Charged particle induced nuclear reactions for the production of 52Fe and 72As were studied. A critical analysis led to consider proton induced nuclear reaction sections on 72Ge, 73Ge, 74Ge and 76Se to investigate for the production of 72As while for the production of 52Fe, the proton induced reactions on 58Ni, 55Mn and alpha induced reaction on 50Cr were chosen. The experimental results obtained via 72Ge(p, n)72As, 73Ge(p, 2n)72As, 74Ge(p, 3n)72As, 76Se (p, x)72As and 58Ni (p, x) 52Fe, 50Cr (4He, 2n) 52Fe and 55Mn(p,4n)52Fe reactions were compared with the results of nuclear model calculations using the codes ALICE-IPPE, EMPIRE 3.2 and TALYS 1.9 to check the reliability and discrepancy in the experimental data. Polynomial fittings were applied using Origin-Lab Pro 2017 to maintain the consistency of experimental and calculated data. Recommended data were generated using the well-established evaluation methodology. The thick target yields (TTY) of 52Fe and 72As is calculated from the recommended excitation functions. Analysis of radionuclidic impurities was also discussed for both radionuclides. Comparison of the various radionuclidic impurities is done. On the basis of TTY and radio-nuclidic impurity analysis; the production routes and optimum energy ranges for the production of 52Fe and 72As are proposed. Our evaluation scheme showed that for the production of 52Fe via 55Mn(p,4n)52Fe reaction, energy ranges from 70→45 MeV could be the method of choice, which gives high yield with minimum impurities to make it as a potential candidate for theranostic applications in nuclear medicine and in particular, Positron Emission Tomography (PET). For the 72As; 72Ge(p, n)72As reaction in the energy ranges 10→20 MeV is the optimized nuclear reaction with a negligible impurity ratio and maximum production yield. Being in the low energy range, a small cyclotron can be engaged for the production of 72As to be used it in the medical applications.
This article focus on the literary aspect of Qur’an. Stylistically it has a rich texture, which in itself is a miracle Qur’an is not only the last message of Allah- bearing finality but it is the root source of all forms of human knowledge. It has a pithy style therefore it offers multiple shades of meanings in it. This article focuses on that so as to open up new pathways into the stylistically rich texture of Holy Qur’an.
In this dissertation, we investigate different types of boundary value problems of nonlinear fractional order differential equations. The concerned research is associated to the existence and uniqueness of solutions, Hyers–Ulam type stability and numerical analysis for fractional order differential equations. We develop sufficient conditions for existence and uniqueness of solutions for fractional differential equations, with the help of classical fixed point theory of Laray Schauder type, Banach contraction type and Topological degree method. Further, we investigate the conditions for stability analysis of fractional differential equations. One of the important area of fraction differential equation is known as hybrid fractional differential equation. Hybrid fractional differential equations has an efficient techniques used for modeling various dynamical phenomenon. Therefore, for investigation sufficient conditions for existence and uniqueness of solutions hybrid fractional differential equations, we have used Hybrid fixed point theory established by Dhage and develop sufficient conditions for the existence and uniqueness of solutions of hybrid fractional differential equations. On the other hand, in most cases the nonlinear fractional differential equations are very complicated to obtained an exact analytic solution. Although, if an exact solution is possible, that needed very complicated calculations. Therefore, we paid a strong attention to the numerical solution of fractional differential equations and fractional partial differential equations. We have developed some powerful and an efficient numerical techniques for the approximate solutions of both linear and nonlinear fractional order differential equations. The established technique are based on Laplace transform coupled with Adomain polynomials to obtain the aforesaid solutions in the form of convergent series. Further, we also develop another interesting and useful method based on operational matrices obtained via using Lagendre polynomials. With the help of these mentioned techniques, we solve both linear and nonlinear ordinary as well as partial fractional order differential equations. We consider some fractional order differential equations for illustrative purposes and numerical approximations of their solutions are obtained using MAPLE and MATLAB. The numerical results obtained via aforesaid techniques, are compared with other standard techniques. Which shows, that how the Laplace transform coupled with Adomain polynomials and operational matrices obtained by Legendre polynomials are more effective and reliable, than the standard ordinary differential equations solvers.