The set Set(n), generated by an arbitrary natural number n, was defined in [2] and some arithmetic functions, over its elements are introduced algebraic aspect. Here, the of two functions similar to modal type operators their basic properties studied.

Introduction In the first part of this article, I identified the correct axioms for the structure 〈P(N),N,+, ·,∈〉 , which is the standard structure for Second Order Number Theory. The axioms, collectively “Projective Determinacy”, solve many of the otherwise unsolvable, classical problems of this structure. Actually working from the axioms of set theory, ZFC, I identified a natural progression ...

Article history: Received 21 July 2010 Available online xxxx

The problem of a uniform transverse flow past a prolate spheroid of arbitrary aspect ratio a t low Reynolds numbers has been analysed by the method of matched asymptotic expansions. The solution is found to depend on two Reynolds numbers, one based on the semi-minor axis b, Rb = Ublv, and the other on the semi-major axis a, Ra = Ualv (U being the free-stream velocity at infinity, which is perpe...

In these notes, Section 2 consists of the number-theoretic discussion, whereas Section 3 provides the probabilistic background (with relatively few proofs). First we draw upon topology and group theory to give some examples of probability spaces. Perhaps the most interesting is the weighted Bernoulli space Bp which models flipping a – fixed but not necessarily fair – coin infinitely many times....

326 NOTICES OF THE AMS VOLUME 47, NUMBER 3 Riemannian Geometry Starting in the late 1970s, MG completely revolutionized Riemannian geometry. I mention in this section some results that reflect my taste. This article contains only a small bibliography; further references may be found in my 1998 survey article in Jahresbericht der Deutschen Mathematiker-Vereinigung.1 Except for obvious cases, eve...

T he aim of this article is to communicate the work of Mikhael Gromov (MG) and its influence in almost all branches of contemporary mathematics and, with a leap of faith, of future mathematics. Because of its length, the article will appear in two parts. It is not meant to be a technical report, and, in order to make it accessible to a wide audience, I have made some difficult choices by highli...