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 pro

Grey system theory is a multidisciplinary scientific approach, which deals with systems that have partially unknown information (small sample and uncertain information). Grey modeling as an important component of such theory gives successful results with limited amount of data. Grey Models are divided into two types; univariate and multivariate grey models. The univariate grey model with one order derivative equation GM (1,1) is the base stone of the theory, it is considered the time series prediction model but it doesn’t take the relative factors in account. The traditional multivariate grey models GM(1,M) takes those factor in account but it has a complex structure and some defects in " modeling mechanism", "parameter estimation "and "m

This paper develops a fuzzy multi-objective model for solving aggregate production planning problems that contain multiple products and multiple periods in uncertain environments. We seek to minimize total production cost and total labor cost. We adopted a new method that utilizes a Zimmermans approach to determine the tolerance and aspiration levels. The actual performance of an industrial company was used to prove the feasibility of the proposed model. The proposed model shows that the method is useful, generalizable, and can be applied to APP problems with other parameters.

Jeder Lernende, der in der Fremdsprache Deutsch kommunizieren möchte, wird sich auch mit der deutschen Aussprache beschäftigen (müssen). Wer eine gute Aussprache hat, wird nicht nur oft und zu Recht bewundert, er hat es auch leichter, die deutsche Sprache zu verstehen, und er wird gut verstanden. Aussprachefehler beeinträchtigen die Kommunikation, sie führen zur Unverständlichkeit von Namen, Wörtern und Äußerungen oder Mißverständnissen, sie bewirken Ermüdung und Konzentrationsverluste und beeinträchtigen die Sprachverarbeitung durch Assoziationen und Emotionen, die beim Hörer entstehen können.’’[1]

Diese vorliegende Forschung befasst sich mit der Wic

This study presents a detailed morphology and taxonomic study of Polysiphonia subtilissima collected from Abdul Rehman Goth, Karachi coast, Pakistan. Polysiphonia is a filamentous heterotrichous red algae, characterized by its branching structures and attachment mechanisms. P. subtilissima is notable for its broad salinity tolerance and wide distribution across marine and freshwater ecosystems. This research provides an in-depth examination of the internal and external structures of P. subtilissima, contributing to its systematic study and documenting its first recorded occurrence in Pakistani coastal areas, bordering the northern Arabian Sea. The findings enhance the understanding of the species taxonomy and its ecological role in

KE Sharquie, HR Al-Hamamy, AA Noaimi, KA Ali, Journal of Cosmetics, Dermatological Sciences and Applications, 2015 - Cited by 3

In this research, the kinetic studies of four isoenzymes of Asprtate aminotransferase, which partially purified from the urine of chronic renal failure patients were carried out .The four isoenzymes were obeyed Michaelis-Menton's equation and the optimum concentration of their substrate (Aspartic acid) was (166.5x10-3) mole/liter,and their Km values were determined. Four isoenzymesI,II,III,IV have shown an optimum pH at 7.4.The four isoenzymes obeyed Arrhenius equation up to 37º C and their Ea and Q10 constants were determined .

   This research deals with the financial reporting for non-current assets impairment from the viewpoint of international accounting standards, particularly IAS 36 "Impairment of non-current assets." The research problems focus on the presence of internal and external indicators on impairment of non-current assets in many of companies listed in Iraqi stock exchange. So it is required to apply IAS 36 to reporting for the impairment loss of assets since this impairment impact certain financial indicators. These indicators help users in their decision-making and forecasting future financial situation and the ability of the company to achieve future profits or maintain current profits. The research aims to shedding lig

Promoting the production of industrially important aromatic chloroamines over transition-metal nitrides catalysts has emerged as a prominent theme in catalysis. This contribution provides an insight into the reduction mechanism of p-chloronitrobenzene (p-CNB) to p-chloroaniline (p-CAN) over the γ-Mo2N(111) surface by means of density functional theory calculations. The adsorption energies of various molecularly adsorbed modes of p-CNB were computed. Our findings display that, p-CNB prefers to be adsorbed over two distinct adsorption sites, namely, Mo-hollow face-centered cubic (fcc) and N-hollow hexagonal close-packed (hcp) sites with adsorption energies of −32.1 and −38.5 kcal/mol, respectively. We establish that the activation of nit

Hepatitis C virus (HCV) is a liver disease that affects14 million people. Feasible research was conducted for identifying the genotypes and allele frequency of some single nucleotide polymorphisms (SNPs) of the IL-28β genes and their predictive role in disease incidence in Iraqi patients. The SNPs (rs28416813, rs4803219, rs11881222, and rs8103142) of IL-28β have been associated with susceptibility to several diseases. Ninety eight (98) HCV patients were included in this research; with average age ± SE (42.28 ± 3.44) years. Also, 80 healthy people (with average age ± SE (29.40 ± 2.84) years) were included as a control group. The SNPs were detected by allele-specific PCR (polymerase chain reaction) using specific primers. The re