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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.
Eells and Sampson introduced the harmonic map heat flow and proved the following fundamental properties: Regularity. Any harmonic map heat flow is smooth as a map (a, b) × M → N given by (t, p) ↦ f t (p). Now suppose that M is a closed manifold and (N, h) is geodesically complete. Existence.
In mathematics, noncommutative harmonic analysis is the field in which results from Fourier analysis are extended to topological groups that are not commutative. [1] Since locally compact abelian groups have a well-understood theory, Pontryagin duality, which includes the basic structures of Fourier series and Fourier transforms, the major business of non-commutative harmonic analysis is ...
In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the fundamental frequency of a periodic signal. The fundamental frequency is also called the 1st harmonic ; the other harmonics are known as higher harmonics .
In projective geometry, the harmonic conjugate point of a point on the real projective line with respect to two other points is defined by the following construction: Given three collinear points A, B, C , let L be a point not lying on their join and let any line through C meet LA, LB at M, N respectively.
The aim of the annual FFT is to bring together researchers from academia, government, and industry, as a means to spur innovation and foster interaction in Harmonic Analysis and its Applications. The FFT lasts two days and consists of approximately 15 half-hour talks, a distinguished lecture, a colloquium, and a keynote lecture.
Florida State head coach Mike Norvell is giving back big time. Norvell is contributing $4.5 million of his salary this year to the university in a one-year restructured contract, sources tell ...
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