This paper studies the oscillation properties and asymptotic behavior of all solutions of the 2×2 system of second-order half-linear neutral differential equations. Four results are obtained in this research. The first and second results are auxiliary results while the third and fourth results are main results. All possible cases of non-oscillating bounded solutions for this system are estimated and analyzed. It is noted that the parameters that affect the volatility of the solutions are Qi,Ri on the one hand and r1 and r2 on the other hand. For this purpose, and through investigation, it is shown that there are only fourteen possible cases of non-oscillating bounded solutions for this system, so all these cases must be treated, in the first result as well as the second, some new necessary and sufficient conditions were obtained to ensure that there are no non-oscillating bounded solutions in these cases, and thus all possible solutions for this system, if they exist, will be only oscillating solutions and there are no non-oscillating solutions for this type of equations. Some examples are included to illustrate all the results obtained.
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
... Show MoreThis 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
... Show Moresix specimens of the Hg0.5Pb0.5Ba2Ca2Cu3-y
الوصف Mixed ligand complexes of Cu (II), Co (II) and Zn (II) with 2-((4-(1-(4-chlorophenylimino) ethyl) phenylimino) methyl) phenol (L) and histidine (His) have been prepared and diagnosed by ¹H and13 C NMR, FT-IR and electronic spectral data, thermal gravimetric, molar conductance and metal analysis measurements. The ligand (L) shows a bidentate nature and the coordination occurs through N and O atoms of imine group and phenol group respectively whereas (His) behave as tridentate ligand, coordinating through the-NH2 group and carboxylate oxygen group and N atoms of imidazole ring. The analytical studies for three complexes have shown octahedral structure. The anticancer activity was screened against human cancer cell such Follicular
... Show MoreThe rise of antibiotic-resistant bacteria necessitates the exploration of novel antimicrobial agents. Yttrium oxide nanoparticles (Y₂O₃) have shown potential due to their unique physicochemical properties and antibacterial activities against various pathogens. This study investigates the cytotoxic and antibacterial effects of Y₂O₃ nanoparticles against Serratia fonticuli and Citrobacter koseri, bacteria isolated from cholangitis patients. Bacterial strains were isolated from bile specimens and confirmed using standard microbiological techniques. The methods of X-ray diffraction (XRD), (SEM), and Frequency transform-infrared spectroscopic (FT-IR) were used to characterize YO₃ particles. Using a microdilution technique, the minimum
... Show MoreConjugated Linoleic Acid (CLA) is an essential polyunsaturated omega fatty acid that occurs naturally in vegetable oils. It also plays an important role in preserving meat for longer periods by preventing oxidation of other fats. Thus, it can be used in the production of functional foods with high biological value and low cholesterol levels by adding poultry diets. Objective: The aim of the present study was to evaluate the effect of adding CLA to broiler diets on production performance and fatty acid content in the meat. Methodology: One-day-old Ross-308 chicks were randomly distributed into four dietary treatment groups: control (0 g CLA kgG1 diet; A1), 0.5 g CLA kgG1 diet (A2), 0.75 g CLA kgG1 diet (A3) and 1 g CLA kgG1 diet (A4). Diets
... Show MoreThe research examines the awareness of the components of responsible citizenship among primary schoolgirls in Jeddah using a descriptive approach. A test was then prepared, which consists of loyalty, affiliation to homeland, conscious citizenship based on the knowledge of rights, the fulfillment of duties, family roles in education and society revival, homeland and preservation of the components and gains, participation in achievements, and of national heritage. To maintain the validity and reliability of the study, 28-item test of multiple-choice and short essays type was applied to a random sample of (303) female students in the (fourth-fifth-sixth) primary school class in Jeddah. Results have shown that the level of awareness of schoo
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