The Hartley transform generalizes to the fractional Hartley transform (FRHT) which gives various uses in different fields of image encryption. Unfortunately, the available literature of fractional Hartley transform is unable to provide its inversion theorem. So accordingly original function cannot retrieve directly, which restrict its applications. The intension of this paper is to propose inversion theorem of fractional Hartley transform to overcome this drawback. Moreover, some properties of fractional Hartley transform are discussed in this paper.

The MTX was converted to MTX nanoparticles by the modified method based on changing the pH gradually with exposure to ultrasound and shaking , changing the pH with exposure to ultrasound plays an significant role in the formation of nanoparticles, and this is shown in some previous studies. As the change in pH affects the nature of bonding between molecules, as well as the strength of bonding that depends on the change of electrical charges The exposure to ultrasound waves will greatly affect the breakdown of large particles into small particles that reach the level of nanoparticles. The MTX NPs formation was characterized by UV-Vis spectra analysis , Atomic force microscopy (AFM) analysis, Scanning electron microscope (SEM) and Fou

In this paper, we introduce a new concept named St-polyform modules, and show that the class of St-polyform modules is contained properly in the well-known classes; polyform, strongly essentially quasi-Dedekind and ?-nonsingular modules. Various properties of such modules are obtained. Another characterization of St-polyform module is given. An existence of St-polyform submodules in certain class of modules is considered. The relationships of St-polyform with some related concepts are investigated. Furthermore, we introduce other new classes which are; St-semisimple and ?-non St-singular modules, and we verify that the class of St-polyform modules lies between them.

In this thesis, we introduce eight types of topologies on a finite digraphs and state the implication between these topologies. Also we studied some pawlak's concepts and generalization rough set theory, we introduce a new types for approximation rough digraphs depending on supra open digraphs. In addition, we present two various standpoints to define generalized membership relations, and state the implication between it, to classify the digraphs and help for measure exactness and roughness of digraphs. On the other hand, we define several kinds of fuzzy digraphs. We also introduce a topological space, which is induced by reflexive graph and tolerance graphs, such that the graph may be infinite. Furthermore, we offered some properties of th

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The research aims to focus on the human rights guarantees as they are subjected to continuous violations due to changes, wars and conflicts between nations and people, especially in the Arab world and the third world due to political, social, economic and environmental conditions and the failure of democratic tracks under the current reality.

Keyword: Human rights, Reality, Ambition.

In this paper introduce some generalizations of some definitions which are, closure converge to a point, closure directed toward a set, almost ω-converges to a set, almost condensation point, a set ωH-closed relative, ω-continuous functions, weakly ω-continuous functions, ω-compact functions, ω-rigid a set, almost ω-closed functions and ω-perfect functions with several results concerning them.

Abstract. This study gives a comprehensive analysis of the properties and interactions of fibrewise maximal and minimal topological spaces. Fibrewise topology extends classical topological concepts to structured spaces, providing a thorough understanding of spaces that vary across different dimensions. We study the basic theories, crucial properties, and characterizations of maximal and minimal fibrewise topological spaces. We investigate their role in different mathematical contexts and draw connections with related topological concepts. By providing exact mathematical formulations and comprehensive examples, this abstract advances the fields of topology and mathematical analysis by elucidating the unique properties and implications of fib

E-learning seeks to create an interactive learning environment between the teacher and the learner through electronic media conveying in more than one direction, regardless of how the environment and its variables are identified. It also develops skills necessary to deal with technology in order to be able to take into account the individual differences between them and helps e-learning teacher and learner to achieve the goals set in advance and identify educational objectives in a clear manner. The research aims to identify e-learning in its benefits and management systems. It has three sections dealt with in the current research. Chapter II concentrates on the research Methodology, which consisted of three sections: The first s