منابع مشابه
Multiples and Divisors
Before discussing multiplication, let us speak about addition. The number A(k) of distinct sums i+ j ≤ k such that 1 ≤ i ≤ k/2, 1 ≤ j ≤ k/2 is clearly 2 bk/2c − 1. Hence the number A(2n) of distinct elements in the n × n addition table involving {1, 2, . . . , n} satisfies limn→∞A(2n)/n = 2, as expected. We turn to multiplication. Let M(k) be the number of distinct products ij ≤ k such that 1 ≤...
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If solutions of a non-linear differential equation are contained in solutions of another equation we say that the former equation is a generalized divisor of the latter one. We design an algorithm which finds first-order quasi-linear generalized divisors of a second-order quasi-linear ordinary differential equation. If solutions of an equation contain solutions of a pair of equations we say tha...
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Pan African Medical Journal. 2016; 25:15 doi:10.11604/pamj.2016.25.15.10626 This article is available online at: http://www.panafrican-med-journal.com/content/article/25/15/full/ © Hakima Elmahi et al. The Pan African Medical Journal ISSN 1937-8688. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0)...
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Information distance is a parameter-free similarity measure based on compression, used in pattern recognition, data mining, phylogeny, clustering, and classification. The notion of information distance is extended from pairs to multiples (finite lists). We study maximal overlap, metricity, universality, minimal overlap, additivity, and normalized information distance in multiples. We use the th...
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We obtain the asymptotic expansion of the sequence with general term $frac{A_n}{G_n}$, where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$, with $d(n)$ denoting the number of positive divisors of $n$. Also, we obtain some explicit bounds concerning $G_n$ and $frac{A_n}{G_n}$.
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 1959
ISSN: 0022-2518
DOI: 10.1512/iumj.1959.8.58062