In this thesis, we introduced the simply* compact spaces which are defined over simply* open set, and study relation between the simply* separation axioms and the compactness were studied and study a new types of functions known as αS^(M* )- irresolte , αS^(M* )- continuous and R S^(M* )- continuous, which are defined between two topological spaces. On the other hand we use the class of soft simply open set to define a new types of separation axioms in soft topological spaces and we introduce the concept of soft simply compactness and study it. We explain and discuss some new concepts in soft topological spaces such as soft simply separated, soft simply disjoint, soft simply division, soft simply limit point and we define soft simply c

The primary purpose of this paper is to introduce the, 2- coprobabilistic normed space, coprobabilistic dual space of 2- coprobabilistic normed space and give some facts that are related of them

In this paper, we characterize normal composition operators induced by holomorphic self-map , when and .Moreover, we study other related classes of operators, and then we generalize these results to polynomials of degree n.

    The objective of this paper is, firstly, we study a new concept noted by algebra and discuss the properties of this concept. Secondly, we introduce a new concept related to the algebra such as smallest algebra. Thirdly, we introduce the notion of the restriction of algebra on a nonempty subset  of and investigate some of its basic properties. Furthermore, we present the relationships between field, monotone class, field and algebra. Finally, we introduce the concept of measure relative to the algebra and prove that every measure relative to the   is complete.

 We use the idea of Grill, this study generalized a new sort of linked space like –connected –hyperconnected and investigated its features, as well as the relationship between it and previously described notation. It also developed new sorts of functions, such as hyperconnected space, and identifying their relationship, by offering numerous instance and attributes that belong to this set. This set will serve as a starting point for further research into the sets many future possibilities. Also, we use some of the theorems and observations previously studied and relate them to the grill and the Alpha group, and benefit from them in order to obtain new results in this research. We applied the concept of Connected to them and obtained

In this research PbS thin film have been prepared by chemical bath deposition technique (CBD).The PbS film with thickness of (1-1.5)μm was thermally treated at temperature of 100°C for 4 hours. Some Structural characteristics was studied by using X-ray diffraction (XRD)and optical microscope photograph some of chemical gas sensing measurements were carried out ,it shown that the sensitivity of (CO2) gas depend on the grain Size and deposition substrate. The grain size of PbS film deposited on on glass closed to 21.4 nm while 37.97nm for Si substrate. The result of current-voltage characterization shwon the sensitivity of prepared film deposited on Si better than film on glass.

In this paper, we introduce an exponential of an operator defined on a Hilbert space H, and we study its properties and find some of properties of T inherited to exponential operator, so we study the spectrum of exponential operator e^T according to the operator T.

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat