Let  be a commutative ring with identity, and  be a unitary left R-module. In this paper we, introduce and study a new class of modules called pure hollow (Pr-hollow) and pure-lifting (Pr-lifting). We give a fundamental, properties of these concept.  also, we, introduce some conditions under which the quotient and direct sum of Pr-lifting modules is Pr-lifting.

RMK Al-Zaid, AT Al-Musawi, SJ Mohammad

The purpose of this paper is to prove the following result: Let R be a 2-torsion free ring and T: R?R an additive mapping such that T is left (right) Jordan ?-centralizers on R. Then T is a left (right) ?-centralizer of R, if one of the following conditions hold (i) R is a semiprime ring has a commutator which is not a zero divisor . (ii) R is a non commutative prime ring . (iii) R is a commutative semiprime ring, where ? be surjective endomorphism of R . It is also proved that if T(x?y)=T(x)??(y)=?(x)?T(y) for all x, y ? R and ?-centralizers of R coincide under same condition and ?(Z(R)) = Z(R) .

The reaction of some new Schiff bases ( 2-[(2-Amino – ethylimino)-methyl]-R , 2-({2-[(R-benzylidene)-amino]-ethylimino}-methyl)-R with Benzoyl chloride or Acetyl chloride were carried out. Subsequent reactions of these products N-(2-Amino-ethyl)-N-[Chloro-(R) –methyl]-benzamide or N-(2-{?-[chloro-(R) –methyl]-amino}-ethyl)-N-[chloro-(R) –methyl]- benzamide with thiourea afforded thioureas compounds. The synthesized compounds were confirmed by their IR,UV,spectra and C.H.N. analysis.

Individual mobility is an outcome of the rapid changes in life; it is revealed in particular literary works within the end of the 19th century. Mobility is clearer in modern time as the individual has become physically freer in his movement. But the individual’s freedom is often conditioned by restrictions. Usually, change stimulates individuals to obtain new structure of feeling; the individual mocks or rages against institutions, or he would comply, suffering rapid personal deterioration as he faces effective stability or institutions. There is a continuous sense of “deadlock.” Sylvia Plath’s novel reflects the depression of an intellectual young woman who fails to find her right path muddled by an inconsistent, confusing

Background: Obesity and diabetes mellitus are the common health problems,and obesity is common cause of the insulin resistance. Aim of studv: Aim of the study is to find any correlation between obesity (insulin resistance) and type I diabetes in children. Patients and methods: This study included (40) children with type I diabetes, in addition to (40) children as control.The age of all studied groups ranged from (8-18) years.This study was attemted from Ibn AlBalady Hospital during from 20 August to 9 Novembar,2008. The subjects wrer divided into (4) groups according to their BMI:- * Obese children,diabetes,n=2O,BMI>30. * Non obese children, diabetes, n=20,BMI<25. Obese children, non diabetes, n=20,BMI>30. * Non obese children,non diabetes

The reaction of(2-oxo-2H-chromen-3-Carbonyl chloride)(k1) with hydrazine in boiling ethanol gives the hydrazide(K2).When compound (k2) reacts with various aromatic aldehydes ,the corres ponding Schiff bases(k3–k4) achieve new series of thiazotidines (k5–k6) and azetidinones (k7–k8) obtained from the reactions of appropriate Schiff bases with mercapto acetic acid and chloro acetyl chloride respectively. All the compounds are characterized by FT-IR,1H-NMR and GC-Ms.

We define and study new ideas of fibrewise topological space namely fibrewise multi-topological space . We also submit the relevance of fibrewise closed and open topological space . Also fibrewise multi-locally sliceable and fibrewise multi-locally section able multi-topological space . Furthermore, we propose and prove a number of statements about these ideas. On the other hand, extend separation axioms of ordinary topology into fibrewise setting. The separation axioms are said to be fibrewise multi-T0. spaces, fibrewise multi-T1spaces, fibrewise multi-R0 spaces, fibrewise multi-Hausdorff spaces, fibrewise multi-functionally Hausdorff spaces, fibrewise multi-regular spaces, fibrewise multi-completely regular spaces, fibrewise multi-normal