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e. In mathematics, a Cauchy (French: [koʃi]) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so as to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative ...
In mathematics, change of base can mean any of several things: Changing numeral bases, such as converting from base 2 (binary) to base 10 (decimal). This is known as base conversion. The logarithmic change-of-base formula, one of the logarithmic identities used frequently in algebra and calculus. The method for changing between polynomial and ...
where E is the expected value operator. Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the two variables. If Y always takes on the same values as X, we have the covariance of a variable with itself (i.e. ), which is called the variance and is more commonly denoted as the square of the ...
In mathematics, a codomain or set of destination of a function is a set into which all of the output of the function is constrained to fall. It is the set Y in the notation f: X → Y. The term range is sometimes ambiguously used to refer to either the codomain or the image of a function. A codomain is part of a function f if f is defined as a ...
Conjugate variables. Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, [1][2] or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation—in physics called the Heisenberg uncertainty principle —between them.
If there was a family tree of pastry, pies and tarts (much like pies versus cobblers) would be on the same delicious branch. Both start out with a bottom layer crust and then are topped with ...
In telecommunications, maximum-ratio combining (MRC) is a method of diversity combining in which: the signals from each channel are added together, the gain of each channel is made proportional to the rms signal level and inversely proportional to the mean square noise level in that channel. different proportionality constants are used for each ...
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