المتغير العشوائي X  له توزيع أسي اذا كان له دالة احتمالية الكثافة بالشكل:

عندما  ، هذه هي الحالة الخاصة لتوزيع كاما.

غالباً جداً ولسبب معقول تأخذ . الحالة الخاصة لـ (1) التي نحصل عليها تسمى بالتوزيع الاسي لمعلمة واحدة.

اذا كانت  ، ، التوزيع في هذه الحالة يسمى التوزيع الاسي القياسي

اما بالنسب

Let R be a commutative ring with identity and let M be a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of semi-essential submodules which introduced by Ali S. Mijbass and Nada K. Abdullah, and we make simple changes to the definition relate with the zero submodule, so we say that a submodule N of an R-module M is called semi-essential, if whenever N ∩ P = (0), then P = (0) for each prime submodule P of M. Various properties of semi-essential submodules are considered.

In this paper we study the notion of preradical on some subcategories of the category of semimodules and homomorphisms of semimodules.
Since some of the known preradicals on modules fail to satisfy the conditions of preradicals, if the category of modules was extended to semimodules, it is necessary to investigate some subcategories of semimodules, like the category of subtractive semimodules with homomorphisms and the category of subtractive semimodules with ҽҟ-regular homomorphisms.

 Let R be a commutative ring with 10 and M is a unitary R-module . In this paper , our aim is to continue studying 2-absorbing submodules which are introduced by  A.Y. Darani and F. Soheilina . Many new properties and characterizations are given .

Let M be an R-module, where R is a commutative ring with unity. A submodule N of M is called e-small (denoted by N e  M) if N + K = M, where K e  M implies K = M. We give many properties related with this type of submodules.

        Let R be a commutative ring with identity, and let M be a unitary R-module. We introduce a concept of almost bounded submodules as follows: A submodule N of an R-module M is called an almost bounded submodule if there exists xÃŽM, xÏN such that ann_R(N)=ann_R(x).

        In this paper, some properties of almost bounded submodules are given. Also, various basic results about almost bounded submodules are considered.

        Moreover, some relations between almost bounded submodules and other types of modules are considered.

The soft sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these concepts to define new types of soft limit points, that we called soft turning points.Finally, we used these points to define new types of soft separation axioms and we study their properties.

Let R be associative; ring; with an identity and let D be unitary left R- module; . In this work we present semiannihilator; supplement submodule as a generalization of R-a- supplement submodule, Let U and V be submodules of an R-module D if D=U+V and whenever Y≤ V and D=U+Y, then annY≪R;. We also introduce the the concept of semiannihilator -supplemented ;modules and semiannihilator weak; supplemented modules, and we give some basic properties of this conseptes.