, 2014 We prove that there exists α ∈ R such that for any N the dicrepancy DN of the sequence 1αn!l, 1 ⩽ n ⩽ N satisfies DN = O(log N)
Aleksenko, Alena
core
$3x+1$ inverse orbit generating functions almost always have natural boundaries [PDF]
, 2014 The $3x+k$ function $T_{k}(n)$ sends $n$ to $(3n+k)/2$ resp. $n/2,$ according as $n$ is odd, resp. even, where $k \equiv \pm 1~(\bmod \, 6)$. The map $T_k(\cdot)$ sends integers to integers, and for $m \ge 1$ let $n \rightarrow m$ mean that $m$ is in the
C. Lagarias, Jason P. Bell, Jeffrey
core
Digital net properties of a polynomial analogue of Frolov's construction
, 2018 Frolov's cubature formula on the unit hypercube has been considered important since it attains an optimal rate of convergence for various function spaces.
Dick, Josef +4 more
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A generating function approach to the automated evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations. [PDF]
, 2018 Based on a previous technique deployed in some specific low order cases, we develop an automated computational procedure to evaluate instances within a class of infinite series comprising exponentiated multiples of generalized linear combinations of ...
Larcombe, Peter J., O'Neill, Sam T.
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On generalised multi-index non-linear recursion identities for terms of the Horadam sequence. [PDF]
, 2019 We state and prove a non-linear recurrence identity for terms of the so called Horadamsequence,andthenofferitsgeneralisationwhichisavailablefromthesamemethodology.
Fennessey, Eric J., Larcombe, Peter J.
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New proofs of linear recurrence identities for terms of the Horadam sequence. [PDF]
, 2019 We state, and prove using matrices, two (related) linear recurrence identities for termsofthesocalledHoradamsequence;eachresultexpressesthegeneraltermofthesequence as a linear combination of terms with particular initial values.
Fennessey, Eric J., Larcombe, Peter J.
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From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules
, 2015 In 1935 J.G. van der Corput introduced a sequence which has excellent uniform distribution properties modulo 1. This sequence is based on a very simple digital construction scheme with respect to the binary digit expansion.
Faure, Henri +2 more
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Weak lensing trispectrum and Kurt-spectra [PDF]
We introduce two kurt-spectra to probe fourth-order statistics of weak lensing convergence maps. Using state-of-the-art numerical simulations, we study the shapes of these kurt-spectra as a function of source redshifts and smoothing angular scales.
Dvorkin, Cora +3 more
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On some oscillating sums [PDF]
, 2008 This paper deals with the sums S α (n)=∑ j=1 n (-1) ⌊jα⌋ where α is any real number. The interest in these sums was initiated by a problem proposed by H. D. Ruderman [Problem 6105, Am. Math. Mon. 83, 573 (1977)] and solved (among other) by D.
Arias de Reyna Martínez, Juan +1 more
core
Exact order of extreme L p discrepancy of infinite sequences in arbitrary dimension. [PDF]
Arch Math, 2022 Kritzinger R, Pillichshammer F.
europepmc +1 more source