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.
Multivariate Analysis (First Edition)
matrix algebra
Linear Equation System
Characteristic root
Eigen value
vectors
Partitioned Matrices
Jacobian Matrix
Hessian matrix
Multivariate Normal Distribution
Publication Date
Fri Jul 29 2022
Journal Name
Journal For Vascular Ultrasound
A Comparative Study of the Right and Left Carotid Arteries in Relation to Age for Patients With Diabetes and Hypertension
Introduction:
Introduction: Age
hypertension
and diabetes can cause significant alterations in arterial structure and function
including
changes in lumen diameter (LD)
intimal-medial thickness (IMT)
flow velocities
and arterial compliance. These are also considered
risk markers of atherosclerosis and cerebrovascular disease. A difference between right and left carotid artery blood flow and
IMT has been reported by some researchers
and a difference in the incidence of nonlacunar stroke has been reported between
the right and left brain hemispheres. The aim of this study was to determine whether there are differences between the right and
left common carotid arteries and internal carotid arteries in patients with hypertension and diabetes for 2 age groups.
Methods: We studied 250 patients with both diabetes and hypertension. Patients were divided into 2 age groups with the
old age group being 56 to 75 years and the young age group 35 to 55 years. The bilateral common carotid and internal carotid
arteries were evaluated with B-mode ultrasound and Doppler examinations. The LD and IMT were measured for both common
carotid arteries
and spectral waveform parameters and indices were recorded for both internal carotid arteries.
Results: The difference in LD between the left and right common carotid arteries for the old age group was 11.64% and for the
young age group was 6.42%
with significant P values of <.05 for both age groups. The difference in IMT between the left and
right common carotid arteries was 18.27% in the old age group compared with 15.38% in the young age group
with significant
P values of <.05. There was a difference in peak systolic velocity between the left and right internal carotid arteries of 4.85%
in the old age group which was not significant
compared with 14.28% in the young age group with a significant P value <.05
whereas the difference in end-diastolic velocity between the left and right internal carotid arteries was not significant for both
age groups. Differences between the right and left internal carotid arteries for resistive index
pulsatility index
and pressure
gradient were significant only in the young age group.
Conclusion: We found significant differences between the right and left common carotid and internal carotid arteries in
patients with diabetes and hypertension which were more prominent in the young age group. Values for common carotid IMT
and LD were significantly higher in the left common carotid artery versus the right common carotid artery in both age groups.
Differences between the 2 carotid sides may be attributed to anatomic variations in the common carotid artery origins which
lead to differences in stress between the 2 sides
Age, hypertension, and diabetes can cause significant alterations in arterial structure and function, including changes in lumen diameter (LD), intimal-medial thickness (IMT), flow velocities, and arterial compliance. These are also considered risk markers of atherosclerosis and cerebrovascular disease. A difference between right and left carotid artery blood flow and IMT has been reported by some researchers, and a difference in the incidence of nonlacunar stroke has been reported between the right and left brain hemispheres. The aim of this study was to determine whether there are differences between the right and left common carotid arteries and internal carotid arteries in patient
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