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.

Background: Insulin resistance (IR) is the primary metabolic disorder associated with obesity. Obesity is a growing worldwide health problem affecting both adults and children. Objectives: To determine the association between leptin and IR, and to identify the ratio of fasting glucose/leptin (G/L) and insulin/leptin (I/L) as a new simple method for the detection of IR in obese children.Methods: This study was done in the National DiabeticCenter/ AL-Mustansiriya University during the period fromMay 2013 until the end of October 2013. Fasting bloodglucose (FBG), serum insulin, leptin, and lipid profile weremeasured in 52 obese children (24 children with IR and 28without IR); their age range was (5-15) years, they werecompared with 38 healt

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In this paper the full stable Banach gamma-algebra modules, fully stable Banach gamma-algebra modules relative to ideal are introduced. Some properties and characterizations of these classes of full stability are studied.

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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

In this paper, we use concepts and results from percolation theory to investigate and characterize the effects of multi-channels on the connectivity of Dynamic Spectrum Access networks. In particular, we focus on the scenario where the secondary nodes have plenty of vacant channels to choose from-a phenomenon which we define as channel abundance. To cope with the existence of multi-channels, we use two types of rendezvous protocols: naive ones which do not guarantee a common channel and advanced ones which do. We show that, with more channel abundance, even with the use of either type of rendezvous protocol, it becomes difficult for two nodes to agree on a common channel, thereby potentially remaining invisible to each other. We model this