This study investigates the influence of five nanomaterials nano-alumina (NA), nano-silica (NS), nano-titanium (NT), nano-zinc oxide (NZ), and carbon nanotubes (CNT)on enhancing the fatigue resistance of asphalt binders. NA, NS, and NT were incorporated at dosages of 2%, 4%, 6%, 8%, and 10%, while NZ and CNT were added at 1%, 2%, 3%, 4%, and 5%. A series of physical, rheological, and performance-based tests were conducted, including penetration, softening point, ductility, and rotational viscosity. Based on the outcomes of the overall desirability evaluation, the first three dosages of each nanomaterial were selected for further testing due to their superior workability and binder flexibility. Subsequent investigations included the high-tem

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

In this work we explain and discuss new notion of fibrewise topological spaces, calledfibrewise soft ideal topological spaces, Also, we show the notions of fibrewise closed soft ideal topological spaces, fibrewise open soft ideal topological spaces and fibrewise soft near ideal topological spaces.

The concept of fully pseudo stable Banach Algebra-module (Banach A-module) which is the generalization of fully stable Banach A-module has been introduced. In this paper we study some properties of fully stable Banach A-module and another characterization of fully pseudo stable Banach A-module has been given.

Abstract. In this study, we shall research the fibrewise micro ideal topological spaces over Ḃ, as well as the relationship between fibrewise micro ideal topological spaces over Ḃ and fibrewise micro topological spaces over Ḃ. At first present introduces a novel notion from fibrewise micro ideal topological spaces over Ḃ, and differentiates it from fibrewise micro topological spaces over Ḃ. Some fundamental characteristics from these spaces are studied. Then show discussed the fibrewise micro ideal closed and micro ideal open topologies. Many propositions relating to these ideas are offered. In the next part will study defines and investigates novel conceptions from fibrewise micro ideal topological spaces over Ḃ, particularly f

Let R be a commutative ring with non-zero identity element. For two fixed positive integers m and n. A right R-module M is called fully (m,n) -stable relative to ideal A of , if for each n-generated submodule of Mm and R-homomorphism . In this paper we give some characterization theorems and properties of fully (m,n) -stable modules relative to an ideal A of . which generalize the results of fully stable modules relative to an ideal A of R.

The main purpose of this paper is to study some results concerning reduced ring with another concepts as semiprime ring ,prime ring,essential ideal ,derivations and homomorphism ,we give some results a bout that.

Iraq is highly dependent on international markets to provide food for its residents. As imported food prices are highly dependent on crude oil prices in global markets, any shock in oil prices will have an impact on food consumption in the country. As a result, it is essential to study the demand for imported food at every time period. To the best of our knowledge as researchers, as not even a single study is available in the literature, this paper is considered the first to study the demand for imported food groups in Iraq. Therefore, the main objective of this research is to estimate demand elasticities for several imported food categories in Iraq. This study uses an Almost Ideal Demand System model to analyze the demand for imported f

A simple technique is proposed in this paper for estimating the coefficient of permeability of an unsaturated soil based on physical properties of soils that include grain size analysis, degree of saturation or water content, and porosity of the soil. The proposed method requires the soil-water characteristic curve for the prediction of the coefficient of permeability as most of the conventional methods. A procedure is proposed to define the hydraulic conductivity function from the soil water characteristic curve which is measured by the filter paper method. Fitting methods are applied through the program (SoilVision), after indentifying the basic properties of the soil such as Attereberg limits, specific gravity, void ratio, porosity, d