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The aliquot sequence starting with a positive integer k can be defined formally in terms of the sum-of-divisors function σ 1 or the aliquot sum function s in the following way: [1] = = = > = = = If the s n-1 = 0 condition is added, then the terms after 0 are all 0, and all aliquot sequences would be infinite, and we can conjecture that all aliquot sequences are convergent, the limit of these ...
A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or (historically) ...
Pascal's calculator (also known as the arithmetic machine or Pascaline) is a mechanical calculator invented by Blaise Pascal in 1642. Pascal was led to develop a calculator by the laborious arithmetical calculations required by his father's work as the supervisor of taxes in Rouen . [ 2 ]
In computability theory, computational complexity theory and proof theory, a fast-growing hierarchy (also called an extended Grzegorczyk hierarchy, or a Schwichtenberg-Wainer hierarchy) [1] is an ordinal-indexed family of rapidly increasing functions f α: N → N (where N is the set of natural numbers {0, 1, ...}, and α ranges up to some large countable ordinal).
The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.
Given the frequency of GC two-nucleotide sequences, the number of CpG dinucleotides is much lower than would be expected. [14] A 2002 study revised the rules of CpG island prediction to exclude other GC-rich genomic sequences such as Alu repeats. Based on an extensive search on the complete sequences of human chromosomes 21 and 22, DNA regions ...
Even though standard Halton sequences perform very well in low dimensions, correlation problems have been noted between sequences generated from higher primes. For example, if we started with the primes 17 and 19, the first 16 pairs of points: (1 ⁄ 17, 1 ⁄ 19), (2 ⁄ 17, 2 ⁄ 19), (3 ⁄ 17, 3 ⁄ 19) ...
Despite the mechanical flaws of the stepped reckoner, it suggested possibilities to future calculator builders. The operating mechanism, invented by Leibniz, called the stepped cylinder or Leibniz wheel, was used in many calculating machines for 200 years, and into the 1970s with the Curta hand calculator.
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