Our aim in this paper is to study the relationships between min-cs modules and some other known generalizations of cs-modules such as ECS-modules, P-extending modules and n-extending modules. Also we introduce and study the relationships between direct sum of mic-cs modules and mc-injectivity.

Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.

The present study examines the main points of differences in the subject of greetings between the English language and the Arabic language. From the review of the related literature on greetings in both languages, it is found that Arabic greeting formulas are more elaborate than the English greetings, because of the differences in the social customs and the Arabic traditions and the Arabic culture. It is also found that Arabic greetings carry a religious meaning basing on the Islamic principle of “the same or more so”, which might lead to untranslatable loopholes when rendered in English.

A total of 61 bat specimens belonging to three species were collected from four distinct sites in the middle of Iraq. Five species of acarine ectoparasites on bats were found. These were: Steatonyssus periblepharus Kolenati, Spinturnix acuminatus (C. L. K.). Cheletonella sp. Rhizoglyphus sp., and Argas sp. Three of the recorded species were new to Iraqi fauna. The abundance and accurence of each parasite was varied from one species to another. S. periblepharus aria S. acuminatus were the most common species found in this study.

In this study, ceramic purifier (CP) was produced from a mixture of Iraqi raw materials. This ceramic mixture was prepared using Bentonite as a Clay, Porcelanite as a Silica, and Limestone as a flux. The produced ceramic filter was formed by semi-dry compressing method and was fired at 1200 C?. Physical properties of the produced CP were measured. A hydraulic test rig was constructed to study the hydraulic conductivity of the produced CP. The average hydraulic conductivity of the produced CP was 55 times that of commercial types of ceramic filters. The mineral composition of the produced ceramics was found by X-Ray tests. Tests results showed that all of the produced ceramics filters composed mainly of low Cristobalte and Tridoymite in addi

The paper is devoted to solve nth order linear delay integro-differential equations of convolution type (DIDE's-CT) using collocation method with the aid of B-spline functions. A new algorithm with the aid of Matlab language is derived to treat numerically three types (retarded, neutral and mixed) of nth order linear DIDE's-CT using B-spline functions and Weddle rule for calculating the required integrals for these equations. Comparison between approximated and exact results has been given in test examples with suitable graphing for every example for solving three types of linear DIDE's-CT of different orders for conciliated the accuracy of the results of the proposed method.