This Book is intended to be textbook studied for undergraduate course in multivariate analysis. This book is designed to be used in semester system. In order to achieve the goals of the book, it is divided into the following chapters. Chapter One introduces matrix algebra. Chapter Two devotes to Linear Equation System Solution with quadratic forms, Characteristic roots & vectors. Chapter Three discusses Partitioned Matrices and how to get Inverse, Jacobi and Hessian matrices. Chapter Four deals with Multivariate Normal Distribution (MVN). Chapter Five concern with Joint, Marginal and Conditional Normal Distribution, independency and correlations. Many solved examples are intended in this book, in addition to a variety of unsolved relied pro

Many of the key stream generators which are used in practice are LFSR-based in the sense that they produce the key stream according to a rule y = C(L(x)), where L(x) denotes an internal linear bit stream, produced by small number of parallel linear feedback shift registers (LFSRs), and C denotes some nonlinear compression function. In this paper we combine between the output sequences from the linear feedback shift registers with the sequences out from non linear key generator to get the final very strong key sequence

This study aims to derive a general relation between line loads that acting on two-way slab system and the equivalent uniformly distributed loads. This relation will be so useful to structural designer that are used to working with a uniformly distributed load and enable them to use the traditional methods for analysis of two-way systems (e.g. Direct Design Method). Two types of slab systems, Slab System with Beams and Flat Slab Systems, have been considered in this study to include the effect of aspect ratio and type of slab on the proposed relation. Five aspect ratios, l2/l1 of 0.5, 0.75, 1.0, 1.5 and 2.0, have been considered for both types of two-way systems.
All necessary finite element analyses have been executed with SAFE Soft

Let G be a graph, each edge e of which is given a weight w(e). The shortest path problem is a path of minimum weight connecting two specified vertices a and b, and from it we have a pre-topology. Furthermore, we study the restriction and separators in pre-topology generated by the shortest path problems. Finally, we study the rate of liaison in pre-topology between two subgraphs. It is formally shown that the new distance measure is a metric

The article considers the main reason for A. I. Herzen's address to obsolete words, which is their ability to acquire a stylistic coloring in the context of speech, as well as the possibility of combining, in some cases, with neutral lexemes of various functional styles. A certain stylistic effect of such characteristics of this type of vocabulary is represented, as a result of which their stylistic coloring in syntagmatic terms does not coincide with stylistic coloring in terms of paradigmatics, that is, in speech they have a completely stylistic meaning. Attention is focused on the role of outdated vocabulary, which consists in the fact that they serve to implement such features of the artistic style as imagery, emotionality, and their

These search summaries in building a mathematical model to the issue of Integer linear Fractional programming and finding the best solution of Integer linear Fractional programming (I.L.F.P) that maximize the productivity of the company^,s revenue by using the largest possible number of production units and maximizing denominator objective which represents^,s proportion of profits to the costs, thus maximizing total profit of the company at the lowest cost through using Dinkelbach algorithm and the complementary method on the Light industries company data for 2013 and comparing results with Goal programming methods results.

It is clear that the final results of resolution and Dinkelbac

دُرِست العوامل المؤثرة في عدد ساعات تجهيز الكهرباء في مدينة بغداد، وتكونت عينة الدراسة من (365) مشاهدة يومية لعام 2018، وتمثلت بستة متغيرات استعملت في الدراسة. كان الهدف الرئيس هو دراسة العلاقة بين هذه المتغيرات، وتقدير تأثيرات المتغيرات التنبؤية في المتغير التابع (عدد ساعات تجهيز الكهرباء في مدينة بغداد). ولتحقيق ذلك استعملت نمذجة المعادلات الهيكلية/ تحليل المسار وبرنامج AMOS

      The main problem when dealing with fuzzy data variables is that it cannot be formed by a model that represents the data through the method of Fuzzy Least Squares Estimator (FLSE) which gives false estimates of the invalidity of the method in the case of the existence of the problem of multicollinearity. To overcome this problem, the Fuzzy Bridge Regression Estimator (FBRE) Method was relied upon to estimate a fuzzy linear regression model by triangular fuzzy numbers. Moreover, the detection of the problem of multicollinearity in the fuzzy data can be done by using Variance Inflation Factor when the inputs variable of the model crisp, output variable, and parameters are fuzzed. The results were compared usin

The aim of this paper is introducing the concept of (ɱ,ɳ) strong full stability B-Algebra-module related to an ideal. Some properties of (ɱ,ɳ)- strong full stability B-Algebra-module related to an ideal have been studied and another characterizations have been given. The relationship of (ɱ,ɳ) strong full stability B-Algebra-module related to an ideal that states,  a B- -module Ӽ is (ɱ,ɳ)- strong full stability B-Algebra-module related to an ideal  , if and only if  for any two ɱ-element sub-sets and of Ӽ^ɳ, if , for each j = 1, …, ɱ,  i = 1,…, ɳ  and   implies _Ạɳ( ) _Ạɳ(  have been proved..