallel}{\theta}-K{\theta}{\parallel}$ is known where K is a projection vector with rank(K) = q. The class of this type estimator is quite general to include the class of the estimators proposed by Merchand and Giri (1993). We can derive the class and obtain the optimal type estimator. Also, this research can be applied to the simple and multiple regression model in the case of rank(K) ${\geq}2$.

• Bulletin of the Korean Chemical Society
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• v.32 no.12
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• pp.4210-4214
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• 2011

Quasiclassical trajectory (QCT) calculations of Ne + ${H_2}^+$ reaction have been carried out on the adiabatic potential energy surface of the ground state $1^2$ A'. The reaction probability of the title reaction for J = 0 has been calculated, and the QCT result is consistent with the previous quantum mechanical wave packet result. Quasiclassical trajectory calculations of the four polarization-dependent differential cross sections have been carried out in the center of mass (CM) frame. The P(${\theta}_r$), P(${\phi}_r$) and P(${\theta}_r$, ${\phi}_r$) distributions, the k-k'-j' correlation and the angular distribution of product rotational vectors are presented in the form of polar plots. Due to the well in $1^2$ A' PES, the reagent vibrational excitation has greater influence on the polarization of the product rotational angular momentum vectors j' than the collision energy.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.649-668
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• 2000

In this paper we prove the following : Let M be a real (2n-1)-dimensional compact minimal semi-invariant submanifold in a complex projective space P(sub)n+1C. If the scalar curvature $\geq$2(n-1)(2n+1), then m is a homogeneous type $A_1$ or $A_2$. Next suppose that the third fundamental form n satisfies dn = 2$\theta\omega$ for a certain scalar $\theta$$\neq$c/2 and $\theta$$\neq$c/4 (4n-1)/(2n-1), where $\omega$(X,Y) = g(X,øY) for any vectors X and Y on a semi-invariant submanifold of codimension 3 in a complex space form M(sub)n+1 (c). Then we prove that M has constant principal curvatures corresponding the shape operator in the direction of the distingusihed normal and the structure vector ξ is an eigenvector of A if and only if M is locally congruent to a homogeneous minimal real hypersurface of M(sub)n (c).

• Honam Mathematical Journal
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• v.23 no.1
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• pp.91-111
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• 2001

In this paper we prove the following : Let M be a semi-invariant submanifold with almost contact metric structure (${\phi}$, ${\xi}$, g) of codimension 3 in a complex hyperbolic space $H_{n+1}{\mathbb{C}}$. Suppose that the third fundamental form n satisfies $dn=2{\theta}{\omega}$ for a certain scalar ${\theta}({\leq}{\frac{c}{2}})$, where ${\omega}(X,\;Y)=g(X,\;{\phi}Y)$ for any vectors X and Y on M. Then M has constant eigenvalues correponding the shape operator A in the direction of the distinguished normal and the structure vector ${\xi}$ is an eigenvector of A if and only if M is locally congruent to one of the type $A_0$, $A_1$, $A_2$ or B in $H_n{\mathbb{C}}$.

• Bulletin of the Korean Chemical Society
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• v.30 no.9
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• pp.1981-1984
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• 2009

Subcellular localization of protein kinase often plays an important role in determining its activity and specificity. Protein kinase C (PKC), a family of multi-gene protein kinases has long been known to be translocated to the particular cellular compartments in response to DAG or its analog phorbol esters. We used C-terminal green fluorescent protein (GFP) fusion proteins of PKC isoforms to visualize the subcellular distribution of individual PKC isoforms. Intracellular localization of PKC-GFP proteins was monitored by fluorescence microscopy after transient transfection of PKC-GFP expression vectors in the HeLa cells. In unstimulated HeLa cells, all PKC isoforms were found to be distributed throughout the cytoplasm with a few exceptions. PKC$\theta$ was mostly localized to the Golgi, and PKC$\gamma$, PKC$\delta$ and PKC$\eta$ showed cytoplasmic distribution with Golgi localization. DAG analog TPA induced translocation of PKC-GFP to the plasma membrane. PKC$\alpha$, PKC$\eta$ and PKC$\theta$ were also localized to the Golgi in response to TPA. Only PKC$\delta$ was found to be associated with the nuclear membrane after transient TPA treatment. These results suggest that specific PKC isoforms are translocated to different intracellular sites and exhibit distinct biological effects.

• Journal of the Korean Solar Energy Society
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• v.21 no.3
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• pp.33-41
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• 2001

This paper showed the a numerical analysis of the thermal and fluid flow in solar concentration absorber with tilt angle, and the purpose of this study is to obtain the optimum tilt angle of the absorber. The boundary conditions of a numerical model were assumed as flows : (1) The heat source is located at the center of absorber (3) The bottom wall is opened and adiabatic. (3) The top, right and left walls are cooled wall. The parameters for the numerical analysis are tilt angles and Rayleigh numbers i.e., tilt angle $\theta=0^{\circ},\;15^{\circ},\;30^{\circ},\;45^{\circ},\;60^{\circ},\;75^{\circ},\;90^{\circ}$ and 101 $\leq$ Ra $\leq$ 103. The velocity vectors and isotherms were dense at wall side and the heat source. The mean Nusselt number had a maximum value at $\theta=0^{\circ}$ and showed a low value as the tilt angles were increased. Finally, the decrease rate of mean Nusselt number was appeared small with tilt angle when Rayleigh numbers were increased.