Related papers: Positive characteristic Ax-Schanuel
Analytic concepts contribute to our understanding of randomness of reals via algorithmic tests. They also influence the interplay between randomness and lowness notions. We provide a survey, written on the occasion of Rod Downey's 60th…
We discuss some examples that illustrate the countability of the positive rational numbers and related sets. Techniques include radix representations, Godel numbering, the fundamental theorem of arithmetic, continued fractions, Egyptian…
In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.
We formulate and explore two basic axiomatic systems of typefree subjective probability. One of them explicates a notion of finitely additive probability. The other explicates a concept of infinitely additive probability. It is argued that…
Using the recently developed mathematical theory of tangles, we re-assess the mathematical foundations for applications of the five factor model in personality tests by a new, mathematically rigorous, quantitative method. Our findings…
Transcendence criteria inspired by Kolberg's paper dated 1962. This is the second part of a note about Kolberg's proof that the values of the sums of a class of certain power series in x, for algebraic values of x, are transcendent. A…
The goal of this note is to introduce Teissier singularities and to explain why they are candidate to play, in positive characteristics, a role for resolution of singularities which is similar to the role played by quasi-ordinary…
The distribution $N(x)$ of citations of scientific papers has recently been illustrated (on ISI and PRE data sets) and analyzed by Redner [Eur. Phys. J. B {\bf 4}, 131 (1998)]. To fit the data, a stretched exponential ($N(x) \propto…
Various algebraic properties of Heilbronn's exponential sum can be deduced through the use of supercharacter theory, a novel extension of classical character theory due to Diaconis-Isaacs and Andre. This perspective yields a variety of…
We define 1-motives of a variety X over a perfect field of positive characteristic which realize the etale cohomology groups of X in dimension and codimension one. This is the analogue in positive characteristic of previous results of…
Characterizing in a constructive way the set of real functions whose Fourier transforms are positive appears to be yet an open problem. Some sufficient conditions are known but they are far from being exhaustive. We propose two constructive…
In this note we continue our investigations of the representation theoretic aspects of reflection positivity, also called Osterwalder--Schrader positivity. We explain how this concept relates to affine isometric actions on real Hilbert…
In this paper, we prove a property of kernels of Brauer characters. We propose a candidate for the kernels of Isaacs' partial characters, and we show that this candidate has the same property.
I present some reminiscences, both personal and scientific, over a lifetime of admiration of, and friendship with, one of the Grandmasters of our subject.
We give a new demonstration of Loewner's characterization of polynomials, solving in the positive a conjecture proposed by Laird and McCann in 1984.
We review the discovery of reflection positivity. We also explain a new geometric approach and proof of the reflection positivity property.
Using the integral representations of the solutions of Schr\"odinger equation, which are the essential ingredients of the Gel'fand-Levitan and Marchenko integral equations of inverse scattering theory, we obtain a general theorem on the…
We address how to robustly interpret natural language refinements (or critiques) in recommender systems. In particular, in human-human recommendation settings people frequently use soft attributes to express preferences about items,…
A piece of music can be expressively performed, or interpreted, in a variety of ways. With the help of an online questionnaire, the Con Espressione Game, we collected some 1,500 descriptions of expressive character relating to 45…
This paper is an update and extension of a result the authors first proved in 2003. The goal of this paper is to study factors which are known to be L^2-characteristic for certain nonconventional averages and prove that these factors are…