相关论文: hankel: A Python library for performing simple and…
Despite being the most popular programming language, Python has not yet received enough attention from the community. To the best of our knowledge, there is no general static analysis framework proposed to facilitate the implementation of…
Connections between Hankel transforms of different order for $L^p$-functions are examined. Well known are the results of Guy [Guy] and Schindler [Sch]. Further relations result from projection formulae for Bessel functions of different…
Complex Gaussian quadrature rules for oscillatory integral transforms have the advantage that they can achieve optimal asymptotic order. However, their existence for Hankel transform can only be guaranteed when the order of the transform…
We propose a spectral Particle-In-Cell (PIC) algorithm that is based on the combination of a Hankel transform and a Fourier transform. For physical problems that have close-to-cylindrical symmetry, this algorithm can be much faster than…
This paper describes open-source scientific contributions in python surrounding the numerical solutions to hyperbolic Hamilton-Jacobi (HJ) partial differential equations viz., their implicit representation on co-dimension one surfaces;…
A Green's function based solver for the modified Bessel equation has been developed with the primary motivation of solving the Poisson equation in cylindrical geometries. The method is implemented using a Discrete Hankel Transform and a…
We present an open-source, performant, pure-python molecular dynamics (MD) suite for non-ideal plasmas. The code, Sarkas, aims to accelerate the research process by providing an MD code but also pre- and post-processing tools. Sarkas offers…
Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the…
Fractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration and complex numbers. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has…
We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms presented in previous work. We present the new software…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
In this paper we offer a review and bibliography of work on Hankel low-rank approximation and completion, with particular emphasis on how this methodology can be used for time series analysis and forecasting. We begin by describing possible…
We describe Rabacus, a Python package for calculating the transfer of hydrogen ionizing radiation in simplified geometries relevant to astronomy and cosmology. We present example solutions for three specific cases: 1) a semi-infinite slab…
Conformal transformations of a Euclidean (complex) plane have some kind of completeness (sufficiency) for the solution of many mathematical and physical-mathematical problems formulated on this plane. There is no such completeness in the…
We present a method to perform the exact convolution of the model prediction for bispectrum multipoles in redshift space with the survey window function. We extend a widely applied method for the power spectrum convolution to the…
We present SPIKE (Spectrometry Processing Innovative KErnel), an open-source Python package dedicated to Fourier spectroscopies. It provides basic functionalities such as apodisation, a complete set of Fourier transforms, phasing for NMR),…
In this paper, we introduce a novel low-rank Hankel tensor completion approach to address the problem of multi-measurement spectral compressed sensing. By lifting the multiple signals to a Hankel tensor, we reformulate this problem into a…
In a recent application of the Bokeh Python library for visualizing physico-chemical properties of chemical entities text-mined from the scientific literature, we found ourselves facing the task of smoothing hexagonally binned data in…
Many applications in the sciences require numerically stable and computationally efficient evaluation of multivariate polynomials. Finding beneficial representations of polynomials, such as Horner factorisations, is therefore crucial.…
Computational analysis has become ubiquitous within the heliophysics community. However, community standards for peer-review of codes and analysis have lagged behind these developments. This absence has contributed to the reproducibility…