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[4] viXra:2307.0124 [pdf] submitted on 2023-07-24 23:34:29
Authors: Robert S. Miller
Comments: 5 Pages. (Correction made by viXra Admin - Please conform!)
This paper details the expression 1^i=1. It uses a known trigonometric substitutions in a mathematical proof showing the accuracy of the expression.
Category: Algebra
[3] viXra:2307.0118 [pdf] submitted on 2023-07-22 03:57:34
Authors: Tai-Choon Yoon
Comments: 7 Pages.
This article presents a solvable quintic equation under the conditions that several coef-ficients of a quintic equation are restricted to become dependent on the other coefficients.We can solve a quintic equation by restricting two coefficients among total four coefficientsavailable. If a quintic equation has a quadratic factor (x^2 + b_1 x + b_0), then we get a twosimultaneous equations, which can be solved by using a sextic equation under restriction.
Category: Algebra
[2] viXra:2307.0100 [pdf] submitted on 2023-07-19 03:16:53
Authors: Yaroslav Shitov
Comments: 85 Pages.
The substitution method of tensor rank computation is a higher dimensional analogue of Gaussian elimination, and it builds on the fact that the removal of a rank one slice s and a subsequent addition of arbitrary scalar multiples of s to all other slices of the same direction decreases the minimum rank exactly by one. We explain how to embed an initial tensor T to a larger linear space and replace its higher rank slice g by a family f of rank one slices in the new space so that the substitutions performed with respect to g in every direction of T have the same effect on the minimum rank as the corresponding substitutions with respect to f. We present several applications, which include a resolution of the well known and widely studied direct sum conjecture for Waring ranks and a strong form of counterexamples to Strassen’s conjecture.
Category: Algebra
[1] viXra:2307.0073 [pdf] submitted on 2023-07-15 00:31:46
Authors: Alexey Kuzmin
Comments: 18 Pages. (Corrections made by viXra Admin to conform with scholarly norm)
I have tried to find a new compact matrix quantum group within actions on a braided noncommutative quadric associated to a solution of Yang- Baxter equation outside of the 8-vertex model. The result appeared to be isomorphic to the circle group.
Category: Algebra
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