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.

Marriage is a characteristic of the human race, as it is one of the oldest organization, asoldas human beign marrige is a legitimale relationsbip between male and female in the name of Allah "o mankind !Be dutiful to your lord, Who created you from a single person (Adam), and from him (Adam) He created his Wife (Eve), and from them both He created mang men and women
Marriage is a requirement of human life to ensure tle continuity and survival of the human species and established it in a legal, social and legitimate frame,according to certain criteria and conditions so that the individual earns psychological and social comfort in the name of Allah and Allah has made for you Azwaj ( mates or wives), sons and grand sons, and has bestowed

The study includes collection of data about cholera disease from six health centers from nine locations with 2500km2 and a population of 750000individual. The average of infection for six centers during the 2000-2003 was recorded. There were 3007 cases of diarrhea diagnosed as cholera caused by Vibrio cholerae. The percentage of male infection was 14. 7% while for female were 13. 2%. The percentage of infection for children (less than one year) was 6.1%, it while for the age (1-5 years) was 6.9%and for the ages more than 5 years was 14.5%.The total percentage of the patients stayed in hospital was 7.7%(4.2%for male and 3.4%for female). The bacteria was isolated and identified from 7cases in the Central Laboratory for Health in Baghdad. In

R. Vasuki [1] proved fixed point theorems for expansive mappings in Menger spaces. R. Gujetiya and et al [2] presented an extension of the main result of Vasuki, for four expansive mappings in Menger space. In this article, an important lemma is given to prove that the iteration sequence is Cauchy under suitable condition in Menger probabilistic G-metric space (shortly, MPGM-space). And then, used to obtain three common fixed point theorems for expansive type mappings.

Authentication is the process of determining whether someone or something is, in fact, who or what it is declared to be. As the dependence upon computers and computer networks grows, the need for user authentication has increased. User’s claimed identity can be verified by one of several methods. One of the most popular of these methods is represented by (something user know), such as password or Personal Identification Number (PIN). Biometrics is the science and technology of authentication by identifying the living individual’s physiological or behavioral attributes. Keystroke authentication is a new behavioral access control system to identify legitimate users via their typing behavior. The objective of this paper is to provide user

In this work we fabrication holographic optical element diffraction grating thickness 40?m and mirror90?m by using dichromated gelatin,to perform that we have to use the Nd-yaG laser doubling frequency of wavelenght (532)nm and its powers of (80)mWatt.we have studyed the thickness and concentration dichromat effect in mirror reflaction ,effect of angle of reconstruction beam in band width and diffraction efficiency ,study effect gelatin hardener of the diffraction efficiency.