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.
Blends of polyvinyl pyrrolidone (PVP) and polyvinyl alcohol (PVA) in equal weight ratios (50 wt.% PVP + 50 wt.% PVA) were doped with 15% of various lithium salts (Li2CO3, LiNO3, Li2SO4H2O, and LiCl) and prepared using the solution-casting method, with dimethylformamide (DMF) as the solvent. The impact of these salts on the blends was analyzed and the results showed that the energy gap was decreased by adding lithium salts Li2CO3, LiNO3 and Li2SO4.H₂O. The minimum energy gap value was 3.5 eV obtained from PVP/PVA:15% Li2CO3. The optical constants were determined in the range of 300-1100 nm. The results showed that all the optical constants for doped blends were grown with the addition of lithium salts. The FTIR study confirms the c
... Show MoreThis study presents the debonding propagation in single NiTi wire shape memory alloy into linear low-density polyethylene matrix composite the study of using the pull-out test. The aim of this study is to investigate the pull-out tests to check the interfacial strength of the polymer composite in two cases, with activation NiTinol wire and without activation. In this study, shape memory alloy NiTinol wire 2 mm diameter and linear fully annealed straight shape were used. The study involved experimental and finite element analysis and eventually comparison between them. This pull-out test is considered a substantial test because its results have a relation with behavior of smart composite materials. The pull-out test was carried out by a u
... Show MoreThis study provides a systematic and bibliometric review of ASTM F75 cobalt–chromium alloys, focusing on microstructure and the shift from conventional to laser-based manufacturing. Using combined analytical methods, it evaluates microstructure, mechanical properties, corrosion behavior, and biocompatibility. Results show that laser-based techniques such as LPBF and DMLS produce finer grain sizes (1–10 µm vs. 50–200 µm), leading to improved hardness (20–40%) and tensile strength (15–30%). Despite challenges like residual stress and process optimization, these methods show strong potential for high-performance and sustainable applications.
Second language learner may commit many mistakes in the process of second language learning. Throughout the Error Analysis Theory, the present study discusses the problems faced by second language learners whose Kurdish is their native language. At the very stages of language learning, second language learners will recognize the errors committed, yet they would not identify the type, the stage and error type shift in the process of language learning. Depending on their educational background of English as basic module, English department students at the university stage would make phonological, morphological, syntactic, semantic and lexical as well as speech errors. The main cause behind such errors goes back to the cultural differences
... Show MoreBackground: The treatment of moderate-to-severe psoriasis has advanced significantly with the use of biologic treatments. Objective: To compare the effectiveness, safety, and impact on quality of life of biologic therapies versus conventional systemic therapies for moderate-to-severe psoriasis, using evidence from 2015 to 2025, focusing on the implications for understudied regions such as Iraq and the Middle East. Methods: Data was collected using "Embase," "MEDLINE," "PubMed," and "Cochrane Central Register." The study includes 45 randomized controlled trials. Additionally, 25 key real-world evidence studies were included for qualitative synthesis to provide context on long-term drug survival, quality of life, and regional applicab
... Show MoreThis study expands the state of the art in studies that assess torsional retrofit of reinforced concrete (RC) multi-cell box girders with carbon fiber reinforced polymer (CFRP) strips. The torsional behavior of non-damaged and pre-damaged RC multi-cell box girder specimens externally retrofitted by CFRP strips was investigated through a series of laboratory experiments. It was found that retrofitting the pre-damaged specimens with CFRP strips increased the ultimate torsional capacity by more than 50% as compared to the un-damaged specimens subjected to equivalent retrofitting. This indicated that the retrofit has been less effective for the girder specimen that did not develop distortion beforehand as a result of pre-loading. From
... Show MoreThe Na-alginate bead is commonly used in biotechnology fields such as adsorption due to ion exchange between Ca and Na with elements. Scanning electron microscopy (SEM-EDX) has proven to be a comparative method in the detections of these adsorbed elements, but the un-flat forming area of beads that can introduce impossible of the detection of element adsorbed. In contrast, X-ray fluorescence (XRF) documents analysis of elements, direct examination, which may analysis the adsorbents of elements. Here, this Study evaluated the possibility by using XRF for the direct analysis for examples of Cd and Ag in a bench stand. This Study compared this to commonly use
... Show MoreThis study expands the state of the art in studies that assess torsional retrofit of reinforced concrete (RC) multi-cell box girders with carbon fiber reinforced polymer (CFRP) strips. The torsional behavior of non-damaged and pre-damaged RC multi-cell box girder specimens externally retrofitted by CFRP strips was investigated through a series of laboratory experiments. It was found that retrofitting the pre-damaged specimens with CFRP strips increased the ultimate torsional capacity by more than 50% as compared to the un-damaged specimens subjected to equivalent retrofitting. This indicated that the retrofit has been less effective for the girder specimen that did not develop distortion beforehand as a result of pre-loading. From
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