Spherical fuzzy set (SFS) as one of several non-standard fuzzy sets, it introduces a number tripl... more Spherical fuzzy set (SFS) as one of several non-standard fuzzy sets, it introduces a number triplet (a,b,c) that satisfies the requirement a 2 þ b 2 þ c 2 1 to express membership grades. Due to the expression, SFS has a more extensive description space when describing fuzzy information, which attracts more attention in scientific research and engineering practice. Just for this reason, how to describe the fuzzy information more reasonably and perfectly is the hot that scholars pay close attention to. In view of this hot, in this paper, the notion of spherical hesitant fuzzy set is introduced as a generalization of spherical fuzzy sets. Some basic operations using sine trigonometric function are presented for spherical hesitant fuzzy sets. We define spherical hesitant fuzzy weighted average and spherical hesitant fuzzy weighted geometric aggregation operators. Based on these new aggregation operators, we propose a method for multi-criteria decision making (MCDM) in the spherical hesitant fuzzy information. Besides, a numerical real-life application about solid waste collection system selection is provided to demonstrate the validity of the proposed approaches along with relevant discussions, the merits of proposed approaches are also analyzed by validity test.
Wreath product, a powerful construction in group theory, has found extensive applications in vari... more Wreath product, a powerful construction in group theory, has found extensive applications in various areas of mathematics and computer science. In this paper, we present a comprehensive analysis of coding matrices associated with wreath products. The coding matrices for the wreath product of two cyclic finite groups were given for the first time. It gives a generalization of the coding matrices for the semi-direct product. We found out that the coding matrix of wreath product really has the same shape as the one for semidirect product and gave the RW-matrix for the coding matrix. An example was showed to illustrate the assertions. Conditions were also given for different wreath products of cyclic groups and that gives different orders for the wreath products.
We parallelly discuss the construction of cyclic linear codes as ideals in the finite cyclic grou... more We parallelly discuss the construction of cyclic linear codes as ideals in the finite cyclic group ring as well as zero-divisors therein. We also determine a complete set of primitive idempotents in the finite cyclic group ring over a field of characteristic p.
We investigate the effect of the restriction and induction functors on the indecomposable modules... more We investigate the effect of the restriction and induction functors on the indecomposable modules of finite cyclic p-group algebra over a field of characteristic. Such functors are significant in studying modules in blocks with cyclic defect groups.
We investigate the effect of the restriction and induction functors on the indecomposable modules... more We investigate the effect of the restriction and induction functors on the indecomposable modules of finite cyclic p-group algebra over a field of characteristic. Such functors are significant in studying modules in blocks with cyclic defect groups.
International Journal of Nonlinear Analysis and Applications, 2017
The purpose of this paper is to investigate the real quadratic number fields Q( √ d) which contai... more The purpose of this paper is to investigate the real quadratic number fields Q( √ d) which contain the specific form of the continued fractions expansions of integral basis element where d ≡ 2, 3(mod4) is a square free positive integer. Besides, the present paper deals with determining the fundamental unit d = ( td + ud √ d ) /2 〉 1 and nd and md Yokoi’s d-invariants by reference to continued fraction expansion of integral basis element where ` (d) is a period length. Moreover, we mention class number for such fields. Also, we give some numerical results concluded in the tables.
Fundamental Journal of Mathematics and Applications, 2018
We use the BN-pair structure for the general linear group to write a suitable listing of the elem... more We use the BN-pair structure for the general linear group to write a suitable listing of the elements of the finite group GL(2, q) which is then used to determine its ring of matrices. This approach of identifying finite group ring with ring of matrices has been used effectively to construct linear codes, benefiting from the ring-theoretic structure of both group rings and the ring of matrices.
We study the points of ( external ) tensor algebras with a concentration on the tensor product of... more We study the points of ( external ) tensor algebras with a concentration on the tensor product of G-algebras. Concepts that are usually associated with G-algebras ( such as Brauer maps , defect pointed groups , source points , multiplicities…etc ) are discussed and shown to be compatible with tensor G-algebras. Finally we present some applications to defect groups of tensor modules and recover some previously known results in this direction.
