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Mathematically, the derivatives of the Gaussian function can be represented using Hermite functions. For unit variance, the n-th derivative of the Gaussian is the Gaussian function itself multiplied by the n-th Hermite polynomial, up to scale. Consequently, Gaussian functions are also associated with the vacuum state in quantum field theory.
RMS, RMS or rms) of a set of numbers is the square root of the set's mean square. [1] Given a set , its RMS is denoted as either or . The RMS is also known as the quadratic mean (denoted ), [2] [3] a special case of the generalized mean.
The MSM package in R has a function, rtnorm, that calculates draws from a truncated normal. The truncnorm package in R also has functions to draw from a truncated normal. Chopin (2011) proposed ( arXiv ) an algorithm inspired from the Ziggurat algorithm of Marsaglia and Tsang (1984, 2000), which is usually considered as the fastest Gaussian ...
In bioinformatics, the root mean square deviation of atomic positions is the measure of the average distance between the atoms of superimposed proteins. In structure based drug design , the RMSD is a measure of the difference between a crystal conformation of the ligand conformation and a docking prediction.
A modulated wave resulting from adding two sine waves of identical amplitude and nearly identical wavelength and frequency. A common situation resulting in an envelope function in both space x and time t is the superposition of two waves of almost the same wavelength and frequency: [2]
where ′ is the irradiance at the center of the pattern, represents the radial distance from the center of the pattern, and is the Gaussian RMS width (in one dimension). If we equate the peak amplitude of the Airy pattern and Gaussian profile, that is, I 0 ′ = I 0 , {\displaystyle I'_{0}=I_{0},} and find the value of ω 0 {\textstyle \omega ...
The distribution is a special case of the folded normal distribution with μ = 0.; It also coincides with a zero-mean normal distribution truncated from below at zero (see truncated normal distribution)
Half width at half maximum (HWHM) is half of the FWHM if the function is symmetric. The term full duration at half maximum (FDHM) is preferred when the independent variable is time . FWHM is applied to such phenomena as the duration of pulse waveforms and the spectral width of sources used for optical communications and the resolution of ...