An optimization calculation is made to find the optimum properties of combined quadrupole lens which consists of electrostatic and magnetic lens. Both chromatic and spherical aberration coefficients are reduced to minimum values and the achromatic aberration is found for many cases. These calculations are achieved with the aid of transfer matrices method and using rectangular model of field distribution, where the path of charged-particles beam traversing the field has been determined by solving the trajectory equation of motion and then the optical properties for lens have been computed with the aid of the beam trajectory along the lens axis. The computations have been concentrated on determining the chromatic and spher

It is shown that if a subset of a topological space (χ, τ) is δ-semi.closed, then it is semi.closed. By use this fact, we introduce the concept regularity of a topological space (χ, τ) via δ-semi.open sets. Many properties and results were investigated and studied. In addition we study some maps that preserve the δ-semi.regularity of spaces.

Let be a commutative ring with unity and let be a non-zero unitary module. In
this work we present a -small projective module concept as a generalization of small
projective. Also we generalize some properties of small epimorphism to δ-small
epimorphism. We also introduce the notation of δ-small hereditary modules and δ-small
projective covers.

     The linear non-polynomial spline is used here to solve the fractional partial differential equation (FPDE). The fractional derivatives are described in the Caputo sense. The tensor products are given for extending the one-dimensional linear non-polynomial spline to a two-dimensional spline  to solve the heat equation. In this paper, the convergence theorem of the method used to the exact solution is proved and the numerical examples show the validity of the method. All computations are implemented by Mathcad15.

In this paper the effect of thermal annealing on the structural and optical properties of Antimony Selenide (Sb2Se3) is investigated. Sb2Se3 powder is evaporated on clean amorphous glass substrates at room temperature under high vacuum pressure (4.5×10-6 mbar) to form thin films. The structural investigation was done with the aid of X-ray diffraction (XRD) and atomic force microscopy (AFM). The amorphous to polycrystalline transformation of these thin films was shown by X-ray diffraction analysis after thermal annealing. These films' morphology is explained. (UV-Vis ) spectra in ranges from 300 to 1100 nm was used to examine the optical properties of the films .The absorption coefficient and optical energy gap of the investigated films are

   In this research we studied  the structural and optical properties of (CdTe) thin films which have been prepared  by thermal evaporation deposition method on the glass substrate at R.T with thickness (450  25) nm., as  a function of doping  ratio with copper element  in (1,3,5) % rate .The structure  measurement  by X-ray diffraction (XRD) analyses shows that the single phase of (CdTe) with polycrystalline structure with a preferred orientation [111].   The optical  measurement shows that the (CdTe) films have a direct energy gap, and they decrease with the increase of doping ratio reaching to 5% . The optical constants are investigated and calculated, such as absorpti

      In this research, the structural and optical properties were studied for Bi2O3 and Bi2O3: Al  thin  films  with   different  doping   ratios  ( 1, 2, 3 ) %  ,  which  were  prepared  by  thermal evaporation  technique under  vacuum , with  thickness  ( 450 ± 20 ) nm  deposited  on  glass substrates  at  room  temperature ( 300 ) K , Structural   measurements by ( XRD)  techniques demonstrated   that  all   samples  prepared   have  polycrystalline  structure   with  tetragonal structure and  a preferred orientation  [ 201 ]   the &n