Most of the known cases of strong gravitational lensing involve multiple imaging of an active galactic nucleus. The properties of lensed active galactic nuclei make them promising systems for astrophysical applications of gravitational lensing. So we present a simple model for strong lensing in the gravitational lensed systems to calculate the age of four lensed galaxies, in the present work we take the freedman models with (k curvature index =0) Euclidian case, and the result show a good agreement with the other models.

The Iraqi-Kuwaiti relations represent a great issue for the Arab-Arab relations. This relation is characterized by specificity for the tension since the foundation of the State of Kuwait until late. There are many factors that prevented the fulfillment of the aspiration towards the development of the relations, perhaps the most important of which is the issue of Mubarak Great Port which is a difficult issue as far as the relation between the two states is concerned. One year after Iraq put the cornerstone of the Great Faw Port. This is considered as the most important hurdle in front of constructing the relations with the neighbor Kuwait

To determine the relationship between infertility and Helicobacter pylori infection, thirty-five infertile patients of ages (20-49) years have been investigated and compared with 10 apparently firtility individuals. All the studied groups were carried out to measure (ASA), (TNF-á), (IL-6), (anti-H.pylori IgA) and (anti-H.pyloriIgG) by Enzyme linked immunosorbent assay (ELISA) technique. The statistical analysis also demonstrated that there were a highly significant differences (P<0.01), when compared between studied group. Also, the statistical analysis demonstrated that there were a highly significant differences (P<0.01) when compare between infertility and fertility in Conc. of sperm. The percentage distribution of ASA in serum and seme

The subgrade soil is the foundation plate form of the roadway; it should sustain its structural characteristics throughout the design life of the roadway with minimal requirements for maintenance. When Gypseous soil is implemented in the construction of subgrade, problems regarding collapsibility and poor structural capacity usually occur when the subgrade came in touch with excess water. Asphalt stabilization could furnish a proper solution to such problems. In this investigation, an attempt has been made to monitor the variations in compressibility characteristics of asphalt stabilized subgrade soil subjected to 30 cycles of (freezing-thawing) and (heating-cooling). Data have been observed after each 10 cycles, and compared with that of r

A factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure. In this paper, the factor groups K(SL(2,121)) and K(SL(2,169)) computed for each group from the character table of rational representations.

Thiamine stimulates the production of a red pigment , which is chromatographically and spectrophotometrically identical to prodigiosin , by growing cultures of serratia marcescens mutant 9-3-3 . this mutant is blocked in the formation of 2- methyl -3- amyl pyrorol( MAP),the monopyrrole moiety of prodigiosin , but accumulates 4-methoxy-2, 2-bipyrrole -5- carboxaldehyde (MBC) and can couple this compound with( MAP) to form prodigiosin . Addition of thiamine caused production of( MAP) , and as little as 0.02 mg of thiamine / ml in peptone- glycerol medium stimulated production of measurable amounts of prodigiosin. Phosphate saltes and another type of peptone decreased the thiamine- induced formation of prodigiosin ,yeast extract and glyc

In the present work theoretical relations are derived for the efficiency evaluation for the generation of the third and the fourth harmonics u$ing crystal cascading configuration. These relations can be applied to a wide class of nonlinear optical materials. Calculations are made for beta barium borate (BBO) crystal with ruby laser /.=694.3 nm . The case study involves producing the third harmonics at X. =231.4 nm of the fundamental beam. The formula of efficiency involves many parameters, which can be changed to enhance the efficiency. The results showed that the behavior of the efficiency is not linear with the crystal length. It is found that the efficiency increases when the input power increases. 'I'he walk-off length is calculated for

A new distribution, the Epsilon Skew Gamma (ESΓ ) distribution, which was first introduced by Abdulah [1], is used on a near Gamma data. We first redefine the ESΓ distribution, its properties, and characteristics, and then we estimate its parameters using the maximum likelihood and moment estimators. We finally use these estimators to fit the data with the ESΓ distribution

Variable selection in Poisson regression with high dimensional data has been widely used in recent years. we proposed in this paper using a penalty function that depends on a function named a penalty. An Atan estimator was compared with Lasso and adaptive lasso. A simulation and application show that an Atan estimator has the advantage in the estimation of coefficient and variables selection.

For a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set Xm = That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric group Sn, the class Cn (n odd positive integer) split into two conjugacy classes in An denoted Cn+ and Cn- . C+ and C- were used for these two parts of Cn. This work we prove that for some odd n ,the class C of 5- cycle in Sn has the property that = An n 7 and C+ has the property that each element of C+ is conjugate to its inverse, the square of each element of it is the element of C-, these results were used to prove that C+ C- = An exceptio