It is well known [4] that the non-Archimedean residue class fields K of the ring of continuous real valued functions on a space are realclosed and 7/i-sets. It does not appear to be known that the exponential function in the reals induces an exponential function in K (definitions to follow) ; thus K is exponentially closed. The property of being exponentially closed is a new invariant which wil...

We give a brief overview of the theory of complex dimensions of real (archimedean) fractal strings via an illustrative example, the ordinary Cantor string, and a detailed survey of the theory of p-adic (nonarchimedean) fractal strings and their complex dimensions. Moreover, we present an explicit volume formula for the tubular neighborhood of a p-adic fractal string Lp, expressed in terms of th...

This paper presents the impact of a class of transformations of copulas in their upper and lower multivariate tail dependence coefficients. In particular we focus on multivariate Archimedean copulas. In the first part of this paper, we calculate multivariate tail dependence coefficients when the generator of the considered copula exhibits some regular variation properties, and we investigate th...

Berarducci (2000) studied irreducible elements of the ring k((G<0))⊕Z, which is an integer part of the power series field k((G)) where G is an ordered divisible abelian group and k is an ordered field. Pitteloud (2001) proved that some of the irreducible elements constructed by Berarducci are actually prime. Both authors mainly concentrated on the case of archimedean G. In this paper, we study ...

Preamble This book written by A. Schumann & F. Smarandache is devoted to advances of non-Archimedean multiple-validity idea and its applications to logical reasoning. Leibnitz was the first who proposed Archimedes' axiom to be rejected. He postulated infinitesimals (infinitely small numbers) of the unit interval [0, 1] which are larger than zero, but smaller than each positive real number. Robi...

In this talk I examine the prospects for a theory of probability aspiring to support a decisiontheoretic interpretation by which principles of probability derive their normative status in virtue of their relationship with principles of rational decision making. More specifically, I investigate the possibility of a theory of expected utility abiding by distinguished dominance principles which ha...