• 충청수학회지
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• 제18권2호
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• pp.205-213
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• 2005

We introduce the conductance and examine its properties. We study the local behavior of quasiconformal mappings on the boundary of a domain $D{\subset}\overline{R}^n$ n and present some geometric applications of conductance.

• 대한수학회지
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• 제55권1호
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• pp.83-99
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• 2018

We introduce the concept of multiplicatively closed subsets of a commutative ring R which split an R-module M and study factorization properties of elements of M with respect to such a set. Also we demonstrate how one can utilize this concept to investigate factorization properties of R and deduce some Nagata type theorems relating factorization properties of R to those of its localizations, when R is an integral domain.

• 대한수학회지
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• 제34권1호
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• pp.43-55
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• 1997

Suppose that D is a domain in the extended complex plane $\overline{C} = C \cup {\infty}$. For each $z_0 \in C$ and $C < r < \infty$, we let $B(z_0, r) = {z \in C : $\mid$z - z_0$\mid$ < r}$ and $S(z_0, r) = \partial B(z_0, r)$. For non-empty sets A, $B \subset \overling{C}$, diam (A) is the diameter of A and d(A, B) is the distance of A and B.

• Korean Journal of Mathematics
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• 제26권4호
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• pp.757-775
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• 2018

For any non-negative real number ${\epsilon}_0$, we shall introduce a concept of the ${\epsilon}_0$-dense subset of $R^m$. Applying this concept, for any sequence {${\epsilon}_n$} of positive real numbers, we also introduce the concept of the {${\epsilon}_n$}-attainable sequence and of the points of {${\epsilon}_n$}-attainable ace in the open subset of $R^m$. We also study the characteristics of those sequences and of the points of {${\epsilon}_n$}-dense ace. And we research the conditions that an {${\epsilon}_n$}-attainable sequence has no {${\epsilon}_n$}-attainable ace. We hope to reconsider the social consideration on the ace in social life by referring to these concepts about the aces.

• ETRI Journal
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• 제44권1호
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• pp.117-124
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• 2022

In this paper, the performance of precoding-aided differential spatial modulation (PDSM) systems with optimal transmit antenna subset (TAS) selection is examined analytically. The average bit error rate (ABER) performance of the optimal TAS selection-based PDSM systems using a zero-forcing (ZF) precoder is evaluated using theoretical upper bound and Monte Carlo simulations. Simulation results validate the analysis and demonstrate a performance penalty < 2.6 dB compared with precoding-aided spatial modulation (PSM) with optimal TAS selection. The performance analysis reveals a transmit diversity gain of (N_T-N_R+1) for the ZF-based PDSM (ZF-PDSM) systems that employ TAS selection with N_T transmit antennas, N_S selected transmit antennas, and N_R receive antennas. It is also shown that reducing the number of activated transmit antennas via optimal TAS selection in the ZF-PDSM systems degrades ABER performance. In addition, the impacts of channel estimation errors on the performance of the ZF-PDSM system with TAS selection are evaluated, and the performance of this system is compared with that of ZF-based PSM with TAS selection.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권1호
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• pp.49-57
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• 2018

We have introduced two new notions of convexity and closedness in functional analysis. Let X be a real normed space, then $C({\subseteq}X)$ is functionally convex (briefly, F-convex), if $T(C){\subseteq}{\mathbb{R}}$ is convex for all bounded linear transformations $T{\in}B$(X, R); and $K({\subseteq}X)$ is functionally closed (briefly, F-closed), if $T(K){\subseteq}{\mathbb{R}}$ is closed for all bounded linear transformations $T{\in}B$(X, R). By using these new notions, the Alaoglu-Bourbaki-Eberlein-${\check{S}}muljan$ theorem has been generalized. Moreover, we show that X is reflexive if and only if the closed unit ball of X is F-closed. James showed that for every closed convex subset C of a Banach space X, C is weakly compact if and only if every $f{\in}X^{\ast}$ attains its supremum over C at some point of C. Now, we show that if A is an F-convex subset of a Banach space X, then A is bounded and F-closed if and only if every element of $X^{\ast}$ attains its supremum over A at some point of A.

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.555-561
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• 1997

In this paper we show that if A is a Banach algebra with radical R and D is a left derivation on A then $D(A){\subset}R$ if and only if $Q_RD^n$ is continuous for all $n{\geq}1$, where $Q_R$ is the canonical quotient map from A onto A/R.

• 대한수학회보
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• 제32권2호
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• pp.179-189
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• 1995

Let $V \subset R^n$ be a convex homogeneous cone which does not contain straight lines, so that the automorphism group $$ G = Aut(R^n, V)^\circ = { g \in GL(R^n) $\mid$ gV = V}^\circ $$ ($\circ$ denoting the identity component) acts transitively on V. A convex cone V is called "self-dual" if V coincides with its dual $$ (1.1) V' = { x' \in R^n $\mid$ < x, x' > > 0 for all x \in \bar{V} - {0}} $$ where $\bar{V}$ denotes the closure of V.sure of V.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.785-794
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• 2022

In this paper we show that if A ∈ L(X) and R ∈ L(X) is a quasinilpotent operator commuting with A then X_A(F) = X_A+R(F) for all subset F ⊆ ℂ and 𝜎_loc(A) = 𝜎_loc(A + R). Moreover, we show that A and A + R share many common local spectral properties such as SVEP, property (C), property (𝛿), property (𝛽) and decomposability. Finally, we show that quasisimility preserves local spectrum.

• 대한수학회지
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• 제36권4호
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• pp.787-811
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• 1999

Let M be the maximal ideal space of the Banach algebra $H^{\infty}$ of bounded analytic functions on the open unit disc $\triangle$. For a positive singular measure ${\mu}\;on\;{\partial\triangle},\;let\;{L_{+}}^1(\mu)$ be the set of measures v with $0\;{\leq}\;{\nu}\;{\ll}\;{\mu}\;and\;{{\psi}_{\nu}}$ the associated singular inner functions. Let $R(\mu)\;and\;R_0(\mu)$ be the union sets of $\{$\mid$\psiv$\mid$\;<\;1\}\;and\;\{$\mid${\psi}_{\nu}$\mid$\;<\;0\}\;in\;M\;{\setminus}\;{\triangle},\;{\nu}\;\in\;{L_{+}}^1(\mu)$, respectively. It is proved that if $S(\mu)\;=\;{\partial\triangle}$, where $S(\mu)$ is the closed support set of $\mu$, then $R(\mu)\;=\;R0(\mu)\;=\;M{\setminus}({\triangle}\;{\cup}\;M(L^{\infty}(\partial\triangle)))$ is generated by $H^{\infty}\;and\;\overline{\psi_{\nu}},\;{\nu}\;{\in}\;{L_1}^{+}(\mu)$. It is proved that %d{\theta}(S(\mu))\;=\;0$ if and only if there exists as Blaschke product b with zeros $\{Zn\}_n$ such that $R(\mu)\;{\subset}\;{$\mid$b$\mid$\;<\;1}\;and\;S(\mu)$ coincides with the set of cluster points of $\{Zn\}_n$. While, we proved that $\mu$ is a sum of finitely many point measure such that $R(\mu)\;{\subset}\;\{$\mid${\psi}_{\lambda}$\mid$\;<\;1}\;and\;S(\lambda)\;=\;S(\mu)$. Also it is studied conditions on \mu for which $R(\mu)\;=\;R0(\mu)$.