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In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...
Differentiation with respect to time or one of the other variables requires application of the chain rule, [1] since most problems involve several variables. Fundamentally, if a function F {\displaystyle F} is defined such that F = f ( x ) {\displaystyle F=f(x)} , then the derivative of the function F {\displaystyle F} can be taken with respect ...
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
For a polynomial-time list-decoding algorithm to exist, we need the combinatorial guarantee that any Hamming ball of radius around a received word (where is the fraction of errors in terms of the block length ) has a small number of codewords. This is because the list size itself is clearly a lower bound on the running time of the algorithm.
In information theory, linguistics, and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences. The Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other.
Borrowing costs on 15-year fixed-rate mortgages, popular with homeowners seeking to refinance their home loan to a lower rate, also eased this week. The average rate fell to 5.84% from 5.96% last ...
Sen. Richard Blumenthal, D-Conn., said the mysterious drones spotted in New Jersey over the past few weeks, and most recently in Connecticut, should be “shot down, if necessary."
If the distance measure is a metric (and thus symmetric), the problem becomes APX-complete, [53] and the algorithm of Christofides and Serdyukov approximates it within 1.5. [ 54 ] [ 55 ] [ 10 ] If the distances are restricted to 1 and 2 (but still are a metric), then the approximation ratio becomes 8/7. [ 56 ]
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