Related papers: Analysis on Metric Spaces
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
These are notes for the Bootcamp volume for the 2015 AMS Summer Institute in Algebraic Geometry. They are based on earlier notes for the "Positive Characteristic Algebraic Geometry Workshop" held at University of Illinois at Chicago in…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
Finding measures for research impact, be it for individuals, institutions, instruments or projects, has gained a lot of popularity. More papers than ever are being written on new impact measures, and problems with existing measures are…
The expected physics and astrophysics capabilities of the AMS experiment on board the International Space Station are briefly reviewed : high statistics study of cosmic rays in a wide range of energies, search for primordial antimatter,…
This volume contains the proceedings of MARS 2024, the sixth workshop on Models for Formal Analysis of Real Systems, held as part of ETAPS 2024, the European Joint Conferences on Theory and Practice of Software. The MARS workshops bring…
Whenever a large group of people are engaged in an activity, communities will form. The nature of these communities depends on the relationship considered. In the group of people who regularly use scholarly literature, a relationship like…
This text is a survey on symmetric matrices. It serves as a script for a module to be taught at university.
This is a write-up of a talk given at the CATMI meeting in Bergen in July 2023, and is an introduction to a category-theoretic perspective on metric spaces. A metric space is a set of points such that between each pair of points there is a…
Pairs of metrics in a three-dimensional linear vector space are considered, one of which is a Minkowski type metric with the signature (+,-,-). Such metric pairs are classified and canonical presentations for them in each class are…
These informal notes deal with some topics related to analysis on metric spaces.
This essay, originally published in the Sept 1990 Notices of the AMS, discusses problems of our mathematical education system that often stem from widespread misconceptions by well-meaning people of the process of learning mathematics. The…
This paper presents an extended version of lecture notes for an introductory course on Berkovich analytic spaces that I gave in 2010 at Summer School "Berkovich spaces" at Institut de Mathmatiques de Jussieu.
In the past, several works have investigated ways for combining quantitative and qualitative methods in research assessment exercises. In this work, we aim at introducing a methodology to explore whether citation-based metrics, calculated…
We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.
Ten years ago, the Mathematics Subject Classification MSC 2010 was released, and a corresponding machine-readable Linked Open Data collection was published using the Simple Knowledge Organization System (SKOS). Now, the new MSC 2020 is out.…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
This paper is to build a primitive framework for a new possible extended system of real mathematical analysis - the Isomorphic Mathematical Analysis System (IMAS). It is based on some new concepts: e.g. isomorphic frame,…
Community detection in a complex network is an important problem of much interest in recent years. In general, a community detection algorithm chooses an objective function and captures the communities of the network by optimizing the…
Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…