Stumpff functions are an infinite series that depends on the value of z. This value results from multiplying the reciprocal semi-major axis with a universal anomaly. The purpose from those functions is to calculate the variation of the universal parameter (variable) using Kepler's equation for different orbits. In this paper, each range for the reciprocal of the semi-major axis, universal anomaly, and z is calculated in order to study the behavior of Stumpff functions C(z) and S(z). The results showed that when z grew, Stumpff functions for hyperbola, parabola, and elliptical orbits were also growing. They intersected and had a tendency towards zero for both hyperbola and parabola orbits, but for elliptical orbits, Stumpff functions

This study focuses for improving the increase the solubility of fiber cellulose in sodium hydroxide solution in concentrations ranging from (4- 12%), from one point of view and from other point of view in (sodium hydroxide and urea) solution concentration (6% NaOH + 4% urea), under  low temperature (- 15, - 20 C^o) , depending on the principle of  reducing the degree of polymerization for  fiber cellulose, which is represented in our tests cotton linter who its represent  (Whatman filter paper, Grade 1), some samples subjected to chemical pretreatment as simulation the method of decomposition of cellulosic materials by white or brown fungi that grow on trees, this method involves the use of

A novel technique Sumudu transform Adomian decomposition method (STADM), is employed to handle some kinds of nonlinear time-fractional equations. We demonstrate that this method finds the solution without discretization or restrictive assumptions. This method is efficient, simple to implement, and produces good results. The fractional derivative is described in the Caputo sense. The solutions are obtained using STADM, and the results show that the suggested technique is valid and applicable and provides a more refined convergent series solution. The MATLAB software carried out all the computations and graphics. Moreover, a graphical representation was made for the solution of some examples. For integer and fractional order problems, solutio

In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi

Internal conversion coefficients (ICC) and electron–positron pair conversion coefficients (PCC) for multipole transition of the core nucleus 88Sr have been calculated theoretically. The calculation is based on the relativistic Dirac–Fock (DF) solutions using the so called ‘‘Frozen Orbital’’ approximation, takes into account the effect of atomic vacancies created in the conversion process, covering a transition energies of 1–5000 keV. A large number of points were used to minimize any errors due to mesh-size effects. The internal conversion coefficients display a smooth monotonic dependence on transition energy, multipolarity and atomic shell. Comparing the values of PCC to ICC, it is interesting to note, that the energy dep

The world's renewable energy sources have taken on great importance, for its cleanness and its environmental effects as well as being a renewable source, Increased demand for fossil energy sources is also causing global warming and climate change. Iraq is an appropriate area for renewable energy This study shows that renewable alternative energy has not been used sufficiently enough at present. But this energy can play an important role in the future of renewable energy in Iraq. This research aims to study the renewable energy in Iraq (solar energy) and it is appropriate to develop this alternative energy for crude oil, which is characterized by the use of the most appropriate and less economical and more environmentally friendly. Solar