In mathematics, statistics, and computer science, particularly in the fields of machine learning inverse problems, regularization is a process introducing additional information order to solve an ill-posed problem or prevent overfitting. The Tikhonov method widely used complex problems engineering. vertical derivative gravity can highlight local anomalies separate horizontal superimposed abnorm...

Experiments on 4He films reveal an attractive Casimir-like force at the bulk lambda point and in the superfluid regime. Previous work has explained the magnitude of this force at the lambda transition and deep in the superfluid region but not the substantial attractive force immediately below the lambda point. Utilizing a simple mean-field calculation renormalized by critical fluctuations we ob...

Aberrations of the coherent wavefront are analyzed using a phase Zernike filter. Developed iterative methods allow us to design a filter that decomposes the analyzed light field into a set of diffraction orders with amplitudes proportional to the circular Zernike polynomials. We also apply the algorithm to the calculation of the light field phase from measurements of the modules of decompositio...

We suggest a new approach for the automatic and fully numerical evaluation of oneloop scattering amplitudes in perturbative quantum field theory. We use suitably formulated dispersion relations to perform the calculation as a convolution of treelevel amplitudes. This allows to take advantage of the iterative numerical algorithms for the evaluation of leading order matrix elements. Preprint subm...

In this paper, a near-field to far-field (NF–FF) transformation for the case of spherical scanning using equivalent magnetic currents (EMCs) and matrix methods is addressed. It is based on the decoupling of the field components and the iterative retrieval of the radial component of the electric field. The technique is applied for far-field calculation as well as for the estimation of the curren...

Numerical algorithms are developed for the centroid molecular dynamics (centroid MD) method to calculate dynamical time correlation functions for general many-body quantum systems. Approaches based on the normal mode path integral molecular dynamics and staging path integral Monte Carlo methods are described to carry out a direct calculation of the force on the centroid variables in the centroi...