Computer theoretical study has been carried out on the design of five electrode immersion electrostatic lens used in electron gun application. The finite element method (FEM) is used in the solution of the Poisson's equation fro determine axial potential distribution, the electron trajectory under Zero magnification condition .      The optical  properties : focal length ,spherical and chromatic aberrations are calculated,From studying the properties of the designed electron gun. we have good futures for these  electron gun where are abeam current 4*10-4A    can be supplied by using cathode tip of radius 100 nm.

Let R be a commutative ring with identity and let M be a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of semi-essential submodules which introduced by Ali S. Mijbass and Nada K. Abdullah, and we make simple changes to the definition relate with the zero submodule, so we say that a submodule N of an R-module M is called semi-essential, if whenever N ∩ P = (0), then P = (0) for each prime submodule P of M. Various properties of semi-essential submodules are considered.

This paper aims to study the quaternary classical continuous optimal control problem consisting of the quaternary nonlinear parabolic boundary value problem, the cost function, and the equality and inequality constraints on the state and the control. Under appropriate hypotheses, it is demonstrated that the quaternary classical continuous optimal control ruling by the quaternary nonlinear parabolic boundary value problem has a quaternary classical continuous optimal control vector that satisfies the equality constraint and inequality state and control constraint. Moreover, mathematical formulation of the quaternary adjoint equations related to the quaternary state equations is discovered, and then the weak form of the quaternary adjoint

Efficient management of treated sewage effluents protects the environment and reuse of municipal, industrial, agricultural and recreational as compensation for water shortages as a second source of water. This study was conducted to investigate the overall performance and evaluate the effluent quality from Al- Rustamiya sewage treatment plant (STP), Baghdad, Iraq by determining the effluent quality index (EQI). This assessment included daily records of major influent and effluent sewage parameters that were obtained from the municipal sewage plant laboratory recorded from January 2011 to December 2018. The result showed that the treated sewage effluent quality from STP was within the Iraqi quality standards (IQS) for disposal and t

One-third of the total waste generated in the world is construction and demolition waste. Reducing the life cycle of building materials includes increasing their recycling and reuse by using recycled aggregates. By preventing, the need to open new aggregate quarries and reducing the amount of construction waste dumped into landfills, the use of recycled concrete aggregate in drum compacted concrete protects the environment. Four samples of PRCC were prepared for testing (compressive strength, tensile strength, flexural strength, density, water absorption, porosity) as the reference mix and (10, 15, and 20%) of fine recycled concrete aggregate as a partial replacement for fine natural aggregate by volume. The mix is designed according to

The dependence of the energy losses or the stopping power for the energies and the related penetrating factor are arrive by using a theoretical approximation models. in this work we reach a compatible agreement between our results and the corresponding experimental results.

          In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

Here, we found an estimation of best approximation of unbounded functions which satisfied weighted Lipschitz condition with respect to convex polynomial by means of weighted Totik-Ditzian modulus of continuity