Combining recent moment and sparse semidefinite programming (SDP) relaxation techniques, we propose an approach to find smooth approximations for solutions of nonlinear differential equations. Given a system of nonlinear differential equations, we apply a technique based on finite differences and sparse SDP relaxations for polynomial optimization problems (POP) to obtain a discrete approximatio...

Even if we disregard all those nominal expressions employed with purely connotative meaning, that is, those which do not refer to any object, and confine our attention to nouns which are names of things, it is clear that no extant lexicon contains anywhere near enough expressions of this kind to suffice even for ordinary daily life. We cannot get along with any single common noun to refer to a ...

Low-frequency spectra for the 1989 Macquarie Ridge earthquake (magnitude 8.2) show an amplitude increase and a phase-delay decrease below 6 millihertz that require a short-term slow precursor. This earthquake can be modeled as a compound event in which a fast-rupturing, ordinary earthquake was initiated by an episode of slow, smooth deformation that began more than 100 seconds before the main s...

We determine which (ordinary) Riordan arrays are the coefficient arrays of a family of orthogonal polynomials. In so doing, we are led to introduce a family of polynomials, which includes the Boubaker polynomials, and a scaled version of the Chebyshev polynomials, using the techniques of Riordan arrays. We classify these polynomials in terms of the Chebyshev polynomials of the first and second ...

We present a perturbation method for determining the moment stability of linear ordinary differential equations with parametric forcing by colored noise. In particular, the forcing arises from passing white noise through an nth order filter. We carry out a perturbation analysis based on a small parameter ε that gives the amplitude of the forcing. Our perturbation analysis is based on a ladder o...

The stochastic counterpart to the deterministic description of continuous fermentation with ordinary differential equation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae. We briefly discuss the continuous fermentation process driven by three-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual ferment...

The heterogeneous multiscale methods (HMM) is a general framework for the numerical approximation of multiscale problems. It is here developed for ordinary differential equations containing different time scales. Stability and convergence results for the proposed HMM methods are presented together with numerical tests. The analysis covers some existing methods and the new algorithms that are ba...

In this paper we study asymptotic behavior of some moment spaces. We consider two different settings. In the first one, we work with ordinary multi-dimensional moments on the standard m-simplex. In the second one, we deal with the trigonometric moments on the unit circle of the complex plane. We state large and moderate deviation principles for uniformly distributed moments. In both cases the r...

We calculate the non-forward quark matrix elements of operators with two covariant derivatives needed for the renormalisation of the second moment of generalised parton distributions in one-loop lattice perturbation theory using Wilson fermions. For some representations of the hypercubic group commonly used in simulations we determine the sets of all possible mixing operators. For those represe...

Recent neutron interferometry experiments have been interpreted as demonstrating a new topological phenomenon similar in principle to the usual Aharonov-Bohm (AB) effect, but with the neutron’s magnetic moment replacing the electron’s charge. We show that the new phenomenon, called Scalar AB (SAB) effect, follows from an ordinary local interaction, contrary to the usual AB effect, and we argue ...