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Squarefree numbers on short intervals
Mathematika, 1982It is a familiar fact that the sequence of K -free numbers, i.e . those having no K -th power divisor greater than 1, has asymptotic density 1/ζ( K ). Let χ ( K ) denote the characteristic function of this sequence, χ (2) = χ.
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Order Relations Between Interval Numbers
2019In addition to fuzzy and stochastic theory, interval analysis is a powerful tool for solving uncertain problems. An important problem in interval analysis is the ranking of interval numbers. This paper analyzes the definitions of satisfaction index for comparing interval numbers.
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Interstimulus Interval and Number Judgment
Nature, 1965D, Jones, A, Elithorn
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Catalan Numbers and Interval Structures
2015There are many interesting families of intervals counted by the Catalan numbers. First, however, let us make a remark about antichains in the poset Int([n]) of intervals on [n]. If \( \mathcal{A} \) is such an antichain, then no two intervals in \( \mathcal{A} \) can share a common left endpoint or a common right endpoint.
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The Elementary Theory of Interval Real Numbers
Mathematical Logic Quarterly, 1985\textit{R. E. Moore} [Interval analysis (1966; Zbl 0176.133)] introduced a model \({\mathcal I}({\mathbb{R}})\) for the ''real numbers'' whose elements are compact real intervals. In this paper the first-order theory of \({\mathcal I}({\mathbb{R}})\) is axiomatized and Tarski's quantifier elimination method for real closed fields is modified to show ...
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Roundoff-Free Number Fields for Interval Computations
Reliable Computing, 2001Let \(F\subseteq \mathbb{R}\) be a field of real numbers. Then \(F\) is called roundoff-free for interval computations if for every polynomial \(f(x_1,\dots, x_n)\) with coefficients from \(F\), and for every set of \(n\) intervals \({\mathbf x}_1= [x^-_1, x^+_1],\dots,{\mathbf x}_n= [x^-_n, x^+_n]\) with \(x^{\pm}_i\in F\), the bounds of the range \(f(
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Social determinants of health and US cancer screening interventions: A systematic review
Ca-A Cancer Journal for Clinicians, 2023Ariella R Korn
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