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.

A new family of nematic liquid crystal dendrimers derived from 3,5-dihydroxybenzoic acid were synthesized. The synthesis of the dendrimers compounds shows the influence of the dendritic core on the mesomorphic properties. The liquid crystalline properties were studied by polarizing optical microscopy (POM) equipped with a hot stage, the structures of the synthesized compounds characterized using FTIR and 1HNMR spectroscopy.

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

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The tourism services provided in the hotel organizations are a set of material and moral elements that represent tourist attractions that are offered to the guests in order to satisfy their needs and desires are accommodation, food, drink and other facilities to reach the satisfaction and satisfaction of guests.Where these tourist services need a mechanism to ensure their quality by working to identify and calculate the costs of these services properly and accurately with the attempt to referendum and reduce the waste and loss to reduce these costs while providing the finest types of tourism services by calculating the cost of production and the administration seeks to reduce Non-essential activities through hotel activities that add val