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In applied mathematics, a discrete Chebyshev transform (DCT) is an analog of the discrete Fourier transform for a function of a real interval, converting in either direction between function values at a set of Chebyshev nodes and coefficients of a function in Chebyshev polynomial basis.
Example of a klm digital I/O expansion card using a large square chip from PLX Technology to handle the PCI bus interface PCI expansion slot Altair 8800b from March 1976 with an 18-slot S-100 backplane which housed both the Intel 8080 mainboard and many expansion boards Rack of IBM Standard Modular System expansion cards in an IBM 1401 computer using a 16-pin gold plated edge connector first ...
The fast multipole method (FMM) is a numerical technique that was developed to speed up the calculation of long-ranged forces in the n-body problem.It does this by expanding the system Green's function using a multipole expansion, which allows one to group sources that lie close together and treat them as if they are a single source.
The equation of a 1-D Gabor wavelet is a Gaussian modulated by a complex exponential, described as follows: [3] = / ()As opposed to other functions commonly used as bases in Fourier Transforms such as and , Gabor wavelets have the property that they are localized, meaning that as the distance from the center increases, the value of the function becomes exponentially suppressed.
The Fourier–Bessel series of a function f(x) with a domain of [0, b] satisfying f(b) = 0. Bessel function for (i) = and (ii) =.: [,] is the representation of that function as a linear combination of many orthogonal versions of the same Bessel function of the first kind J α, where the argument to each version n is differently scaled, according to [1] [2] ():= (,) where u α,n is a root ...
The function was tabulated by Vera Faddeeva and N. N. Terentyev in 1954. [8] It appears as nameless function w(z) in Abramowitz and Stegun (1964), formula 7.1.3. The name Faddeeva function was apparently introduced by G. P. M. Poppe and C. M. J. Wijers in 1990; [9] [better source needed] previously, it was known as Kramp's function (probably after Christian Kramp).
Jimmy Carter dies at 100. 179 people were killed in South Korea in a deadliest place crash of 2024. Trump praises H-1B visas. Putin apologizes to Azerbaijan.
Eigenmode expansion is a linear frequency-domain method. It offers very strong benefits compared with FDTD , FEM and the beam propagation method for the modelling of optical waveguides , [ 3 ] and it is a popular tool for the modelling linear effects in fiber optics and silicon photonics devices.