The presentwork is a theoretical study in the field of charged particle optics. It concentrates on the design of electrostatic enzil lens for focusing charge particles beams, using inverse method in designingthe electrostatic lens. The paraxial ray equation was solved to obtain the trajectory of the particles, the optical properties such as the focal length and spherical and chromatic aberration coefficients were determined. The shape of the electrode of the electrostatic lens were determined by solving poison equation and the results showed low values of spherical and chromatic aberrations, which are considered as good criteria for good design.

    A theoretical calculation of the binding and excitation energies have been used at low – lying energies based on shell model and quantum theory. In this model, we evaluated the energies under assume Ni 28 56 30 as inert core with two nucleon extra, nucleons in the  2P3/2 ,  1f 5/2  and 2P1/2  configuration. Modified Surface Delta Interaction (MSDI) and Reid's Potential (RP) theory for two body matrix elements are evaluated by using a Matlab program to calculate the energies of experimental and Reid single particle energies. Our results of the theoretical calculation have been compared with the experimental results, which show no good agreement with the experiment but have a good agreement wit

   In this paper, we find the two solutions of two dimensional stochastic Fredholm integral equations contain two gamma processes differ by the parameters in two cases and equal in the third are solved by the Adomain decomposition method. As a result of the solutions probability density functions and their variances at the time t are derived by depending upon the maximum variances of each probability density function with respect to the three cases. The auto covariance and the power spectral density functions are also derived. To indicate which of the three cases is the best, the auto correlation coefficients are calculated.

The primary aim of this paper, is to introduce the rough probability from topological view. We used the Gm-topological spaces which result from the digraph on the stochastic approximation spaces to upper and lower distribution functions, the upper and lower mathematical expectations, the upper and lower variances, the upper and lower standard deviation and the upper and lower r th moment. Different levels for those concepts are introduced, also we introduced some results based upon those concepts.

Watermelon is known to be infested by multiple insect pests both simultaneously and in sequence. Interactions by pests have been shown to have positive or negative, additive or non additive, compensatory or over compensatory effects on yields. Hardly has this sort of relationship been defined for watermelon vis-à-vis insect herbivores. A 2-year, 2-season (4 trials) field experiments were laid in the Research Farm of Federal University Wukari, to investigate the interactive effects of key insect pests of watermelon on fruit yield of Watermelon in 2016 and 2017 using natural infestations. The relationship between the dominant insect pests and fruit yield were determined by correlation (r) and linear regression (simple and multiple) analys