The goal of this discussion is to study the twigged of pure-small (pr-small) sub- moduleof a module W as recirculation of a small sub-module, and we give some basic idiosyncrasy and instances of this kind of sub-module. Also, we give the acquaint of pure radical of a module W (pr-radical) with peculiarities.

The main goal of this paper is to dualize the two concepts St-closed submodule and semi-extending module which were given by Ahmed and Abbas in 2015. These dualizations are called CSt-closed submodule and cosemi-extending mod- ule. Many important properties of these dualizations are investigated, as well as some others useful results which mentioned by those authors are dualized. Furthermore, the relationships of cosemi-extending and other related modules are considered.

Abstract The purpose of this paper is to preparing small games for fifth graders. And to identify the impact of these small games in developing some concepts of traffic safety for fifth graders. The two researchers used the experimental method to solve the research problem, and the research community was identified with students. The fifth grade of primary school in the province of Baghdad and a sample was chosen from the private Baghdad Primary School, which numbered (60) male and female students. They were distributed equally into two groups by simple random method (experimental and control groups). As for the most important conclusions reached by the two researchers, it is the presence of an effect of small games in developing some conce

Solar energy usage in Iraq is facing many issues; one of those is the accumulation “of the dust on the surface of the solar module which” would highly lower its efficiency. The present work study the effect of dust accumulation” on installing fixed solar modules with different inclined angles 15^o, 33^o, 45^o, 60^o. Evaluation of the solar modules performance under different circumstance conditions such as rain, wind and humidity are considered in study of dust effect on solar module performance. The results show that the lowest output average efficiencies of solar modules occurs at 15^o horizontally inclined angle are 7.4% , 6.7% , 8.0% , 8.1%, and 8.4% for the cor

Let A be a unital algebra, a Banach algebra module M is strongly fully stable Banach A-module relative to ideal K of A, if for every submodule N of M and for each multiplier θ : N → M such that θ(N) ⊆ N ∩ KM. In this paper, we adopt the concept of strongly fully stable Banach Algebra modules relative to an ideal which generalizes that of fully stable Banach Algebra modules and we study the properties and characterizations of strongly fully stable Banach A-module relative to ideal K of A.

The importance of topology as a tool in preference theory is what motivates this study in which we characterize topologies generating by digraphs. In this paper, we generalized the notions of rough set concepts using two topological structures generated by out (resp. in)-degree sets of vertices on general digraph. New types of topological rough sets are initiated and studied using new types of topological sets. Some properties of topological rough approximations are studied by many propositions.

Rice is a major staple food for more than two thirds of the world population. Pathogenesis-related proteins-10 (PR10) have a range of 154 to 163 amino acid with molecular weight ~ 17 kDa.  They are acidic and generally intracellular and cytosolic proteins accumulate in plants in response to biotic and abiotic stresses. In the present study, a PR10 gene and its corresponding protein were characterized in O. sativa, O.  barthii, O. glaberrima, O. glumipatula, O. meridionalis, O. nivara, O. rufipogon and  O. punctata. The results revealed a narrow range of variation at both DNA and protein levels in all examined species except O. glumipatula. The latter showed a relatively

Security reflects a permanent and complex movement that complies with international and societal needs and developments in all its dimensions, interactions and levels. To constitute a universal demand for all States, communities and individuals. The question of security is one of the most important motivations and motivations that govern the behavior, and even the objectives of those societies and States. These groups or individuals have always sought to avoid fear and harm, and to provide stability, safety and security. In the light of this, security studies have been among the important fields of study in the field of international and strategic relations. The field witnessed many theoretical efforts, from the traditional perspective,