• Journal of applied mathematics & informatics
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• v.1 no.1
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• pp.31-42
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• 1994

In this paper we investigate an functional central limit theorem for a nonstatioary d-parameter array of associated random variables applying the crite-rion of the tightness condition in Bickel and Wichura[1971]. Our results imply an extension to the nonstatioary case of invariance principle of Burton and Kim(1988) and analogous results for the d-dimensional associated random measure. These re-sults are also applied to show a new functional central limit theorem for Poisson cluster random variables.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.3
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• pp.321-325
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• 2006

The purpose of this paper is to establish the common fixed point theorem in the intuitionistic fuzzy metric space in which it is a little revised in Park [11]. Our research are an extension of Jungck's common fixed point theorem [8] in the intuitionistic fuzzy metric space.

• Journal of applied mathematics & informatics
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• v.3 no.1
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• pp.89-100
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• 1996

In this paper we investigate a limit theorem for a non-statioary d-parameter array of associated random variables applying the criterion of the tightness condition in Donsker, M[1951]. Our re-sults imply an extension to the nonstatioary case of Convergence of Probability Measure of billingsley. P[1986]. and analogous results for the d-dimensional associated random measure. These results are also applied to show a new limit theorem for Poisson cluster random mea-sures.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.273-285
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• 2006

In this paper, we shall give an affirmative answer to the question raised by Kim and Tan [1] dealing with generalized vector quasi-variational inequalities which generalize many existence results on (VVI) and (GVQVI) in the literature. Using the maximal element theorem, we derive two theorems on the existence of weak solutions of (GVQVI), one theorem on the existence of strong solution of (GVQVI), and one theorem on strong solution in the 1-dimensional case.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.757-764
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• 2013

In this paper, we give sufficient conditions for a map with nonconvex values to have a continuous selection and the selection extension property in LC-metric spaces under the one-point extension property. And we apply it to weakly lower semicontinuous maps and generalize previous results. We also get a continuous selection theorem for almost lower semicontinuous maps with closed sub-admissible values in $\mathbb{R}$-trees.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1235-1245
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• 2021

Using recent L² extension theorems, we give an analytic proof under some conditions of Zariski's theorem on zero-dimensional base loci. This motivates further discussions on the crucial curvature conditions in L² extension theorems.

• East Asian mathematical journal
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• v.16 no.2
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• pp.331-337
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• 2000

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.83-85
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• 1985

Let K be a real function field over a real closed field F. Then there exists an F-place .phi.:K.rarw.F.cup.{.inf.}. This is Lang's Existence of Rational Place Theorem (6). There is an equivalent version of Lang's Theorem in (4). That is, if K is a function field over a field F, then, for any ordering P$_{0}$ on F which extends to K, there exists an F-place .phi.: K.rarw.F'.cup.{.inf.} where F' is a real closure of (F, P$_{0}$). In [2], Knebusch pointed out the converse of the version of Lang's Theorem is also true. By a valuation theoretic approach to Lang's Theorem, we have found out the following generalization of Lang and Knebusch's Theorem. Let K be an arbitrary extension field of a field F. then an ordering P$_{0}$ on F can be extended to an ordering P on K if there exists an F-place of K into some real closed field R containing F. Of course R$^{2}$.cap.F=P$_{0}$. The restriction K being a function field of F is vanished, though the codomain of the F-place is slightly varied. Therefore our theorem is a generalization of Lang and Knebusch's theorem.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.655-668
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• 2012

An operator $T\;{\varepsilon}\;B(\mathcal{H})$ is said to be $k$-quasi-paranormal operator if $||T^{k+1}x||^2\;{\leq}\;||T^{k+2}x||\;||T^kx||$ for every $x\;{\epsilon}\;\mathcal{H}$, $k$ is a natural number. This class of operators contains the class of paranormal operators and the class of quasi - class A operators. In this paper, using the operator matrix representation of $k$-quasi-paranormal operators which is related to the paranormal operators, we show that every algebraically $k$-quasi-paranormal operator has Bishop's property ($\beta$), which is an extension of the result proved for paranormal operators in [32]. Also we prove that (i) generalized Weyl's theorem holds for $f(T)$ for every $f\;{\epsilon}\;H({\sigma}(T))$; (ii) generalized a - Browder's theorem holds for $f(S)$ for every $S\;{\prec}\;T$ and $f\;{\epsilon}\;H({\sigma}(S))$; (iii) the spectral mapping theorem holds for the B - Weyl spectrum of T.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.235-246
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• 2010

A Banach space operator A $\in$ B(X) is polaroid if the isolated points of the spectrum of A are poles of the resolvent of A; A is hereditarily polaroid, A $\in$ ($\mathcal{H}\mathcal{P}$), if every part of A is polaroid. Let $X^n\;=\;\oplus^n_{t=i}X_i$, where $X_i$ are Banach spaces, and let A denote the class of upper triangular operators A = $(A_{ij})_{1{\leq}i,j{\leq}n$, $A_{ij}\;{\in}\;B(X_j,X_i)$ and $A_{ij}$ = 0 for i > j. We prove that operators A $\in$ A such that $A_{ii}$ for all $1{\leq}i{\leq}n$, and $A^*$ have the single-valued extension property have spectral properties remarkably close to those of Jordan operators of order n and n-normal operators. Operators A $\in$ A such that $A_{ii}$ $\in$ ($\mathcal{H}\mathcal{P}$) for all $1{\leq}i{\leq}n$ are polaroid and have SVEP; hence they satisfy Weyl's theorem. Furthermore, A+R satisfies Browder's theorem for all upper triangular operators R, such that $\oplus^n_{i=1}R_{ii}$ is a Riesz operator, which commutes with A.