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In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration ...
The analytical solution of SV-wave in a half-space indicates that the plane SV wave reflects back to the domain as a P and SV waves, leaving out special cases. The angle of the reflected SV wave is identical to the incidence wave, while the angle of the reflected P wave is greater than the SV wave.
Bessel functions describe the radial part of vibrations of a circular membrane.. Bessel functions, first defined by the mathematician Daniel Bernoulli [1] [failed verification] and then generalized by Friedrich Bessel, [citation needed] are canonical solutions y(x) of Bessel's differential equation + + = for an arbitrary complex number, which represents the order of the Bessel function.
There have been efforts to put a select subset of Wikipedia's articles into printed book form. [246] [W 108] Since 2009, tens of thousands of print-on-demand books that reproduced English, German, Russian, and French Wikipedia articles have been produced by the American company Books LLC and by three Mauritian subsidiaries of the German ...
The P versus NP problem, which remains open to this day, is also important for discrete mathematics, since its solution would potentially impact a large number of computationally difficult problems. [45] Discrete mathematics includes: [14] Combinatorics, the art of enumerating mathematical objects that satisfy some given constraints.
Maxwell's equations may be combined to demonstrate how fluctuations in electromagnetic fields (waves) propagate at a constant speed in vacuum, c (299 792 458 m/s [2]). Known as electromagnetic radiation, these waves occur at various wavelengths to produce a spectrum of radiation from radio waves to gamma rays.
The best-known exact solutions, and also those most interesting from a physics point of view, are the Schwarzschild solution, the Reissner–Nordström solution and the Kerr metric, each corresponding to a certain type of black hole in an otherwise empty universe, [56] and the Friedmann–Lemaître–Robertson–Walker and de Sitter universes ...
High and low tide in the Bay of Fundy. The theory of tides is the application of continuum mechanics to interpret and predict the tidal deformations of planetary and satellite bodies and their atmospheres and oceans (especially Earth's oceans) under the gravitational loading of another astronomical body or bodies (especially the Moon and Sun).