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Calculus. The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. [a] Functionals are often expressed as definite integrals involving ...
In mathematical analysis, p-variation is a collection of seminorms on functions from an ordered set to a metric space, indexed by a real number . p -variation is a measure of the regularity or smoothness of a function. Specifically, if , where is a metric space and I a totally ordered set, its p -variation is. where D ranges over all finite ...
Reserves and resource reporting. An oil or gas resource refers to known (discovered fields) or potential accumulations of oil and/or gas (i.e undiscovered prospects and leads) in the subsurface of the Earth's crust. All reserve and resource estimates involve uncertainty in volume estimates (expressed below as Low, Mid or High uncertainty), as ...
Therefore, a naïve algorithm to calculate the estimated variance is given by the following: Let n ← 0, Sum ← 0, SumSq ← 0. For each datum x: n ← n + 1. Sum ← Sum + x. SumSq ← SumSq + x × x. Var = (SumSq − (Sum × Sum) / n) / (n − 1) This algorithm can easily be adapted to compute the variance of a finite population: simply ...
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. [1] Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered ...
Propagation of uncertainty. In statistics, propagation of uncertainty (or propagation of error) is the effect of variables ' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of experimental measurements they have uncertainties due to measurement ...
In probability theory and statistics, complex random variables are a generalization of real-valued random variables to complex numbers, i.e. the possible values a complex random variable may take are complex numbers. [1] Complex random variables can always be considered as pairs of real random variables: their real and imaginary parts.
The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved ...