• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.657-663
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• 2005

In this paper, we consider groups of permutations S on a set A acting on subsets X of A. In particular, we show that if $X_2{\subseteq}X_1{\subseteq}A$ and Y is an S-normal extension of $X_2 in X_1$, then the Galois group $G_{S}(X_1/Y){\;}of{\;}X_1{\;}over{\;}X_2$ relative to S is an S-closed subgroup of $G_{S}(X_1/X_2)$ in the setting of a Galois theory (correspondence) for this situation.

• 대한수학회논문집
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• 제22권2호
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• pp.297-303
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• 2007

In this paper, we study on C-closed spaces, SC-closed spaces and related spaces. We show that a sequentially compact SC-closed space is sequential and as corollaries obtain that a sequentially compact space with unique sequential limits is sequential if and only if it is C-closed [7, 1.19 Proposition] and every sequentially compact SC-closed space is C-closed. We also show that a countably compact WAP and C-closed space is sequential and obtain that a countably compact (or compact or sequentially compact) WAP-space with unique sequential limits is sequential if and only if it is C-closed as a corollary. Finally we prove that a weakly discretely generated AP-space is C-closed. We then obtain that every countably compact (or compact or sequentially compact) weakly discretely generated AP-space is $Fr\acute{e}chet$-Urysohn with unique sequential limits, for weakly discretely generated AP-spaces, unique sequential limits ${\equiv}KC{\equiv}C-closed{\equiv}SC-closed$, and every continuous surjective function from a countably compact (or compact or sequentially compact) space onto a weakly discretely generated AP-space is closed as corollaries.

• 호남수학학술지
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• 제35권2호
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• pp.303-310
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• 2013

In this paper, we first show that $z_{{\kappa}X}:E_{cc}({\kappa}X){\rightarrow}{\kappa}X$ is $z^{\sharp}$-irreducible and that if $\mathcal{G}(E_{cc}({\beta}X))$ is a base for closed sets in ${\beta}X$, then $E_{cc}({\kappa}X)$ is $C^*$-embedded in $E_{cc}({\beta}X)$, where ${\kappa}X$ is the extension of X such that $vX{\subseteq}{\kappa}X{\subseteq}{\beta}X$ and ${\kappa}X$ is weakly Lindel$\ddot{o}$f. Using these, we will show that if $\mathcal{G}({\beta}X)$ is a base for closed sets in ${\beta}X$ and for any weakly Lindel$\ddot{o}$f space Y with $X{\subseteq}Y{\subseteq}{\kappa}X$, ${\kappa}X=Y$, then $kE_{cc}(X)=E_{cc}({\kappa}X)$ if and only if ${\beta}E_{cc}(X)=E_{cc}({\beta}X)$.

• 대한수학회보
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• 제21권2호
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• pp.87-89
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• 1984

Let X be a Banach space, and let B(X) (resp. CB(X), K(X), CV(X)) denote the family of all nonvoid (resp. closed bounded, compact, convex) subsets of X. The Kuratowski measure of noncompactness is defined by the mapping .alpha.$_{k}$: B(X).rarw. $R_{+}$ with .alpha.$_{k}$(A) = inf {r>0 vertical bar A can be covered by a finite number of sets with diameter less than r}.an r}.

• 대한수학회지
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• 제32권2호
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• pp.311-319
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• 1995

Let $H$ be a separable, infinite dimensional, complex Hilbert space and let $L(H)$ be the algebra of all bounded linear operaors on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $I_H$ and is closed in the $weak^*$ topology on $L(H)$. Note that the ultraweak operator topology coincides with the $weak^*$ topology on $L(H)$ (see [5]).

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제10권2호
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• pp.134-141
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• 2010

We introduce the category IVSet(H) of interval-valued H-fuzzy sets and show that IVSet(H) satisfies all the conditions of a topological universe except the terminal separator property. And we study some relations among IVSet (H), ISet (H) and Set (H).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권1호
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• pp.33-45
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• 2005

We introduce the category ISet(H) of intuitionistic H-fuzzy sets and show that ISet(H) satisfies all the conditions of a topological universe except the terminal separator property. And we study the relation between Set(H) and ISet(H).

• 로봇학회논문지
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• 제15권3호
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• pp.212-220
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• 2020

This paper deals with a strategy of gain optimization for the kinematic control algorithm of a wire-driven surgical robot. The proposed controller consists of the closed-loop inverse kinematics with the back-calculation method. The closed-loop inverse kinematics has 18 PID control gains, and the back-calculation method has 6 gains. An efficient strategy is designed to optimize 18 values first and then the remaining 6 values. The optimal gain sets are searched under the step input with performance indices. In this gain optimization, the objective function is defined as the minimum value of signal-to-noise ratio of the performance indices for 6 DoF (Degree-of-Freedom) motion that is based on the Taguchi method, and the constraints are applied to obtain stable responses for each motion evenly. The gain sets obtained are verified by simulations using the test trajectories. In comparative results, the optimal gain value based on the performance index combined with ISE (integral of square error) and settling time showed the best control performance.

• 호남수학학술지
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• 제32권2호
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• pp.333-362
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• 2010

We define H*H-fuzzy set and form a new category Set(H*H) consisting of H*H-fuzzy sets and morphisms between them. First, we study it in the sense of topological universe and obtain an exponential objects of Set(H*H). Second, we investigate some relationships among the categories Set(H*H), Set(H) and ISet(H).

• 대한수학회보
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• 제51권3호
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• pp.667-680
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• 2014

In this paper, $\mathcal{I}$-scattered spaces are introduced, and their characterizations and properties are given. We prove that (X, ${\tau}$) is scattered if and only if (X, ${\tau}$, $\mathcal{I}$) is $\mathcal{I}$-scattered for any ideal $\mathcal{I}$ on X.