The concept of a small f- subm was presented in a previous study. This work introduced a concept of a hollow f- module, where a module is said to be hollow fuzzy when every subm of it is a small f- subm. Some new types of hollow modules are provided namely, Loc- hollow f- modules as a strength of the hollow module, where every Loc- hollow f- module is a hollow module, but the converse is not true. Many properties and characterizations of these concepts are proved, also the relationship between all these types is researched. Many important results that explain this relationship are demonstrated also several characterizations and properties related to these concepts are given.

   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.

A submodule Ϝ of an R-module Ε is called small in Ε if whenever  , for some submodule W of Ε , implies  . In this paper , we introduce the notion of Ζ-small submodule , where a proper submodule Ϝ of an R-module Ε is said to be Ζ-small in Ε if  , such that  , then  , where  is the second singular submodule of Ε . We give some properties of Ζ-small submodules . Moreover , by using this concept , we generalize the notions of hollow modules , supplement submodules, and supplemented modules into Ζ-hollow modules, Ζ-supplement submodules, and Ζ-supplemented modules. We study these concepts and provide some of their relations .

         The main goal of this paper is to give  a new generalizations for two important classes in the category of modules, namely the class of small submodules and the class of hollow modules. They are purely small submodules and purely hollow modules respectively. Various properties of these classes of modules are investigated. The relationship between purely small submodules and P-small submodules which is introduced by Hadi and Ibrahim, is studied. Moreover, another characterization of  purely hollow modules is considered.

Human cytomegalovirus (CMV) infection is associated with higher risk of cardiovascular diseases in immunocompromised organ transplant patients; it has been linked with the elevated arterial blood pressure. This study aimed to find a relationship between CMV antibody titers and blood pressure elevation by using the enzyme-linked immunosorbent assay (ELISA) to measure CMV IgG levels in the serum of 60 patients with high blood pressure, in comparison to 30 healthy persons with normal blood pressure as a control. All patients and control were 25-50 years old. The results showed that CMV antibody titers were higher in those who undergo blood pressure elevation. This finding supports the hypothesis that; the common CMV infection may leads to i

Multiphase flow is a very common phenomenon in oil wells. Several correlation models, either analytical or experimental, have been investigated by various studies to investigate this phenomenon. However, no single correlation model was found to produce good results in all flow conditions. 14 models available on the Prosper software were selected for the purpose of calculating the pressure gradient inside wells within a range of different flow conditions. The pressure gradient was calculated using Prosper software, then compared with the measured gradient based on the production log test (PLT) data. This study was conducted on 31 wells from five different oil fields (Kirkuk, Jambur, Bai-Hassan, Al-Ahdab, and Rumaila). It is worth noting t

A session is a period of time linked to a user, which is initiated when he/she arrives at a web application and it ends when his/her browser is closed or after a certain time of inactivity. Attackers can hijack a user's session by exploiting session management vulnerabilities by means of session fixation and cross-site request forgery attacks.
Very often, session IDs are not only identification tokens, but also authenticators. This means that upon login, users are authenticated based on their credentials (e.g., usernames/passwords or digital certificates) and issued session IDs that will effectively serve as temporary static passwords for accessing their sessions. This makes session IDs a very appealing target for attackers. In many c

This Book is the second edition that intended to be textbook studied for undergraduate/ postgraduate course in mathematical statistics. In order to achieve the goals of the book, it is divided into the following chapters. Chapter One introduces events and probability review. Chapter Two devotes to random variables in their two types: discrete and continuous with definitions of probability mass function, probability density function and cumulative distribution function as well. Chapter Three discusses mathematical expectation with its special types such as: moments, moment generating function and other related topics. Chapter Four deals with some special discrete distributions: (Discrete Uniform, Bernoulli, Binomial, Poisson, Geometric, Neg