The main purpose of this work is to introduce the concept of higher N-derivation and study this concept into 2-torsion free prime ring we proved that:Let R be a prime ring of char. 2, U be a Jordan ideal of R and be a higher N-derivation of R, then , for all u U , r R , n N .

This study examined the correlation between binder-level fatigue properties and mixture-level cracking resistance in asphalt binders modified with five Nanomaterials (NMs): Nano-Silica (NS), Nano-Alumina (NA), and Nano-Titanium dioxide (NT) at 2%, 4%, and 6% as well as Nano-Zinc oxide (NZ) and Carbon Nanotubes (CNTs) at 1%, 2%, and 3%. Modified binders were subjected to Rolling Thin-Film Oven Test (RTFOT) and Pressure Aging Vessel (PAV) aging and tested at 25 °C using the Linear Amplitude Sweep (LAS) test to determine fatigue life (Nf) and the fatigue parameter G*.sin δ. The corresponding asphalt mixtures were evaluated using the IDEAL-CT test. The results indicated strong correlations between binder and mixture performance for

Raising children occupies a prominent place in Islam as a step paving the way for the success of reform projects on the level of diverse human life, and for this reason the recommendation for education was mentioned in the mission entrusted to the Prophet (PBUH), the Almighty said:

(( هُوَ الَّذِي بَعَثَ فِي الْأُمِّيِّينَ رَسُولًا مِّنْهُمْ يَتْلُو عَلَيْهِمْ آيَاتِهِ وَيُزَكِّيهِمْ وَيُعَلِّمُهُمُ الْكِتَابَ وَالْحِكْمَةَ وَإِن كَانُوا مِن قَبْلُ لَفِي ضَلَالٍ مُّبِينٍ))  Jumaa verse /38

The topic of the research that is in your hands deals with the

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.