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 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.
In this paper, we define a new type of pairwise separation axioms called pairwise semi-p- separation axioms in bitopological spaces, also we study some properties of these spaces and relationships of each one with the ordinary separation axioms in the bitopological spaces.
Multipole mixing ratios for gamma transition populated in from reaction have been studied by least square fitting method also transition strength ] for pure gamma transitions have been calculated taking into account the mean life time for these levels .
This paper aimed to investigate the effect of the height-to-length ratio of unreinforced masonry (URM) walls when loaded by a vertical load. The finite element (FE) method was implemented for modeling and analysis of URM wall. In this paper, ABAQUS, FE software with implicit solver was used to model and analysis URM walls subjected to a vertical load. In order to ensure the validity of Detailed Micro Model (DMM) in predicting the behavior of URM walls under vertical load, the results of the proposed model are compared with experimental results. Load-displacement relationship of the proposed numerical model is found of a good agreement with that of the published experimental results. Evidence shows that load-displacement curve obtained fro
... Show MoreThe two parameters of Exponential-Rayleigh distribution were estimated using the maximum likelihood estimation method (MLE) for progressively censoring data. To find estimated values for these two scale parameters using real data for COVID-19 which was taken from the Iraqi Ministry of Health and Environment, AL-Karkh General Hospital. Then the Chi-square test was utilized to determine if the sample (data) corresponded with the Exponential-Rayleigh distribution (ER). Employing the nonlinear membership function (s-function) to find fuzzy numbers for these parameters estimators. Then utilizing the ranking function transforms the fuzzy numbers into crisp numbers. Finally, using mean square error (MSE) to compare the outcomes of the survival
... 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 MoreIt is commonly known that Euler-Bernoulli’s thin beam theorem is not applicable whenever a nonlinear distribution of strain/stress occurs, such as in deep beams, or the stress distribution is discontinuous. In order to design the members experiencing such distorted stress regions, the Strut-and-Tie Model (STM) could be utilized. In this paper, experimental investigation of STM technique for three identical small-scale deep beams was conducted. The beams were simply supported and loaded statically with a concentrated load at the mid span of the beams. These deep beams had two symmetrical openings near the application point of loading. Both the deep beam, where the stress distribution cannot be assumed linear, and the ex
... 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 MoreANN 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 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
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