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.
This study introduces a highly sensitive trapezium-shaped PCF based on an SPR refractometric sensor with unique design features. The structure of a sensor was designed and analyzed using COMSOL Multiphysics v5.6 based on Finite Element Method (FEM) with a focus on investigating the influence of various geometric parameters on its performance. The two channels were coated with a metallic gold layer to provide chemical stability, and a thin layer of TiO₂ improved the gold's adhesion to the fiber. The findings indicate that the proposed sensor achieves maximum amplitude and wavelength sensitivities of 1,779 RIU⁻¹ and 30,500 nm/RIU, respectively, with corresponding resolutions of 3.2
This article deals with the study of theories about verbal periphrasis as a grammatical construction; the aim of this point it offers good and valid guidelines to improve the linguistic description. The interest in the subject comes from its importance in the process of language teaching for the students of Spanish and to clarify this type of curriculum of this research we analyzed a literary text. From "Zurita"
Were analyzed curved optical fates Almarchih absolute colony of the binary type, the Great Palmstqrh using mathematical relationships derived for that and that gave us the results closer to the results of the observed spectral Great Colonial
Reducing a structure’s self-weight is the main goal and a major challenge for most civil constructions, especially in tall buildings and earthquake-affected buildings. One of the most adopted techniques to reduce the self-weight of concrete structures is applying voids in certain positions through the structure, just like a voided slab or BubbleDeck slab. This research aims to study, experimentally and theoretically, the structural behavior of BubbleDeck reinforced concrete slabs under the effect of harmonic load. Tow-way BubbleDeck slab of 2500mm×2500m×200mm dimensions and uniformly distributed bubbles of 120mm diameter and 160mm spacing c/c was tested experimentally under the effect of harmonic load. Numerical analysis was als
... Show MoreIn this study, a cholera model with asymptomatic carriers was examined. A Holling type-II functional response function was used to describe disease transmission. For analyzing the dynamical behavior of cholera disease, a fractional-order model was developed. First, the positivity and boundedness of the system's solutions were established. The local stability of the equilibrium points was also analyzed. Second, a Lyapunov function was used to construct the global asymptotic stability of the system for both endemic and disease-free equilibrium points. Finally, numerical simulations and sensitivity analysis were carried out using matlab software to demonstrate the accuracy and validate the obtained results.
This study focused on the synthesis of novel polymers incorporating the 1,3,4-oxadiazole ring. Four polymers were specifically prepared by blending polymers (6-9) with polyvinyl alcohol (PVA) in defined ratios, resulting in the formation of blended polymers (10-13). The synthesized polymers were characterized using Fourier Transform Infrared (FTIR) spectroscopy and proton nuclear magnetic resonance (1H-NMR). The results showed that the structure aligned with the proposed synthetic polymers. Furthermore, the physical and thermal properties were studied using scanning electron microscopy (SEM), thermogravimetric analysis (TGA) and Differential Scanning Calorimetry (DSC). Additionally, the biological activity was examined against two s
... Show MoreThis paper presents a numerical analysis of the piled-raft foundation (PRF) based on the actual behavior of supporting piles. The raft was modeled as a thin plate, while the piles were modeled as springs in different ways. This research also aims to propose an analytical model of piles based on actual behavior at fieldwork. The results proved that the structural behavior of raft member can be improved through utilizing the actual behavior of supporting piles. When the piles were modeled as non-linear stiffness springs, settlements and bending stresses of raft foundation were reduce marginally as compared with those obtained from piles with linear stiffness springs.
This paper presents a nonlinear finite element modeling and analysis of steel fiber reinforced concrete (SFRC) deep beams with and without openings in web subjected to two- point loading. In this study, the beams were modeled using ANSYS nonlinear finite element
software. The percentage of steel fiber was varied from 0 to 1.0%.The influence of fiber content in the concrete deep beams has been studied by measuring the deflection of the deep beams at mid- span and marking the cracking patterns, compute the failure loads for each deep beam, and also study the shearing and first principal stresses for the deep beams with and without openings and with different steel fiber ratios. The above study indicates that the location of openings an
A time series analysis can help to observe the behavior of the system and specify the system faults. In addition, it also helps to explain the various energy flows in the system and further aid in reducing the thermodynamic losses. The intelligent supervisory LabVIEW software can monitor the incoming data from the system by using Arduino microcontroller and calculates the important parameters. Energy, exergy, and anergy analysis present in this paper to investigate the system performance as well as its components. To accomplish this, a 4-ton vertical split air conditioner based on vapor compression refrigeration cycle charged with refrigerant R-22 was modified for experimental analysis. The results showed that during 540
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