Related papers: Analysis on Metric Spaces
With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many…
An array of large observational programs using ground-based and space-borne telescopes is planned in the next decade. The forthcoming wide-field sky surveys are expected to deliver a sheer volume of data exceeding an exabyte. Processing the…
The new era of technology has brought us to the point where it is convenient for people to share their opinions over an abundance of platforms. These platforms have a provision for the users to express themselves in multiple forms of…
These notes are loosely based on an introductory course in algebraic geometry given at Rutgers University in Spring of 2024. We introduce some relatively advanced topics at the expense of the technical details.
This article is an introduction for a theme issue following a Scientific Discussion Meeting on \emph{The next generation of analogue gravity experiments} held at the Royal Society in December 2019. This theme issue comprises a collection of…
This set of lecture notes constitutes the free textbook project I initiated towards the end of Summer 2015, while preparing for the Fall 2015 Analytical Methods in Physics course I taught to upper level undergraduates at the University of…
The notion of machine companions has long been embedded in social-technological imaginaries. Recent advances in AI have moved those media musings into believable sociality manifested in interfaces, robotic bodies, and devices. Those…
The definition of weighted distance measure involves weights. The paper proposes a weighted distance measure without the help of weights. Here, weights are intrinsically added to the measure, and for this, the concept of metric space is…
In this paper we study Probability Measures (PM) from a functional point of view: we show that PMs can be considered as functionals (generalized functions) that belong to some functional space endowed with an inner product. This approach…
This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.
The first aim of this study is to define soft sequential compact metric spaces and to investigate some important theorems on soft sequential compact metric space. Second is to introduce net and totally bounded soft metric space and study…
This is just a note for \cite[Chapter$3{1/2}_+$]{gromov}. Maybe this note is obvious for a reader who knows metric geometry. I wish that someone study further in this direction.
In the present paper, a notion of M-basis and multi dimension of a multi vector space is introduced and some of its properties are studied.
These lecture notes are an expanded write-up of my short lecture series "Noncommutative Resolutions" given to the MSRI Graduate Student Workshop "Noncommutative Algebraic Geometry" during June 2012. The notes include five chapters, an…
This survey is based on lectures given by the authors during the program "Noncommutative algebraic geometry and representation theory" at the MSRI, Berkeley, in the spring of 2013. It covers the recent work of the authors on noncommutative…
These are lecture notes on scale calculus and M-polyfolds written for a graduate course at UNICAMP March-June 2018 and an advanced mini-course given during the biannual meeting of Brazilian mathematicians, CBM-32, at IMPA in August 2019.
The research field of spatial scientometrics is dedicated to measuring and analyzing science with spatial components (e.g., location, place, mapping). Because of the dynamic nature of this field, researchers from multidisciplinary domains…
This is an overview of math.AG/0310186, math.AG/0309290, math.AG/0501247, math.AG/0401002 and math.AG/0504584 written for the Proceedings of the AMS Meeting on Algebraic Geometry, Seattle, 2005.
This article deals with peer-assessment in the context of higher education teaching in mathematics, and examines the nature of student activity when assessing work produced by peers. After an overview of research on peer assessment, we…
We present the contribution of the Unbabel team to the WMT 2020 Shared Task on Metrics. We intend to participate on the segment-level, document-level and system-level tracks on all language pairs, as well as the 'QE as a Metric' track.…