Related papers: Simple Linear and Nonlinear Examples of Truncated …
Given an algebraic ordinary differential equation (AODE), we propose a computational method to determine when a truncated power series can be extended to a formal power series solution. If a certain regularity condition on the given AODE or…
We analyze a simple textbook approach to nonlinear oscillators proposed recently, disclose its errors, limitations and misconceptions and complete the calculations that the authors failed to perform.
Consider the following truncated Freud linear functional $\mathbf{u}_z$ depending on a parameter $z$, $$\langle\mathbf{u}_z,p\rangle=\int_0^\infty p(x)e^{-zx^4}dx,\quad z>0.$$ The aim of this work is to analyze the properties of the…
In this paper, we introduce two focussed sequent calculi, LKp(T) and LK+(T), that are based on Miller-Liang's LKF system for polarised classical logic. The novelty is that those sequent calculi integrate the possibility to call a decision…
Puiseux series are power series in which the exponents can be fractional and/or negative rational numbers. Several computer algebra systems have one or more built-in or loadable functions for computing truncated Puiseux series. Some are…
Cycloids are particular Petri nets for modelling processes of actions or events. They belong to the fundaments of Petri's general systems theory and have very different interpretations, ranging from Einstein's relativity theory and…
From tabulated nuclear and degenerate equations of state to photon and neutrino opacities, to nuclear reaction rates: tabulated data is ubiquitous in computational astrophysics. The dynamic range that must be covered by these tables…
A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the…
Contingency table analysis routinely relies on log linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a low rank tensor factorization of the probability mass function for…
The linearization of nonlinear systems is an important digital enhancement technique. In this paper, a real-time capable post- and pre-linearization method for the widely applicable time-varying discrete-time Volterra series is presented.…
Cadabra is an open access program ideally suited to complex tensor commutations in General Relativity. Tensor expressions are written in LaTeX while an enhanced version of Python is used to control the computations. This tutorial assumes no…
This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…
In recent years, twisted Alexander polynomial has been playing an important role in low-dimensional topology. For Montesinos links, we develop an efficient method to compute the twisted Alexander polynomial associated to any linear…
An effective radius of convergence is defined and computed for any truncated Taylor series. Applications to well known series are performed and is shown that a range of good coincidence for actual and approximative plot can always be found.…
We estimate the truncated double trigonometric series $\sum_{n=0}^{N}\sum_{m=0}^{M}a_{mn} {e}^{2\pi \imath \left(m x+n y\right)}$, $a_{mn} \in\mathbb{C}$, in Lebesgue spaces with mixed norms in terms of the $p^{th}-q^{th}$ power finite…
We state and analyze a generalization of the "truncation trick" suggested by Gourdon and Sebah to improve the performance of power series evaluation by binary splitting. It follows from our analysis that the values of D-finite functions…
Transient stability analysis (TSA) plays an important role in power system analysis to investigate the stability of power system. Traditionally, transient stability analysis methods have been developed using time domain simulation by means…
In this technical paper we introduce the Tensor Network Theory (TNT) library -- an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…