Let R be an associative ring with identity, and let M be a unital left R-module, M is called totally generalized *cofinitely supplemented module for short ( T G*CS), if every submodule of M is a Generalized *cofinitely supplemented ( G*CS ). In this paper we prove among the results under certain condition the factor module of T G*CS is T G*CS and the finite sum of T G*CS is T G*CS.

      Faintly continuous (FC) functions, entitled faintly S-continuous and faintly δS-continuous functions have been introduced and investigated via a -open and -open sets. Several characterizations and properties of faintly S-continuous and faintly -Continuous functions were obtained. In addition, relationships between faintly s- Continuous and faintly S-continuous function and other forms of FC function were investigated. Also, it is shown that every faintly  S-continuous is weakly S-continuous. The Convers is shown to be satisfied only if the co-domain of the function is almost regular.

Background: Human leukocyte antigen (HLA) is the most polymorphic genetic system in man. The genes of this region influence susceptibility to certain diseases.
Patients and methods: Immunofixation test is the method used to asses C4 polymorphism of 100 blood samples of 60 AIH patients and 40 healthy normal controls.
Results: An increased frequency of C4A*Q0 was observed for patients group versus control group with P-value (0.003).
Conclusions: This finding demonstrated that C4A*Q0 might play a role in AIH susceptibility.

        A new generalizations of coretractable modules are introduced where a module  is called t-essentially (weakly t-essentially) coretractable if for all proper submodule  of , there exists f End( ), f( )=0 and Imf _tes  (Im f + _tes ). Some basic properties are studied and many relationships between these classes and other related one are presented.

The method of incineration was chosen to treat the most commonly used antimicrobial agents in Iraq (Triclabendazol, Oxfendazol, Mebendazole), which are antibiotics for children. The moisture content and chemical oxygen demand (COD) were examined and the results were (93.34, 94.88, 92.97)%, (52000, 33200, and 64000) mg/ L. The temperature was determined as a variable in the burning process (600, 500, 400)° C for the purpose of calculating the loss of ignition LOI and determining the ideal temperature. The results of the models (Triclabendazol, Oxfendazol, Mebendazole) (94.92, 93.12, 58.81% and 88.87), (62.61, 44.08%, 98.75, 84.98 and 55.086)% respectively. When mixing the three models in equal proportions, the percentage of loss was 92.8

The contract of participation ended with ownership is considered as a new contract which preceded the legislations and accompanying the reality in which the parties of contract go into partnership in a certain project and sharing its profit and loss where any party shall own the project through buying the portion of the other party or parties from the incomes of that project or any other resources as a single payment or in form of payments as agreed.

This type of contract has special provisions that made us to choose the specialty of contract of participation that ended with ownership as a subject to be discussed in this research through three research works:

1. The specialty of the concept of contract of participatio

The aim of this paper is introducing the concept of (ɱ,ɳ) strong full stability B-Algebra-module related to an ideal. Some properties of (ɱ,ɳ)- strong full stability B-Algebra-module related to an ideal have been studied and another characterizations have been given. The relationship of (ɱ,ɳ) strong full stability B-Algebra-module related to an ideal that states,  a B- -module Ӽ is (ɱ,ɳ)- strong full stability B-Algebra-module related to an ideal  , if and only if  for any two ɱ-element sub-sets and of Ӽ^ɳ, if , for each j = 1, …, ɱ,  i = 1,…, ɳ  and   implies _Ạɳ( ) _Ạɳ(  have been proved..

Often phenomena suffer from disturbances in their data as well as the difficulty of formulation, especially with a lack of clarity in the response, or the large number of essential differences plaguing the experimental units that have been taking this data from them. Thus emerged the need to include an estimation method implicit rating of these experimental units using the method of discrimination or create blocks for each item of these experimental units in the hope of controlling their responses and make it more homogeneous. Because of the development in the field of computers and taking the principle of the integration of sciences it has been found that modern algorithms used in the field of Computer Science genetic algorithm or ant colo

The present experimental work is conducted to examine the influence of adding Alumina (Al₂O₃) nanoparticles and Titanium oxide (TiO₂) nanoparticles each alone to diesel fuel on the characteristic of the emissions. The size of both Alumina and Titanium oxide nanoparticles which have been added to diesel fuel to obtain nano-fuel is about 20 nm and 25 nm respectively. Three doses of (Al₂O₃) and (TiO₂) were prepared (25, 50, and 100) ppm. The nanoparticles mixed with gas oil fuel by mechanical homogenous (manual electrical mixer) and ultrasonic processor. The study reveals that the adding of Aluminum oxide (Al₂O₃) and Titanium oxide (TiO₂) to g

    Let R be a commutative ring with unity and let M, N be unitary R-modules. In this research, we give generalizations for the concepts: weakly relative injectivity, relative tightness and weakly injectivity of modules. We call M weakly N-quasi-injective, if for each f  Hom(N,) there exists a submodule X of  such that  f (N)  X ≈ M, where  is the quasi-injective hull of M. And we call M N-quasi-tight, if every quotient N / K of N which embeds in  embeds in M. While we call M weakly quasi-injective if M is weakly N-quasiinjective for every finitely generated R-module N.         Moreover, we generalize some properties of weakly N-injectiv