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One of the main limitation of the Taylor diagram is the absence of explicit information about model biases. One approach suggested by Taylor (2001) was to add lines, whose length is equal to the bias to each data point. An alternative approach, originally described by Elvidge et al., 2014, [17] is to show the bias of the models via a color ...
Taylor columns were first observed by William Thomson, Lord Kelvin, in 1868. [1] [2] Taylor columns were featured in lecture demonstrations by Kelvin in 1881 [3] and by John Perry in 1890. [4] The phenomenon is explained via the Taylor–Proudman theorem, and it has been investigated by Taylor, [5] Grace, [6] Stewartson, [7] and Maxworthy [8 ...
The standard map (also known as the Chirikov–Taylor map or as the Chirikov standard map) is an area-preserving chaotic map from a square with side onto itself. [1] It is constructed by a Poincaré's surface of section of the kicked rotator , and is defined by:
That is, the Taylor series diverges at x if the distance between x and b is larger than the radius of convergence. The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for analytic functions ...
Taylor's derivation is based on two assumptions: (1) that the surface of the cone is an equipotential surface and (2) that the cone exists in a steady state equilibrium. To meet both of these criteria the electric field must have azimuthal symmetry and have R {\displaystyle {\sqrt {R}}\,} dependence to counter the surface tension to produce the ...
The butterfly diagram show a data-flow diagram connecting the inputs x (left) to the outputs y that depend on them (right) for a "butterfly" step of a radix-2 Cooley–Tukey FFT algorithm. This diagram resembles a butterfly as in the Morpho butterfly shown for comparison, hence the name. A commutative diagram depicting the five lemma
A popular window function, the Hann window.Most popular window functions are similar bell-shaped curves. In signal processing and statistics, a window function (also known as an apodization function or tapering function [1]) is a mathematical function that is zero-valued outside of some chosen interval.
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.