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The smallest constant is sometimes called the (best) Lipschitz constant [4] of f or the dilation or dilatation [5]: p. 9, Definition 1.4.1 [6] [7] of f. If K = 1 the function is called a short map, and if 0 ≤ K < 1 and f maps a metric space to itself, the function is called a contraction.
By default, a Pandas index is a series of integers ascending from 0, similar to the indices of Python arrays. However, indices can use any NumPy data type, including floating point, timestamps, or strings. [4]: 112 Pandas' syntax for mapping index values to relevant data is the same syntax Python uses to map dictionary keys to values.
In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of discrete values.. The DTFT is often used to analyze samples of a continuous function.
In calculus, the differential represents the principal part of the change in a function = with respect to changes in the independent variable. The differential is defined by = ′ (), where ′ is the derivative of f with respect to , and is an additional real variable (so that is a function of and ).
For example, in Python, to print the string Hello, World! followed by a newline, one only needs to write print ("Hello, World!" In contrast, the equivalent code in C++ [ 7 ] requires the import of the input/output (I/O) software library , the manual declaration of an entry point , and the explicit instruction that the output string should be ...
There exist programs for the numerical computation of the Pfaffian on various platforms (Python, Matlab, Mathematica) (Wimmer 2012). The Pfaffian is an invariant polynomial of a skew-symmetric matrix under a proper orthogonal change of basis. As such, it is important in the theory of characteristic classes.
The F-test statistic is the ratio, after scaling by the degrees of freedom. If there is no difference between population means this ratio follows an F-distribution with 2 and 3n − 3 degrees of freedom. In some complicated settings, such as unbalanced split-plot designs, the sums-of-squares no longer have scaled chi-squared distributions ...
Shortly after Van Rossum joined the Corporation for National Research Initiatives, the term appeared in a follow-up mail by Ken Manheimer to a meeting trying to create a semi-formal group that would oversee Python development and workshops; this initial use included an additional joke of naming Van Rossum the "First Interim BDFL".