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.
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 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 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 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 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 MoreThe challenge in studying fusion reaction when the projectile is neutron or proton rich halo nuclei is the coupling mechanism between the elastic and the breakup channel, therefore the motivation from the present calculations is to estimate the best coupling parameter to introduce the effect of coupled-channels for the calculations of the total cross section of the fusion , the barrier distribution of the fusion and the average angular momentum 〈L〉 for the systems 6He+206Pb, 8B+28Si, 11Be+209Bi, 17F+208Pb, 6He+238U, 8He+197Au and 15C+232Th using quantum mechanical approach. A
... 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 MoreIn the current digitalized world, cloud computing becomes a feasible solution for the virtualization of cloud computing resources. Though cloud computing has many advantages to outsourcing an organization’s information, but the strong security is the main aspect of cloud computing. Identity authentication theft becomes a vital part of the protection of cloud computing data. In this process, the intruders violate the security protocols and perform attacks on the organizations or user’s data. The situation of cloud data disclosure leads to the cloud user feeling insecure while using the cloud platform. The different traditional cryptographic techniques are not able to stop such kinds of attacks. BB84 protocol is the first quantum cry
... Show MoreEfficient management of treated sewage effluents protects the environment and reuse of municipal, industrial, agricultural and recreational as compensation for water shortages as a second source of water. This study was conducted to investigate the overall performance and evaluate the effluent quality from Al- Rustamiya sewage treatment plant (STP), Baghdad, Iraq by determining the effluent quality index (EQI). This assessment included daily records of major influent and effluent sewage parameters that were obtained from the municipal sewage plant laboratory recorded from January 2011 to December 2018. The result showed that the treated sewage effluent quality from STP was within the Iraqi quality standards (IQS) for disposal and t
... Show MoreA stochastic process {Xk, k = 1, 2, ...} is a doubly geometric stochastic process if there exists the ratio (a > 0) and the positive function (h(k) > 0), so that {α 1 h-k }; k ak X k = 1, 2, ... is a generalization of a geometric stochastic process. This process is stochastically monotone and can be used to model a point process with multiple trends. In this paper, we use nonparametric methods to investigate statistical inference for doubly geometric stochastic processes. A graphical technique for determining whether a process is in agreement with a doubly geometric stochastic process is proposed. Further, we can estimate the parameters a, b, μ and σ2 of the doubly geometric stochastic process by using the least squares estimate for Xk a
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