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We introduce some early considerations of physical and mathematical impossibility as preludes to the Goedel incompleteness theorems. We consider some informal aspects of these theorems and their underlying assumptions and discuss some the…
This paper is a complement of our recent works on the semilinear Tricomi equations in [8] and[9].
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
We give a shorter simpler proof of a result of Szalay on the equation $2^a + 2^b + 1 = z^2$. We give an elementary proof of a result of Luca on the equation of the title for prime $p > 2$. The elementary treatment is made possible by a…
The book gives a detailed exposition of basic concepts and results of a theory of processes. The presentation of theoretical concepts and results is accompanied with illustrations of their application to solving various problems of…
This is a survey article describing some recent results at the interface of homogeneous dynamics and Diophantine approximation.
The author surveys the problem of piecing together integral or rational solutions to Diophantine equations (global structure) from solutions modulo congruences and real solutions (local structure).
In this written version of a pre-dinner-speech at the workshop "The Nature of Gravity" at ISSI I illustrate Pauli's science primarily with material that has not formally been published by him, but was communicated in detailed letters to…
This paper reports on the current status of the project in which we order all polynomial Diophantine equations by an appropriate version of "size", and then solve the equations in that order. We list the "smallest" equations that are…
We present a list of open questions in the theory of holomorphic foliations, possibly with singularities. Some problems have been around for a while, others are very accessible.
We show that Peliti's Comment [arXiv:0808.2855] fails to appreciate basic physical principles and consequently misrepresents both our work as well as the classical work of Gibbs and Tolman.
We formalise the well-known rules of partial differentiation in a version of equational logic with function variables and binding constructs. We prove the resulting theory is complete with respect to polynomial interpretations. The proof…
We discuss the common existential theory of all or almost all completions of a global function field.
An assessment of the present status of the theory, some immediate tasks which are suggested thereby and some questions whose answers may require a longer breath since they relate to significant changes in the conceptual and mathematical…
Fifteen years after their discovery, ample fields now stand at the center of research in contemporary Galois theory and attract more and more attention also from other areas of mathematics. This survey gives an introduction to the theory of…
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…
A list of open problems in the field of analysis of boolean functions, compiled February 2012 for the Simons Symposium.
Many statistical issues arise in the analysis of Particle Physics experiments. We give a brief introduction to Particle Physics, before describing the techniques used by Particle Physicists for dealing with statistical problems, and also…
In this paper we give solutions of certain diophantine equations related to triangular and tetrahedral numbers and propose several problems connected with these numbers. The material of this paper was presented in part at the 11th…
In this paper, we will address broader concepts for Dunford-Pettis operators, presenting new classes and results that correlate this class with others already well-studied in the literature, as well as an approach outside the origin. We…