General Mathematics

2002 Submissions

[9] viXra:2002.0594 [pdf] submitted on 2020-02-28 22:17:24

Cycles Universels et Cycles Dérivés en 3x +1 Généralisé

Authors: Pierre Lamothe
Comments: 10 Pages. En français, 4 tableaux

In Collatz-Kakutani sequences that are generalized to px + q, the beginning x and the end y of a sequence are connected by a diophantine equation pm x - 2d y + qc = 0, where m and d are the numbers of multiplication and division. There is a cycle (x = y) if δ (= 2d - pm) divide qc. It is shown that all c are included in parametric rotation cycles (c1 c2 ... cm) for px + δ, and that the rare numerical cycles (x1 x2 ... xm) derive from them when xi = qci / δ are integers. The universal cycles are purely algebrical but the derived cycles result from a numerical coincidence. Assuming that the possible values of qc mod δ are equiprobable, a formula is given for the ocurrence probability of a derived cycle.


Category: General Mathematics

[8] viXra:2002.0571 [pdf] replaced on 2020-03-06 01:11:03

Approche Algébrique du Problème 3n + 1 Généralisé

Authors: Pierre Lamothe
Comments: 38 Pages. 10 figures, 9 tableaux. En français.

This essay describes the steps of an algebraic approach to Collatz's conjecture that led to the discovery of algebraic cycles from which the rare numerical cycles are derived. The derivation criterion is used to calculate the probability of a derived cycle in a given class. The probability drops exponentially with the length of the cycle. The steps : From numbers to functions – Monoid algebra of chain functions – Algebraic cycles and derived cycles – Triplet operator of linear functions – From functions to numbers – Paths in a lattice of classes – Discrimination of cycle possibilities – Probability that a new cycle exists in 3n + 1.
Category: General Mathematics

[7] viXra:2002.0506 [pdf] submitted on 2020-02-25 13:14:17

An Imaginary pi Formula

Authors: Doug Jensen
Comments: 1 Page.

This is the first pi formula based on imaginary numbers. It is the imaginary version of the famous Leibniz pi formula.
Category: General Mathematics

[6] viXra:2002.0439 [pdf] submitted on 2020-02-22 19:43:18

Methods of the Global Optimization by Deformation of Functions (Part 1)

Authors: Alexander Bolonkin
Comments: 29 Pages.

A new method of optimization by means of a redefinition of the function over a wider set and a deformation of the function on the initial and additional sets is proposed. The method (a) reduces the initial complex problem of optimization to series of simplified problems, (b) finds the subsets containing the point of global minimum and finds the subsets containing better solutions that the given one, and (c) obtains a lower estimation of the global minimum.
Category: General Mathematics

[5] viXra:2002.0438 [pdf] submitted on 2020-02-22 19:50:10

Global Optimization. Methods of α – Functions. Estimations (Part 2).

Authors: Alexander Bolonkin
Comments: 26 Pages.

Author develop ideas of Global Optimization offered in article “Methods of the Global Optimization by Deformation of Functions” [9]: A new method of optimization by means of a redefinition of the function over a wider set and a deformation of the function on the initial and additional sets is proposed. The method (a) reduces the initial complex problem of optimization to series of simplified problems, (b) finds the subsets containing the point of global minimum and finds the subsets containing better solutions that the given one, and (c) obtains a lower estimation of the global minimum.
Category: General Mathematics

[4] viXra:2002.0255 [pdf] submitted on 2020-02-13 04:56:22

Resolvement of the St. Petersburg Paradox and Improvement of Pricing Theory

Authors: Dahang Li
Comments: 8 Pages.

The St. Petersburg Paradox was proposed before two centuries. In the paper we proposed a new pricing theory with several rules to solve the paradox and state that the fair pricing should be judged by buyer and seller independently. The pricing theory we proposed can be applied to financial market to solve the confusion with fat tails.
Category: General Mathematics

[3] viXra:2002.0070 [pdf] replaced on 2020-02-17 17:41:41

Understanding of Numbers a Short Introduction to Division by Zero

Authors: Leszek Mazurek
Comments: 2 Pages, Full text about Division by zero here -> https://vixra.org/abs/2001.0475

This paper presents the concept how to understand numbers properly.
Category: General Mathematics

[2] viXra:2002.0036 [pdf] submitted on 2020-02-03 01:50:39

Infinity Furthers Anomaly in the Complex Numbers

Authors: Han Geurdes
Comments: 5 Pages. Extension of earlier studies

In the paper an anomaly in complex number theory is reported. Similar to a previousnote, the ingredients of the analysis are Euler’s identity and the DeMoivre rule for n =2. If a quadratic and definitely not weak equation has two solutions, then, acontradiction can be derived from ±1 functions in complex number theory. Aconstructivist finite approach to cos and sin is briefly discussed to resolve the anomaly.
Category: General Mathematics

[1] viXra:2002.0028 [pdf] submitted on 2020-02-02 12:56:16

A proof of Riemann Hypothesis

Authors: Francisco Moga Moscoso
Comments: 5 Pages.

This article is very important because the objective is to contribute to research related to the riemann hypothesis. In this article, we will prove Riemann Hypothesis by a new novel vision.In research each positive result as negative must be published.He is an independent researcher and not known in the mathematical community for this reason magazines reject his papers.We need mathematicians with an open mind to assess any contribution to research from other disciplines.Thanks for reading this.
Category: General Mathematics