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

One of the important objectives of the varistor is for a sustainable environment and reduce the pollution resulting from the frequent damage of the electrical devices and power station waste. In present work, the influence of Al2O3 additives on the non –linear electrical features of SnO2 varistors, has been investigated, where SnO2 ceramic powder doped with Al2O3 in three rates (0.005, 0.01, and 0.05), the XRD test improved that SnO2 is the primary phase, while CoCr2O4, and Al2O3 represent the secondary phases. The electrical tests of all prepared samples confirmed that the increasing of Al2O3 rates and sintering temperature improves and increase the electrical features, where the best results obtained at Al2O3 (0.05) and 1000℃, the non

Background: Fixed orthodontic appliances impede the maintenance of oral hygiene and result in plaque accumulation leads to enamel demineralization caused by acids produced by bacteria. Studies on plaque control strategies in orthodontic populations are limited. This might be caused by difficulties in the quantitative evaluation of dental plaque because the teeth have various levels of bracket coverage, and different tooth sizes and malocclusions, making the traditional categorical indices complex. The present study aims to evaluate the effect of different hygiene protocols on plaque quantity on bands with different attachments. Materials and method: Twenty patients had four bands within the orthodontic appliance. Then randomly divided into

Based on the diazotization-coupling reaction, a new, simple, and sensitive spectrophotometric method for determining of a trace amount of (BPF) is presented in this paper. Diazotized metoclopramide reagent react with bisphenol F produces an orange azo-compound with a maximum absorbance at 461 nm in alkaline solution. The experimental parameters were optimized such as type of alkaline medium, concentration of NaOH, diazotized metoclopramide amount, order additions, reaction time, temperature, and effect of organic solvents to achieve the optimal performance for the proposed method. The absorbance increased linearly with increasing bisphenol F concentration in the range of 0.5-10 μg mL^-1 under ideal conditions, with a correlati

Electronic properties such as density of state, energy gap, HOMO (the highest occupied molecular orbital) level, LUMO (the lowest unoccupied molecular orbital) level and density of bonds, as well as spectroscopic properties like infrared (IR), Raman scattering, force constant, and reduced masses for coronene C₂₄, reduced graphene oxide (rGO) C₂₄O₅and interaction between C₂₄O₅and NO₂gas molecules were investigated. Density functional theory (DFT) with the exchange hybrid function B3LYP with 6-311G** basis sets through the Gaussian 09 W software program was used to do these calculations. Gaussian view 05 was em

Hybrid architecture of ZnO nanorods/graphene oxide ZnO-NRs@GO synthesized by electrostatic self-assembly methods. The morphological, optical and luminescence characteristics of ZnO-NRs@GO and ZnO-NRs thin films have been described by FESEM, TEM, HRTEM, and AFM, which refers to graphene oxide have been coated ZnO-NRs with five layers. Here we synthesis ZnO-NRs@GO by simple, cheap and environmentally friendly method, which made it favorable for huge -scale preparation in many applications such as photocatalyst. ZnO-NRs@GO was applied as a photocatalyst Rodamin 6 G (R6G) dye from water using 532 nm diode laser-induced photocatalytic process. Overall degradation of R6G/ ZnO-NRs@GO was achieved after 90 minutes of laser irradiation while it ne