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.

In this paper, the dynamic behaviour of the stage-structure prey-predator fractional-order derivative system is considered and discussed. In this model, the Crowley–Martin functional response describes the interaction between mature preys with a predator.  e existence, uniqueness, non-negativity, and the boundedness of solutions are proved. All possible equilibrium points of this system are investigated.  e su‰cient conditions of local stability of equilibrium points for the considered system are determined. Finally, numerical simulation results are carried out to con‹rm the theoretical results.

     Chromium oxide (Cr₂O₃) doped ZnO nanoparticles were prepared by pulsed laser deposition (PLD) technique at different concentration ratios (0, 3, 5, 7 and 9 wt %) of ZnO on glass substrate. The effects of ZnO dopant on the average crystallite size of the synthesized nanoparticles was examined By X-ray diffraction. The morphological features were detected using atomic force microscopy (AFM). The optical band gap value was observed to range between 2.78 to 2.50 eV by UV-Vis absorption spectroscopy, with longer wavelength shifted in comparison with that of the bulk Cr₂O₃ (~3eV). Gas sensitivity, response, and recovery times of the sensor in the presence of NH₃

In this paper a stage structure prey-predator model with Hollimg type IV functional response is proposed and analyzed. The local stability analysis of the system is carried out. The occurrence of a simple Hopf bifurcation and local bifurcation are investigated. The global dynamics of the system is investigated with the help of the Lyapunov function. Finally, the analytical obtained results are supported with numerical simulation and the effects of parameters system are discussed. It is observed that, the system has either stable point or periodic dynamics.

Production sites suffer from idle in marketing of their products because of the lack in the efficient systems that analyze and track the evaluation of customers to products; therefore some products remain untargeted despite their good quality. This research aims to build a modest model intended to take two aspects into considerations. The first aspect is diagnosing dependable users on the site depending on the number of products evaluated and the user's positive impact on rating. The second aspect is diagnosing products with low weights (unknown) to be generated and recommended to users depending on logarithm equation and the number of co-rated users. Collaborative filtering is one of the most knowledge discovery techniques used positive

     This paper is used for solving component Volterra nonlinear systems by means of the combined Sumudu transform with Adomian decomposition process. We equate the numerical results with the exact solutions to demonstrate the high accuracy of the solution results. The results show that the approach is very straightforward and effective.

In this research, beam expander, BEX, is explained and designed for illuminating the
remote flying target. The BEX is optically designed to be suited for Nd:YAG laser of given
specifications. The BEX is modified to be zoom one to meet the conditions of preventing the
receiving unit; i.e the photodetector, from getting saturated at near and far laser tracking.
Decollimation could be achieved by automatic motor, which controls zoom lens of the BEX
according to the required expansion ratio of beam expander