Differential operators | Partial differential equations | Multivariable calculus
The factorization of a linear partial differential operator (LPDO) is an important issue in the theory of integrability, due to the Laplace-Darboux transformations, which allow construction of integrable LPDEs. Laplace solved the factorization problem for a bivariate hyperbolic operator of the second order (see Hyperbolic partial differential equation), constructing two Laplace invariants. Each Laplace invariant is an explicit polynomial condition of factorization; coefficients of this polynomial are explicit functions of the coefficients of the initial LPDO. The polynomial conditions of factorization are called invariants because they have the same form for equivalent (i.e. self-adjoint) operators. Beals-Kartashova-factorization (also called BK-factorization) is a constructive procedure to factorize a bivariate operator of the arbitrary order and arbitrary form. Correspondingly, the factorization conditions in this case also have polynomial form, are invariants and coincide with Laplace invariants for bivariate hyperbolic operators of the second order. The factorization procedure is purely algebraic, the number of possible factorizations depending on the number of simple roots of the Characteristic polynomial (also called symbol) of the initial LPDO and reduced LPDOs appearing at each factorization step. Below the factorization procedure is described for a bivariate operator of arbitrary form, of order 2 and 3. Explicit factorization formulas for an operator of the order can be found in General invariants are defined in and invariant formulation of the Beals-Kartashova factorization is given in (Wikipedia).
Is d⁴x really Lorentz Invariant? | Physics Riddle
The integral measure d4x is Lorentz invariant. The easiest way to see this, is to consider a Lorentz transformation Lambda, under which x goes to Lambda times x. Under a coordinate transformation, the integration measure d4x picks up the Jacobian, the determinant of the transformation matr
From playlist Special Relativity, General Relativity
Lorentz Covariance VS Lorentz Invariance: What's the Difference? | Special Relativity
In special relativity, Lorentz covariance and Lorentz invariance are two very important concepts. But what exactly are these concepts? In this video, we will find out! Contents: 00:00 Definitions 00:51 Examples If you want to help us get rid of ads on YouTube, you can support us on Patr
From playlist Special Relativity, General Relativity
Ex 2: Derivatives of Inverse Trig Functions
This video provides two examples of how to find the derivative of an inverse trigonometric function. One example does not require the chain rule and one example requires the chain rule. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Differentiation of Inverse Trigonometric Functions
Calculus 3.03f - Derivative Example 6
Another of example of finding a derivative using the definition of the derivative.
From playlist Calculus Ch 3 - Derivatives
Math 030 Calculus I 031315: Inverse Functions and Differentiation
Inverse functions. Examples of determining the inverse. Relation between the graphs of a function and its inverse. One-to-one functions. Restricting the domain of a function so that it is invertible. Differentiability of inverse functions; relation between derivatives of function and
From playlist Course 2: Calculus I
Heuristics for lambda Invariants - Sonal Jain
Sonal Jain New York University February 17, 2011 The λλ-invariant is an invariant of an imaginary quadratic field that measures the growth of class numbers in cyclotomic towers over the field. It also measures the number of zeroes of an associated pp-adic L-function. In this talk, I will d
From playlist Mathematics
An introduction to Invariant Theory - Harm Derksen
Optimization, Complexity and Invariant Theory Topic: An introduction to Invariant Theory Speaker: Harm Derksen Affiliation: University of Michigan Date: June 4, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Ex 1: Find the Inverse of a Function
This video provides two examples of how to determine the inverse function of a one-to-one function. A graph is used to verify the inverse function was found correctly. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com
From playlist Determining Inverse Functions
Lecture: Numerical Differentiation Methods
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From playlist Beginning Scientific Computing
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 3/4
We motivate, define and study Donaldson-Thomas invariants and Cohomological Hall algebras associated to quivers, relate them to the geometry of moduli spaces of quiver representations and (in special cases) to Gromov-Witten invariants, and discuss the algebraic structure of Cohomological H
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Beyond Eigenspaces: Real Invariant Planes
Linear Algebra: In the context of real vector spaces, one often needs to work with complex eigenvalues. Let A be a real nxn matrix A. We show that, in R^n, there exists at least one of: an (nonzero) eigenvector for A, or a 2-dimensional subspace (plane) invariant under A.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Stefaan Vaes: "Outer actions of amenable groups on von Neumann algebras"
Actions of Tensor Categories on C*-algebras 2021 Mini Course: "Outer actions of amenable groups on von Neumann algebras" Stefaan Vaes - KU Leuven Abstract: I will give a survey lecture on the classification of outer actions of amenable groups on von Neumann algebras with the main focus b
From playlist Actions of Tensor Categories on C*-algebras 2021
GPDE Workshop - Alexakis' theorem on conformally invariant integrals - Charles Fefferman
Charles Fefferman Princeton University February 25, 2009 For more videos, visit http://video.ias.edu
From playlist Mathematics
Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group
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From playlist Lie Groups and Lie Algebras
Lie Groups and Lie Algebras: Lesson 38 - Preparation for the concept of a Universal Covering Group
Lie Groups and Lie Algebras: Lesson 38 - Preparation for the Universal Covering Group concept In this lesson we examine another amazing connection between the algebraic properties of the Lie groups with topological properties. We will lay the foundation to understand how discrete invaria
From playlist Lie Groups and Lie Algebras
Lecture 6, Systems Represented by Differential Equations | MIT RES.6.007 Signals and Systems
Lecture 6, Systems Represented by Differential Equations Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES-6.007S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT RES.6.007 Signals and Systems, 1987
R - Multigroup Confirmatory Factor Analysis Lecture
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From playlist Structural Equation Modeling
17. Five more problems (numbers 30-34)
I was on a bit of a roll today but although I did the first three questions very quickly, it wasn't 100% satisfying because for the first one I couldn't see what it had to do with invariants, and for the second and third I relied on happening to have the right piece of knowledge, though th
From playlist Thinking about maths problems in real time: mostly invariants problems
Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum), Lecture 5
Quiver moduli spaces are algebraic varieties encoding the continuous parameters of linear algebra type classification problems. In recent years their topological and geometric properties have been explored, and applications to, among others, Donaldson-Thomas and Gromov-Witten theory have
From playlist Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum)
Determine Derivative Function Values Using a Free Online Calculator (MathAS)
This video explains how to determine derivative function values using a free online graphing calculator. https://dlippman.imathas.com/graphcalc/graphcalc.html
From playlist Introduction and Formal Definition of the Derivative