Search results for "Mathematics::General Mathematics"
showing 10 items of 36 documents
On a Category of Extensional Fuzzy Rough Approximation L-valued Spaces
2016
We establish extensionality of some upper and lower fuzzy rough approximation operators on an L-valued set. Taking as the ground basic properties of these operators, we introduce the concept of an (extensional) fuzzy rough approximation L-valued space. We apply fuzzy functions satisfying certain continuity-type conditions, as morphisms between such spaces, and in the result obtain a category \(\mathcal{FRA}{} \mathbf{SPA}(L)\) of fuzzy rough approximation L-valued spaces. An interpretation of fuzzy rough approximation L-valued spaces as L-fuzzy (di)topological spaces is presented and applied for constructing examples in category \(\mathcal{FRA}{} \mathbf{SPA}(L)\).
On another approach to the definition of an L-fuzzy valued integral
2011
We continue to develop a construction of an L-fuzzy valued measure extending a crisp measure defined on a σ-algebra of crisp sets to an L-fuzzy valued measure defined on a T M -tribe. We describe two equivalent approaches to define an L-fuzzy valued integral of non-negative measurable functions.
L-fuzzy syntopogenous structures, Part I: Fundamentals and application to L-fuzzy topologies, L-fuzzy proximities and L-fuzzy uniformities
2013
Abstract We introduce the concept of an L-fuzzy syntopogenous structure where L is a complete lattice endowed with an implicator ↦ : L × L → L satisfying certain properties (in particular, as L one can take an MV-algebra). As special cases our L-fuzzy syntopogenous structures contain classical Csaszar syntopogenous structures, Katsaras–Petalas fuzzy syntopogenous structures as well as fuzzy syntopogeneous structures introduced in the previous work of the second named author (A. Sostak, Fuzzy syntopogenous structures, Quaest. Math. 20 (1997) 431–461). Basic properties of the category of L-fuzzy syntopogenous spaces are studied; categories of L-fuzzy topological spaces, L-fuzzy proximity spac…
A Decomposition Theorem for the Fuzzy Henstock Integral
2012
We study the fuzzy Henstock and the fuzzy McShane integrals for fuzzy-number valued functions. The main purpose of this paper is to establish the following decomposition theorem: a fuzzy-number valued function is fuzzy Henstock integrable if and only if it can be represented as a sum of a fuzzy McShane integrable fuzzy-number valued function and of a fuzzy Henstock integrable fuzzy number valued function generated by a Henstock integrable function.
Green’s Function of a Spin- 1 2 $$\tfrac {1}{2}$$ Particle in a Constant External Magnetic Field
2020
Our objective here is to find the Green’s function of a spin-\(\tfrac {1}{2}\) particle in an external electromagnetic field. Accordingly we start with the defining equation
An Approach to the Concept of Soft Fuzzy Proximity
2014
The purpose of this paper is to introduce the concept of soft fuzzy proximity. Firstly, we give the definitions of soft fuzzy proximity and Katsaras soft fuzzy proximity, and also we investigate the relations between the soft fuzzy proximity and slightly modified version of Katsaras soft fuzzy proximity. Secondly, we induce a soft fuzzy topology from a given soft fuzzy proximity by using soft fuzzy closure operator. Then, we obtain the initial soft fuzzy proximity from a given family of soft fuzzy proximities. So, we describe products in the category of soft fuzzy proximities. Finally, we show that a family of all soft fuzzy proximities on a given set constitutes a complete lattice.
Fuzzy fixed points of generalized F2-geraghty type fuzzy mappings and complementary results
2016
The aim of this paper is to introduce generalized F2-Geraghty type fuzzy mappings on a metric space for establishing the existence of fuzzy fixed points of such mappings. As an application of our result, we obtain the existence of common fuzzy fixed point for a generalized F2-Geraghty type fuzzy hybrid pair. These results unify, generalize and complement various known comparable results in the literature. An example and an application to theoretical computer science are presented to support the theory proved herein. Also, to suggest further research on fuzzy mappings, a Feng–Liu type theorem is proved.
Field Reconstruction for Modeling Multiple Faults in Permanent Magnet Synchronous Motors in Transient States
2021
Conventional field reconstruction model (FRM) for electrical machines has proved its main strength in efficient computations of magnetic fields and forces in healthy permanent magnet synchronous machines (PMSM) or faulty machines in steady states. This study aims to develop a magnet library of different magnet defects and include inter-turn short-circuit (ITSC) in the FRM for PMSM. The developed FRM can model a combination fault between ITSC, and magnet defect in a PMSM in transient states. Within the framework, an 8-turn ITSC was modelled in both finite element analysis (FEA) and FRM, and then identified by the extended Park’s vector approach. The air-gap magnetic field reproduced b…
"Table 8" of "Measurement of charged-particle event shape variables in sqrt(s) = 7 TeV proton-proton interactions with the ATLAS detector"
2014
Mean Values of Thrust, Thrust Minor and Sphericity verses charged particle PT scalar sum.
Fractal photon sieve
2006
A novel focusing structure with fractal properties is presented. It is a photon sieve in which the pinholes are appropriately distributed over the zones of a fractal zone plate. The focusing properties of the fractal photon sieve are analyzed. The good performance of our proposal is demonstrated experimentally with a series of images obtained under white light illumination. It is shown that compared with a conventional photon sieve, the fractal photon sieve exhibits an extended depth of field and a reduced chromatic aberration.