A submoduleA of amodule M is said to be strongly pure , if for each finite subset {ai} in A , (equivalently, for each a ?A) there exists ahomomorphism f : M ?A such that f(ai) = ai, ?i(f(a)=a).A module M is said to be strongly F–regular if each submodule of M is strongly pure .The main purpose of this paper is to develop the properties of strongly F–regular modules and study modules with the property that the intersection of any two strongly pure submodules is strongly pure .

     The purpose of this paper is to introduce dual notions of two known concepts which are semi-essential submodules and semi-uniform modules. We call these concepts; cosemi-essential submodules and cosemi-uniform modules respectively. Also, we verify that these concepts form generalizations of two well-known classes; coessential submodules and couniform modules respectively. Some conditions are considered to obtain the equivalence between cosemi-uniform and couniform. Furthermore, the relationships of cosemi-uniform module with other related concepts are studied, and some conditional characterizations of cosemi-uniform modules are investigated.

Naidid worms were sorted from 27 samples of aquatic macrophyta including ceratophyllum demersum , Potamogeton crispus and, Hydrilla verticellat with associated filamentous algae were collected from Euphrates River at Al-Mussayab city, 60 Km southwest Baghdad. The result of sorted worms revealed the presence of eight species of subfamily Naidinae, which are consider as new records for Iraq, including Stephensoniana trivandrana; Paranais frici, Ophidonais serpentine, Specaria josinae, Dero (Dero) evelinae , Dero (Aulophorus) indicus , Nais pseudobtusa and finally N. stolci. This investigation includes morphological descriptions for each species illustrated by identification criteria photos.

Let R be a commutative ring with non-zero identity element. For two fixed positive integers m and n. A right R-module M is called fully (m,n) -stable relative to ideal A of , if for each n-generated submodule of Mm and R-homomorphism . In this paper we give some characterization theorems and properties of fully (m,n) -stable modules relative to an ideal A of . which generalize the results of fully stable modules relative to an ideal A of R.

To evaluate and improve the efficiency of photovoltaic solar modules connected with linear pipes for water supply, a three-dimensional numerical simulation is created and simulated via commercial software (Ansys-Fluent). The optimization utilizes the principles of the 1st and 2nd laws of thermodynamics by employing the Response Surface Method (RSM). Various design parameters, including the coolant inlet velocity, tube diameter, panel dimensions, and solar radiation intensity, are systematically varied to investigate their impacts on energetic and exergitic efficiencies and destroyed exergy. The relationship between the design parameters and the system responses is validated through the development of a predictive model. Both single and mult

Based on the theoretical ideas of E. Cassirer, a methodology is developed and an analysis of the painting work by J. Saleem, a representative of modern Iraqi painting, is carried out. While comparing the artistic programme of J. Saleem and the views of E. Cassirer, the methodological potential of the theory of the symbol for the art criticism analysis of the regional painting is clarified. Comparative analysis with the inclusion of the works of B. Buffet, B. Turetsky, J. Miro helps to see the multiple meanings of the same cultural symbol in thematically similar works of different years, created in different socio-cultural circumstances. The article shows that for regions with a shorter history (France, Russia, Spain, etc.), which have lo

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.

      Let S be a commutative ring with identity, and A is an S-module. This paper introduced an important concept, namely strongly maximal submodule. Some properties and many results were proved as well as the behavior of that concept with its localization was studied and shown.

    The main objective of this research is to study and to introduce a concept of strong fully stable Banach -algebra modules related to an ideal.. Some properties and characterizations of full stability are studied.

Tests were performed on Marshall samples and were implemented for permanent deformation and resilient modulus (Mr) under indirect tensile repeated loading (ITRL), with constant stress level. Two types of liquid asphalt (cutback and emulsion) were tried as recycling agents, aged materials that were reclaimed from field (100% RAP), samples were prepared from the aged mixture, and two types of liquid asphalt (cutback and emulsion) with a weight content of 0.5% were utilized to prepare a recycled mixture. A group of twelve samples was prepared for each mixture; six samples were tested directly for ITRL test (three samples at 25˚C and three samples at 40˚C), an average value for ITRL for every three samples was calculated (