Mathematica as an Efficient Tool to Optimize the Kinetic Study of Ethyl Acetate Hydrolysis

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. We report here, optimizing the kinetic data for the hydrolysis of ethyl acetate through caustic soda via using Mathematica

The Kinetic Study of DPT Using Mathematica as an Efficient Optimization Tool

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 Dinitrate - as 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

Kannan Contraction Operator on the Domain of r.-Cesàro Matrix in ℓt. and Related Prequasi Ideal with an Application of Nonlinear Difference Equations

In this article, the sequence space Ξr,tυ has been built by the domain of rl-Cesàro matrix in Nakano sequence space ℓtl, where t=tl and r=rl are sequences of positive reals with 1≤tl<∞, and υf=∑l=0∞∑z=0lrzfz/∑z=0lrztl, with f=fz∈Ξr,t. Some topological and geometric behavior of Ξr,tυ, the multiplication maps acting on Ξr,tυ, and the eigenvalues distribution of operator ideal constructed by Ξr,tυ and s-numbers have been examined. The existence of a fixed point of Kannan prequasi norm contraction mapping on this sequence space and on its prequasi operator ideal are investigated. Moreover, we indicate our results by some explanative examples and actions to the existence of solutions of nonlinear difference equations

A Generalization of Caristi’s Fixed Point Theorem in the Variable Exponent Weighted Formal Power Series Space

Suppose pn be sequence of positive reals. By Hwpn, we represent the space of all formal power series ∑n=0∞anzn equipped with ∑n=0∞λan/n+1pn0. Various topological and geometric behavior of Hwpn and the prequasi ideal constructs by s-numbers and Hwpn have been considered. The upper bounds for s-numbers of infinite series of the weighted n-th power forward shift operator on Hwpn with applications to some entire functions are granted. Moreover, we investigate an extrapolation of Caristi’s fixed point theorem in Hwpn