scholarly journals Fuzzy Hypervector Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
R. Ameri ◽  
O. R. Dehghan
Keyword(s):  
Fundamental Theorem ◽  
The Other ◽  
Vector Spaces ◽  
Fuzzy Subset ◽  
Fuzzy Vector

The aim of this paper is the generalization of the notion of fuzzy vector spaces to fuzzy hypervector spaces. In this regard, by considering the notion of fuzzy hypervector spaces, we characterized a fuzzy hypervector space based on its level sub-hyperspace. The algebraic nature of fuzzy hypervector space under transformations is studied. Certain conditions are obtained under which a given fuzzy hypervector space can or cannot be realized as a union of two fuzzy hypervector spaces such that none is contained in the other. The construction of a fuzzy hypervector space generated by a given fuzzy subset of a hypervector space is given. The set of all fuzzy cosets of a fuzzy hypervector space is shown to be a hypervector space. Finally, a fuzzy quotient hypervector space is defined and an analogue of a consequence of the “fundamental theorem of homomorphisms” is obtained.

Spectral statistics of orthogonal and symplectic ensembles

2018 ◽  
Author(s):  
Greg W. Anderson
Keyword(s):  
Orthogonal Polynomials ◽  
Fundamental Theorem ◽  
The Other ◽  
Classical Orthogonal Polynomials ◽  
The Matrix ◽  
Spectral Statistics ◽  
Orthogonal And Symplectic Ensembles ◽  
The One ◽  
Gap Probabilities ◽  
Matrix Kernels

This article describes a direct approach for computing scalar and matrix kernels, respectively for the unitary ensembles on the one hand and the orthogonal and symplectic ensembles on the other hand, leading to correlation functions and gap probabilities. In the classical orthogonal polynomials (Hermite, Laguerre, and Jacobi), the matrix kernels for the orthogonal and symplectic ensemble are expressed in terms of the scalar kernel for the unitary case, using the relation between the classical orthogonal polynomials going with the unitary ensembles and the skew-orthogonal polynomials going with the orthogonal and symplectic ensembles. The article states the fundamental theorem relating the orthonormal and skew-orthonormal polynomials that enter into the Christoffel-Darboux kernels

Bases of fuzzy vector spaces

1993 ◽  
Vol 67 (1-2) ◽  
pp. 87-92 ◽  
Author(s):  
John N. Mordeson
Keyword(s):  
Vector Spaces ◽  
Fuzzy Vector

scholarly journals Fundamental theorem of prehomogeneous vector spaces of characteristic p

1997 ◽  
Vol 56 (2) ◽  
pp. 331-341
Author(s):  
Tatsuo Kimura ◽  
Takeyoshi Kogiso ◽  
Makiko Fujinaga
Keyword(s):  
Local Field ◽  
Fundamental Theorem ◽  
Functional Equations ◽  
Local Fields ◽  
Vector Spaces ◽  
Characteristic P ◽  
Prehomogeneous Vector Spaces

For a local field of characteristic 0, the functional equations of zeta distributions of prehomogeneous vector spaces have been obtained by M. Sato, Shintani, Igusa, F. Sato and Gyoja. In this paper, we shall consider the case of local fields of characteristic p > 0.

GLOBAL ZETA FUNCTIONS OF FREUDENTHAL QUARTICS

2002 ◽  
Vol 13 (08) ◽  
pp. 797-820
Author(s):  
HIROSHI SAITO
Keyword(s):  
Vector Space ◽  
Zeta Function ◽  
Explicit Formula ◽  
Explicit Form ◽  
Zeta Functions ◽  
The Other ◽  
Vector Spaces ◽  
Prehomogeneous Vector Space ◽  
Prehomogeneous Vector Spaces

We give two applications of an explicit formula for global zeta functions of prehomogeneous vector spaces in Math. Ann.315 (1999), 587–615. One is concerned with an explicit form of global zeta functions associated with Freudenthal quartics, and the other the comparison of the zeta function of a unsaturated prehomogeneous vector space with that of the saturated one obtained from it.

scholarly journals Conorms over anti fuzzy vector spaces

2020 ◽  
Vol 4 (1) ◽  
pp. 158-167
Author(s):  
Rasul Rasuli ◽  
Keyword(s):  
Vector Spaces ◽  
Fuzzy Vector

scholarly journals Weighted Fuzzy Sets

2020 ◽  
Vol 8 (5) ◽  
pp. 766-769
Keyword(s):  
Fuzzy Sets ◽  
External Factors ◽  
The Other ◽  
Fuzzy Subset ◽  
Factors Influencing ◽  
Internal And External Factors

The weighted fuzzy subset is to describe the importance of each element in the set through the characteristi3c function. In this paper, we study how an element and its presence in the set, namely, the degree of belongingness plays a role in determining the characteristic level of the set. Presence of an element in the set strengthens the set to a greater extent. Set gets its weightage, because of its elements and its association with the other elements. Association depicts the internal and external factors influencing over an element. In other words, the proposed weighted fuzzy subset has 3-tuple representation such as elements in a set, degree of presence of an elements and degree of impact of the set because of each elements presence.

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