General Mathematics

2507 Submissions

[9] viXra:2507.0222 [pdf] submitted on 2025-07-31 15:11:19

Generalized Random Measures.double Stochastic Processes and Generalized Chapman Kolmogorov Equations.random Feinman Measure

Authors: Jaykov Foukzon
Comments: 34 Pages.

In this paper generalized Chapman-Kolmogorov equation is derived.
Category: General Mathematics

[8] viXra:2507.0219 [pdf] replaced on 2025-09-27 21:30:23

The Knotted Cords and the Origins of the Sexagesimal System

Authors: Jaime Vladimir Torres-Heredia Julca
Comments: 7 Pages. 5 figures

This paper presents an explanation of the origins of the sexagesimal system linked to theuse of a knotted cord 12 lengths long closed to form a loop. This device can suggest a groupingof elements by 60. We will see that this device has also important geometrical properties linkedto the division of the circle in 360 equal parts. Historical and cultural arguments will also begiven to support this thesis. We will see how the grouping of the Old Mesopotamian unitsof measurement of capacity, weight, mass and time confirm this thesis. We will see also howimportant groupings of the Old Mesopotamian units of measurement of length and area use thenumber 12 which is also suggested by this device.
Category: General Mathematics

[7] viXra:2507.0188 [pdf] submitted on 2025-07-26 01:23:01

A Relationship Between Golden Ratio and the Length of the Arc of the Parabola Y = X^2

Authors: Jaime Vladimir Torres-Heredia Julca
Comments: 3 Pages.

This paper presents a simple relationship between Golden Ratio φ and the length of the arcfrom x = 0 to x = 1 of the curve defined by the equation y = x².
Category: General Mathematics

[6] viXra:2507.0160 [pdf] submitted on 2025-07-22 19:36:52

Remarks on a paper by K. Adegoke

Authors: Edgar Valdebenito
Comments: 4 Pages.

Recently, K. Adegoke et al.(arXiv:2505.11575v1,16 May 2025) established a number of results on binomial series. In this note, we explore some particular cases of these series.
Category: General Mathematics

[5] viXra:2507.0125 [pdf] submitted on 2025-07-17 20:03:13

U4 (Unified Foundation): T0=2 A Four-Symbol Foundation of Mathematics

Authors: Kleschev Anton Alevtinowitch
Comments: 2 Pages.

We present U4, a 4-symbol axiom that encodes the entire birth—dissolution cycle of natural- number arithmetic. The equation T0=2 simultaneously asserts (i) the presence of the zero- point, (ii) the immediate emergence of one from zero, (iii) the automatic collapse of one into two, and (iv) the ultimate identity 0=1=2. No external primitives are presupposed.
Category: General Mathematics

[4] viXra:2507.0108 [pdf] submitted on 2025-07-15 19:10:04

Uf0: τ(0)⊕0=τ(1)⊕1 a One-Line Axiomatization of the Birth and Dissolution of Mathematics

Authors: Kleschev Anton Alevtinowitch
Comments: 2 Pages.

We present UF0(Unified Foundation 0), a minimal formal system in which the entire edificeof natural-number arithmetic is generated and dissolved by a single equation. u2022 0 is the pre-numerical, non-dual point. u2022 τ is a unary "tear" operator enacting the primal split. u2022 ⊕ is a non-repeating union. The sole axiom τ (0) ⊕ 0 = τ (1) ⊕ 1 simultaneously encodes 1. the birth of mathematics (0 → 1), and 2. the fundamental duality (1 → 2), while collapsing both into identity when 0 = 1 = 2. No external arithmetic, set theory, or category theory is presupposed. UF0 is therefore the first fully formal, one-sentence foundation that captures both the emergence and the illusoriness of number.
Category: General Mathematics

[3] viXra:2507.0062 [pdf] submitted on 2025-07-08 12:45:51

Deformed Lie Products and Involution - Second Part: in a Four-dimensional Space.

Authors: Thierry L.A. Periat
Comments: 40 Pages.

A previous document laid the foundations for the study of involution in any three-dimensional spaces, [c]. This exploration continues the exploration of the topic in focusing now attention on four-dimensional spaces. The repetition of a deformed Lie product on a given argument carries two concepts with it: (i) the eventual invariance of this argument and (ii) the existence of an involution. The work discovers two distinct classes of decomposition without residual part for each deformed Lie product. It explains why only one of both (the simplest one) can characterize the involution when the deforming cube is anti-symmetric and anti-reduced. The document also starts a confrontation between the simplest representation and the electromagnetic duality in Maxwell's vacuum.
Category: General Mathematics

[2] viXra:2507.0048 [pdf] submitted on 2025-07-06 21:11:22

Sum of Three Cubes =sum of Another Three Cubes

Authors: Oliver Couto
Comments: 4 Pages.

In math literature,(eg: ref. #3), most solutions to the above equations are dealt with using elliptic curve theory. In this paper the author has, by imposing certain conditions, provided a parametric solution of the equation by using Algebra only.
Category: General Mathematics

[1] viXra:2507.0042 [pdf] submitted on 2025-07-05 17:58:18

Theoretical and Formal Proof of "P Versus NP" Theorem

Authors: Mirzakhmet Syzdykov
Comments: 2 Pages.

After making the number of sufficient and successful experiments on account of "P versus NP" theorem, specifically according to the equivalence of complexity classes, we are giving the final and formal theoretical proof by contradiction in this paper summarizing all the results before and giving the definition of our functional hypothesis or conjecture.
Category: General Mathematics