The restriction concept is a basic feature in the field of measure theory and has many important properties. This article introduces the notion of restriction of a non-empty class of subset of the power set on a nonempty subset of a universal set. Characterization and examples of the proposed concept are given, and several properties of restriction are investigated. Furthermore, the relation between the P*–field and the restriction of the P*–field is studied, explaining that the restriction of the P*–field is a P*–field too. In addition, it has been shown that the restriction of the P*–field is not necessarily contained in the P*–field, and the converse is true. We provide a necessary condition for the P*–field to obtain th

A standard theoretical neutron energy flux distribution is achieved for the triton-triton nuclear fusion reaction in the range of triton energy about ≤10 MeV. This distribution give raises an evidence to provide the global calculations including the characteristics fusion parameters governing the T-T fusion reaction.

We study in this paper the composition operator that is induced by ?(z) = sz + t. We give a characterization of the adjoint of composiotion operators generated by self-maps of the unit ball of form ?(z) = sz + t for which |s|?1, |t|<1 and |s|+|t|?1. In fact we prove that the adjoint is a product of toeplitz operators and composition operator. Also, we have studied the compactness of C? and give some other partial results.

              -convex sets and -convex functions, which are considered as an important class of generalized convex sets and convex functions, have been introduced and studied by Youness [5] and other researchers. This class has recently extended, by Youness, to strongly -convex sets and strongly -convex functions. In these generalized classes, the definitions of the classical convex sets and convex functions are relaxed and introduced with respect to a mapping . In this paper, new properties of strongly -convex sets are presented. We define strongly -convex hull, strongly -convex cone, and strongly -convex cone hull and we proof some of their properties.  Some examples to illustrate the aforementioned concepts and to cl

A cap of size  and degree  in a projective space, (briefly; (k,r)-cap) is a set of  points with the property that each line in the space meet it in at most  points. The aim of this research is to extend the size and degree of complete caps and incomplete caps, (k, r)-caps of degree r<12 in the finite projective space of dimension three over the finite field of order eleven, which already exist and founded by the action of subgroups of the general linear group over the finite field of order eleven and degree four, to (k+i,r+1) -complete caps. These caps have been classified by giving the t_i-distribution and -distribution. The Gap programming has been used to execute the designed algorit

  Let â„› be a commutative ring with unity and let ℬ be a unitary R-module. Let ℵ be a proper submodule of ℬ, ℵ is called semisecond submodule if for any r∈ℛ, r≠0, n∈Z_+, either rⁿℵ=0 or rⁿℵ=rℵ.

In this work, we introduce the concept of semisecond submodule and confer numerous properties concerning with this notion. Also we study semisecond modules as a popularization of second modules, where an ℛ-module ℬ is called semisecond, if ℬ is semisecond submodul of ℬ.

     Let Ḿ be a unitary R-module and R is a commutative ring with identity. Our aim in this paper  to study the concepts T-ABSO fuzzy ideals, T-ABSO fuzzy submodules and T-ABSO quasi primary fuzzy submodules, also we discuss these concepts in the class of multiplication fuzzy modules and relationships between these concepts. Many new basic properties and characterizations on these concepts are given.