Polynomials | Stability theory
In the context of the characteristic polynomial of a differential equation or difference equation, a polynomial is said to be stable if either: * all its roots lie in the open left half-plane, or * all its roots lie in the open unit disk. The first condition provides stability for continuous-time linear systems, and the second case relates to stabilityof discrete-time linear systems. A polynomial with the first property is called at times a Hurwitz polynomial and with the second property a Schur polynomial. Stable polynomials arise in control theory and in mathematical theoryof differential and difference equations. A linear, time-invariant system (see LTI system theory) is said to be BIBO stable if every bounded input produces bounded output. A linear system is BIBO stable if its characteristic polynomial is stable. The denominator is required to be Hurwitz stable if the system is in continuous-time and Schur stable if it is in discrete-time. In practice, stability is determined by applying any one of several stability criteria. (Wikipedia).
Determining if a equation is a polynomial or not
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
Is it a polynomial with two variables
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
Classify a polynomial then determining if it is a polynomial or not
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
Learn how to identify if a function is a polynomial and identify the degree and LC
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
C07 Homogeneous linear differential equations with constant coefficients
An explanation of the method that will be used to solve for higher-order, linear, homogeneous ODE's with constant coefficients. Using the auxiliary equation and its roots.
From playlist Differential Equations
Determining if a function is a polynomial or not then determine degree and LC
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
Differential Equations | Homogeneous linear equations with constant coefficients
We introduce the strategy used for solving homogeneous linear differential equations with constant coefficients.
From playlist Linear Differential Equations
Learn how to write a polynomial in standard form and classify
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
How to reorder and classify a polynomial based on it's degree and number of terms
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Log-concavity, matroids and expanders - Cynthia Vinzant
Members' Seminar Topic: Log-concavity, matroids and expanders Speaker: Cynthia Vinzant Affiliation: North Carolina State University; von Neumann Fellow, School of Mathematics Date: October 19, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Amir Ali Ahmadi, Princeton University
January 31, Amir Ali Ahmadi, Princeton University Two Problems at the Interface of Optimization and Dynamical Systems We propose and/or analyze semidefinite programming-based algorithms for two problems at the interface of optimization and dynamical systems: In part (i), we study the po
From playlist Spring 2020 Kolchin Seminar in Differential Algebra
Shaoshi Chen, Chinese Academy of Sciences
May 3, Shaoshi Chen, Chinese Academy of Sciences Stability Problems in Symbolic Integration
From playlist Spring 2022 Online Kolchin seminar in Differential Algebra
Elise Goujard: Volumes of odd strata of quadratic differentials
CONFERENCE Recording during the thematic meeting : "Combinatorics, Dynamics and Geometry on Moduli Spaces" the September 20, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwid
From playlist Combinatorics
Kac polynomials and Lie algebras associated to quivers and curves – Olivier Schiffmann – ICM2018
Lie Theory and Generalizations Invited Lecture 7.1 Kac polynomials and Lie algebras associated to quivers and curves Olivier Schiffmann Abstract: We provide an explicit formula for the following enumerative problem: how many (absolutely) indecomposable vector bundles of a given rank r an
From playlist Lie Theory and Generalizations
Log-concave polynomials in theory and applications - Cynthia Vinzant
Computer Science/Discrete Mathematics Seminar II Topic: Log-concave polynomials in theory and applications Speaker: Cynthia Vinzant Affiliation: Member, School of Mathematics Date: January 26, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
The solution of the Kadison-Singer problem - Daniel Spielman
Daniel Spielman Yale University November 5, 2014 We will explain our recent solution of the Kadison-Singer Problem and the equivalent Bourgain-Tzafriri and Paving Conjectures. We will begin by introducing the method of interlacing families of polynomials and use of barrier function argume
From playlist Mathematics
A solution to Weaver's KS2KS2 - Adam Marcus
A solution to Weaver's KS2KS2Primary tabs Adam Marcus Yale University December 2, 2013 We will outline the proof that gives a positive solution of to Weaver's conjecture KS2KS2. That is, we will show that any isotropic collection of vectors whose outer products sum to twice the identity ca
From playlist Mathematics
CONFERENCE Recording during the thematic meeting : « ALEA Days» the March 16, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathemat
From playlist Mathematical Aspects of Computer Science
Classifying a polynomial based on its degree and number of terms
👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1
From playlist Classify Polynomials | Equations
Spectrahedral lifts of convex sets – Rekha Thomas – ICM2018
Control Theory and Optimization Invited Lecture 16.6 Spectrahedral lifts of convex sets Rekha Thomas Abstract: Efficient representations of convex sets are of crucial importance for many algorithms that work with them. It is well-known that sometimes, a complicated convex set can be expr
From playlist Control Theory and Optimization