Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure [PDF]
, 2021 We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems.
Marwan, Norbert +4 more
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Matrix interpretation of multiple orthogonality [PDF]
, 2010 In this work we give an interpretation of a (s(d + 1) + 1)-term recurrence relation in terms of type II multiple orthogonal polynomials.We rewrite this recurrence relation in matrix form and we obtain a three-term recurrence relation for vector ...
Branquinho, Amílcar +2 more
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GB-splines of arbitrary order [PDF]
, 1998 Explicit formulae and recurrence relations for the calculation of generalized B-splines (GB-splines) of arbitrary order are given. We derive main properties of GB-splines and their series, i.e.
Sattayatham, Pairote +3 more
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Anomalous dynamics and the choice of Poincaré recurrence set [PDF]
, 2016 We investigate the dependence of Poincaré recurrence-time statistics on the choice of recurrence set by sampling the dynamics of two- and four-dimensional Hamiltonian maps.
Sala, Matteo +2 more
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Fast computation of sine/cosine series coefficients of associated Legendre function of arbitrary high degree and order [PDF]
, 2018 In order to accelerate the spherical/spheroidal harmonic synthesis of any function, we developed a new recursive method to compute the sine/cosine series coefficient of the 4π fully- and Schmidt quasi-normalized associated Legendre functions.
Fukushima T.
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No-neighbours recurrence schemes for space-time Green’s functions on a 3D simple cubic lattice [PDF]
, 2018 Application of multivariate creative telescoping to a finite triple sum representation of the discrete space-time Green's function for an arbitrary numeric (non-symbolic) lattice point on a 3D simple cubic lattice produces a fast, no-neighbours, seventh ...
John M Arnold +8 more
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Decoherence and thermalization of Unruh-DeWitt detector in arbitrary dimensions [PDF]
, 2023 We study the decoherence and thermalization of an Unruh-DeWitt detector linearly coupled to the free massless scalar field in flat spacetime of arbitrary dimensions ($d\geq 2$). The initial state of the detector is chosen to be a pure state consisting of
Hao Xu, Xu, Hao
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Fast and rigorous arbitrary-precision computation of Gauss-Legendre quadrature nodes and weights [PDF]
, 2018 International audienceWe describe a strategy for rigorous arbitrary-precision evaluation of Legendre polynomials on the unit interval and its application in the generation of Gauss-Legendre quadrature rules.
Mezzarobba, Marc, Johansson, Fredrik
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Differential-Difference Properties of Hypergeometric Series [PDF]
, 2022 14 pagesSix families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$.
Brisebarre, Nicolas, Salvy, Bruno
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Approximating conic sections by constrained Bézier curves of arbitrary degree [PDF]
, 2012 In this paper, an algorithm for approximating conic sections by constrained Bézier curves of arbitrary degree is proposed. First, using the eigenvalues of recurrence equations and the method of undetermined coefficients, some exact integral formulas for ...
Hu, Qian-Qian
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