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 (as done in the first edition 2019). 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. While the revised new chapters have been added (as the current second edition 2024). Chapter six introduces mean vector estimation and covariance matrix estimation. Chapter seven devotes to testing concerning mean: one sample mean, and two sample mean. Chapter eight discusses special case of factorial analysis which is principal components analysis. Chapter nine deals with discriminant analysis. While chapter ten deals with cluster analysis. 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 the readers.
The flow in a manifolds considered as an advanced problem in hydraulic engineering applications. The objectives of this study are to determine; the uniformity qn/q1 (ratio of the discharge at last outlet, qn to the discharge at first outlet, q1) and total head losses of the flow along straight and rectangular loop manifolds with different flow conditions. The straight pipes were with 18 m and 19 m long and with of 25.4 mm (1.0 in) in diameter each. While, the rectangular close loop configuration was with length of 19 m and with diameter of 25.4 mm (1.0 in) also. Constant head in the supply tank was used and the head is 2.10 m. It is found that outlets spacing and manifold configuration are the main factors aff
... Show MoreFinite element modeling of transient temperature distribution is used to understand physical phenomena occurring during the dwell (penetration) phase and moving of welding tool in friction stir welding (FSW) of 5mm plate made of 7020-T53 aluminum alloy at 1400rpm and 40mm/min.
Thermocouples are used in locations near to the pin and under shoulder surface to study the welding tool penetration in the workpiece in advance and retreate sides along welding line in three positions (penetrate (start welding) , mid, pullout (end welding)).
Numerical results of ANSYS 12.0 package are compared to experimental data including axial load measurements at different tool rotational speeds (710rpm.900rpm.1120rpm and 1400rpm) Based on the experiment
The ground state proton, neutron, and matter density distributions and corresponding root-mean-square (rms) of P19PC exotic nucleus are studied in terms of two-frequency shell model (TFSM) approach. The single-particle wave functions of harmonic-oscillator (HO) potential are used with two different oscillator parameters bRcoreR and bRhaloR. According to this model, the core nucleons of P18PC nucleus are assumed to move in the model space of spsdpf. The shell model calculations are carried out for core nucleons with w)20(+ truncations using the realistic WBPinteraction. The outer (halo) neutron in P19PC is assumed to move in the pure 2sR1/2R-orbit. The halo structure in P19PC is confirmed with 2sR1/2R-dominant configuration.Elastic electr
... Show MoreThe porosity of materials is important in many applications, products and processes, such as electrochemical devices (electrodes, separator, active components in batteries), porous thin film, ceramics, soils, construction materials, ..etc. This can be characterized in many different methods, and the most important methods for industrial purposes are the N2 gas adsorption and mercury porosimetry. In the present paper, both of these techniques have been used to characterize some of Iraqi natural raw materials deposits. These are Glass Sand, Standard Sand, Flint Clay and Bentonite. Data from both analyses on the different types of natural raw materials deposits are critically examined and discussed. The results of specific surface are
... Show MoreA checklist of the wild mammals of Syria including their current status and geographical distribution is provided. Data related to 110 mammalian species were collected following a comprehensive review of available literature records, grey data, and online observations combined with photographic evidence and in situ surveys carried out between 2006 and 2023. The checklist comprises seven orders, 36 families, 73 genera (subgenera), and 110 species, and includes data on 15 globally threatened species of wild mammals. Overall, we report up-to-date information on taxonomic revisions, historical and current geographical range, as well as the conservation status recently assessed by the International Union for Conservation of Nature (IUCN)
... Show Moreٳن العلاقة بين التخطيط والتنمية، تكتسب᾽ شكلها وطبيعتها من خلال دور التخطيط في ٳخضاع عملية التغيير والتحوّل للأوضاع الاقتصادية من وضع الى وضع آخر أكثر تقدما̋ عن طريق ٳعتماد منهج التخطيط لتحديد معالم خطوط السير المجدول زمنيا̋ لعملية التغيير والتحوّل وفقا̋ لرؤية الحكومة وفلسفتها باتجاه الانتقال من وضع ٳقتصادي وٳجتماعي متخلف الى وضع ٳقتصادي وٳجتماعي آخر يسمح بجعل عملية النمو مستمرة، ويمكن تبيّن تلك
... Show MoreElectrical distribution system loads are permanently not fixed and alter in value and nature with time. Therefore, accurate consumer load data and models are required for performing system planning, system operation, and analysis studies. Moreover, realistic consumer load data are vital for load management, services, and billing purposes. In this work, a realistic aggregate electric load model is developed and proposed for a sample operative substation in Baghdad distribution network. The model involves aggregation of hundreds of thousands of individual components devices such as motors, appliances, and lighting fixtures. Sana’a substation in Al-kadhimiya area supplies mainly residential grade loads. Measurement-based
... Show MoreThe calculation. of the nuclear. charge. density. distributions. ρ(r) and root. mean. square. radius.( RMS ) by elastic. electron. scattering. of medium. mass. nuclei. such. as (90Zr, 92Mo) based. on the model. of the modified. shell. and the use of the probability. of occupation. on the surface. orbits. of level 2p, 2s eroding. shells. and 1g gaining. shells. The occupation probabilities of these states differ noticeably from the predictions of the SSM. We have found. an improvement. in the determination. of ground. charge. density. and this improvement. allow. more precise. identification. of (CDD) between. (92Mo- 90Zr) to illustrate the influence of the extra
... Show MoreThe purpose of this paper is to consider fibrewise near versions of the more important separation axioms of ordinary topology namely fibrewise near T0 spaces, fibrewise near T1 spaces, fibrewise near R0 spaces, fibrewise near Hausdorff spaces, fibrewise near functionally Hausdorff spaces, fibrewise near regular spaces, fibrewise near completely regular spaces, fibrewise near normal spaces and fibrewise near functionally normal spaces. Also we give several results concerning it.
The aim of this paper is to look at fibrewise slightly issuances of the more important separation axioms of ordinary topology namely fibrewise said to be fibrewise slightly T0 spaces, fibrewise slightly T1spaces, fibrewise slightly R0 spaces, fibrewise slightly T2 spaces, fibrewise slightly functionally T2 spaces, fibrewise slightly regular spaces, fibrewise slightly completely regular spaces, fibrewise slightly normal spaces. In addition, we announce and confirm many proposals related to these concepts.