• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1027-1039
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• 2005

Consider the problem of estimating a $p{\times}1$ mean vector $\theta(p\geq4)$ under the quadratic loss, based on a sample $X_1$, $X_2$, $\cdots$, $X_n$. We find a Lindley type decision rule which shrinks the usual one toward the mean of observations when the underlying distribution is that of a variance mixture of normals and when the norm $\parallel\;{\theta}-\bar{{\theta}}1\;{\parallel}$ is restricted to a known interval, where $bar{{\theta}}=\frac{1}{p}\;\sum\limits_{i=1}^{p}{\theta}_i$ and 1 is the column vector of ones. In this case, we characterize a minimal complete class within the class of Lindley type decision rules. We also characterize the subclass of Lindley type decision rules that dominate the sample mean.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.343-352
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• 2006

A real matrix A is called a sign-central matrix if for, every matrix $\tilde{A}$ with the same sign pattern as A, the convex hull of columns of $\tilde{A}$ contains the zero vector. A sign-central matrix A is called a tight sign-central matrix if the Hadamard (entrywise) product of any two columns of A contains a negative component. A real vector x = $(x_1,{\ldots},x_n)^T$ is called stable if $\|x_1\|{\leq}\|x_2\|{\leq}{\cdots}{\leq}\|x_n\|$. A tight sign-central matrix is called a $tight^*$ sign-central matrix if each of its columns is stable. In this paper, for a matrix B, we characterize those matrices C such that [B, C] is tight ($tight^*$) sign-central. We also construct the matrix C with smallest number of columns among all matrices C such that [B, C] is $tight^*$ sign-central.

• Journal of Microbiology and Biotechnology
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• v.25 no.2
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• pp.247-254
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• 2015

In this presentation, I describe the expression and purification of the recombinant liver X receptor β-ligand binding domain proteins in E. coli using a commercially available double cistronic vector, pACYCDuet-1, to express the receptor heterodimer in a single cell as the soluble form. I describe here the expression and characterization of a biologically active heterodimer composed of the liver X receptor β-ligand binding domain and retinoid X receptor α-ligand binding domain. Although many of these proteins were previously seen to be produced in E. coli as insoluble aggregates or "inclusion bodies", I show here that as a form of heterodimer they can be made in soluble forms that are biologically active. This suggests that co-expression of the liver X receptor β-ligand binding domain with its binding partner improves the solubility of the complex and probably assists in their correct folding, thereby functioning as a type of molecular chaperone.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.573-586
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• 2016

We study the conditional integral transforms and conditional convolutions of functionals defined on K[0, T]. We consider a general vector-valued conditioning functions $X_k(x)=({\gamma}_1(x),{\ldots},{\gamma}_k(x))$ where ${\gamma}_j(x)$ are Gaussian random variables on the Wiener space which need not depend upon the values of x at only finitely many points in (0, T]. We then obtain several relationships and formulas for the conditioning functions that exist among conditional integral transform, conditional convolution and first variation of functionals in $E_{\sigma}$.

• The Pure and Applied Mathematics
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• v.11 no.2
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• pp.155-166
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• 2004

In this paper, we introduce new monotone concepts for set-valued mappings, called generalized C(x)-L-pseudomonotonicity and weakly C(x)-L-pseudomonotonicity. And we obtain generalized Minty-type lemma and the existence of solutions to vector variational inequality problems for weakly C(x)-L-pseudomonotone set-valued mappings, which generalizes and extends some results of Konnov & Yao [11], Yu & Yao [20], and others Chen & Yang [6], Lai & Yao [12], Lee, Kim, Lee & Cho [16] and Lin, Yang & Yao [18].

• Korean Journal of Mathematics
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• v.19 no.1
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• pp.77-85
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• 2011

In [7], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $${\sum_{i=1}^{n}}\left\|x_i-{\frac{1}{n}}{\sum_{j=1}^{n}}x_j \right\|^2={\sum_{i=1}^{n}}{\parallel}x_i{\parallel}^2-n\left\|{\frac{1}{n}}{\sum_{i=1}^{n}}x_i \right\|^2$$ holds for all $x_1$, ${\cdots}$, $x_n{\in}V$. Let V, W be real vector spaces. It is shown that if an even mapping $f:V{\rightarrow}W$ satisfies $$(0.1)\;{\sum_{i=1}^{2n}f}\(x_i-{\frac{1}{2n}}{\sum_{j=1}^{2n}}x_j\)={\sum_{i=1}^{2n}}f(x_i)-2nf\({\frac{1}{2n}}{\sum_{i=1}^{2n}}x_i\)$$ for all $x_1$, ${\cdots}$, $x_{2n}{\in}V$, then the even mapping $f:V{\rightarrow}W$ is quadratic. Furthermore, we prove the generalized Hyers-Ulam stability of the quadratic functional equation (0.1) in Banach spaces.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.783-791
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• 1998

A random vector X on $R^{d}$ with the following properties is constructed: the distribution of X is infinitely divisible and not selfdecomposable, but every linear transformation of X to a lower-dimensional space has a selfdecomposable distribution.

• Proceedings of the KSMRM Conference
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• 2001.11a
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• pp.57-63
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• 2001

Tensor 하면 최근 3D로 white matter내의 섬유질을 멋있게 그려내는 diffusion tensor를 연상합니다. 하지만 여기서 다룰 tensor는 수학적 연산자(operator)입니다. NMR 혹은 MRI에서 스핀을 vector로 표시하고, 이 vector 스핀이 90도 rf pulse에 의해서 z축에서 x-y Plane으로 rotation되는 것을 vector diagram으로 나타냅니다. 그런데 이 vector notation으로는 스핀에 일어나는 여러 현상들을 수식적으로 모델 하는데 한계가 있습니다. 그래서 도입된 모델이 product operator와 tensor operator입니다 (1, 2, 3). 한 예로 우리가 다루는 proton NMR 신호가 single quantum인데 23Na 등에는 multiple quantum 신호가 생기게 되며 이는 vector로는 나타낼 수가 없으며 tensor로 분석이 가능합니다 (4, 5).

• Honam Mathematical Journal
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• v.25 no.1
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• pp.163-172
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• 2003

In this paper we study the property of harmonic vector fields. We call a vector fields ${\xi}$ harmonic if it is a harmonic map from the manifold into its tangent bundle with the Sasaki metric. We show that the characteristic polynomial of operator $A={\nabla}{\xi}\;in\;S^{2n+1}\;is\;(x^2+1)^n$.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1677-1703
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• 2008

In this paper, we introduce and study various locally convex vector topologies on the space of bounded linear operators between Banach spaces. We also apply these topologies to approximation properties.