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2. Hodge theory - Wikipedia

   en.wikipedia.org/wiki/Hodge_theory

   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.

3. Harmonic generation - Wikipedia

   en.wikipedia.org/wiki/Harmonic_generation

   N-th harmonic generation. Harmonic generation (HG, also called multiple harmonic generation) is a nonlinear optical process in which photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with times the energy of the initial photons (equivalently, times the frequency and the wavelength divided by ).

4. AOL

   search.aol.com

   The search engine that helps you find exactly what you're looking for. Find the most relevant information, video, images, and answers from all across the Web.

5. Optical autocorrelation - Wikipedia

   en.wikipedia.org/wiki/Optical_autocorrelation

   Classification of the different kinds of optical autocorrelation. In optics, various autocorrelation functions can be experimentally realized. The field autocorrelation may be used to calculate the spectrum of a source of light, while the intensity autocorrelation and the interferometric autocorrelation are commonly used to estimate the duration of ultrashort pulses produced by modelocked lasers.

6. Biharmonic equation - Wikipedia

   en.wikipedia.org/wiki/Biharmonic_equation

   Just as harmonic functions in 2 variables are closely related to complex analytic functions, so are biharmonic functions in 2 variables. The general form of a biharmonic function in 2 variables can also be written as Im ⁡ ( z ¯ f ( z ) + g ( z ) ) {\displaystyle \operatorname {Im} ({\bar {z}}f(z)+g(z))} where f ( z ) {\displaystyle f(z)} and ...

7. Projective harmonic conjugate - Wikipedia

   en.wikipedia.org/wiki/Projective_harmonic_conjugate

   Four ordered points on a projective range are called harmonic points when there is a tetrastigm in the plane such that the first and third are codots and the other two points are on the connectors of the third codot. [6] If p is a point not on a straight with harmonic points, the joins of p with the points are harmonic straights.

8. Optical parametric oscillator - Wikipedia

   en.wikipedia.org/wiki/Optical_parametric_oscillator

   A special case is the degenerate OPO, when the output frequency is one-half the pump frequency, = = /, which can result in half-harmonic generation when signal and idler have the same polarization. The first optical parametric oscillator was demonstrated by Joseph A. Giordmaine and Robert C. Miller in 1965, [ 2 ] five years after the invention ...

9. Desmos - Wikipedia

   en.wikipedia.org/wiki/Desmos

   In it, geometrical shapes can be made, as well as expressions from the normal graphing calculator, with extra features. [8] In September 2023, Desmos released a beta for a 3D calculator, which added features on top of the 2D calculator, including cross products, partial derivatives and double-variable parametric equations.