Related papers: Analysis on Metric Spaces
In this manuscript, we provide a concise review of the concept of metric dimension for both deterministic as well as random graphs. Algorithms to approximate this quantity, as well as potential applications, are also reviewed. This work has…
A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.
In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be…
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
These informal notes briefly discuss some basic topics involving Lipschitz functions, connectedness, and Hausdorff content in particular.
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
This is a survey on special metrics. We shall present some results and open questions on special metrics mainly appeared in the last 10 years
Two-page paper on the notion of cost of groups and measured equivalence relations to appear in the "What is?" series in the Notices of the AMS.
This paper presents a bibliometric analysis that examines the works cited in, as well as those citing, NIME papers; for brevity, we refer to these as `references` and `citations`. Utilizing existing tools, we have computationally extracted…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…
This is a draft of my textbook on mathematical analysis and the areas of mathematics on which it is based. The idea is to fill the gaps in the existing textbooks. Any remarks from readers are welcome.
These are notes on adic spaces. They are made available upon some requests in order to make quoting them easier.
Multiscale and multiphysics applications are now commonplace, and many researchers focus on combining existing models to construct combined multiscale models. Here we present a concise review of multiscale applications and their source…
This volume contains the proceedings of MARS 2022, the fifth workshop on Models for Formal Analysis of Real Systems, held as part of ETAPS 2022, the European Joint Conferences on Theory and Practice of Software. The MARS workshops bring…
This paper focuses on defining a measure, appropriate for obtaining optimally sparse solutions to underdetermined systems of linear equations.* The general idea is the extension of metrics in n-dimensional spaces via the Cartesian product…
Learning analytics is a research topic that is gaining increasing popularity in recent time. It analyzes the learning data available in order to make aware or improvise the process itself and/or the outcome such as student performance. In…
Here we consider a few topics related to Lipschitz classes for functions and curves in metric spaces.
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches…