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 problems at the end of each chapter to enrich the statistical knowledge of our students.
In this paper an attempt to provide a single degree of freedom lumped model for fluid structure interaction (FSI) dynamical analysis will be presented. The model can be used to clarify some important concept in the FSI dynamics such as the added mass, added stiffness, added damping, wave coupling ,influence mass coefficient and critical fluid depth . The numerical results of the model show that the natural frequency decrease with the increasing of many parameters related to the structure and the fluid .It is found that the interaction phenomena can become weak or strong depending on the depth of the containing fluid .The damped and un damped free response are plotted in time domain and phase plane for different model parameters It is fou
... Show MoreThe last decade of this 20th century provides a wide spread of applications of one of the computer techniques, which is called Fuzzy Logic. This technique depends mainly on the fuzzy set theory, which is considered as a general domain with respect to the conventional set theory. This paper presents in initiative the fuzzy sets theory and fuzzy logic as a complete mathematics system. Here it was explained the concept of fuzzy set and defined the operations of fuzzy logic. It contains eleven operations beside the other operations which related to fuzzy algebra. Such search is considered as an enhancement for supporting the others waiting search activities in this field.
Most statistical research generally relies on the study of the behaviour of different phenomena during specific time periods and the use of the results of these studies in the development of appropriate recommendations and decision-making and for the purpose of statistical inference on the parameters of the statistical distribution of life times in The technical staff of most of the manufacturers in the research units of these companies deals with censored data, the main objective of the study of survival is the need to provide information that is the basis for decision making and must clarify the problem and then the goals and limitations of this study and that It may have different possibilities to perform the
... Show MoreBackground: The rapid evolution of Artificial Intelligence (AI) has significantly influenced Education, demonstrating substantial potential to transform traditional teaching and learning methods. AI reshapes teacher-student interactions and the relationship with knowledge. Objective: To analyze the potential benefits, ethical challenges, and limitations of AI in Education based on recent scientific literature, emphasizing the balance between technology and human interaction. Methods: A documentary research approach with a descriptive focus was employed, following the PRISMA protocol for systematic reviews. The search strategy involved analyzing evidence from 18 scientific articles published within the last six years. Results:AI o
... Show MoreThis study investigates the effects of Al-Doura oil refinery effluent, in Baghdad city, on the water quality of the Tigris River using the Canadian Water Quality Index (CCME WQI) and Rivers Maintaining System (1967). Water samples were collected monthly from Tigris River at three stations, which are Al-Muthanna Bridge (upstream), Al-Doura Refinery (point source), and Al–Zafaraniya city (downstream) from October 2020 to April 2021. Fourteen water quality parameters were studied, namely pH (6.50-8.10), Water Temperature (WT) (5.00-27.00 °C), Electrical Conductivity (EC) (877.00-1192.00 μs/cm), Dissolved Oxygen (DO) (5.03-7.57 mg/L), Biological Oxygen demand (BOD) (0.53-2.23 mg/L), Total Dissolved S
In this paper, the probabilistic behavior of plain concrete beams subjected to flexure is studied using a continuous mesoscale model. The model is two-dimensional where aggregate and mortar are treated as separate constituents having their own characteristic properties. The aggregate is represented as ellipses and generated under prescribed grading curves. Ellipses are randomly placed so it requires probabilistic analysis for model using the Monte Carlo simulation with 20 realizations to represent geometry uncertainty. The nonlinear behavior is simulated with an isotropic damage model for the mortar, while the aggregate is assumed to be elastic. The isotropic damage model softening be
Passive optical network (PON) is a point to multipoint, bidirectional, high rate optical network for data communication. Different standards of PONs are being implemented, first of all PON was ATM PON (APON) which evolved in Broadband PON (BPON). The two major types are Ethernet PON (EPON) and Gigabit passive optical network (GPON). PON with these different standards is called xPON. To have an efficient performance for the last two standards of PON, some important issues will considered. In our work we will integrate a network with different queuing models such M/M/1 and M/M/m model. After analyzing IPACT as a DBA scheme for this integrated network, we modulate cycle time, traffic load, throughput, utilization and overall delay
... Show MoreThere are different types of corruptions such as administrative, political, economic and financial corruption. The corruption forms also varied such as bribery, nepotism and extortion. All types and forms of corruption play significant role in the all economic variables generally and on investments in particular, and the corruption used to be an intermediate means in reducing the rate of economic growth. The corruption contributes in reducing the domestic investments via pay bribery by investors to officials’ persons for supplemental contracts and tenders which finally leads to reduction in the investment efficiency. The corruption also contributes in rise of operational costs for the investment projects. In additio
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