Related papers: Perfect Powers: Pillai's works and their developme…
Recursive formulas are derived for the number of solutions of linear and quadratic Diophantine equations with positive coefficients. This result is further extended to general non-linear additive Diophantine equations. It is shown that all…
In this paper, we define Tribonacci-Lucas polynomials and present Tribonacci-Lucas numbers and polynomials as a binomial sum. Then, we introduce incomplete Tribonacci-Lucas numbers and polynomials. In addition we derive recurrence…
A brief introduction into Idempotent Mathematics and an idempotent version of Interval Analysis are presented. Some applications are discussed.
Several open problems in algebraic logic are solved.
We review Extended Theories of Gravity in metric and Palatini formalism pointing out their cosmological and astrophysical application. The aim is to propose an alternative approach to solve the puzzles connected to dark components.
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
Telegraphic notes on the historical bibliography of the Gamma function and Eulerian integrals. Correction to some classical references. Some topics of the interest of the author. We provide some extensive (but not exhaustive) bibliography.…
In this small note we ask several questions which are relevant to the construction of the self-consistent neutrino theory of light. The previous confusions in such attempts are explained in the more detailed publication.
A range of issues in the field of hyperon physics is presented, together with an assessment of where important challenges remain.
After reviewing the basics, topics in this talk include an attempted survey of theoretical contributions to this workshop, some extra specific comments on quark models, and a summary.
An introduction to the methods and ideas of Chiral Perturbation Theory is presented in this talk. The discussion is illustrated with some phenomenological predictions that can be compared with available experimental results.
We give an overview of publications on partial actions and related concepts, paying main attention to some recent developments.
We give solutions of a Diophantine equation containing factorials, which can be written as a cubic form, or as a sum of binomial coefficients. We also give some solutions to higher degree forms and relate some solutions to an unsolvable…
We present some reflections concerning two papers by H. Poincar\'e concerning the theory of quanta.
We survey old and new conjectures and results on various types of spherical maximal functions, emphasizing problems with a fractal dilation set.
The necessity of the FORM project is discussed. Then the evolutionary needs in particle physics are considered, looking at the trends over the years. A guess is made at what will be needed in the (near) future. The whole is concluded with…
An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut
In this paper we study the polynomial version of Pillai's conjecture on the exponential Diophantine equation \begin{equation*} p^n - q^m = f. \end{equation*} We prove that for any non-constant polynomial $ f $ there are only finitely many…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
A very short, non-technical review of the main problems which are presently open in the context of the gravitational theory and of its cosmological applications, and which are currently under investigation and deep discussion. We will talk…