The present work represents a theoretical study for the correction of spherical aberration of an immersion lens of axial symmetry operating under the effect of space charge, represented by a second order function and preassigned magnification conditions in a focusing of high current ion beams. The space charge depends strongly on the value of the ionic beam current which is found to be very effective and represents an important factor effecting the value of spherical aberration .The distribution of the space charge was measured from knowing it's density .It is effect on the trajectory of the ion beam was studied. To obtain the trajectories of the charged particles which satisfy the preassined potential the axial electrostatic potential w

In this article the unsteady magnetohydrodynamics oscillating flow of third order fluid with free stream velocity is proposed. It is found that the motion equation is controlled by five dimensionless parameters namely the coecostic parameter 4, viscoelostic parameter ?,acceleration/deceleration c,suction/blowing d and material constants ? . The effect of each of these parameters upon the velocity distribution is analysised

In this paper, third order non-polynomial spline function is used to solve 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of this method, and to compare the computed results with other known methods.

         The optimum balance values for different coefficient of spherical aberration (third and fifth degree also focal shift) were studied, the optical system includes different apertures (circle, ellipse, square and triangle) using point spread function (PSF).       By using (Marechal) method; the minimum value of mean square of variance in wave front was founded, so we can get the maximum of central intensity according to (Strehl) criterion.

In this paper, we study the effects of coherent and incoherent illumination on the optical imaging system. The effects were studied qualitatively in terms of Point Spread Function (PSF) and Modulation Transfer Function (MTF), and quantitatively in terms of Root Mean Square Error (RMSE). Different values of radius of aperture were investigated in the presence and absence of spherical aberration with various magnitudes of spherical aberration (M=1, 2, and 3). The experiments were performed using homogeneous media.

     The results show that imaging with incoherent illumination is better than imaging with coherent illumination, especially for small aperture. Also, we found that the effects of spherical aberration

In this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.

The study aims to identify the third instar larvae of fly species (Order : Diptera) feeding on carcasses (Fishes and Rabbits). Two families (Calliphoridae and Sarcophagidae), were recorded with highest rate in Calliphoridae species. The following species had been registered in accordance with their prevalence respectively; Calliphora vicina Rob.-Desvoidy, Chrysomya albiceps (Wiedmann), Chrysomy megacephala (Fabricius), Sarcophaga sp. and Lucilia sericata (Meigen). The highest rate has been registered Calliphora vicina during February, November, December and January at rate 100%, the larvae of this fly have not been observed during July, August, September and October. The highest rate of Ch

The aim of this paper is to present a method for solving third order ordinary differential equations with two point boundary condition , we propose two-point osculatory interpolation to construct polynomial solution. The original problem is concerned using two-points osculatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by compared with conventional method .

In this work dithine complexes prepared from dithiol benzil ligand and central ion to the Ni,Pd,Pt, element the ligand and complexes have been investigated using FTIR spectrophotometer and uv-vis-NIR spectral reigns show higher intensity represents the ?-?* transition in the chromopher cycle .These absorption which appear in visible and near IR spectral regions ,According to the complexes of one group ,the spectral shifting due to the change of central ion has been found to be related to atomic number of central ion .This shifting is increased while decreasing the central ion atom number These complexes have been implemented in Nd+2:YAG cavity because each posses resonant absorption band near Nd+2:YAG, Nd+2:Glass emitting at (106