In this paper, cubic trigonometric spline is used to solve nonlinear Volterra integral equations of second kind. Examples are illustrated to show the presented method’s efficiency and convenience.

This paper is concerned with introducing and studying the first new approximation operators using mixed degree system and second new approximation operators using mixed degree system which are the core concept in this paper. In addition, the approximations of graphs using the operators first lower and first upper are accurate then the approximations obtained by using the operators second lower and second upper sincefirst accuracy less then second accuracy. For this reason, we study in detail the properties of second lower and second upper in this paper. Furthermore, we summarize the results for the properties of approximation operators second lower and second upper when the graph G is arbitrary, serial 1, serial 2, reflexive, symmetric, tra

      Let  R  be a commutative ring  with identity  and  E  be a unitary left  R – module .We introduce  and study the concept Weak Pseudo – 2 – Absorbing submodules as  generalization of weakle – 2 – Absorbing submodules , where a proper submodule  A of  an  R – module  E is  called  Weak Pseudo – 2 – Absorbing  if   0 ≠ rsx   A   for  r, s  R , x  E , implies that  rx   A + soc ( E ) or  sx  A + soc (E)  or   rs  [ A + soc ( E ) E ]. Many basic  properties, char

The current study is designed to investigate the histological and immunohistochemical characteristics of the thyroid gland in adult male Sciurus anamalus. This study found that the thyroid gland of the Caucasian squirrel is located in the neck area, below the larynx, on both sides of the trachea. It has two lobes (right and left) with cylindrical shape. The histological studies revealed that the thyroid gland is surrounded by a capsule which consists of connective tissue and forming of two layers which are outer layer and inner layer, and a layer of adipose tissue appears overlapping the outer layer. The inner tissue of the gland consists of follicles with different shapes and sizes, and is lined with simple cuboidal epithelial tissue (foll

The current study is designed to investigate the histological and immunohistochemical characteristics of the thyroid gland in adult male Sciurus anamalus. This study found that the thyroid gland of the Caucasian squirrel is located in the neck area, below the larynx, on both sides of the trachea. It has two lobes (right and left) with cylindrical shape. The histological studies revealed that the thyroid gland is surrounded by a capsule which consists of connective tissue and forming of two layers which are outer layer and inner layer, and a layer of adipose tissue appears overlapping the outer layer. The inner tissue of the gland consists of follicles with different shapes and sizes, and is lined with simple cuboidal epithelial tissue (foll

The behavior of externally prestressed composite beams under short term loading has been studied. A computer program developed originally by Oukaili to evaluate curvature is modified to evaluate the deflection of prestressed composite beam under flexural load. The analysis model based on the deformation compatibility of entire structure that allows to determine the full history of strain and stress distribution along cross section depth, deflection and stress increment in the external tendons .
The evaluation of curvatures for the composite beam involves iterations for computing the strains vectors at each node at any loading stage. The stress increment determined using equations depended on the member deflection at points of connecti

Being a doctoral student is not easy because it presupposes having a number of technical skills, among which digital skills, defined by the European Commission (2006) as "the safe and critical use of the technologies of the society of the information". and the variety of digital use in the personal and professional context, allows us to ask the question that any doctoral student should master and acquire in terms of digital skills? And on what basis can we define these skills?
In this work we expect to develop a baseline of digital skills, is a document that includes the set of essential digital skills that represents a fundamental tool for the doctoral student who can in no way bypass it. And for this, we conducted interviews with ab

The aim of the current paper is to resolve the non-uniqueness in gravity interpretation through searching for singular points in the gravity field that are coincide with causative body vertices. The Absolute Second Horizontal Gradient (ASHG) method is used to locate the horizontal reference location of the body, while its amplitude could be used to define body corner depth. Intelligent use of the ASHG method could help in differentiating between basin and intrusion structures from their gravity effect and could facilitate the interpretation in forward modeling and constrain inversion modeling to maximum limit. The method is tested by using many synthetic examples with different types of shapes. A real data is used to examine the method a

The topological indices are functions on the graph that do not depend on the labeling of their vertices. They are used by chemists for studying the properties of chemical compounds.  Let  be a simple connected graph. The Hyper-Zagreb index of the graph ,  is defined as  ,where  and  are the degrees of vertex  and , respectively. In this paper, we study the Hyper-Zagreb index and give upper and lower bounds for .

    Let R be a commutative ring with identity, and M be a left untial module. In this paper we introduce and study the concept w-closed submodules, that is stronger form of the concept of closed submodules, where asubmodule K of a module M is called w-closed in M, "if it has no proper weak essential extension in M", that is if there exists a submodule L of M with K is weak essential submodule of L then K=L. Some basic properties, examples of w-closed submodules are investigated, and some relationships between w-closed submodules and other related modules are studied. Furthermore, modules with chain condition on w-closed submodules are studied.