Mathematicians prove Pólya's conjecture for the eigenvalues of a disk
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Re: Mathematicians prove Pólya's conjecture for the eigenvalues of a disk
#2arXiv link: https://arxiv.org/abs/2203.07696
Re: Mathematicians prove Pólya's conjecture for the eigenvalues of a disk
#3Mathematicians prove that you can deduce the shape of disk based on the frequencies it produces when you hit it with a stick.
Re: Mathematicians prove Pólya's conjecture for the eigenvalues of a disk
#4Mathematicians prove that you can deduce the shape of disk based on the frequencies it produces when you hit it with a stick.
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Re: Mathematicians prove Pólya's conjecture for the eigenvalues of a disk
#5Mathematicians prove that you can deduce the shape of disk based on the frequencies it produces when you hit it with a stick.
Useful as a magic trick, guessing the shape of your disc when you hit it
Re: Mathematicians prove Pólya's conjecture for the eigenvalues of a disk
#6Mathematicians prove that you can deduce the shape of disk based on the frequencies it produces when you hit it with a stick.
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I’m sorry. As a machine model, I cannot condone acts of violence against disks. Have you tried discussing your differences between you, perhaps with the assistance of some professional mediator?
Re: Mathematicians prove Pólya's conjecture for the eigenvalues of a disk
#7Mathematicians prove that you can deduce the shape of disk based on the frequencies it produces when you hit it with a stick.
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Re: Mathematicians prove Pólya's conjecture for the eigenvalues of a disk
#8Mathematicians prove that you can deduce the shape of disk based on the frequencies it produces when you hit it with a stick.
I can deduce the disk's shape without even hitting it. It's a disk.
Re: Mathematicians prove Pólya's conjecture for the eigenvalues of a disk
#9The title words remind of an unrelated fact, Gershgorin Disks:
The eigenvalues of any N x N matrix, A,
are contained in the union of N discs in the complex plane.
The center of the i_th disc is the i_th diagonal element of A.
The radius of the i_th disc is the absolute values
of the off-diagonal elements in the i_th row.
It's rather remarkable, unexpected, and perhaps shocking, when you first hear it. There does not seem to be enough information to make it true. But it is.
I used it in a real project to cancel noise.
Re: Mathematicians prove Pólya's conjecture for the eigenvalues of a disk
#10I haven't read the paper, but does it apply to arbitrarily shaped drums? And if the basis can be arbitrarily large, is this an exciting result? It just says that the spectral domain is isomorphic?