This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

We have provided in this research model multi assignment  with  fuzzy function goal has been to build programming model is correct Integer Programming fogging  after removing the case from the objective function data and convert it to real data .Pascal triangular graded mean using Pascal way to the center of the triangular.

The data processing to get rid of the case fogging which is surrounded by using an Excel 2007 either model multi assignment  has been used program LNDO to reach the optimal solution, which represents less than what can be from time to accomplish a number of tasks by the number of employees on the specific amount of the Internet, also included a search on some of the

In this work, a composite material was prepared from Low-density polyethylene (LDPE) with different weight percent of grain and calcinations kaolin at temperature of (850^oC) using single screw extruder and a mixing machine operated at a temperature between (190-200^oC). Some of mechanical and physical properties such as tensile strength, tensile strength at break, Young modulus, and elongation at break, shore hardness and water absorption were determined at different weight fraction of filler (0, 2, 7, 10 and 15%). It was found that the addition of filler increases the modulus of elasticity, elongation at break, shore hardness and impact strength; on other hand, it decreases the tensile strength and tensile strength

The study of cohomology groups is one of the most intensive and exciting researches that arises from algebraic topology. Particularly, the dimension of cohomology groups is a highly useful invariant which plays a rigorous role in the geometric classification of associative algebras. This work focuses on the applications of low dimensional cohomology groups. In this regards, the cohomology groups of degree zero and degree one of nilpotent associative algebras in dimension four are described in matrix form.

This contribution aims to investigate volume-dependent thermal and mechanical properties of the two most studied phases of molybdenum nitride (c-MoN and h-MoN) by means of the quasi-harmonic approximation approach (QHA) via first-principles calculations up to their melting point and a pressure of 12 GPa. Lattice constants, band gaps, and bulk modulus at 0 K match corresponding experimental measurements well. Calculated Bader’s charges indicate that Mo–N bonds exhibit a more ionic nature in the cubic MoN phase. Based on estimated Gibbs free energies, the cubic phase presents thermodynamic stability higher than that detected for hexagonl, with no phase transition observed in the selected T–P conditions as detected experimentall

                The electrical characteristics of polyvinyl alcohol PVA doped with different concentrations (0, 1, 2, 3 and 4wt%) of sodium  iodide NaI powder were studied. The films are prepared using solution casting technique, in order to investigate the effect of sodium iodide NaI additions on the electrical properties of PVA host. The D.C conductivity measured by measuring the D.C electrical resistance using the Keithly Electrometer type 616C, and for different temperatures ranging from 30 – 70^oC.

          The dielectric properties measured by measuring the capacitor and the loss

This study presents the design of flash-lamps for pumped solid-state lasers. In this research have been study some of characters for flash lamp. The optimum pressure operation is found using different flash lamps about (600-4000) mbar. In conclusion, it was shown that the increase in pressure due to improve efficiency of radiation and decrease of temperature. Also this study illustrated the reason of decrease temperature is atomic number and due to increase of radiation efficiency.

Vanadium dioxide nanofilms are one of the most essential materials in electronic applications like smart windows. Therefore, studying and understanding the optical properties of such films is crucial to modify the parameters that control these properties. To this end, this work focuses on investigating the opacity as a function of the energy directed at the nanofilms with different thicknesses(1–100) nm. Effective mediator theories(EMTs), which are considered as the application of Bruggeman’s formalism and the Looyenga mixing rule, have been used to estimate the dielectric constant of VO2 nanofilms. The results show different opacity behaviors at different wavelength ranges(ultraviolet, visible, and infrared). The results depict that th

Thin films of tin sulfide (SnS) were prepared by thermal evaporation technique on glass substrates, with thickness in the range of 100, 200 and 300nm and their physical properties were studied with appropriate techniques. The phase of the synthesized thin films was confirmed by X-ray diffraction analysis. Further, the crystallite size was calculated by Scherer formula and found to increase from 58 to 79 nm with increase of thickness. The obtained results were discussed in view of testing the suitability of SnS film as an absorber for the fabrication of low-cost and non toxic solar cell. For thickness, t=300nm, the films showed orthorhombic OR phase with a strong (111) preferred orientation. The films deposited with thickness < 200nm deviate