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This paper presents a lightweight, open-source and high-performance python package for solving peridynamics problems in solid mechanics. The development of this solver is motivated by the need for fast analysis tools to achieve the large…
In general dimension, there is no known total polynomial algorithm for either convex hull or vertex enumeration, i.e. an algorithm whose complexity depends polynomially on the input and output sizes. It is thus important to identify…
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…
The aim of this work is to report on several ladder operators for generalized Zernike polynomials which are orthogonal polynomials on the unit disk $\mathbf{D}\,=\,\{(x,y)\in \mathbb{R}^2: \; x^2+y^2\leqslant 1\}$ with respect to the weight…
The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects. A large part of this paper is dedicated to a tutorial which exemplifies the usage. Later sections…
Zernike moments can be used to generate invariant features that are applied in various machine vision applications. They, however, suffer from slow implementation and numerical stability problems. We propose a novel method for computing…
We consider 3D versions of the Zernike polynomials that are commonly used in 2D in optics and lithography. We generalize the 3D Zernike polynomials to functions that vanish to a prescribed degree $\alpha\geq0$ at the rim of their supporting…
We establish the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field. In…
The Epstein zeta function generalizes the Riemann zeta function to oscillatory lattice sums in higher dimensions. Beyond its numerous applications in pure mathematics, it has recently been identified as a key component in simulating exotic…
FEniCS Mechanics is a Python package to facilitate computational mechanics simulations. The Python library dolfin, from the FEniCS Project, is used to formulate and numerically solve the problem in variational form. The general balance laws…
We show that a nonvanishing analytic function on a domain in the unit disc can be approximated by (a scalar multiple of) a Blaschke product whose zeros lie on a prescribed circle enclosing the domain. We also give a new proof of the…
We present zea (pronounced ze-yah), a Python package for cognitive ultrasound imaging that offers a flexible, modular, and differentiable pipeline for ultrasound data processing. Additionally, it includes a collection of pre-defined models…
The Bernstein polynomial basis sees significant use owing to its unique properties, particularly in the field of optimal control. However, the basis is known to have a slow rate of convergence to the function it approximates. With this in…
We sharpen the bound $n^{2k}$ on the maximum modulus of the $k^{{\rm th}}$ radial derivative of the Zernike circle polynomials (disk polynomials) of degree $n$ to $n^2(n^2-1^2)\cdot ... \cdot(n^2-(k-1)^2)/2^k(1/2)_k$. This bound is obtained…
This paper presents \textsc{hankel}, a pure-python code for solving Hankel-type integrals and transforms. Such transforms are common in the physical sciences, especially appearing as the radial solution to angularly symmetric Fourier…
In this paper, a new python package (optipoly) is described that solves box-constrained optimization problem over multivariate polynomial cost functions. The principle of the algorithm is described before its performance is compared to…
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…
In this work we report on a new version of FeynCalc, a Mathematica package widely used in the particle physics community for manipulating quantum field theoretical expressions and calculating Feynman diagrams. Highlights of the new version…
Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built…
The interpolation-regression approximation is a powerful tool in numerical analysis for reconstructing functions defined on square or triangular domains from their evaluations at a regular set of nodes. The importance of this technique lies…