Related papers: Intuitive dyadic calculus: the basics
This article provides an accessible introduction to fractional derivatives, a concept that extends classical calculus by allowing derivatives of non-integer order. It explores both the fundamental definitions and some of the most relevant…
This short introductory category theory textbook is for readers with relatively little mathematical background (e.g. the first half of an undergraduate mathematics degree). At its heart is the concept of a universal property, important…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
This book aims to provide a brief overview of recent advancements in the theory of inverse problems for stochastic partial differential equations. In order to keep the content concise, we will only discuss the inverse problems of two…
This paper presents a brief survey of the most important and the most remarkable inequalities involving the basic arithmetic functions.
Dimensional analysis is a simple qualitative method for determining essential connections between physical quantities. It is applicable to a multitude of physics problems, many of which canbe introduced early on in a university physics…
We present in this article a general approach (in the form of recommendations and guidelines) for tackling Diophantine equation problems (whether single equations or systems of simultaneous equations). The article should be useful in…
This paper describes the classification of analytic $q$-difference equations. The difference Galois groups are computed. A tentative description of the universal difference Galois group is given.
We give new and elementary proofs of one weight norm inequalities for fractional integral operators and commutators. Our proofs are based on the machinery of dyadic grids and sparse operators used in the proof of the A2 conjecture.
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…
We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without…
The main objective of the paper is to establish explicit estimates on some applicable inequalities in two variables on time scales which can be used in the study of certain qualitative properties of dynamical equations on time scales.
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
This paper is concerned with inference in the linear model with dyadic data. Dyadic data is data that is indexed by pairs of "units", for example trade data between pairs of countries. Because of the potential for observations with a unit…
The book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalist. List of topics: Euclidean geometry: The Axioms / Half-planes / Congruent triangles / Perpendicular…
We offer the proofs that complete our article introducing the propositional calculus called semi-intuitionistic logic with strong negation.
In this paper the double-sided Taylor's approximations are studied. A short proof of a well-known theorem on the double-sided Taylor's approximations is introduced. Also, two new theorems are proved regarding the monotonicity of such…
We discuss how a class of difficult kinematic problems can play an important role in an introductory course in stimulating students' reasoning on more complex physical situations. The problems presented here have an elementary analysis once…
This book is a detailed introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. It is intended to serve both as a textbook for readers with no or little background in this area, and…
A short tutorial on non-standard analysis, made in particular for people working in the Categorical Quantum Mechanics crowd.