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

The Weibull distribution is considered one of the Type-I Generalized Extreme Value (GEV) distribution, and it plays a crucial role in modeling extreme events in various fields, such as hydrology, finance, and environmental sciences. Bayesian methods play a strong, decisive role in estimating the parameters of the GEV distribution due to their ability to incorporate prior knowledge and handle small sample sizes effectively. In this research, we compare several shrinkage Bayesian estimation methods based on the squared error and the linear exponential loss functions. They were adopted and compared by the Monte Carlo simulation method. The performance of these methods is assessed based on their accuracy and computational efficiency in estimati

Moisture damage is one of the most significant troubles that destroy asphaltic pavement and reduces road serviceability. Recently, academics have noticed a trend to utilize fibers to enhance the efficiency of asphalt pavement. This research explores the effect of low-cost ceramic fiber, which has high tensile strength and a very high thermal insulation coefficient, on the asphalt mixture's characteristics by adding three different proportions (0.75%, 1.5%, and 2.25%). The Marshall test and the Tensile Strength Ratio Test (TSR) were utilized to describe the impact of ceramic fiber on the characteristics of Marshall and the moisture susceptibility of the hot mix asphalt mixture. The Field Emission Scanning Electron Microsc

Introduction: This study was designed to examine the effects of addition of the combination of polymerized polymethyl methacrylate (PMMA) and zirconia (ZrO2) particles to heat cure PMMA resin on impact strength, surface hardness, and roughness. Methods: The 70% (w/w) of polymerized PMMA powder (particle size: 0.70mm) was mixed with 30% (w/w) of zirconia powder (ZrO2) (1mm) to produce PMMA-ZrO2 filler. Ninety acrylic specimens created were divided into three groups containing 0% wt (Control group), 2% wt, and 4% wt, PMMA-ZrO2 filler. Ten specimens were used for impact strength, surface hardness and roughness test, blindly. Data were analyzed via oneway ANOVA and the Tukey post hoc test using R 3.6.3. Results: There was statistically signific

Rock engineers widely use the uniaxial compressive strength (UCS) of rocks in designing
surface and underground structures. The procedure for measuring this rock strength has been
standardized by both the International Society for Rock Mechanics (ISRM) and American Society
for Testing and Materials (ASTM), Akram and Bakar(2007).
In this paper, an experimental study was performed to correlate of Point Load Index ( Is(50))
and Pulse Wave Velocity (Vp) to the Unconfined Compressive Strength (UCS) of Rocks. The effect
of several parameters was studied. Point load test, Unconfined Compressive Strength (UCS) and
Pulse Wave Velocity (Vp) were used for testing several rock samples with different diameters.
The predicted e

A reinforced concrete frame is referred as "RIGID FRAMES". However, researches indicate that the Beam-Column joint (BCJ) is definitely not rigid. In addition, extensive research shows that failure may occur at the joint instead of in the beam or the column. Joint failure is known to be a catastrophic type which is difficult to repair.
This study was carried out to investigate the effect of hoops and column axial load on the shear strength of high-strength fiber reinforced Beam-Column Joints by using a numerical model based on finite element method using computer program ANSYS (Version 11.0). The variables are: diameter of hoops and magnitude of column axial load.
The theoretical results obtained from ANSYS program are in a good a

Most dinoflagellate had a resting cyst in their life cycle.  This cyst was developed in unfavorable environmental condition. The conventional method for identifying dinoflagellate cyst in natural sediment requires morphological observation, isolating, germinating and cultivating the cysts.  PCR is a highly sensitive method for detecting dinoflagellate cyst in the sediment.  The aim of this study is to examine whether CO1 primer could detect DNA of multispecies dinoflagellate cysts in the sediment from our sampling sites. Dinoflagellate cyst DNA was extracted from 16 sediment samples. PCR method using COI primer was running. The sequencing of dinoflagellate cyst DNA was using BLAST. Results showed that there were two clades of dinoflag

The most significant water supply, which is the basis of agriculture, industry and human and wildlife needs, is the river. In order to determine its suitability for drinking purposes, this study aims to measure the Water Quality Index (WQI) of the Tigris River in the Salah Al-Din Province (center of Tikrit), north of Baghdad. For ten (9) physio-chemical parameters, namely turbidity, total suspended sediments, PH, electrical conductivity, total dissolved solids, alkalinity, chloride, nitrogen as nitrate, sulphate, and then transported for examination to the laboratory, water samples were collected from 13 locations along the Tigris river. Using the weighted arithmetic index method, the WQI was measured and found to be 105,87 in up-stream, wh

The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient