Related papers: On the averaging principle for one-frequency syste…
In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved…
We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right hand side are available. A natural approach is to take the average of the measurements as an approximation of the…
Multiple sets of synthetic spectra of OB-binary stars are used to test the suitability of disentangling for deriving accurate spectroscopic orbits. Given a set of spectra with broad phase coverage and sufficient total integration time…
We consider the problem of estimating the distance, or range, between two locations by measuring the phase of multiple sinusoidal signals transmitted between the locations. Traditional estimators developed for optical interferometry include…
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…
A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
First and second order corrections for the scattering of different types of particles by a weak gravitational field, treated as an external field, are calculated. These computations indicate a violation of the Equivalence Principle: to…
In this paper, we analyze the error estimate of a wavelet frame based image restoration method from degraded and incomplete measurements. We present the error between the underlying original discrete image and the approximate solution which…
A phase-space semiclassical approximation valid to $O(\hbar)$ at short times is used to compare semiclassical accuracy for long-time and stationary observables in chaotic, stable, and mixed systems. Given the same level of semiclassical…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…
In the setting of entangled single-sample distributions, the goal is to estimate some common parameter shared by a family of $n$ distributions, given one single sample from each distribution. This paper studies mean estimation for entangled…
For a family of second-order elliptic systems in divergence form with rapidly oscillating almost-periodic coefficients, we obtain estimates for approximate correctors in terms of a function that quantifies the almost periodicity of the…
We provide stability estimates, obtained by implementing the Nekhoroshev theorem, in reference to the orbital motion of a small body (satellite or space debris) around the Earth. We consider a Hamiltonian model, averaged over fast angles,…
In this paper, we propose a fully distributed algorithm for frequency offsets estimation in decentralized systems. With the proposed algorithm, each node estimates its frequency offsets by local computations and limited exchange of…
We propose a new embedding method for a single vector and for a pair of vectors. This embedding method enables: a) efficient classification and regression of functions of single vectors; b) efficient approximation of distance functions; and…
The influence of low-spatial frequency errors of an optical component of an imaging system on the point spread function can be quantified using Zernike polynomials. High-spatial frequency errors cause strong scattering due to which the…
This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634--658,…