We show that Brauer-Fitting correspondence as well as the notion of pseudo-blocks of endomorphism... more We show that Brauer-Fitting correspondence as well as the notion of pseudo-blocks of endomorphism algebras are both compatible with the external tensor product of modules and algebras.
The Hecke algebras associated with the Young subgroups of S n acts on the corresponding Specht mo... more The Hecke algebras associated with the Young subgroups of S n acts on the corresponding Specht module by scalars given by Green character. This partially (and in some cases completely) characterizes the Specht module as being eigenvectors for the elements of the Hecke algebra with eigenvalues given by the values of Green character. We define an equivalence relation which simplifies the problem of calculating the values of such character and reduce it to a combinatorial one. We also determine the values of that character in the case of two parts partition of n.
This paper is a survey report on some results on properties of modules which are being indicated ... more This paper is a survey report on some results on properties of modules which are being indicated by the Brauer-Fitting correspondence that links the representation theory of the endomorphism algebra E(Y) of a module Y over a finite dimensional algebra with the -components of the module Y. The invistigations include properties of -components of Y such as projectivity, the socle structure of projective indecomposable -modules and the -block distribution of such components. This approch is applied to invistigate modules over certain concrete examples of finite groups [e.g. the Steinberg module of finite groups of Lie type and Young modules for the symmetric groups]. It turns out that; although the E(Y) -block linkage of the simple E(Y) -modules implies the -block linkage of the corresponding component of Y , the two relations are not completely compatible except for special kinds of endomorphism algebras. To provide such compatibility we introduce the notion of psudoblocks o...
This paper is based on the fact that the non-stable blocks of the modular Hecke algebra for the g... more This paper is based on the fact that the non-stable blocks of the modular Hecke algebra for the general linear group can be parametrized by the partitions of n. We study the central elements of such blocks and determine basis elements of the block that involved in the center.
Spherical fuzzy set (SFS) as one of several non-standard fuzzy sets, it introduces a number tripl... more Spherical fuzzy set (SFS) as one of several non-standard fuzzy sets, it introduces a number triplet (a,b,c) that satisfies the requirement a 2 þ b 2 þ c 2 1 to express membership grades. Due to the expression, SFS has a more extensive description space when describing fuzzy information, which attracts more attention in scientific research and engineering practice. Just for this reason, how to describe the fuzzy information more reasonably and perfectly is the hot that scholars pay close attention to. In view of this hot, in this paper, the notion of spherical hesitant fuzzy set is introduced as a generalization of spherical fuzzy sets. Some basic operations using sine trigonometric function are presented for spherical hesitant fuzzy sets. We define spherical hesitant fuzzy weighted average and spherical hesitant fuzzy weighted geometric aggregation operators. Based on these new aggregation operators, we propose a method for multi-criteria decision making (MCDM) in the spherical hesitant fuzzy information. Besides, a numerical real-life application about solid waste collection system selection is provided to demonstrate the validity of the proposed approaches along with relevant discussions, the merits of proposed approaches are also analyzed by validity test.
Wreath product, a powerful construction in group theory, has found extensive applications in vari... more Wreath product, a powerful construction in group theory, has found extensive applications in various areas of mathematics and computer science. In this paper, we present a comprehensive analysis of coding matrices associated with wreath products. The coding matrices for the wreath product of two cyclic finite groups were given for the first time. It gives a generalization of the coding matrices for the semi-direct product. We found out that the coding matrix of wreath product really has the same shape as the one for semidirect product and gave the RW-matrix for the coding matrix. An example was showed to illustrate the assertions. Conditions were also given for different wreath products of cyclic groups and that gives different orders for the wreath products.
We parallelly discuss the construction of cyclic linear codes as ideals in the finite cyclic grou... more We parallelly discuss the construction of cyclic linear codes as ideals in the finite cyclic group ring as well as zero-divisors therein. We also determine a complete set of primitive idempotents in the finite cyclic group ring over a field of characteristic p.
