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The stretched exponential function. is obtained by inserting a fractional power law into the exponential function. In most applications, it is meaningful only for arguments t between 0 and +∞. With β = 1, the usual exponential function is recovered. With a stretching exponent β between 0 and 1, the graph of log f versus t is ...
The natural logarithm function can be defined as the integral from 1 to of /, and the exponential function can then be defined as the inverse function of the natural logarithm. The number e is the value of the exponential function evaluated at x = 1 {\displaystyle x=1} , or equivalently, the number whose natural logarithm is 1.
The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718 281 828 459. [1] The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.
The Weibull plot is a plot of the empirical cumulative distribution function of data on special axes in a type of Q–Q plot. The axes are versus . The reason for this change of variables is the cumulative distribution function can be linearized: which can be seen to be in the standard form of a straight line.
The difference in these decay behaviors, where correlations between microscopic random variables become zero versus non-zero at large distances, is one way of defining short- versus long-range order. In statistical mechanics, the correlation function is a measure of the order in a system, as characterized by a mathematical correlation function ...
In linear algebra, a linear function is a map f between two vector spaces such that. Here a denotes a constant belonging to some field K of scalars (for example, the real numbers) and x and y are elements of a vector space, which might be K itself. In other terms the linear function preserves vector addition and scalar multiplication .
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