General topology | Compactification (mathematics)
In the mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact. It is named after the Russian mathematician Pavel Alexandroff.More precisely, let X be a topological space. Then the Alexandroff extension of X is a certain compact space X* together with an open embedding c : X → X* such that the complement of X in X* consists of a single point, typically denoted ∞. The map c is a Hausdorff compactification if and only if X is a locally compact, noncompact Hausdorff space. For such spaces the Alexandroff extension is called the one-point compactification or Alexandroff compactification. The advantages of the Alexandroff compactification lie in its simple, often geometrically meaningful structure and the fact that it is in a precise sense minimal among all compactifications; the disadvantage lies in the fact that it only gives a Hausdorff compactification on the class of locally compact, noncompact Hausdorff spaces, unlike the Stone–Čech compactification which exists for any topological space (but provides an embedding exactly for Tychonoff spaces). (Wikipedia).
Andrey Minchenko 4/11/14 Part 1
Title: Central Extensions of Simple Linear Differential Algebraic Groups
From playlist Spring 2014
Andrey Minchenko 4/11/14 Part 2
Title: Central Extensions of Simple Linear Differential Algebraic Groups
From playlist Spring 2014
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This lecture begins with how to construct a gluing tree. Combinatorial bounds and algorithms are proved for gluing results, which
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
Inspired by http://www.youtube.com/watch?v=PQOjkuJtBfM
From playlist Projects & Installations
Ricardo Nochetto: Two-scale FEMs for non-variational elliptic PDEs ...
We show that the finite element method (FEM) is able to approximate non-variational elliptic PDEs provided we add a larger scale ε to the usual meshsize h. We use the ε-scale to compute centered second differences of continuous functions which are piecewise linear at the h-scale, thereby r
From playlist HIM Lectures: Trimester Program "Multiscale Problems"
Andrey Zinovyev - Reduced Google Matrix approach for exploring biological networks
https://indico.math.cnrs.fr/event/3475/attachments/2180/2566/Zinovyev_GoMaxSlides.pdf
From playlist Google matrix: fundamentals, applications and beyond
GCSE Science Revision Biology "Sizes of Cells"
Find my revision workbooks here: https://www.freesciencelessons.co.uk/workbooks In this video, we look at the sizes of cells. We explore the meaning of the words millimetre, micrometre and nanometre and how these relate to cells and the objects within cells. Image credits: Helicobacter
From playlist 9-1 GCSE Biology Paper 1 Cell Biology
FIT2.3.3. Algebraic Extensions
Field Theory: We define an algebraic extension of a field F and show that successive algebraic extensions are also algebraic. This gives a useful criterion for checking algberaic elements. We finish with algebraic closures.
From playlist Abstract Algebra
Animated Mandelbrot transform - linear interpolation
http://code.google.com/p/mandelstir/
From playlist mandelstir
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Mikhail Gromov - 3/4 Old, New and Unknown around Scalar Curvature
Geometry of scalar curvature, that is comparable in scope to symplectic geometry, mediates between two worlds: the domain of rigidity, one sees in convexity and the realm of softness, characteristic of topology, such as the cobordism theory. The aim of this course is threefold: 1. An ove
From playlist Mikhail Gromov - Old, New and Unknown around Scalar Curvature
Russian Multiplication Algorithm Solution - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Isoperimetry and boundaries with almost constant mean curvature - Francesco Maggi
Variational Methods in Geometry Seminar Topic: Isoperimetry and boundaries with almost constant mean curvature Speaker: Francesco Maggi Affiliation: The University of Texas at Austin; Member, School of Mathematics Date: February 12, 2019 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
Russian Multiplication Algorithm - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Alessandro Desantis - Extensions Are Dead, Long Live Extensions! | SolidusConf 2019
Alessandro Desantis takes us through the future of extensions on Solidus. "Extensions Are Dead, Long Live Extensions!" What is the true place of extensions in the Solidus ecosystem and what does their future look like? In this talk, I will walk you through the challenges Solidus extension
From playlist SolidusConf 2019
Terraforming Jupyter: Changing JupyterLab to suit your needs
Terraforming Jupyter: Changing JupyterLab to suit your needs Stephanie Stattel (Bloomberg LP), Paul Ivanov (Bloomberg LP) As the next-generation user interface for Project Jupyter, JupyterLab is at its core an extensible environment. JupyterLab extensions can be created to modify themes,
From playlist JupyterCon in New York 2018
Evolving Chrome Extensions with Manifest V3 - Simeon Vincent - JSConf US 2019
Browser extensions are a defining feature of the web experience, but they're far from perfect. The Chrome team is planning to make a number of changes to improve privacy, security, and performance. In this session we’ll dive into some of the biggest issues with the current platform, where
From playlist JSConf US 2019
Galois theory: Infinite Galois extensions
This lecture is part of an online graduate course on Galois theory. We show how to extend Galois theory to infinite Galois extensions. The main difference is that the Galois group has a topology, and intermediate field extensions now correspond to closed subgroups of the Galois group. We
From playlist Galois theory
Iwasawa invariants for elliptic curves in a family by Sujatha Ramdorai
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
23 Algebraic system isomorphism
Isomorphic algebraic systems are systems in which there is a mapping from one to the other that is a one-to-one correspondence, with all relations and operations preserved in the correspondence.
From playlist Abstract algebra