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 ground state proton, neutron and matter densities of exotic 11Be and 15C nuclei are studied by means of the TFSM and BCM. In TFSM, the calculations are based on using different model spaces for the core and the valence (halo) neutron. Besides single particle harmonic oscillator wave functions are employed with two different size parameters Bc and Bv. In BCM, the halo nucleus is considered as a composite projectile consisting of core and valence clusters bounded in a state of relative motion. The internal densities of the clusters are described by single particle Gaussian wave functions.
Elastic electron scattering proton f
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Lightweight materials is used in the sheet metal hydroforming process, because it can be adapted to the manufacturing of complex structural components into a single body with high structural stiffness. Sheet hydroforming has been successfully developed in industry such as in the manufacturing of the components of automotive.The aim of this study is to simulate the experimental results ( such as the amount of pressure required to hydroforming process, stresses, and strains distribution) with results of finite element analyses (FEA) (ANSYS 11) for aluminum alloy (AA5652) sheets with thickness (1.2mm) before heat treatm
... Show MoreThe present work investigates the effect of; superficial air velocities of: 1, 3, and 6 cm/s for two types of perforated distributor on hydrodynamic characteristic in a gas-liquid dispersion column of; air-water, and airaqueous-n-propanol solution. Bubble distribution, gas holdup, and power consumption are parameters take in consideration. Experimental work was carried out in perspex column of 8.5 cm inside diameter and 1.5 m height. Two types of bubble generator (perforated plate) were fixed at the bottom of the column; plate A (99 holes of 0.5 mm diameter and free area of 0.34%), plate B (20 holes of 1.5 mm diameter and free area of 0.62%). Photographic technique was used to measure the bubble parameters. The experimental results were
... Show MoreThe inelastic C2 form factors and the charge density distribution (CDD) for 58,60,62Ni and 64,66,68Zn nuclei has been investigated by employing the Skyrme-Hartree-Fock method with (Sk35-Skzs*) parametrization. The inelastic C2 form factor is calculated by using the shape of Tassie and Bohr-Mottelson models with appropriate proton and neutron effective charges to account for the core-polarization effects contribution. The comparison of the predicted theoretical values was conducted with the available measured data for C2 and CDD form factors and showed very good agreement.
In this work, the calculation of matter density distributions, elastic charge form factors and size radii for halo 11Be, 19C and 11Li nuclei are calculated. Each nuclide under study are divided into two parts; one for core part and the second for halo part. The core part are studied using harmonic-oscillator radial wave functions, while the halo part are studied using the radial wave functions of Woods-Saxon potential. A very good agreement are obtained with experimental data for matter density distributions and available size radii. Besides, the quadrupole moment for 11Li are generated.
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.
The 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.
ANN modeling is used here to predict missing monthly precipitation data in one station of the eight weather stations network in Sulaimani Governorate. Eight models were developed, one for each station as for prediction. The accuracy of prediction obtain is excellent with correlation coefficients between the predicted and the measured values of monthly precipitation ranged from (90% to 97.2%). The eight ANN models are found after many trials for each station and those with the highest correlation coefficient were selected. All the ANN models are found to have a hyperbolic tangent and identity activation functions for the hidden and output layers respectively, with learning rate of (0.4) and momentum term of (0.9), but with different data
... Show MoreThe 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