In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.

In this work a model of a source generating truly random quadrature phase shift keying (QPSK) signal constellation required for quantum key distribution (QKD) system based on BB84 protocol using phase coding is implemented by using the software package OPTISYSTEM9. The randomness of the sequence generated is achieved by building an optical setup based on a weak laser source, beam splitters and single-photon avalanche photodiodes operating in Geiger mode. The random string obtained from the optical setup is used to generate the quadrature phase shift keying signal constellation required for phase coding in quantum key distribution system based on BB84 protocol with a bit rate of 2GHz/s.

In this research , design and study a (beam expander) for the Nd – YAG laser with (1.06 ?m) Wavelength has been studied at 5X zoom with narrow diversion in the room temperature. by using (ZEMAX) to study the system. Evaluate its performance via (ZEMAX) outputs, as bright Spot Diagram via (RMS), Ray Fan Plot, Geometric Encircled Energy and the value of Focal shift. Then study the effect of field of view on the outputs in the room temperature.

The finishing operation of the electrochemical finishing technology (ECF) for tube of steel was investigated In this study. Experimental procedures included qualitative
and quantitative analyses for surface roughness and material removal. Qualitative analyses utilized finishing optimization of a specific specimen in various design and operating conditions; value of gap from 0.2 to 10mm, flow rate of electrolytes from 5 to 15liter/min, finishing time from 1 to 4min and the applied voltage from 6 to 12v, to find out the value of surface roughness and material removal at each electrochemical state. From the measured material removal for each process state was used to verify the relationship with finishing time of work piece. Electrochemi

Abstract
A two electrode immersion electrostatic lens used in the design
of an electron gun, with small aberration, has been designed using
the finite element method (FEM). By choosing the appropriate
geometrical shape of there electrodes the potential V(r,z) and the
axial potential distribution have been computed using the FEM to
solve Laplace's equation.
The trajectory of the electron beam and the optical properties of
this lens combination of electrodes have been computed under
different magnification conditions (Zero and infinite magnification
conditions) from studying the properties of the designed electron
gun can be supplied with Abeam current of 5.7*10-6 A , electron
gun with half acceptance

A computerized investigation has been carried out on the design of six electrodes electrostatic lenses used in electron gun application. The Finite-Element Method (FEM) was used in the solution of Laplace equation for determine the axial potential distribution. The electron trajectory under zero magnification condition. The optical properties, spherical and chromatic aberrations, the object and image focal length and object and image position are calculated. A very good futures for the electron gun with these lenses have been computed where are a beam current of 8.7*10-7A can be supplied using cathode tip of radius 10nm.