This paper including a gravitational lens time delays study for a general family of lensing potentials, the popular singular isothermal elliptical potential (SIEP), and singular isothermal elliptical density distribution (SIED) but allows general angular structure. At first section there is an introduction for the selected observations from the gravitationally lensed systems. Then section two shows that the time delays for singular isothermal elliptical potential (SIEP) and singular isothermal elliptical density distributions (SIED) have a remarkably simple and elegant form, and that the result for Hubble constant estimations actually holds for a general family of potentials by combining the analytic results with data for the time dela

Elastic magnetic electron scattering form factors in Ca-41 have been investigated. 1f7/2 subshell has been adopted as a model space with one neutron, and Millinar, Baymann and Zamick 1f7/2 model space effective interaction (F7MBZ) has been used as a model space effective interaction to generate the model space vectors for the M1, M3, M5, M7, and total form factors. Discarded space (core and higher configuration orbits) have been included through the first order perturbation theory to couple the partice-hole pair of excitation with 2ћω excitation energy in the calculation of the form factors and regarding the realistic interaction density dependence M3Y as a core polarization interaction with five sets of modern fitting parameters. Fina

Numerous physiological and biochemical changes are linked to menopause. The current study was intended to examine the transforms linked to anthropometric measurements and bone-related factors. In this study of 80 women which included; they comprised 40 premenopausal women and 40 postmenopausal women. waist circumference (WC), body mass index (BMI), hip circumference (HC), moreover waist to hip ratio are among the anthropometric measurements (W-HR) recorded by standard procedures. The plasma samples were tested for the following biochemical parameters: bone-related parameters [calcium (Ca), phosphorus (P), uric acid (UA), alkaline phosphatase (ALP), and erythrocyte sedimentation rate (ESR)] and serological agglutination tests [rheumat

Physiological status and litter size can indeed have a significant impact on ewes' ‎hematological parameters, which are essential indicators of their health. Therefore, this study ‎examined the hematological profiles of ewes during pregnancy with single and twins in the ‎Awassi ewes. The present study involved 232 ewes in good health and at sexual maturity. ‎Among them, 123 ewes had single pregnancies, while 109 ewes had twin pregnancies. The age ‎range of the ewes included in the study was between 3.5 and 4.5 years. Hematological tests ‎were conducted on the sheep's blood samples promptly following collection. The findings ‎demonstrated variations in hematological parameters among pregnant

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

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

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 curr

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 curr

Shoulder immobilization is one of the injuries that lead to disability and loss of movement in the joint within a short time, which called the researchers to find appropriate therapeutic means to rehabilitate this injury. They prepared a rehabilitation program accompanying the reflexology technique to rehabilitate the injury of the immobilized shoulder of the small degree and improve the range of movement and muscle strength working on the shoulder joint The sample was selected from the male patients aged (40-50) years. The muscle strength test was used using the force sensor, the shoulder range test from the flexion and extension position and the visual analog test to measure the level of pain. The study concluded that the pre-rehabilitati