Manifolds | Differential geometry
In mathematics, and specifically differential geometry, a density is a spatially varying quantity on a differentiable manifold that can be integrated in an intrinsic manner. Abstractly, a density is a section of a certain line bundle, called the density bundle. An element of the density bundle at x is a function that assigns a volume for the parallelotope spanned by the n given tangent vectors at x. From the operational point of view, a density is a collection of functions on coordinate charts which become multiplied by the absolute value of the Jacobian determinant in the change of coordinates. Densities can be generalized into s-densities, whose coordinate representations become multiplied by the s-th power of the absolute value of the jacobian determinant. On an oriented manifold, 1-densities can be canonically identified with the n-forms on M. On non-orientable manifolds this identification cannot be made, since the density bundle is the tensor product of the orientation bundle of M and the n-th exterior product bundle of T∗M (see pseudotensor). (Wikipedia).
Physical Science 3.4b - Density
Density. The definition of density, the equation for density, and some numerical examples.
From playlist Physical Science Chapter 3 (Complete chapter)
Keep going! Check out the next lesson and practice what you’re learning: https://www.khanacademy.org/math/geometry/hs-geo-solids/hs-geo-density/e/surface-and-volume-density-word-problems Volume density is the amount of a quantity (often mass) per unit of volume. Density=Quantity/Volume
From playlist High School Geometry | High School Math | Khan Academy
From playlist h. Three-Dimensional Measurement
Physics - Ch 33A Test Your Knowledge: Fluid Statics (18 of 36) Floating Hollow Sphere
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the density=? of the hollow sphere floating half way in a liquid of density=0.89g/cm^3. To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 Next video in this
From playlist PHYSICS 33A TEST YOUR KNOWLEDGE: FLUID STATICS
A Visual Example Of MASS Density!! #Chemistry #Physics #Engineering #Density #NicholasGKK #Shorts
From playlist Heat and Chemistry
In this video, the Flipping Physics team discusses the concept of mass and density by comparing the mass and density of steel and wood. The team first addresses the misconception that steel is always more massive than wood, explaining that the mass of an object cannot be determined without
From playlist Fluids
What is Density? | Gravitation | Physics | Don't Memorise
Understanding the concept of Density is very important in order to understand Physics. Watch this video to fully grasp the idea of density. To get access to the entire course based on Gravitation, enroll here: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&u
From playlist Physics
Rod Gover - An introduction to conformal geometry and tractor calculus (Part 1)
After recalling some features (and the value of) the invariant « Ricci calculus » of pseudo‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
Learn how to determine the volume of a sphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
Alberto Cattaneo: An introduction to the BV-BFV Formalism
Abstract: The BV-BFV formalism unifies the BV formalism (which deals with the problem of fixing the gauge of field theories on closed manifolds) with the BFV formalism (which yields a cohomological resolution of the reduced phase space of a classical field theory). I will explain how this
From playlist Topology
From playlist Plenary talks One World Symposium 2020
Davorin Lešnik (9/9/20) Sampling smooth manifolds using ellipsoids
Title: Sampling smooth manifolds using ellipsoids Abstract: A common problem in data science is to determine properties of a space from a sample. For instance, under certain assumptions a subspace of a Euclidean space may be homotopy equivalent to the union of balls around sample points,
From playlist AATRN 2020
Ximena Fernández - Intrinsic persistent homology via density-based metric learning
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Ximena Fernández, Swansea University Title: Intrinsic persistent homology via density-based metric learning Abstract: Typically, persistence diagrams computed from a sample depend strongly on the distance associated to th
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
Singular Learning Theory - Seminar 5 - Introduction to density of states
This seminar series is an introduction to Watanabe's Singular Learning Theory, a theory about algebraic geometry and statistical learning theory. In this seminar Dan Murfet talks about density of states, which is a concept from physics that plays an important role in Watanabe's work. The
From playlist Singular Learning Theory
Benjamin Stamm - Acceleration of quantum mechanical systems by exploiting similarity - IPAM at UCLA
Recorded 05 May 2022. Benjamin Stamm of RWTH Aachen University presents "Acceleration of quantum mechanical systems by exploiting similarity" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Abstract: In this talk, we will present two examples of exploiting
From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics
Yoshua Bengio: "Representation Learning and Deep Learning, Pt. 3"
Graduate Summer School 2012: Deep Learning, Feature Learning "Representation Learning and Deep Learning, Pt. 3" Yoshua Bengio, University of Montreal Institute for Pure and Applied Mathematics, UCLA July 17, 2012 For more information: https://www.ipam.ucla.edu/programs/summer-schools/gr
From playlist GSS2012: Deep Learning, Feature Learning
Mokshay Madiman : Minicourse on information-theoretic geometry of metric measure
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 28, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician
From playlist Geometry
Another practice problem dealing with the volume of a sphere
From playlist Middle School - Worked Examples
Rod Gover - Geometric Compactification, Cartan holonomy, and asymptotics
Conformal compactification has long been recognised as an effective geometric framework for relating conformal geometry, and associated field theories « at infinity », to the asymptotic phenomena of an interior (pseudo‐)‐Riemannian geometry of one higher dimension. It provides an effective
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale