In this study, the modified Rayleigh-Ritz method and Fourier series are used to determine the thermal buckling behavior of laminated composite thin plates with a general elastic boundary condition applied to in-plane uniform temperature distribution depending upon classical laminated plate theory(CLPT). A generalized procedure solution is developed for the Rayleigh-Ritz method combined with the synthetic spring technique. The transverse displacement of the orthotropic rectangular plates is not a different term as a new shape expansion of trigonometric series. In this solution approach, the plate transverse deflection and rotation due to bending are developed into principle Fourier series with a sufficient smoothness auxiliary polynomial function, the variable of boundary condition can be easily done by only change the boundary spring stiffness of at the all boundaries of laminated composite plate without achieving any replacement to the solution. The accuracy of the current outcome is verified by comparing with the result obtained from other analytical methods in addition to the finite element method (FEM), so the excellent of this technique is proving during numerical examples.
This research has come out with that strategies made by Porter as generally strategies applicable to any size and type of economic units cannot be applied to many of the economic units in the world in generally and in Iraq especially not a lot of economic units have the resources and competencies that enable them to provide a unique product of its kind in the minds of customers and then adopt a differentiation strategy and not a lot of economic units have the resources and competencies that make them the cost leader. Differentiators and cost leaders are minority in the world while not differentiators and not cost leaders are majority in the world.
The economic units are not differentiators and not c
... Show MoreThis research shows the problem of the economic development of underdeveloped countries in an unconventional way, as these papers explain the problems of the economic development. This research not only reviews the problems, but it illustrates them in a philosophical way, basis of the data of modernity, this mean it is a process of connecting between the absence of the modernity values and the failure of development in underdeveloped countries. The Search follows the descriptive approach to get to the goal of search by four main axes. The first axis includes clarifying modernity and its principles, the second axis includes clarifying the economic development , the third axis includes the features of the mod
... 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 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 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 (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
... 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 (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
... Show MoreThis study presents a mathematical model describing the interaction of gut bacteria in the participation of probiotics and antibiotics, assuming that some good bacteria become harmful through mutations due to antibiotic exposure. The qualitative analysis exposes twelve equilibrium points, such as a good-bacteria equilibrium, a bad-bacteria equilibrium, and a coexisting endemic equilibrium in which both bacteria exist while being exposed to antibiotics. The theory of the Sotomayor theorem is applied to study the local bifurcation around all possible equilibrium points. It’s noticed that the transcritical and saddle-node bifurcation could occur near some of the system’s equilibrium points, while pitchfork bifurcation cannot be accrued at
... Show MoreThe combined system of electrocoagulation (EC) and electro-oxidation (EO) is one of the most promising methods in dye removal. In this work, a solution of 200 mg/l of Congo red was used to examine the removal of anionic dye using an EC-EO system with three stainless steel electrodes as the auxiliary electrodes and an aluminum electrode as anode for the EC process, Cu-Mn-Ni Nanocomposite as anode for the EO process. This composite oxide was simultaneously synthesized by anodic and cathodic deposition of Cu (NO3)2, MnCl2, and Ni (NO3)2 salts with 0.075 M as concentrations of each salt with a fixed molar ratio (1:1:1) at a constant current density of 25 mA/cm2. The characteristics structure and surface morphology of the depo
... Show MoreBackground: the aim of this study was to evaluate the effect of different surface acids treatments (37%phospjoric acid, 5%hydrofluoric acid, 1.23 acidulated phosphate fluoride) of feldspathic ceramic VITA 3D MASTER , and the effect of thermocycling on shear bond strength using a ceramic repair kit (ivoclar/vivadent). Material and Methods: sixty Nickel-Chromium metal base plates were prepared(9mm diameter,3mm depth) using lost wax technique, 2mm thick layer of ceramic(VITA 3D MASTER) fused to metal plates, all specimens were embedded in acrylic resin blocks except their examined surfaces and divided into 3 main groups 20 specimens each, Grp A: treatment with 37%phosphoric acid for 2 mins, Grp B: etching with 5% hydrofluoric acid for 2mins,
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