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The Koutecký–Levich equation models the measured electric current at an electrode from an electrochemical reaction in relation to the kinetic activity and the mass transport of reactants. A visualization of the Koutecký–Levich equation. The graph shows the measured current as a function of the mass transport current for given kinetic current.
In mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence [1]), denoted (), is a type of statistical distance: a measure of how much a model probability distribution Q is different from a true probability distribution P.
The Levich equation is written as: = where I L is the Levich current (A), n is the number of moles of electrons transferred in the half reaction (number), F is the Faraday constant (C/mol), A is the electrode area (cm 2), D is the diffusion coefficient (see Fick's law of diffusion) (cm 2 /s), ω is the angular rotation rate of the electrode (rad/s), ν is the kinematic viscosity (cm 2 /s), C ...
Add-in to convert formulas into equations. Works offline and can also request 100% LaTaX from the online CodeCogs servers. Collabora Office Math [1] Yes Yes No No Yes No Yes No Online and Windows, Linux, Mac Tool to create formulae that can be embedded inside other suite documents png, jpg, pdf, html, xml, OLE.
where is the Kullback–Leibler divergence, and is the outer product distribution which assigns probability () to each (,).. Notice, as per property of the Kullback–Leibler divergence, that (;) is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when and are independent (and hence observing tells you nothing about ).
Note that the expression of Pinsker inequality depends on what basis of logarithm is used in the definition of KL-divergence. D K L {\displaystyle D_{KL}} is defined using ln {\displaystyle \ln } (logarithm in base e {\displaystyle e} ), whereas D {\displaystyle D} is typically defined with log 2 {\displaystyle \log _{2}} (logarithm in base 2).
The B can be defined as: [2] = where n is the number of moles of electrons transferred in the half reaction (number) F is the Faraday constant (C/mol) A is the electrode area (cm 2) D is the diffusion coefficient (see Fick's law of diffusion) (cm 2 /s)
The covariance function K X satisfies the definition of a Mercer kernel. By Mercer's theorem, there consequently exists a set λ k, e k (t) of eigenvalues and eigenfunctions of T K X forming an orthonormal basis of L 2 ([a,b]), and K X can be expressed as