Elementary Evaluation of the Zeta and Related Functions

A simple and elementary derivation of values at integer points for the Riemann's zeta and related functions is reported.Comment: ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics, Rhodes, Greece, 19-25 September 201

A conceptual model of a transition from technogenic to human-induced globalization

Globalization is a fundamental integrative social mechanism, in which two stages can be distinguished: “technogenic globalization” and “human-induced globalization”. The result of a phase transition from the first stage to the second should be the final formation of an information society. The aim of the study was the theoretical substantiation of globalization as a mechanism for a transition to an information society, and identification of the role and place of technogenesis in it. The paper considers the essence of a transition to an information society in the context of the replacement of technogenic globalization with human-induced globalization, and draws a conclusion about the place of technogenesis and artificial intelligence, as its institution, in human-induced globalization. It is shown that at the present stage, human-induced globalization should be implemented with a focus on the following directions of technogenesis: a) formation of breakthrough directions of development of the “Human Variable of society”; b) ensuring the demand for innovative development; c) acquisition by society of a new development resource – “human-energy-informational plasma”;  d) formation of a new “capital” mechanism – the mechanism of self-growth of the value of social life on the basis of the investment flow of human-energy-informational plasma

The Lebesgue Universal Covering Problem

In 1914 Lebesgue defined a "universal covering" to be a convex subset of the plane that contains an isometric copy of any subset of diameter 1. His challenge of finding a universal covering with the least possible area has been addressed by various mathematicians: Pal, Sprague and Hansen have each created a smaller universal covering by removing regions from those known before. However, Hansen's last reduction was microsopic: he claimed to remove an area of $6 \cdot 10^{-18}$, but we show that he actually removed an area of just $8 \cdot 10^{-21}$. In the following, with the help of Greg Egan, we find a new, smaller universal covering with area less than $0.8441153$. This reduces the area of the previous best universal covering by a whopping $2.2 \cdot 10^{-5}$.Comment: 11 pages, 5 jpeg figures, numerical errors correcte

An elementary and real approach to values of the Riemann zeta function

An elementary approach for computing the values at negative integers of the Riemann zeta function is presented. The approach is based on a new method for ordering the integers and a new method for summation of divergent series. We show that the values of the Riemann zeta function can be computed, without using the theory of analytic continuation and functions of complex variable.Comment: added comments on zeroes of $\eta(s)$ on page 3 and some new ref