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

Well dispersed Cu2FeSnSe4 (CFTSe) nanofilms were synthesized by hot-injection method. The structural and morphological measurements were characterized using XRD (X-ray diffraction), Raman spectroscopy, SEM (scanning electron microscopy), and TEM (transmission electron microscopy). Chemical composition and optical properties of as-synthesized CFTSe nanoparticles were characterized using EDS (energy dispersive spectroscopy) and UV-Vis spectrophotometry. The average particle size of the nanoparticles was about 7-10 nm. The UV-Vis absorption spectra showed that the synthesized CFTS nanofilms have a band gap (Eg) of about 1.16 eV. Photo-electrochemical characteristics of CFTSe nanoparticles were studied and indicated their potential application

In this paper we investigated some new properties of π-Armendariz rings and studied the relationships between π-Armendariz rings and central Armendariz rings, nil-Armendariz rings, semicommutative rings, skew Armendariz rings, α-compatible rings and others. We proved that if R is a central Armendariz, then R is π-Armendariz ring. Also we explained how skew Armendariz rings can be ?-Armendariz, for that we proved that if R is a skew Armendariz π-compatible ring, then R is π-Armendariz. Examples are given to illustrate the relations between concepts.