• 충청수학회지
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• 제35권2호
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• pp.103-113
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• 2022

The notions of soft rough pre open set, soft rough pre closed set, soft rough dense set, soft rough sub maximal, soft rough pre interior and soft rough pre closure are introduced and studied. We also investigate some related properties of these concepts.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.265-272
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• 2023

This article presents a novel notion of hesitant fuzzy cleanly covered in hesitant fuzzy topological spaces;moreover two strong hesitant fuzzy separation axioms are investigated. Based on fuzzy maximal open sets few properties of hesitant fuzzy cleanly covered are obtained. By dint of hesitant fuzzy minimal open and fuzzy maximal closed sets two strong hesitant fuzzy separation axioms are extended.

• 한국실내디자인학회논문집
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• 제25권1호
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• pp.3-12
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• 2016

This study analyses characteristics of space to facilitate community centering on cases of collective houses in Japan and uses the results as basic data to activate collective houses as an alternative form of housing in our country. To identify the characteristics of space for active communities with collective living space, this study conducted a theoretical examination on collective houses and housing, derived territoriality, accessibility, comfort and safety as factors of community activation and analysed various cases, and the results are presented as follows: First, territoriality is a necessary condition for formation of community, and a confined and physical space. It indicates the proper size of a space and diverse spacial areas which meet the needs of residents with the proper size and amount of space (space which can accommodate diverse generations including women, the aged and the young, flexible space which changes according to the purposes and program, space which supports leisure and hobby activities, and space which can accommodate outsiders). Second, accessibility indicates an environment which supports residents' easy use of space. As the more accessible it is, the higher the frequency of its use, spatial factors (piloti, backyards, benches and tables) should be provided, community space should be arranged in a central or decentralized way and community living space should be made for each floor. As for exits, accessibility should be considered in every way; entrances connected with community spaces, open entrances and entrances accessible from outside or individual living spaces. Third, comfort satisfies the physical and mental needs of residents through separation of floors and flows between the community and individual spaces for privacy and formation of eco-friendly spaces including vegetable gardens, gardens and plant arrangements. Fourth, safety should be considered for a higher quality environment with psychological stability and comfort, for which the following are recommended: installation of hand-rails, removal of thresholds, spacial design for the socially weak, duplex and open type structures for community space, open stages and halls, as well as indoor and outdoor openness through the use of windows.

• Korean Journal of Mathematics
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• 제12권2호
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• pp.177-183
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• 2004

In this paper, we introduce the concepts of half-interior, half-closure, half-gp-maps and half-gp-open maps defined by intuitionistic gradations of openness.

• Korean Journal of Mathematics
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• 제15권1호
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• pp.27-37
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• 2007

In this paper, we introduce the concepts of r-semi-generalized fuzzy closed sets, r-semi-generalized fuzzy open sets, r-semi-generalized fuzzy continuous maps in fuzzy topological spaces and investigate some of their properties.

• 대한수학회보
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• 제54권5호
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• pp.1485-1526
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• 2017

We show that birational rigidity of Mori fibre spaces is not open in moduli.

• 대한수학회보
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• 제48권6호
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• pp.1195-1205
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• 2011

Let $H(\mathbb{D})$ denote the class of all analytic functions on the open unit disk $\mathbb{D}$ of the complex plane $\mathbb{C}$. Let n be a nonnegative integer, ${\varphi}$ be an analytic self-map of $\mathbb{D}$ and $u{\in}H(\mathbb{D})$. The generalized weighted composition operator is defined by $$D_{{\varphi},u}^nf=uf^{(n)}{\circ}{\varphi},\;f{\in}H(\mathbb{D})$$. The boundedness and compactness of the generalized weighted composition operator from area Nevanlinna spaces to weighted-type spaces and little weighted-type spaces are characterized in this paper.

• 대한수학회지
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• 제45권5호
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• pp.1203-1220
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• 2008

Let V be an arbitrary system of weights on an open connected subset G of ${\mathbb{C}}^N(N{\geq}1)$ and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let $HV_b$ (G, E) and $HV_0$ (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings ${\phi}:G{\rightarrow}G$ and operator-valued analytic mappings ${\Psi}:G{\rightarrow}B(E)$ which generate weighted composition operators and invertible weighted composition operators on the spaces $HV_b$ (G, E) and $HV_0$ (G, E) for different systems of weights V on G. Also, we obtained compact weighted composition operators on these spaces for some nice classes of weights.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권4호
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• pp.281-284
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• 2009

In [8], we introduced the concept of fuzzy r-minimal structure which is an extension of smooth fuzzy topological spaces and fuzzy topological spaces in Chang's sense. And we also introduced and studied the fuzzy r-M continuity. In this paper, we introduce the concepts of fuzzy r-minimal compactness on fuzzy r-minimal compactness and nearly fuzzy r-minimal compactness, almost fuzzy r-minimal spaces and investigate the relationships between fuzzy r-M continuous mappings and such types of fuzzy r-minimal compactness.

• 대한수학회지
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• 제35권1호
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• pp.177-189
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• 1998

In this paper, weighted Bloch spaces $B_q (q > 0)$ are considered on the open unit ball in $C^n$. These spaces extend the notion of Bloch spaces to wider classes of holomorphic functions. It is proved that the functions in a weighted Bloch space admit certain integral representation. This representation formula is then used to determine the degree of growth of the functions in the space $B_q$. It is also proved that weighted Bloch space is a Banach space for each weight q > 0, and the little Bloch space $B_q,0$ associated with $B_q$ is a separable subspace of $B_q$ which is the closure of the polynomials for each $q \geq 1$.