Related papers: Analytical Guide and updates for "Cardinal Arithme…
We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.
We give a corrected version of Corollary 3.33 in: H. Flenner, S. Kaliman, and M. Zaidenberg, Birational transformations of weighted graphs. Affine algebraic geometry. Osaka Univ. Press, 2007, 107-147.
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
This is a replacement paper. There are 6 chapters. The first two chapters are introductory. The third chapter is on extremal graph theory. The fourth chapter is about algebra in graph theory. The fifth chapter is focused on algorithms. The…
This paper provides a new approach to derive various arbitrary high order finite difference formulae for the numerical differentiation of analytic functions. In this approach, various first and second order formulae for the numerical…
This is part one of a series of four methodological papers on (bi)quaternions and their use in theoretical and mathematical physics: 1- Alphabetical bibliography, 2- Analytical bibliography, 3- Notations and terminology, and 4- Formulas and…
This manuscript is intended as an accompaniment to Guth's "A restriction estimate using polynomial partitioning". We begin by summarizing the core ideas of the proof, elaborating the history and development of the techniques therein. From…
We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the…
Some recent approaches for scalable offline partial evaluation of logic programs include a size-change analysis for ensuring both so called local and global termination. In this work|inspired by experimental evaluation|we introduce several…
We present a brief overview of fractional analytic QCD, basically following the results recently obtained in Refs. [1,2].
Corrections are brought to an article of Friesen on continued fractions of a given period.
We provide an algorithmic description of a family of graded decomposition numbers for rational Cherednik algebras.
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…
Preliminary version of a book on univariate real analysis, with 14 chapters and 2 appendices. 1. Real numbers; 2. Limits of real sequences; 3. Series; 4. Limits of real functions. 5. Elementary functions; 6. Continuous functions; 7.…
This update to my article on Congruent numbers, elliptic curves, and the passage from the local to the global, which appeared in Resonance, December 2009, pp. 1183--1205 (https://www.ias.ac.in/describe/article/reso/014/12/1183-1205) and was…
We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.
Introduction revised, representations of generalized power series reformulated, references updated.
This text is a support for different courses of the master of Mechanics of the University Paris-Saclay. The content of this text is an introduction, for graduate students, to tensor algebra and analysis. Far from being exhaustive, the text…
In this revised version, we add some expository material and references and make some minor corrections.
In the revised version of the paper, we correct misprints and add some new statements.