Internet: Culture Diversity and Unification

Culture specifics of the Internet usage is analysed. The analysis done is a preliminary work for the application of the socio-historical theory of human mental development. The practice of the Internet usage is ambigious as it gives rise to both the unification and the diversity. The parameters analysed include the techniques of the hypertexts browsing,\ud and the status/position/rank of the communicators - its influence on holding the floor and turntaking rules, the ways the emotions are expressed while Internet communication, and the way the English language serves the functions of world-wide medium

The Hecke Bicategory

We present an application of the program of groupoidification leading up to a sketch of a categorification of the Hecke algebroid --- the category of permutation representations of a finite group. As an immediate consequence, we obtain a categorification of the Hecke algebra. We suggest an explicit connection to new higher isomorphisms arising from incidence geometries, which are solutions of the Zamolodchikov tetrahedron equation. This paper is expository in style and is meant as a companion to Higher Dimensional Algebra VII: Groupoidification and an exploration of structures arising in the work in progress, Higher Dimensional Algebra VIII: The Hecke Bicategory, which introduces the Hecke bicategory in detail.Comment: 27 pages, 11 .eps figures, Major revision of expositio

On Some Families of Integrals Connected to the Hurwitz Zeta Function

Expressions for a family of integrals involving the Hurwitz zeta function are established using standard properties of the Fourier transform

On Arithmetic Series involving the fractional part function

We present new relationships between the work of H. Davenport and A. I. Popov. A new general formula involving the Von Mangoldt function is presented, as well as a criteria for the Riemann Hypothesis

Another Smallest Part Function related to Andrews' spt function

In this note, we offer some relations and congruences for an interesting $spt$-type function.Comment: Updated previous versio