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For common optical glasses, the refractive index calculated with the three-term Sellmeier equation deviates from the actual refractive index by less than 5×10 −6 over the wavelengths' range [5] of 365 nm to 2.3 μm, which is of the order of the homogeneity of a glass sample. [6]
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
A closely related yet independent quantity is the group-delay dispersion (GDD), defined such that group-velocity dispersion is the group-delay dispersion per unit length. GDD is commonly used as a parameter in characterizing layered mirrors, where the group-velocity dispersion is not particularly well-defined, yet the chirp induced after ...
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. [1] The variable denoting time is usually written as t {\displaystyle t} .
Given the dispersion relation, one can calculate the frequency-dependent phase velocity and group velocity of each sinusoidal component of a wave in the medium, as a function of frequency. In addition to the geometry-dependent and material-dependent dispersion relations, the overarching Kramers–Kronig relations describe the frequency ...
As another example, consider a distribution in which 6/10 of the time returns a standard normal distribution, and 4/10 of the time returns exactly the value 3.5 (i.e. a partly continuous, partly discrete mixture distribution). The density function of this distribution can be written as
The function must be discretized spatially with a central difference scheme. This is an explicit method which means that, u i n + 1 {\displaystyle u_{i}^{n+1}} can be explicitly computed (no need of solving a system of algebraic equations) if values of u {\displaystyle u} at previous time level ( n ) {\displaystyle (n)} are known.
In the univariate case, a real-valued random variable belongs to the additive exponential dispersion model with canonical parameter and index parameter , (,), if its probability density function can be written as