Related papers: Perfect Powers: Pillai's works and their developme…
We answer a question of Samir Siksek, asked at the open problems session of the conference ``Rational Points 2022'', which, in a broader sense, can be viewed as a reverse engineering of Diophantine equations. For any finite set $S$ of…
Some properties and relations satisfied by the polynomial solutions of the bispectral problem are studied. Given a differential operator, under certain restrictions its polynomial eigenfunctions are explicitly obtained, as well as the…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
The original derivation of Power Functional Theory, Schmidt and Brader, JCP 138, 214101 (2013), is reworked in some detail with a view to clarifying and simplifying the logic and making explicit the various functional dependencies. We note…
In this paper we summarize the existing principles for building unconventional computing devices that involve delayed signals for encoding solutions to NP-complete problems. We are interested in the following aspects: the properties of the…
In this paper we are interested in developments of elliptic functions of Jacobi. In particular a trigonometric expansion of the classical theta functions introduced by the author (Algebraic methods and q-special functions, Editors: C.R.M.…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approximation; such as theorems of Khintchine, Jarn\'{\i}k, Duffin-Schaeffer and Gallagher. We then describe recent strengthening of various…
This is the first in a series of papers whereby we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of…
We expand upon some topics reviewed and sketched in a book to appear with more details, embellishments, and some new material of a speculative nature.
We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…
We contribute to the knowledge of the quantifier completions and their applications by using the language of doctrines. This algebraic presentation allows us to properly analyse the behaviour of the existential and universal quantifiers. We…
We offer a careful development of the Dixonian elliptic functions with parameter $\alpha = 0$ from the initial value problem of which they are solutions.
Some thoughts are presented on the inter-relation between beauty and truth in science in general and theoretical physics in particular. Some conjectural procedures that can be used to create new ideas, concepts and results are illustrated…
A brief recollection is made of the many scientific collaborations of Bologna with colleagues from Developing Countries. In particular are discussed in detail the collaborations in some recent Astroparticle Physics experiments.
Starting from Ritt's classical theorems, we give a survey of results in functional decomposition of polynomials and of applications in Diophantine equations. This includes sufficient conditions for the indecomposability of polynomials, the…
An introduction to the basic ideas and methods of Chiral Perturbation Theory is presented. Several phenomenological applications of the effective Lagrangian technique to strong, electromagnetic and weak interactions are discussed.
The present status of the problems in my book "Cardinal Invariants on Boolean algebras" (Birkhauser 1996) is described, with a description of solutions or partial solutions, and references.
Clarified certain points and related it to other work.
We present a technique for deriving certain new natural dualities for any variety of algebras generated by a finite Heyting chain. The dualities we construct are tailored to admit a transparent translation to the more pictorial…