Theorems in analysis | Inequalities
In mathematical analysis, Agmon's inequalities, named after Shmuel Agmon, consist of two closely related interpolation inequalities between the Lebesgue space and the Sobolev spaces . It is useful in the study of partial differential equations. Let where . Then Agmon's inequalities in 3D state that there exists a constant such that and In 2D, the first inequality still holds, but not the second: let where . Then Agmon's inequality in 2D states that there exists a constant such that For the -dimensional case, choose and such that . Then, if and , the following inequality holds for any (Wikipedia).
Phase separation of oil and water, in a grid model
Following work by Eran Agmon et al.: http://mitpress.mit.edu/sites/default/files/titles/content/alife14/978-0-262-32621-6-ch082.pdf At every grid point there are two numbers, representing the concentration of oil and water respectively. We compute how these numbers should change based on
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Phase separation of oil and water in a grid model
Following work of Eran Agmon at al. in their paper "Quantifying robustness in a spatial model of metabolism-boundary co-construction": http://mitpress.mit.edu/sites/default/files/titles/content/alife14/978-0-262-32621-6-ch082.pdf The details are in a Ready file: Patterns/Agmon2014/oil-wat
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The hidden landscape of localization of eigenfunctions - Svitlana Mayboroda
Analysis Seminar Topic: The hidden landscape of localization of eigenfunctions Speaker: Svitlana Mayboroda Date: Tuesday, March 8 Numerous manifestations of wave localization permeate acoustics, quantum physics, mechanical and energy engineering. It was used in construction of noise a
From playlist Mathematics
Solving and graphing a two step absolute value inequality
๐ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems
From playlist Solve Absolute Value Inequalities
Solving an absolute value inequality by switching the signs
๐ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems
From playlist Solve Absolute Value Inequalities
From PhD to PhD: A Conference Mapping the Network on Lebanese Mathematics - Day 3 - June 3, 2021
โI dislike frontiers, political or intellectual, and I find that ignoring them is an essential catalyst for creative thought. Ideas should flow without hindrance in their natural course.โ Michael Atiyah In the midst of social-political turmoil, financial meltdown, disease induced lockdown,
From playlist From PhD to PhD: A Conference Mapping the Network on Lebanese Mathematics - June 1-3, 2021
Solving an absolute value inequality
๐ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems
From playlist Solve Absolute Value Inequalities
Solving and graphing an absolute value inequality with an or inequality
๐ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems
From playlist Solve Absolute Value Inequalities
Solve and graph an absolute value inequality
๐ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems
From playlist Solve Absolute Value Inequalities
Solve and graph an absolute value inequality
๐ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems
From playlist Solve Absolute Value Inequalities
How to solve and graph an absolute value inequality
๐ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems
From playlist Solve Absolute Value Inequalities
Learn how to solve an graph an absolute value inequality
๐ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems
From playlist Solve Absolute Value Inequalities
Solving and graphing a absolute value inequality with infinite many solutions
๐ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems
From playlist Solve Absolute Value Inequalities
How to Solve Inequalities (NancyPi)
MIT grad explains solving inequalities. This video focuses on solving linear inequalities. It shows when to switch the sign of the inequality, if you divide or multiply by a negative number, and is an introduction to how to solve inequalities in algebra. To skip ahead: 1) For a basic examp
From playlist Algebra
Compound Inequalities 9 Examples including Fractions & Interval Notation
I start by defining Compound Inequalities & explaining the difference between "and" and "or" statements Inequality to Number Line examples at 2:03 7:01 8:44 Number Line to Inequality examples at 11:01 14:19 16:55 These examples include Interval Notation. Solving a Compound Inequality exa
From playlist Algebra 1
Concentration of quantum states from quantum functional (...) - N. Datta - Workshop 2 - CEB T3 2017
Nilanjana Datta / 24.10.17 Concentration of quantum states from quantum functional and transportation cost inequalities Quantum functional inequalities (e.g. the logarithmic Sobolev- and Poincarรฉ inequalities) have found widespread application in the study of the behavior of primitive q
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Radek Adamczak: Functional inequalities and concentration of measure II
Concentration inequalities are one of the basic tools of probability and asymptotic geo- metric analysis, underlying the proofs of limit theorems and existential results in high dimensions. Original arguments leading to concentration estimates were based on isoperimetric inequalities, whic
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
Solving an absolute value inequality using an and compound inequality
๐ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems
From playlist Solve Absolute Value Inequalities
8ECM Invited Lecture: Rupert Frank
From playlist 8ECM Invited Lectures