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

Stabilization of phenol trapped by agricultural waste: a study of the influence of ambient temperature on the adsorbed phenol

  This work discusses the beginning of fractional calculus and how the Sumudu and Elzaki transforms are applied to fractional derivatives. This approach combines a double Sumudu-Elzaki transform strategy to discover analytic solutions to space-time fractional partial differential equations in Mittag-Leffler functions subject to initial and boundary conditions. Where this method gets closer and closer to the correct answer, and the technique's efficacy is demonstrated using numerical examples performed with Matlab R2015a.

The synthesis and structural characterization of new dithiocarbamate (DTC) ligand and some of its dinuclear transition metal complexes are described. The free dithiocarbamate ligand was prepared through several synthetic routes, including Schiff-base formation. The reaction of 2-aminopropane with terephthaldehyde leads to the formation of Schiff^_base which is reduced by methanolic NaBH₄ to the corresponding secondary diamine. Diamine( N,N'^_ (1,4 phenylenebis (methylene)) bis(propan-2 amine))  reacts with (CS₂) in a basic solution of (KOH) to provide the corresponding bis(dithiocarbamate) free^_ligand, which undergoes complexation with the appropriate metal   (II) chlori

This work is aiming to study and compare the removal of lead (II) from simulated wastewater by activated carbon and bentonite as adsorbents with particle size of 0.32-0.5 mm. A mathematical model was applied to describe the mass transfer kinetic.

The batch experiments were carried out to determine the adsorption isotherm constants for each adsorbent, and five isotherm models were tested to choose the best fit model for the experimental data. The pore, surface diffusion coefficients and mass transfer coefficient were found by fitting the experimental data to a theoretical model. Partial differential equations were used to describe the adsorption in the bulk and solid phases. These equations were simplified and the