Related papers: Alcune Note di Analisi Matematica
This is a survey on the usage of the module theoretic notion of a "retractable module" in the study of algebras with actions. We explain how classical results can be interpreted using module theory and end the paper with some open…
One-loop functions with loop masses larger than external masses and momenta can always be expanded in terms of external masses and momenta. The precision requested for observables determines the number of the expansion terms retained in the…
In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…
A didactical survey of the foundations of Algorithmic Information Theory. These notes are short on motivation, history and background but introduce some of the main techniques and concepts of the field. The "manuscript" has been evolving…
This is the second volume of a textbook for a two-semester course in mathematical analysis. This second volume is about analysis of multi-variable functions. The topics covered include Euclidean spaces, convergence of sequences, open sets…
These lecture notes concern information-theoretic notions of entropy. They are intended for, and have been successfully taught to, undergraduate students interested inresearch careers. Besides basic notions of analysis related to…
These few pages briefly present the way in which Activity Theory has been adopted for several years now by French researchers in didactics of mathematics and has been adapted to study the learning of school mathematics in relation with the…
These informal notes concern some basic themes of harmonic analysis related to representations of groups.
The annotation of textual information is a fundamental activity in Linguistics and Computational Linguistics. This article presents various observations on annotations. It approaches the topic from several angles including Hypertext,…
These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
We present a brief introduction to analytic capacity, with an emphasis on its numerical computation. We also discuss several related open problems.
Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods,…
Colombeau algebras constitute a convenient framework for performing nonlinear operations like multiplication on Schwartz distributions. Many variants and modifications of these algebras exist for various applications. We present a…
This article serves as the regression analysis lecture notes in the Intelligent Computing course cluster (including the courses of Artificial Intelligence, Data Mining, Machine Learning, and Pattern Recognition). It aims to provide students…
Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.
We provide a theoretical framework for analysing and comparing different forms of organizing introductions to mathematical analysis at the secondary level, then illustrate it by two characteristic examples from certain periods of change in…
This is a collection of (mostly) pen-and-paper exercises in machine learning. The exercises are on the following topics: linear algebra, optimisation, directed graphical models, undirected graphical models, expressive power of graphical…
This is a chapter destined for the book "Handbook of the Tutte Polynomial". The chapter is a composite. The first part is a brief introduction to Orlik-Solomon algebras. The second part sketches the theory of evaluative functions on matroid…
Linear typed $\lambda$-calculi are more delicate than their simply typed siblings when it comes to metatheoretic results like preservation of typing under renaming and substitution. Tracking the usage of variables in contexts places more…