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With the aid of these rules the UV absorption maximum can be predicted, for example in these two compounds: [8] In the compound on the left, the base value is 214 nm (a heteroannular diene). This diene group has 4 alkyl substituents (labeled 1,2,3,4) and the double bond in one ring is exocyclic to the other (adding 5 nm for an exocyclic double ...
The Lagrange multiplier theorem states that at any local maximum (or minimum) of the function evaluated under the equality constraints, if constraint qualification applies (explained below), then the gradient of the function (at that point) can be expressed as a linear combination of the gradients of the constraints (at that point), with the ...
is the line broadening at half the maximum intensity , after subtracting the instrumental line broadening, in radians. This quantity is also sometimes denoted as Δ ( 2 θ ) {\displaystyle \Delta \left(2\theta \right)} ;
Full width at half maximum. In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the y-axis which are half the maximum ...
The wavelengths chosen are usually the wavelengths of maximum absorption (absorbance maxima) for the individual species. None of the wavelengths may be an isosbestic point for a pair of species. The set of the following simultaneous equations can be solved to find the concentrations of each absorbing species: {() = = (), …
The primary application of the Levenberg–Marquardt algorithm is in the least-squares curve fitting problem: given a set of empirical pairs (,) of independent and dependent variables, find the parameters of the model curve (,) so that the sum of the squares of the deviations () is minimized:
The plasma parameter is a dimensionless number, denoted by capital Lambda, Λ.The plasma parameter is usually interpreted to be the argument of the Coulomb logarithm, which is the ratio of the maximum impact parameter to the classical distance of closest approach in Coulomb scattering.
In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories.