is known to have only finitely many triples of positive integer solutions x, y, z for a given n > 2 (Faltings, 1983). In Chapter 11, special situations are described in which more precise information is accessible. For example, if x is in S, then n is bounded by a computable number C5 = Cb(pv ..., p8). From these examples, it should be clear that the book is a mine of information for workers in...

Various ethical theories recommend developing a morally sound character, and therefore require an understanding of the nature and development of traits. Philosophers usually accept the Aristotelian view that traits are a combination of habit and insight. Sartre’s early work offers an alternative: traits consist in projects. One aim of this paper is to show that this is indeed Sartre’s view, by ...

We revisit the classical theorem of Euler regarding special values of the Riemann zeta function as well as Hecke’s generalization of this to Dirichlet’s Lfunctions and derive an elliptic analogue. We also discuss transcendence questions that arise from this analogue.

These notes discuss formalizing contexts as first class objects. The basic relation is ist(c, p). It asserts that the proposition p is true in the context c. The most important formulas relate the propositions true in different contexts. Introducing contexts as formal objects will permit axiomatizations in limited contexts to be expanded to transcend the original limitations. This seems necessa...

Spirituality" has often been framed in social science research as an alternative to organized "religion," implicitly or explicitly extending theoretical arguments about the privatization of religion. This article uses in-depth qualitative data from a religiously-diverse U.S. sample to argue that this either-or distinction not only fails to capture the empirical reality of American religion, but...

We express the zeros of the Weierstass ℘-function in terms of generalized hypergeometric functions. As an application of our main result we prove the transcendence of two specific hypergeometric functions at algebraic arguments in the unit disc. We also give a Saalschützian 4F3–evaluation.

This essay about the phenomenon of human self-overlapping presents an evident plurality of approaches and theoretical definitions of this phenomenon. On the basis of historical, philosophical, psychological and sociological starting points the author tries to systemise knowledge and creates his own, temporary dual structure of the selfoverlapping phenomenon. The given phenomenon is suitable for...

In the present paper, we derive transcendence measures for the numbers log a, e, aP, (log aj)/(log 02) from a previous lower bound of ours on linear forms in the logarithms of algebraic numbers. Subject classification (Amer. Math Soc. (MOS) 1970): 10 F 05, 10 F 35

We give the first transcendence results for the Rosen continued fractions. Introduced over half a century ago, these fractions expand real numbers in terms of certain algebraic numbers.

This paper is concerned with difference equations on elliptic curves. We establish some general properties of the difference Galois groups of equations of order two, and give applications to the calculation of some difference Galois groups. For instance, our results combined with a result from transcendence theory due to Schneider allow us to identify a large class of discrete Lamé equations wi...