Let  be a commutative ring with identity. The aim of this paper is introduce the notion of a pseudo primary-2-absorbing submodule as generalization of 2-absorbing submodule and a pseudo-2-absorbing submodules. A proper submodule  of an -module  is called pseudo primary-2-absorbing if whenever , for , , implies that either                  or  or . Many basic properties, examples and characterizations of these concepts are given. Furthermore, characterizations of pseudo primary-2-absorbing submodules in some classes of modules are introduced. Moreover, the behavior of a pseudo primary-2-absorbing submodul

Let R be a ring and let A be a unitary left R-module. A proper submodule H of an R-module A is called 2-absorbing , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H or rs∈[H:A], and a proper submodule H of an R-module A is called quasi-prime , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H. This led us to introduce the concept pseudo quasi-2-absorbing submodule, as a generalization of both concepts above, where a proper submodule H of an R-module A is called a pseudo quasi-2-absorbing submodule of A, if whenever rsta∈H,where r,s,t∈R,a∈A, implies that either rsa∈H+soc(A) or sta∈H+soc(A) or rta∈H+soc(A), where soc(A) is socal of an

Statistical learning theory serves as the foundational bedrock of Machine learning (ML), which in turn represents the backbone of artificial intelligence, ushering in innovative solutions for real-world challenges. Its origins can be linked to the point where statistics and the field of computing meet, evolving into a distinct scientific discipline. Machine learning can be distinguished by its fundamental branches, encompassing supervised learning, unsupervised learning, semi-supervised learning, and reinforcement learning. Within this tapestry, supervised learning takes center stage, divided in two fundamental forms: classification and regression. Regression is tailored for continuous outcomes, while classification specializes in c

BOOK REVIEW

The aim of this paper is to introduce the concept of N  and Nβ -closed sets in terms of neutrosophic topological spaces. Some of its properties are also discussed.

This paper introduces some properties of separation axioms called α -feeble regular and α -feeble normal spaces (which are weaker than the usual axioms) by using elements of graph which are the essential parts of our α -topological spaces that we study them. Also, it presents some dependent concepts and studies their properties and some relationships between them.

Excerption and inclusion are two terms in Arabic rhetoric. The excerption is defined as a taking a part of text from Holly Quran or Hadith and put it in a poem, verse line, or put it in a prose text. But the linguistics expand the concept of this term to include taking from another sciences and knowledge, like Grammar, Philology, and Prosody.
Inclusion is defined as taking a verse line or part of verse line from another poet to put it in a new poem, it is necessary that the poet who take the text should declare it, and if he hides it, it will be plagiarism.
This search is use these two terms in architecture, we have now new two terms in architecture, first one; architectural excerption, it means the designer takes a part of religio

Perhaps one of the most pillars in building communities, and to achieve consistency between its members, is the volunteer work, he is a humanitarian exercise been closely associated with all the meanings of goodness and righteousness since ancient times, but it differs in size and shape and motivations and trends from one community to another, and from time to time; while at least in the stages of calm and stability, it increases in disasters and calamities and wars times, and perhaps (the popular crowd) is the best proof of that, they answered a call reference, and volunteered to defend their land and their holy places. In terms of form it may be donating money or effort or profession or otherwise, either in terms of the trend may be di