The definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X ,  ) be a topological space, and let  A ⊆,    then A is called semi-preopen set if ⊆∘ .        In this paper, we study the properties of semi-preopen sets but by another  definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.

     In this paper, we study a new concept of fuzzy sub-module, called  fuzzy socle semi-prime sub-module that is a generalization the concept of semi-prime fuzzy sub-module and fuzzy of approximately semi-prime sub-module in the ordinary sense.  This leads us to introduce level property which studies the relation between the ordinary and fuzzy sense of approximately semi-prime sub-module. Also, some of its characteristics and notions such as the intersection, image and external direct sum of fuzzy socle semi-prime sub-modules are introduced. Furthermore, the relation between the fuzzy socle semi-prime sub-module and other types of fuzzy sub-module presented.

In this work the concept of semi-generalized regular topological space was introduced and studied via semi generalized open sets. Many properties and results was investigated and studied, also it was shown that the quotient space of semi-generalized regular topological space is not, in general semi-generalizedspace.

    The definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X ,  ) be a topological space, and let  A ⊆,    then Ais called semi-preopen set if ⊆∘ .        In this paper, we study the properties of semi-preopen sets but by another  definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.

Dans la langue française, une forme d'auxiliarité, composée de deux éléments cohérents l'auxiliant et l'auxilié, fournit, en effet, à la phrase une diversité significative et structurale. L'auxiliarité, renvoie à l'unification de deux éléments grammaticaux afin de localiser l'énoncé sur l'axe du temps, d'aspect ou de mode. É. Benveniste définit l'auxiliarité en : « Il s'agit d'une forme linguistique unitaire qui se réalise, à travers des paradigmes entiers, en  deux éléments, dont chacun assume une partie des fonctions grammaticales, et qui sont à la fois liés et autonomes, distincts et complémentaires »[1]. Ces deux éléments d'auxiliarité possèden

               In this research, the semiparametric Bayesian method is compared with the classical  method to  estimate reliability function of three  systems :  k-out of-n system, series system, and parallel system. Each system consists of three components, the first one represents the composite parametric in which failure times distributed as exponential, whereas the second and the third components are nonparametric ones in which reliability estimations depend on Kernel method using two methods to estimate bandwidth parameter h method and Kaplan-Meier method. To indicate a better method for system reliability function estimation, it has be

In this study, the modified size-strain plot (SSP) method was used to analyze the x-ray diffraction lines pattern of diffraction lines (1 0 1), (1 2 1), (2 0 2), (0 4 2), (2 4 2) for the calcium titanate(CaTiO3) nanoparticles, and to calculate lattice strain, crystallite size, stress, and energy density, using three models: uniform (USDM). With a lattice strain of (2.147201889), a stress of (0.267452615X10), and an energy density of (2.900651X10-3 KJ/m3), the crystallite was 32.29477611 nm in size, and to calculate lattice strain of Scherrer (4.1644598X10−3), and (1.509066023X10−6 KJ/m3), a stress of(6.403949183X10−4MPa) and (26.019894 nm).

The influence of adding metal foam fins on the heat transfer characteristics of an air to water double pipe heat exchanger is numerically investigated. The hot fluid is water which flows in the inner cylinder whereas the cold fluid is air which circulates in the annular gap in parallel flow with water. Ten fins of metal foam (Porosity = 0.93), are added in the gap between the two cylinder, and distributed periodically with the axial distance. Finite volume method is used to solve the governing equations in porous and non-porous regions. The numerical investigations cover three values for Reynolds number (1000 ,1500, 2000), and Darcy number (1 x10^-1, 1 x10^-2, 1x10^-3). The comparison betwee

In this research we study a variance component model, Which is the one of the most important models widely used in the analysis of the data, this model is one type of a multilevel models, and it is considered as linear models , there are three types of linear variance component models ,Fixed effect of linear variance component model, Random effect of linear variance component model and Mixed effect of linear variance component model . In this paper we will examine the model of mixed effect of linear variance component model with one –way random effect ,and the mixed model is a mixture of fixed effect and random effect in the same model, where it contains the parameter (μ) and treatment effect (τ_i ) which  has