The restriction concept is a basic feature in the field of measure theory and has many important properties. This article introduces the notion of restriction of a non-empty class of subset of the power set on a nonempty subset of a universal set. Characterization and examples of the proposed concept are given, and several properties of restriction are investigated. Furthermore, the relation between the P*–field and the restriction of the P*–field is studied, explaining that the restriction of the P*–field is a P*–field too. In addition, it has been shown that the restriction of the P*–field is not necessarily contained in the P*–field, and the converse is true. We provide a necessary condition for the P*–field to obtain th

 In this research, analytical study for simulating a Fabry-Perot bistable etalon (F-P cavity) filled with a dispersive optimized nonlinear optical material (Kerr type) such as semiconductors Indium Antimonide (InSb). An optimization procedure using reflective (~85%) InSb etalon (~50µm) thick is described. For this etalon with a (50 µm) spot diameter beam, the minimum switching power is (~0.078 mW) and switching time is (~150 ns), leading to a switching energy of (~11.77 pJ) for this device. Also, the main role played by the temperature to change the etalon characteristic from nonlinear to linear dynamics.

The present research aims to study the efficiency of infrared material lenses compared with the glass material lenses by determining LSF and CLSF for perfect optical system having circular aperture, Arnorphous(1,2) material transmitting infrared radiation (AMTIR) is used for infrared window, lenses and prisms when transmission in the range of 1-14 pm is desired in application like thermal imaging, astronomical and forward looking infrared (FLIR), AMTIR is the low thermal change in refractive index 72 * 10-6 /C ° is an advantage in lenses design to prevent defocussing.

The Electric Discharge (EDM) method is a novel thermoelectric manufacturing technique in which materials are removed by a controlled spark erosion process between two electrodes immersed in a dielectric medium. Because of the difficulties of EDM, determining the optimum cutting parameters to improve cutting performance is extremely tough. As a result, optimizing operating parameters is a critical processing step, particularly for non-traditional machining process like EDM. Adequate selection of processing parameters for the EDM process does not provide ideal conditions, due to the unpredictable processing time required for a given function. Models of Multiple Regression and Genetic Algorithm are considered as effective methods for determ

Water pollution has created a critical threat to the environment.‎‎ A lot of research has been done ‎recently to use surface-enhanced Raman spectroscopy (SERS) to detect multiple pollutants in water. This study aims to use Ag colloid nanoflowers as liquid SERS enhancer. Tri sodium phosphate (Na₃PO₄) was investigated as a pollutant using liquid SERS ‎based on colloidal Ag ‎nanoflowers. The chemical method was used to synthesize nanoflowers from silver ‎ions. Atomic Force Microscope (AFM), Scanning Electron Microscope (SEM), and X-ray diffractometer (XRD) were employed to characterize the silver nanoflowers. This ‎nanoflowers SERS action in detecting Na₃PO₄ was reported and analyzed

A set of ten drug compounds containing an amino group in the structure were determined theoretically. The parameters were entered into a model to forecast the optimal values of practical (log P) medicinal molecules. The drugs were evaluated theoretically using different types of calculations which are AM1, PM3, and Hartree Fock at the basis set (HF/STO-3G). The Physico-chemical data like (entropy, total energy, Gibbs Free Energy,…etc were computed and played an important role in the predictions of the practical lipophilicity values. Besides, Eigenvalues named HOMO and LUMO were determined. Linearity was shown when correlated between the experimental data with the evaluated physical properties. The statistical analysis was used to analy

A theoretical study by using computer model is presented to study the energy characteristics of the vibrational – rotational levels as a function of the vibrational and rotational quantum number, respectively. The calculations were based on the basis of a multilevel model taking into account the non-equilibrium population of the rotational levels. The computational investigation has been performed to examine the vibrational-rotational characteristics of some hydrogen halides chemical laser molecules. This program takes into account the various molecules of chemical lasers such as, Hydrogen Fluoride (HF), Deuterium Fluoride (DF), Hydrogen Chloride (HCl), and Deuterium Chloride (DCl). The practical difficulties associated with this