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[2] viXra:2209.0097 [pdf] submitted on 2022-09-15 08:51:09
Authors: Hans Hermann Otto
Comments: 9 Pages.
The best-known profile function is the Gaussian function, which can be used, for instance, to fit successfully optical absorption bands or neutron scattering patterns. However, peaks of X-ray powder pattern can hardly be fitted well with such a simple function. Whereas combined functions are widely in use for such purpose, we applied Cauchy functions to fit our well resolved Guinier powder diffraction data. The Cauchy function of second order is well suited and will be described in more detail as a didactic exercise in crystallography as well as mathematics. In addition, a profile function with an exotic non-integer exponent based on the golden mean is supplemented. This contribution will be continuously revised before its final publication to react of Fewster’s new diffraction theory that will change the matter in future. As an example beyond crystallography the author fitted German Covid-19 data to correlate virus infection peak maxima with causal events.
Category: Algebra
[1] viXra:2209.0060 [pdf] submitted on 2022-09-09 14:28:46
Authors: Mehsin Jabel Atteya
Comments: 24 Pages.
The main purpose of this paper is to study a number of results concerning the generalized (σ, τ )-derivation D associated with the derivation d of semiprime ring and prime ring R such that D and d are zero power valued on R, where the mappings σ and τ act as automorphism mappings.Precisely, this article divided into two sections, in the first section, we emphasize on generalized (σ, τ )-derivation D associated with the derivation d of the semiprime ring and prime ring R while in the second section, we study the effect of the compositions of generalized (σ, τ )-derivations of semiprime ring and prime ring R such that D is period (n − 1) on R, for some positive integer n.
Category: Algebra
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