ARTICLE | doi:10.20944/preprints202108.0176.v1
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: consecutive sum of the digits; algebraic equations; diophantine equations; arithmetic functions
Online: 9 August 2021 (07:52:49 CEST)
In this paper defines the consecutive sum of the digits of a natural number, so far as it becomes less than ten, as an arithmetic function called and then introduces some important properties of this function by proving a few theorems in a way that they can be used as a powerful tool in many cases. As an instance, by introducing a test called test, it has been shown that we are able to examine many algebraic equalities in the form of in which and are arithmetic functions and to easily study many of the algebraic and diophantine equations in the domain of whole numbers. The importance of test for algebraic equalities can be considered equivalent to dimensional equation in physics relations and formulas. Additionally, this arithmetic function can also be useful in factorizing the composite odd numbers.
Subject: Engineering, Automotive Engineering Keywords: Reaction engineering; Catalysis; particle; multiplicity; parallel reactions; consecutive reactions;
Online: 17 March 2021 (11:13:56 CET)
The steady-state multiplicity of the porous, non-isothermal, catalyst pellet when two parallel and consecutive chemical reactions take place was analysed in this work. The geometry selected for the catalyst pellet is finite hollow cylinder. A numerical multigrid continuation technique with the preconditioned conjugate gradient squared as coarse grid solver was used. The continuation parameter is the dimensionless adiabatic heat rise (Prater number) for the first chemical reaction. The effect of the other governing parameters was analysed and the results are compared to those provided by the single chemical reaction.