General Mathematics

2006 Submissions

[4] viXra:2006.0204 [pdf] replaced on 2020-06-28 02:05:25

Cycles in Generalized Collatz Sequences

Authors: Pierre Lamothe
Comments: 26 Pages. En français. 4 figures.

The generalized Collatz sequences are set by D(x) = x/r if x mod r = 0 and T(x) = floor (px/r) otherwise. It has previously been shown (2002.0594) with px + q sequences that numerical cycles are derived from algebraic cycles. The same is shown here in a richer framework where the number of elementary functions increases from 2 to r. Again, the beginning and the end of each sequence are connected by a diophantine equation, pm x - rd y - q = 0, where m and d are the respective numbers of multiplications and divisions. There are still always rotation cycles (q1 q2 ... qm) while derived cycles (x1 x2 ... xm) are present only when qi / (rd - pm) are integers. The function R outlined by Rm(q) = q proves to be a powerful computational tool. In addition, the subsequences are numbered and one can easily find a subsequence from its rank ρ in the base r.
Category: General Mathematics

[3] viXra:2006.0201 [pdf] replaced on 2020-09-14 05:29:09

Extensions of Some Trigonometric Double Angle and Product Formulae

Authors: Suaib Lateef
Comments: 6 pages

I present some new trigonometric identities which generalize trigonometric product formulae, power reduction formulae and double angle formulae. Also, some conjectures on further generalizations of the proven new identities are stated for further research.
Category: General Mathematics

[2] viXra:2006.0072 [pdf] submitted on 2020-06-09 12:32:50

Essence of Millennium Problems

Authors: Vaibhav Gupta
Comments: 3 Pages.

This article contains seven Millennium problem simple explanation. The most of things are from different sources and I just arranged it in simple manner so that even general person can understand that. The problems contain diverse fields including Pure Mathematics (Topology and Number Theory), Theoretical Computer Science, Physics etc.
Category: General Mathematics

[1] viXra:2006.0047 [pdf] submitted on 2020-06-05 18:01:47

New Square Power Algorithm (in Spanish)

Authors: Zeolla Gabriel Martin
Comments: 9 Pages.

Solving a square power without a calculator for middle school students is possible. A new and previously unknown method is presented in this document. Resolver una potencia cuadrada sin calculadora para alumnos de la escuela media es posible. Un método nuevo y desconocido se presenta en este documento.
Category: General Mathematics