Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials [PDF]
, 2009 Two sets of infinitely many exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials are presented. They are derived as the eigenfunctions of shape invariant and thus exactly solvable quantum mechanical Hamiltonians, which ...
Alberto Grünbaum +35 more
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Exceptional Sets in Uniform Distribution [PDF]
Proceedings of the Edinburgh Mathematical Society, 1979 Let B be a measurable set of real numbers in (0,1) of Lebesgue measure |B| and letx1, …,xnbe real. Thendenotes the number ofj(1 ≦j≦n) for which the fractional part {xj}∈B. Thediscrepancyofx1, …,xniswhere the supremum is taken over all intervalsIin [0,1].
openaire +1 more source
Exceptional Sets for Inner Functions [PDF]
Journal of the London Mathematical Society, 1972 Peer Reviewed ; http://deepblue.lib.umich.edu/bitstream/2027.42/135322/1/jlms0696 ...
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From m-clusters to m-noncrossing partitions via exceptional sequences [PDF]
, 2011 Let W be a finite crystallographic reflection group. The generalized Catalan number of W coincides both with the number of clusters in the cluster algebra associated to W, and with the number of noncrossing partitions for W.
Buan, Aslak Bakke +2 more
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A Nurse in the Great War: The Exceptional Voice of Mary Borden
Miranda: Revue Pluridisciplinaire du Monde Anglophone, 2021 This essay focuses on the experience and literary testimony of Mary Borden, an outstanding figure in the landscape of World War I nursing. Beyond gender issues or questions of traumatic writing, what emerges out of Borden’s disjointed sketches is a ...
Isabelle Brasme
doaj +1 more source
The relative growth rate for the digits in Lüroth expansions
Comptes Rendus. Mathématique, 2020 In this note, the rate of growth of digits in the Lüroth expansion of an irrational number is studied relative to the rate of approximation of the number by its convergents.
Tan, Xiaoyan, Zhang, Zhenliang
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Counting sets with exceptions [PDF]
Mathematical Inequalities & Applications, 2004 The paper studies the tail of the hypergeometric distribution as a combinatorial problem and misses to mention the terms ``tail'' or ``hypergeometric distribution''. The main result is that if \(N+E< X\) and and \(K\leq \min\{N,E\}\), then \(1-{NE\over (K+1)X} \leq {1\over {X\choose N}}\sum_{j=0}^K {X-E\choose N-j}{E\choose j}\), where all letters ...
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A capacity approach to box and packing dimensions of projections of sets and exceptional directions [PDF]
Journal of Fractal Geometry, 2019 Dimension profiles were introduced in [8,11] to give a formula for the box-counting and packing dimensions of the orthogonal projections of a set $R^n$ onto almost all $m$-dimensional subspaces.
K. Falconer
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Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem
Open Mathematics, 2017 In this paper, we are able to prove that almost all integers n satisfying some necessary congruence conditions are the sum of j almost equal prime cubes with j = 7, 8, i.e., N=p13+…+pj3$\begin{array}{} N=p_1^3+ \ldots +p_j^3 \end{array} $ with |pi−(N ...
Feng Zhao
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Exceptional sets for nonuniformly expanding maps [PDF]
, 2015 Given a rational map of the Riemann sphere and a subset A of its Julia set, we study the A-exceptional set, that is, the set of points whose orbit does not accumulate at A.
Sara Campos, K. Gelfert
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