arXiv subjects

Jose E. Martínez Serra

Publications and source records attributed to Jose E. Martínez Serra.

2 recordsLinked to original sources

arXiv2017

Some elements of a possible demonstration of the Collatz conjecture

In this paper we are shown the following facts: The probability of increased $ A_{k}=P(T^{k} (x_{0})>T^{k-1} (x_{0})) $, and the probability of decrease $B_{k}=P(T^{k} (x_{0})<T^{k-1} (x_{0}))$ in step $ k $ of a Collataz procedure initiated in $ x_ {0} \in \mathbb{N} $ arbitrary, they are equal for all values of $ k $. This influences on the law that generates the numbers of a Collatz sequence so that it is forced to decrease until the unit. Also is shown in the Collatz conjecture is false for every problem $an +b$ such that $a\geq 5\geq b+2$, and your probabilistic caracter can not be ignored if you want to get to the definitive solution, among other interesting arguments.

math.NT↗

arXiv2016

Proposed method to reduce the determinant of order n

This paper presents a theorem which solves the problem of reduction of the determinant order by means of a transformation of it, into other determinant whose each element are a determinant of second order. This implies that, if the process continues, desired result is obtained by solving always determinants of second order. It also assesses the degree of efficiency compared to the method by minors and with the method of Gauss, as well as the ability to reflect small variations in the data. This method should have a good impact also in the area of teaching mathematics, due to its ease of assimilation and application.

math.GM↗