相关论文: General self-similarity: an overview

Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).

This is a write up on some sections of convex geometry, functional analysis, optimization, and nonstandard models that attract the author.

Equivalencies of many basic elementary inequalities are given

This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the "entropy distance" and "information distance". Their…

I give an overview of the motivations for and theory/phenomenology of supersymmetry.

A short informal survey on the topics listed in the title. For the proceedings of the International Conference on Rings and Algebras X.

A method is developed for calculating effective sums of divergent series. This approach is a variant of the self-similar approximation theory. The novelty here is in using an algebraic transformation with a power providing the maximal…

This short note contains elementary evaluations of some Euler sums.

These notes were originally intended to be complementary material for an introductory course on self-similar graphs and their algebras, presented by the author at the CIMPA School ``K-theory and Operator Algebras'', held in La Plata and…

Lecture notes for a minicourse to given in the XVII Brazilian School of Geometry, UFAM (Amazonas), Brazil, July 2012.

Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…

These are the revised notes of my lectures at the 1995 Santa Cruz summer institute. Changes from the Jan.26,1996 version: Major: 7.1--2; Medium: 3.7, 3.11, 5.3.3, 7.9.2, 9.8.

This entry for the SIGSPATIAL Special July 2010 issue on Similarity Searching in Metric Spaces discusses the notion of intrinsic dimensionality of data in the context of similarity search.

In this paper, we propose new generalizations of amicable numbers. We also give examples and prove properties of these new concepts.

These are the notes from my courses on the arithmetic of quadratic forms.

These lectures are a brief introduction to supersymmetry.

In this note, we demonstrate the convergence of the Demailly approximation of a general (weakly) upper semi-continuous weight.

We define the concept of self-similarity of an object by considering endomorphisms of the object as `similarity' maps. A variety of interesting examples of self-similar objects in geometry, algebra and arithmetic are introduced.…

These notes are the write-up of my 2008 PCMI lectures on multiplier ideals. They aim to give an introduction to the algebro-geometric side of the theory, with an emphasis on its global aspects. The focus is on concrete examples and…

The purpose of this short note is to show the interplay between math outreach and conducting original research, in particular how each can build off the other.