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In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations.The key observation is that, given a Riemannian metric on M, every cohomology class has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric.
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Download as PDF; Printable version; In other projects ... Pages in category "Harmonic functions" ... out of 26 total.
In mathematics, a number of concepts employ the word harmonic. The similarity of this terminology to that of music is not accidental: the equations of motion of vibrating strings, drums and columns of air are given by formulas involving Laplacians ; the solutions to which are given by eigenvalues corresponding to their modes of vibration.
The New York City Ballet has been performing "The Nutcracker" for decades. Each year, young dancers make their mark on the ballet.
Euler's Tonnetz. The Tonnetz originally appeared in Leonhard Euler's 1739 Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae.Euler's Tonnetz, pictured at left, shows the triadic relationships of the perfect fifth and the major third: at the top of the image is the note F, and to the left underneath is C (a perfect fifth above F), and to the right is A (a ...
Ellen DeGeneres is setting the record straight about the status of her new U.K. home amid severe storms that devastated parts of the U.K.. After reports circulated over the weekend that the former ...
Then Marsh pointed out that all the plagues were still written on a chalkboard behind them after their last session. The Bible study burst into laughter. “Y’all remember.