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[2] viXra:2112.0100 [pdf] replaced on 2024-01-30 10:37:06
Authors: Ruslan Enikeev
Comments: 23 Pages.
A solution is proposed for the so-called Collatz conjecture, also known as the "3��+1 problem". The idea of the proof involves representing the algorithm's operations through an infinite sequence as a formal object. Hypotheses regarding the convergence or divergence are considered within the framework of sequence theory corresponds to hypotheses about the output values of the algorithm.
Category: Functions and Analysis
[1] viXra:2112.0011 [pdf] submitted on 2021-12-02 18:09:58
Authors: Claude Michael Cassano
Comments: 46 Pages.
The d'alembertian operator on vector doublets may be factored with a pair of four-by-four matrices via simple partial derivatives as elements. As a generalization of the d'alembertian operator,the Helmholtzian operator on vector doublets may be factored with a pair of four-by-four matrices via simple partial derivatives augmented by adding certain constants as elements thereto. The Covariant Helmholtzian operator generalizes these, where the elements of the pair of four-by-four matrices are covariant derivatives applying to the vector doublet operated on. Thus, the d'alembertian operator is a Covariant Helmholtzian operator operated in a flat rectangular Cartesian space; the Helmholtzian operator is a Covariant Helmholtzian operator operated in a space of curvature where all the Christoffel symbols are appropriate constants.
Category: Functions and Analysis
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