Introduction: The theory and application of linear and nonlinear delay differential equations is an important subject within physics and applied mathematics. There are several numerical approaches for solving linear and nonlinear delay differential equations. Aim: In this paper, differential transform method ( DTM ) is applied to numerical solution of linear and nonlinear delay differential equ...

We present two new algorithms, ADT and MDT, for solving order-n Toeplitz systems of linear equations Tz = b in time O(n log n) and space O(n). The fastest algorithms previously known, such as Trench’s algorithm, require time Ω(n2) and require that all principal submatrices of T be nonsingular. Our algorithm ADT requires only that T be nonsingular. Both our algorithms for Toeplitz systems are de...

Introduction: An accurate and representative catalog of impact craters on the surface of the Moon is necessary to infer information about the age of surfaces and the sequence of geological events [1]. The existing global catalogs of lunar craters contain ~2700 craters [2] and ~8500 craters [3], respectively. They suffer from uneven areal coverage as they were compiled from images having differe...

This work presents the first results of an experiment aiming to derive a high resolution Digital Terrain Model (DTM) by kinematic GPS surveying. The accuracy of the DTM depends on both the operational GPS precision and the density of GPS samples. The operational GPS precision, measured in the field, is about 10 cm. A Monte Carlo analysis is performed to study the dependence of the DTM error on ...

In this paper, we introduce the notion of DTM-signature, a measure on R+ that can be associated to any metric-measure space. This signature is based on the distance to a measure (DTM) introduced by Chazal, Cohen-Steiner and Mérigot. It leads to a pseudo-metric between metric-measure spaces, upper-bounded by the Gromov-Wasserstein distance. Under some geometric assumptions, we derive lower bound...

Checkpointing and closed nesting are mechanisms typically used for implementing partial roll-back in transactional systems. Closed nesting limits the amount of work to redo on an abort by allowing sub-transactions to abort and retry independently from their parents. Checkpointing goes further and allows a transaction to be rolled back to any previous point where a checkpoint was saved. Checkpoi...

In this paper we show that certain piecewiselinear Lyapunov functions are preserved for LTI systems under Padé approximations. In particular, we present a simple method to find a piecewise-linear Lyapunov function that is so preserved under the Padé discretization of any order and sampling time. This result may be of interest in the discretisation of switched linear systems for both simulation ...

In univariate Padé approximation we learn from the Froissart phenomenon that Padé approximants to perturbed Taylor series exhibit almost cancelling pole–zero combinations that are unwanted. The location of these pole–zero doublets was recently characterized for rational functions by the so-called Froissart polynomial. In this paper the occurrence of the Froissart phenomenon is explored for the ...

We compare Monte Carlo results for the interface tension and interface energy of the 3-dimensional Ising model with Padé and inhomogeneous differential approximants of the low temperature series that was recently extended by Arisue to 17 order in u = exp(−4β). The series is expected to suffer from the roughening singularity at u ≈ 0.196. The comparison with the Monte Carlo data shows that the P...

We study recurrence relations and biorthogonality properties for polynomials and rational functions in the problem of the Padé interpolation in the usual scheme and in the scheme with prescribed poles and zeros. The main result is deriving explicit orthogonality and biorthogonality relations for polynomials and rational functions in both schemes. We show that the simplest linear restrictions in...