Related papers: hankel: A Python library for performing simple and…
We use the concept of the half of a lower-triangular matrix to define a transformation on integer sequences. We explore the properties of this transformation, including in some cases a study of the Hankel transform of the transformed…
This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the…
The problem of accurately measuring the similarity between graphs is at the core of many applications in a variety of disciplines. Graph kernels have recently emerged as a promising approach to this problem. There are now many kernels, each…
A common task in astronomical research is to estimate the physical parameters (temperature, mass, density etc.) of a gas by using observed line emission. This often requires a calculation of how the radiation propagates via emission and…
This paper presents rerankers, a Python library which provides an easy-to-use interface to the most commonly used re-ranking approaches. Re-ranking is an integral component of many retrieval pipelines; however, there exist numerous…
This article analyzes and develops a method to solve fractional ordinary differential equations using the Monte Carlo Method. A numerical simulation is performed for some differential equations, comparing the results with what exists in the…
The purpose of this paper is to present an algorithm for evaluating Hankel transform of the null and the first kind. The result is the exact analytical representation as the series of the Bessel and Struve functions multiplied by the…
Many standard conversion matrices between coefficients in classical orthogonal polynomial expansions can be decomposed using diagonally-scaled Hadamard products involving Toeplitz and Hankel matrices. This allows us to derive…
Fractional calculus has become widely studied and applied to physical problems in recent years. As a result, many methods for the numerical computation of fractional derivatives and integrals have been defined. However, these algorithms are…
In high energy physics, the standard convention for expressing physical quantities is natural units. The standard paradigm sets $c = \hbar = \epsilon_0 = 1$ and hence implicitly rescales all physical quantities that depend on unit…
We present trainsum, a versatile Python package for doing computations with multidimensional quantics tensor trains: https://github.com/fh-igd-iet/trainsum. Using the Array API standard together with opt_einsum, trainsum allows the…
While functional programming is an efficient way to express complex software, functional programming languages have a steep learning curve. Haskell can be challenging to learn for students who were only introduced to imperative programming.…
Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…
We describe a fast algorithm for computing discrete Hankel transforms of moderate orders from $n$ nonuniform points to $m$ nonuniform frequencies in $O((m+n)\log\min(n,m))$ operations. Our approach combines local and asymptotic Bessel…
HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincar\'e disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of…
Zernike polynomials serve as an orthogonal basis on the unit disc, and have proven to be effective in optics simulations, astrophysics, and more recently in plasma simulations. Unlike Bessel functions, Zernike polynomials are inherently…
We obtain necessary and sufficient conditions on weights for the generalized Fourier-type transforms to be bounded between weighted $L^p-L^q$ spaces. As an important example, we investigate transforms with kernel of power type, as for…
One of the happiest accidents in all math is the ease of transforming a function to and taking derivatives in the Fourier frequency domain. But in order to exploit this extraordinary fact without serious artefacting, and in order to be able…
We give a new and simple proof of the Hankel inversion formula for the classical Hankel transform which holds for a complex order with real part greater than -1. Using the proof of this formula we obtain the full description of the Kirillov…
Quaternion-valued representations provide a convenient way to model coupled multi-channel signals (e.g., RGB imagery, polarization data, vector fields, and multi-detector time series). Yet practical and numerically reliable software support…