Hamiltonians, momentum operators, and other quantum-mechanical perceptible take the form of self-adjoint operators when understood in quantized physical schemes. Unbounded and self-adjoint recognition are required in the situation of positive measurements. The selection of the proper Hilbert space(s) and the selection of the self-adjoint extension must be made in order for this to operate. In this effort, we define a new extension positive measure depending on the measurable field of nonzero positive self-adjoint operator in unbounded Hilbert space of analytic functions of complex variables. Consequently, we define an extension norm in the same space. We show several new properties of the suggested operator and its adjoin operator. These pr

A variety of oxides were examined as additives to a V2O5/Al2O3 catalyst in order to enhance the catalytic performance for the vapor phase oxidation of toluene to benzoic acid. It was found that the modification with MoO3 greatly promoted the little reaction leading to improve catalyst performance in terms of toluene conversion and benzoic acid selectivity. The effect of catalyst surface area, catalyst promoters, reaction temperature, O2/toluene, steam/toluene, space velocity, and catalyst composition to catalyst performance were examined in order to increase the benzoic acid selectivity and yield.

Simple, sensitive and accurate two methods were described for the determination of terazosin. The spectrophotometric method (A) is based on measuring the spectral absorption of the ion-pair complex formed between terazosin with eosin Y in the acetate buffer medium pH 3 at 545 nm. Method (B) is based on the quantitative quenching effect of terazosin on the native fluorescence of Eosin Y at the pH 3. The quenching of the fluorescence of Eosin Y was measured at 556 nm after excitation at 345 nm. The two methods obeyed Beer’s law over the concentration ranges of 0.1-8 and 0.05-7 µg/mL for method A and B respectively. Both methods succeeded in the determination of terazosin in its tablets

Lactococcus lactis ssp. lactis isolated from raw milk was used for titanium dioxide (TiO2) nanoparticles biosynthesis. Biosynthesized TiO2 nanoparticles were characterized using UV-vis spectroscopy, Atomic Force Microscopy (AFM) (1.97 nm), X-ray diffraction (XRD) appa-ratus, Field Emission Scanning Electron Microscopy (FE-SEM), Energy dispersive X-ray anal-ysis (EDX) spectra and Fourier Transform Infrared Spectroscopy (FTIR). Result was 408.21 cm-1 that belong to anatase Titania. L. lactis ssp. Lactis isolates had the ability to synthesize TiO2 nanoparticles, the characterization results presented that the biosynthesized nanoparti-cles were at wavelength (344-347) nm; approving the formation of anatase phase of TiO2 NPs; spherical c