[2111.07719] Eigenvalue ratios for vibrating String equations with concave densities
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2026-07-25 09:43:02
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划选高亮2026-07-25 13:04:02
原文高亮摘录
“arXivLabs: experimental projects with community collaborators”
Whisper 随想笔记
Wish more platforms did this, collaborative experiments are the future.
划选高亮2026-07-25 12:55:02
原文高亮摘录
“arXivLabs: experimental projects with community collaborators”
Whisper 随想笔记
So this is where they test the wild ideas before they go mainstream?
划选高亮2026-07-25 10:01:02
原文高亮摘录
“optimal lower bound $\frac{\lambda_n}{\lambda_m}\geq(\frac{n}{m})^2$ of vibrating string”
Whisper 随想笔记
Huang's method again—that trick with zeros of eigenfunctions is really neat.
划选高亮2026-07-25 09:52:02
原文高亮摘录
“optimal lower bound $\frac{\lambda_n}{\lambda_m}\geq(\frac{n}{m})^2$ of vibrating string”
Whisper 随想笔记
I've seen this ratio before for constant density, but concave makes it way more interesting.
划选高亮2026-07-25 09:43:02
原文高亮摘录
“optimal lower bound $\frac{\lambda_n}{\lambda_m}\geq(\frac{n}{m})^2$ of vibrating string”
Whisper 随想笔记
So the bound is optimal only when the density is concave—that's a pretty strong condition.
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