Commutative algebra | Ideals (ring theory)
In mathematics, a system of parameters for a local Noetherian ring of Krull dimension d with maximal ideal m is a set of elements x1, ..., xd that satisfies any of the following equivalent conditions: 1. * m is a minimal prime over (x1, ..., xd). 2. * The radical of (x1, ..., xd) is m. 3. * Some power of m is contained in (x1, ..., xd). 4. * (x1, ..., xd) is m-primary. Every local Noetherian ring admits a system of parameters. It is not possible for fewer than d elements to generate an ideal whose radical is m because then the dimension of R would be less than d. If M is a k-dimensional module over a local ring, then x1, ..., xk is a system of parameters for M if the length of M / (x1, ..., xk). (Wikipedia).
Analyze the characteristics of multiple functions
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
Determine the domain, range and if a relation is a function
๐ Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Determine if the equation represents a function
๐ Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
Using the vertical line test to determine if a graph is a function or not
๐ Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
Structural Identifiability of Rational ODE Models in Biological Systems: a real-world application of differential algebra
From playlist Spring 2019 Kolchin Seminar
Parameter identifiability through canonical bases In joint work with Alexey Ovchnnikov, Anand Pillay, and Gleb Pogudin we study the problem of whether and how parameters in input-output equations may be recovered from experiments. Specifically, we relate the problem to a problem in the mo
From playlist DART X
Olivier Le Maรฎtre: Global Sensitivity Analysis in Stochastic Systems
Abstract: In this talk we first quickly present a classical and simple model used to describe flow in porous media (based on Darcy's Law). The high heterogeneity of the media and the lack of data are taken into account by the use of random permability fields. We then present some mathemati
From playlist Probability and Statistics
Working with Parameter Uncertainty | Robust Control, Part 4
Watch the first videos in this series: Robust Control, Part 1: What Is Robust Control? - https://youtu.be/A7wHSr6GRnc Robust Control, Part 2: Understanding Disk Margin - https://youtu.be/XazdN6eZF80 Robust Control, Part 3: Disk Margins for MIMO Systems - https://youtu.be/sac_IYBjcq0 The
From playlist Robust Control
Overview of various methods for sensitivity analysis in the UQ of subsurface systems
From playlist Uncertainty Quantification
Sloppiness and Parameter Identifiability, Information Geometry by Mark Transtrum
26 December 2016 to 07 January 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore Information theory and computational complexity have emerged as central concepts in the study of biological and physical systems, in both the classical and quantum realm. The low-energy landscape of classical
From playlist US-India Advanced Studies Institute: Classical and Quantum Information
Wolfram SystemModeler and Mathematica Quick Start
Speaker: Anneli Mossberg This talk focuses on analyzing models and simulation results with Mathematica. Learn about the link between Mathematica and SystemModeler, and get an overview of the powerful Mathematica functionality relevant to modeling and analysis. For more training resource
From playlist Wolfram SystemModeler Virtual Conference 2014
Dynamical model selection and estimation near the (...) - J. Ralph - Workshop 2 - CEB T2 2018
Jason Ralph (Univ. Liverpool) / 06.06.2018 Dynamical model selection and estimation near the quantum-classical boundary Joint work with Marko Toros, Simon Maskell, Kurt Jacobs and Hendrik Ulbricht. We discuss a general method of model selection from experimentally recorded time-trace dat
From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments
Dynamic Eigen Decomposition I: Parameter Variation in System Dynamics
Video 1 in a series about dynamic eigen decomposition (DED) theory and applications. Here we cover basic theoretical aspects of the DED as applied to a 2 degree of freedom mechanical oscillator with parameter variation. The surprising fact we uncover is that dynamic eigenvectors are preser
From playlist Summer of Math Exposition Youtube Videos
What are the important things to know about the graph of a function
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
Seminar on Applied Geometry and Algebra (SIAM SAGA): Jonathan Hauenstein
Title: Some applications of homotopy continuation in science and engineering Date: Tuesday, November 16 at 11:00am Eastern Speaker: Jonathan Hauenstein, University of Notre Dame Abstract: Homotopy continuation is a foundational computational approach in numerical algebraic geometry which
From playlist Seminar on Applied Geometry and Algebra (SIAM SAGA)