scholarly journals Fuzzy Bases of Fuzzy Domains

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Sanping Rao ◽  
Qingguo Li
Keyword(s):  
Domain Theory ◽  
Galois Connections ◽  
Algebraic Domains ◽  
Algebraic Domain

This paper is an attempt to develop quantitative domain theory over frames. Firstly, we propose the notion of a fuzzy basis, and several equivalent characterizations of fuzzy bases are obtained. Furthermore, the concept of a fuzzy algebraic domain is introduced, and a relationship between fuzzy algebraic domains and fuzzy domains is discussed from the viewpoint of fuzzy basis. We finally give an application of fuzzy bases, where the image of a fuzzy domain can be preserved under some special kinds of fuzzy Galois connections.

scholarly journals The local triangle axiom in topology and domain theory

2003 ◽  
Vol 4 (1) ◽  
pp. 47 ◽  
Author(s):  
Pawel Waszkiewicz
Keyword(s):  
Complete Characterization ◽  
Domain Theory ◽  
General Context ◽  
Topological Spaces ◽  
General Notion ◽  
Algebraic Domains ◽  
Partial Metrics ◽  
Semimetric Spaces ◽  
Metrization Theorem

We introduce a general notion of distance in weakly separated topological spaces. Our approach differs from existing ones since we do not assume the reflexivity axiom in general. We demonstrate that our partial semimetric spaces provide a common generalization of semimetrics known from Topology and both partial metrics and measurements studied in Quantitative Domain Theory. In the paper, we focus on the local triangle axiom, which is a substitute for the triangle inequality in our distance spaces. We use it to prove a counterpart of the famous Archangelskij Metrization Theorem in the more general context of partial semimetric spaces. Finally, we consider the framework of algebraic domains and employ Lebesgue measurements to obtain a complete characterization of partial metrizability of the Scott topology.

Domain theory of polarization echoes in ferroelectrics

1982 ◽  
Vol 43 (3) ◽  
pp. 567-574 ◽  
Author(s):  
U. Kh. Kopvillem ◽  
S.V. Prants
Keyword(s):  
Domain Theory

scholarly journals Learning From a Complementary-Label Source Domain: Theory and Algorithms

2021 ◽  
pp. 1-15
Author(s):  
Yiyang Zhang ◽  
Feng Liu ◽  
Zhen Fang ◽  
Bo Yuan ◽  
Guangquan Zhang ◽  
...  
Keyword(s):  
Domain Theory ◽  
Source Domain

scholarly journals Continuous Domains in Formal Concept Analysis*

2021 ◽  
Vol 179 (3) ◽  
pp. 295-319
Author(s):  
Longchun Wang ◽  
Lankun Guo ◽  
Qingguo Li
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Continuous Functions ◽  
Formal Context ◽  
Formal Concept ◽  
Contractive Mappings ◽  
Continuous Domains ◽  
Algebraic Domains ◽  
Scott Continuous ◽  
Continuous Domain

Formal Concept Analysis (FCA) has been proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notion of contractive mappings over formal contexts is proposed, which can be viewed as a generalization of interior operators on sets into the framework of FCA. Then, by considering subset-selections consistent with contractive mappings, the notions of attribute continuous formal contexts and continuous concepts are introduced. It is shown that the set of continuous concepts of an attribute continuous formal context forms a continuous domain, and every continuous domain can be restructured in this way. Moreover, the notion of F-morphisms is identified to produce a category equivalent to that of continuous domains with Scott continuous functions. The paper also investigates the representations of various subclasses of continuous domains including algebraic domains and stably continuous semilattices.

Determination of Intrinsic Magnetic Parameters of SmCo5 Phase in Sintered Samples

2005 ◽  
Vol 498-499 ◽  
pp. 129-133 ◽  
Author(s):  
Marcos Flavio de Campos ◽  
Fernando José Gomes Landgraf
Keyword(s):  
Powder Metallurgy ◽  
Domain Wall ◽  
Kerr Effect ◽  
Critical Diameter ◽  
Optical Microscope ◽  
Domain Theory ◽  
Magnetic Domains ◽  
Magnetic Parameters ◽  
Intrinsic Parameters

SmCo5 magnets are usually produced by powder metallurgy route, including milling, compaction and orientation under magnetic field, sintering and heat treatment. The samples produced by powder metallurgy, with grain size around 10 μm, are ideal for determination of intrinsic parameters. The first step for determination of intrinsic magnetic parameters is obtaining images of domain structure in demagnetized samples. In the present study, the domain images were produced by means of Kerr effect, in a optical microscope. After the test of several etchings, Nital appears as the most appropriate for observation of magnetic domains by Kerr effect. Applying Stereology and Domain Theory, several intrinsic parameters of SmCo5 phase were determined: domain wall energy 120 erg/cm2, critical diameter for single domain particle size 2 μm and domain wall thickness 60 Å. In the case of SmCo5, and also other phases with high magnetocrystalline anisotropy, Domain Theory presents several advantages when compared with Micromagnetics.

scholarly journals Fuzzy Galois connections on fuzzy sets

2018 ◽  
Vol 352 ◽  
pp. 26-55 ◽  
Author(s):  
Javier Gutiérrez García ◽  
Hongliang Lai ◽  
Lili Shen
Keyword(s):  
Fuzzy Sets ◽  
Galois Connections
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