Suppose p n be sequence of positive reals. By H w p n , we represent the space of all formal power series ∑ n = 0 ∞ a n z n equipped with ∑ n = 0 ∞ λ a n / n + 1 p n < ∞ , for some λ > 0 . Various topological and geometric behavior of H w p n and the prequasi ideal constructs by s -numbers and H w p n have been considered. The upper bounds for s -numbers of infinite series of the weighted n -th power forward shift operator on H w p n with applications to some entire functions are granted. Moreover, we investigate an extrapolation of Caristi’s fixed point theorem in H w p n .

The algebraic structure of the linear system appears in solving fractional order Poisson’s equation by Haar wavelet collocation approach is considered. The fractional derivative is described in the Caputo sense. Comparison with the classical integer case as a limiting process is illustrated. Numerical comparison is made between the solution using the Haar wavelet method and the finite difference method. The results confirms the accuracy for the Haar wavelet method.

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The present work aims at constructing an atlas of the balanced Earth satellite orbits with respect to the secular and long periodic effects of Earth oblateness with the harmonics of the geopotential retained up to the 4th zonal harmonic. The variations of the elements are averaged over the fast and medium angles, thus retaining only the secular and long periodic terms. The models obtained cover the values of the semi-major axis from 1.1 to 2 Earth’s radii, although this is applicable only for 1.1 to 1.3 Earth’s radii due to the radiation belts. The atlas obtained is useful for different purposes, with those having the semi-major axis in this range particularly for remote sensing and meteorology.

Mathematica is a powerful program for computing both numeric and algebraic calculations as well as graphing two and three dimensional curves and surfaces. It is used increasingly in many fields of science now such as physics, engineering, chemistry and even biology because of the fast interaction of mathematics with almost the fields of science nowadays. Synthesis of Cyclotetramethylene Tetramine through the action of nitrating mixture formed of ammonium nitrate and fuming nitric acid on hexamine in presence of acetic acid, acetic anhydride and p-formaldehyde has been proven. The pathway is relatively long and Hexamine Dinitrate and Dinitro Pentamethylene Tetramine (DPT) are two of the main intermediate compounds. The former was prepared, purified, and then characterized. Conversion of this compound into the latter has been followed up experimentally. Herein, we report the Preparation of Dinitro Pentamethylene Tetramine (DPT) from Hexamine Dinitrateas an alternative synthetic route -which is an important intermediate appears through preparation of DPT from Hexamine directly. DPT was prepared at different temperatures. The variation of some factors like: temperature and time has been investigated. The obtained results were reliable and consistent with the literature. The conversion of Hexamine Dinitrate to HMX as another synthetic route was not fully studied from the point of view of kinetics. In this paper, it is intended to study the effect of time and temperature on the conversion rate of hexamine dinitrate to DPT. This scientific approach is considered as a bridge through which we aim to initiate a complete kinetic study of an important intermediate in the synthesis route of one of the most powerful energetic materials. We report here, optimizing the kinetic data for the synthesis of DPT via using Mathematica.