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 effect of short range correlations on the inelastic longitudinal
Coulomb form factors for different states of J 4 , T 1with
excitation energies 3.553,7.114, 8.960 and 10.310 MeV in 18O is
analyzed. This effect (which depends on the correlation parameter )
is inserted into the ground state charge density distribution through
the Jastrow type correlation function. The single particle harmonic
oscillator wave function is used with an oscillator size parameter b.
The parameters and b are considered as free parameters, adjusted
for each excited state separately so as to reproduce the experimental
root mean square charge radius of 18O. The model space of 18O does
not contribute to the tra
The growth curves of the children are the most commonly used tools to assess the general welfare of society. Particularity child being one of the pillars to develop society; through these tools, we can path a child's growth physiology. The Centile line is of the important tools to build these curves, which give an accurate interpretation of the information society, also respond with illustration variable age. To build standard growth curves for BMI, we use BMI as an index. LMSP method used for finding the Centile line which depends on four curves represents Median, Coefficient of Variation, Skews, and Kurtosis. These can be obtained by modeling four parameters as nonparametric Smoothing functions for the illustration variable. Ma
... Show MoreForward-swept wings were researched and introduced to improve maneuverability, control, and fuel efficiency while reducing drag and they are often used alongside canards, to further enhance their characteristics. In this research, the effects of canard dihedral angles on the wing loading of a forward-swept wing in transonic flow conditions were studied, as the wing loading provides a measure of wing’s efficiency (lift/drag). A generic aircraft model from literatures was selected, simulated, and compared to, using CFD software ANSYS/Fluent where the flow equations were solved to calculate the aerodynamic characteristics. The research was carried at two different Mach numbers, 0.6 and 0.9, for five different canard dihedral angles which tra
... Show MoreImage compression plays an important role in reducing the size and storage of data while increasing the speed of its transmission through the Internet significantly. Image compression is an important research topic for several decades and recently, with the great successes achieved by deep learning in many areas of image processing, especially image compression, and its use is increasing Gradually in the field of image compression. The deep learning neural network has also achieved great success in the field of processing and compressing various images of different sizes. In this paper, we present a structure for image compression based on the use of a Convolutional AutoEncoder (CAE) for deep learning, inspired by the diversity of human eye
... Show MoreThe charge density distributions (CDD) and the elastic electron
scattering form factors F(q) of the ground state for some even mass
nuclei in the 2s 1d shell ( Ne Mg Si 20 24 28 , , and S 32 ) nuclei have
been calculated based on the use of occupation numbers of the states
and the single particle wave functions of the harmonic oscillator
potential with size parameters chosen to reproduce the observed root
mean square charge radii for all considered nuclei. It is found that
introducing additional parameters, namely 1 , and , 2 which
reflect the difference of the occupation numbers of the states from
the prediction of the simple shell model leads to a remarkable
agreement between the calculated an
The effects of short-range correlation on elastic Coulomb (charge) form factors, charge density distributions as well as root mean square charge radii of various nuclei (for instance, 46, 48, 50Ti, 52, 54Cr, 56, 58Fe, and 72, 74, 76Ge nuclei) are examined. The one- and two body terms of the cluster expansion together with the single-particle harmonic oscillator wave functions are utilized. For the purpose of embedding these effects into the formulae of charge density and form factor we employ the correlation function of Jastrow-type. These formulae depend upon the short-range correlation parameter (which instigates from the Jastr
... Show MoreIn this work lactone (1) was prepared from the reaction of p-nitro phenyl hydrazine with ethylacetoacetate, which upon treatment with benzoyl chloride afforded the lactame (2). The reaction of (2) with 2-amino phenol produced a new Schiff base (L) in good yield. Complexes of V(IV), Zr(IV), Rh(III), Pd(II), Cd(II) and Hg(II) with the new Schiff base (L) have been prepared. The compounds (1, 2) were characterized by FT-IR and UV spectroscopy, as well as characterizing ligand (L) by the same techniques with elemental analysis (C.H.N) and (1H-NMR). The prepared complexes were identified and their structural geometries were suggested by using elemental analysis (C.H.N), flame atomic absorption technique, FT-IR and UV-Vis spectroscopy, in additio
... Show MoreThe main aim of image compression is to reduce the its size to be able for transforming and storage, therefore many methods appeared to compress the image, one of these methods is "Multilayer Perceptron ". Multilayer Perceptron (MLP) method which is artificial neural network based on the Back-Propagation algorithm for compressing the image. In case this algorithm depends upon the number of neurons in the hidden layer only the above mentioned will not be quite enough to reach the desired results, then we have to take into consideration the standards which the compression process depend on to get the best results. We have trained a group of TIFF images with the size of (256*256) in our research, compressed them by using MLP for each
... Show MoreA watermark is a pattern or image defined in a paper that seems as different shades of light/darkness when viewed by the transmitted light which used for improving the robustness and security. There are many ways to work Watermark, including the addition of an image or text to the original image, but in this paper was proposed another type of watermark is add curves, line or forms have been drawn by interpolation, which produces watermark difficult to falsify and manipulate it. Our work suggests new techniques of watermark images which is embedding Cubic-spline interpolation inside the image using Bit Plane Slicing. The Peak to Signal Noise Ratio (PSNR) and Mean Square Error (MSE) value is calculated so that the quality of the original i
... Show MoreIn this work, thermodynamic efficiency of individual cell and stack of cells (two cells) has been computed by studying the variation of voltage produced during an operation time of 30 min as a result of the affected parameters:- stoichiometric feed ratio, flow field design on single cell and feed distribution on stack of cells. The experiments were carried out by using two cells, one with serpentine flow field and the other with spiral flow field. These cells were fed with hydrogen and oxygen at low volumetric flow rates from 1 to 2 ml/sec and stoichiometric ratios of fuel (H2) to oxidant (O2) as 1:2, 1:1 and 2:1 respectively. The results showed that
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