We investigate the effect of the restriction and induction functors on the indecomposable modules... more We investigate the effect of the restriction and induction functors on the indecomposable modules of finite cyclic p-group algebra over a field of characteristic. Such functors are significant in studying modules in blocks with cyclic defect groups.
We investigate the effect of the restriction and induction functors on the indecomposable modules... more We investigate the effect of the restriction and induction functors on the indecomposable modules of finite cyclic p-group algebra over a field of characteristic. Such functors are significant in studying modules in blocks with cyclic defect groups.
International Journal of Nonlinear Analysis and Applications, 2017
The purpose of this paper is to investigate the real quadratic number fields Q( √ d) which contai... more The purpose of this paper is to investigate the real quadratic number fields Q( √ d) which contain the specific form of the continued fractions expansions of integral basis element where d ≡ 2, 3(mod4) is a square free positive integer. Besides, the present paper deals with determining the fundamental unit d = ( td + ud √ d ) /2 〉 1 and nd and md Yokoi’s d-invariants by reference to continued fraction expansion of integral basis element where ` (d) is a period length. Moreover, we mention class number for such fields. Also, we give some numerical results concluded in the tables.
Fundamental Journal of Mathematics and Applications, 2018
We use the BN-pair structure for the general linear group to write a suitable listing of the elem... more We use the BN-pair structure for the general linear group to write a suitable listing of the elements of the finite group GL(2, q) which is then used to determine its ring of matrices. This approach of identifying finite group ring with ring of matrices has been used effectively to construct linear codes, benefiting from the ring-theoretic structure of both group rings and the ring of matrices.
We study the points of ( external ) tensor algebras with a concentration on the tensor product of... more We study the points of ( external ) tensor algebras with a concentration on the tensor product of G-algebras. Concepts that are usually associated with G-algebras ( such as Brauer maps , defect pointed groups , source points , multiplicities…etc ) are discussed and shown to be compatible with tensor G-algebras. Finally we present some applications to defect groups of tensor modules and recover some previously known results in this direction.
We show that Brauer-Fitting correspondence as well as the notion of pseudo-blocks of endomorphism... more We show that Brauer-Fitting correspondence as well as the notion of pseudo-blocks of endomorphism algebras are both compatible with the external tensor product of modules and algebras.
The Hecke algebras associated with the Young subgroups of S n acts on the corresponding Specht mo... more The Hecke algebras associated with the Young subgroups of S n acts on the corresponding Specht module by scalars given by Green character. This partially (and in some cases completely) characterizes the Specht module as being eigenvectors for the elements of the Hecke algebra with eigenvalues given by the values of Green character. We define an equivalence relation which simplifies the problem of calculating the values of such character and reduce it to a combinatorial one. We also determine the values of that character in the case of two parts partition of n.
This paper is a survey report on some results on properties of modules which are being indicated ... more This paper is a survey report on some results on properties of modules which are being indicated by the Brauer-Fitting correspondence that links the representation theory of the endomorphism algebra E(Y) of a module Y over a finite dimensional algebra with the -components of the module Y. The invistigations include properties of -components of Y such as projectivity, the socle structure of projective indecomposable -modules and the -block distribution of such components. This approch is applied to invistigate modules over certain concrete examples of finite groups [e.g. the Steinberg module of finite groups of Lie type and Young modules for the symmetric groups]. It turns out that; although the E(Y) -block linkage of the simple E(Y) -modules implies the -block linkage of the corresponding component of Y , the two relations are not completely compatible except for special kinds of endomorphism algebras. To provide such compatibility we introduce the notion of psudoblocks o...
This paper is based on the fact that the non-stable blocks of the modular Hecke algebra for the g... more This paper is based on the fact that the non-stable blocks of the modular Hecke algebra for the general linear group can be parametrized by the partitions of n. We study the central elements of such blocks and determine basis elements of the block that involved in the center.
Uploads
Papers by Ahmed Khammash