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.

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.

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

The subject of this research involves studying adsorption to remove hexavalent chromium Cr(VI) from aqueous solutions. Adsorption process on bentonite clay as adsorbent was used in the Cr(VI) concentration range (10-100) ppm at different temperatures (298, 303, 308 and 313)K, for different periods of time. The adsorption isotherms were obtained by obeying Langmuir and Freundlich adsorption isotherm with R2 (0.9921-0.9060) and (0.994-0.9998), respectively. The thermodynamic parameters were calculated by using the adsorption process at four different temperatures the values of ?H, ?G and ?S was [(+6.582 ? +6.547) kJ.mol-1, (-284.560 ? -343.070) kJ.mol-1 and (+0.977 ? +1.117) kJ.K-1.mol-1] respectively. This data indicates the spontaneous sorp

Bending effects on the transmission of optical signal are investigated on a single mode
optical fiber (SMOF) of 10 m length, core radius of 5 μm and optical refractive index difference
0.003. The bending radii (R) were between 0.08 and 0.0015 m. A great decrease in the amplitude is
shown for radii below 0.01 m. Sudden break down occurs for radii less than 0.0015 m. Birefringence
(B) is difficult to measure for long fibers. Meanwhile, B was found by comparing with calibrated
fiber of the same properties but of length of 0.075 m. The results show an increase in propagation
constant (Δβ) and the decrease in beat length (Lb), and show that bending decreases the critical radius
of curvature (Rc) related to B. The chang

The quality of Global Navigation Satellite Systems (GNSS) networks are considerably influenced by the configuration of the observed baselines. Where, this study aims to find an optimal configuration for GNSS baselines in terms of the number and distribution  of baselines to improve the quality criteria of the GNSS networks. First order design problem (FOD) was applied in this research to optimize GNSS network baselines configuration, and based on sequential adjustment method to solve its objective functions.

FOD for optimum precision (FOD-p) was the proposed model which based on the design criteria of A-optimality and E-optimality. These design criteria were selected as objective functions of precision, whic

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.

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.