• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.527-540
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• 2010

We characterize the boundedness and compactness of the weighted composition operator on the logarithmic Bloch space $\mathcal{L}\ss=\{f{\in}H(D):sup_D(1-|z|^2)ln(\frac{2}{1-|z|})|f'(z)|$<+$\infty$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$. The results generalize the known corresponding results on the composition operator and the pointwise multiplier on the logarithmic Bloch space ${\mathcal{L}\ss$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.751-759
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• 2015

In this paper, we give new characterizations of the boundedness and compactness of composition operators $C_{\varphi}$ between Bloch type spaces in the unit ball $\mathbb{B}^n$, in terms of the power of the components of ${\varphi}$, where ${\varphi}$ is a holomorphic self-map of $\mathbb{B}^n$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1225-1233
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• 2011

In this paper, without assumption of monotonicity, we study the compactness and the connectedness of the weakly efficient solutions set to vector equilibrium problems by using scalarization method in locally convex spaces. Our results improve the corresponding results in [X. H. Gong, Connectedness of the solution sets and scalarization for vector equilibrium problems, J. Optim. Theory Appl. 133 (2007), 151-161].

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.253-292
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• 2018

In this paper, we introduce a general Ricci flow system, which is closely linked with the Ricci flow and the renormalization group flow, etc. We prove the short-time existence, the entropy functionals, the higher derivatives estimates and the compactness theorem for this general Ricci flow system on closed Riemannian manifolds. These basic results are useful tools to understand the singularities of this system.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.10a
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• pp.57-59
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• 1997

The concept of fuzzy sets was introduced by Zad도 in his highly influential paper [5]. Using this concept, Chang [1] introduced a notion of fuzzy topological spaces which formally is the same one as for ordinary topological spaces. Observing that with Chang's definition constant maps between fuzzy topological spaces are not necessarily continuous, Lowen [2] gave an alternative and more natural definition for a fuzzy topological spaces and characterized the fuzzy compact spaces by means of prefilters in [4]. In this paper we give new characterizations of fuzzy compact spaces introduced in [2]. These results explain more clearly fuzzy compactness in fuzzy topological spaces.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.223-234
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• 2005

We introduce the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set and obtain some of their structural properties. We also introduce the concepts of several types of quasi-smooth ${\alpha}$- compactness in terms of the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set and investigate some of their properties.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.233-240
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• 2006

In this paper we introduce the concepts of several types of $weak^*$ quasi-smooth ${\alpha}$-compactness in terms of the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set in smooth topological spaces and investigate some of their properties.

• East Asian mathematical journal
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• v.23 no.2
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• pp.213-227
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• 2007

In this paper the concept of fuzzy nearly C-compactness is introduced in Generalized fuzzy topological spaces. Several characterizations and some interesting properties of these spaces in Generalized fuzzy topological spaces are discussed. The properties of fuzzy almost continuous and fuzzy almost open functions in Generalized fuzzy topological spaces are also studied.

• Journal of the Chungcheong Mathematical Society
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• v.14 no.1
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• pp.29-40
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• 2001

In this note, we get the conditions such that strong continuity ${\Rightarrow}$ weak continuity plus interiority condition( wc+ic), and continuity ${\Rightarrow}$ wc+ic are true. And we investigate some equivalent conditions with weak continuity, some properties of weak continuity. And we show that almost compactness is preserved by weakly continuous function, and we improve some known results with respect to strong continuity.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.4
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• pp.261-268
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• 2009

In this paper we introduce stronger form of the notion of cover so-called p-cover which is more appropriate. According to this cover we introduce and study another type of compactness in L-fuzzy topology so-called $C^*$-compact and study some of its properties with some interrelation.