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Like approximate entropy (ApEn), Sample entropy (SampEn) is a measure of complexity. [1] But it does not include self-similar patterns as ApEn does. For a given embedding dimension, tolerance and number of data points, SampEn is the negative natural logarithm of the probability that if two sets of simultaneous data points of length have distance < then two sets of simultaneous data points of ...
The companion Pell numbers can be expressed by the closed form formula Q n = ( 1 + 2 ) n + ( 1 − 2 ) n . {\displaystyle Q_{n}=\left(1+{\sqrt {2}}\right)^{n}+\left(1-{\sqrt {2}}\right)^{n}.} These numbers are all even ; each such number is twice the numerator in one of the rational approximations to 2 {\displaystyle {\sqrt {2}}} discussed above.
The general expression for the spin angular momentum is [1] =, where is the speed of light in free space and is the conjugate canonical momentum of the vector potential.The general expression for the orbital angular momentum of light is =, where = {,,,} denotes four indices of the spacetime and Einstein's summation convention has been applied.
Self-assembled monolayers (SAM) of organic molecules are molecular assemblies formed spontaneously on surfaces by adsorption and are organized into more or less large ordered domains. [ 1 ] [ 2 ] In some cases molecules that form the monolayer do not interact strongly with the substrate.
A one-vertex crease pattern consists of a set of rays or creases drawn on a flat sheet of paper, all emanating from the same point interior to the sheet. (This point is called the vertex of the pattern.) Each crease must be folded, but the pattern does not specify whether the folds should be mountain folds or valley folds. The goal is to ...
A Taxicab number is the smallest positive number that can be expressed as a sum of two positive integer cubes in n distinct ways. The smallest taxicab number after Ta(1) = 1, is Ta(2) = 1729, [4] expressed as
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Symmetrical pattern made by the denominators of the Farey sequence, F 9. Symmetrical pattern made by the denominators of the Farey sequence, F 25 . In mathematics , the Farey sequence of order n is the sequence of completely reduced fractions , either between 0 and 1, or without this restriction, [ a ] which when in lowest terms have ...
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