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| viXra.org > General Mathematics > 2603 |
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[6] viXra:2603.0128 [pdf] submitted on 2026-03-27 01:45:12
Authors: Edgar Valdebenito
Comments: 5 Pages. (Note by viXra Admin: Please cite listed scientific references!)
In this note, we give some formulas for the Goh-Schmutz constant
Category: General Mathematics
[5] viXra:2603.0104 [pdf] submitted on 2026-03-19 23:45:33
Authors: Saburou Saitoh
Comments: 3 Pages. (Note by viXra Admin: Further repetition will not be accepted; please cite and list scientific references)
We consider the degenerate case of the general circle equation. By applying Division by Zero Calculus, we observe that two different finite quantities arise depending on the algebraic form of the radius. One corresponds to zero area, while the other gives the signed distance from the origin to the line.
Category: General Mathematics
[4] viXra:2603.0103 [pdf] submitted on 2026-03-19 02:12:51
Authors: Taiyou Ikiru
Comments: 31 Pages. In Japanses (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)
I demonstrate that, within mathematical operations, there inevitably exist instances where the axiomatic principles governing the mathematical axioms A=A, ¬(A∧¬A), and ¬A=¬A are not adhered to. In doing so, I reflect upon the relationship between logic and mathematics.
Category: General Mathematics
[3] viXra:2603.0094 [pdf] submitted on 2026-03-18 09:36:37
Authors: Zhi Li, Hua Li
Comments: 5 Pages.
The continuum hypothesis states that the set of real numbers is the power set of the countable set of natural numbers, the smallest uncountable set, and its cardinality is greater than that of natural numbers. There is no set whose cardinality is absolutely greater than that of countable sets and absolutely less than that of the set of real numbers.This paper proposes a method for constructing a subset of real numbers and proves that itscardinality exceeds that given by the continuum hypothesis. This result refutes the continuumhypothesis and pushes the cardinality of real numbers to a higher order of magnitude.
Category: General Mathematics
[2] viXra:2603.0033 [pdf] submitted on 2026-03-06 21:47:45
Authors: Abdelmajid Ben Hadj Salem
Comments: 5 Pages. In French
A new approach finds solutions to fluid dynamics equations and could be applied to solve one of the Millennium Prize Problems.
Category: General Mathematics
[1] viXra:2603.0001 [pdf] submitted on 2026-03-01 01:16:32
Authors: Jaime Vladimir Torres-Heredia Julca
Comments: 27 Pages. 9 figures
This paper is a continuation of our previous paper viXra:2512.0150, in which we expressed all vectors of the 3D Euclidean vector space with operations involving rotations and homotheties of the unit vector of the x-axis. We defined also a new vector multiplication and in this paper we will show that with the usual vector addition, we have a K-algebra. We will also study the 4D case and we will also express all vectors with simple rotations and homotheties of the unit vector of the x-axis about 3 planes, we will define a vector multiplication analogous to what we have seen in the 3D case, and we will show that we have again a K-algebra with the usual vector addition. We will construct also a 4D fractal set which contains the 3D fractal set (which contains the Mandelbrot set) seen in our previous paper and we will show several 4D projections of that set in the 3D space. We will show also that there are no quaternion numbers, because there are actually geometrical operations involving the unit vector of the x-axis. In that case we will use compositions of 2 rotations of the unit vector of the x-axis about different planes to express all the vectors. In that case we will have also a division algebra. Finally, we will show that for all dimensions, we have K-algebras if we express all vectors with operations involving homotheties and simple rotations of the unit vector of the first axis (x_1), with the usual vector addition and a generalization of the multiplication that we have seen in our previous papers for the 2D and 3D cases and for the 4D case in this paper. One advantage of the simple rotations, among other ones, is that they allow to construct interesting n-dimensional fractal sets linked to the Mandelbrot set.
Category: General Mathematics
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