相关论文: Pad\'e Approximants and Resonance Poles

A particular instance of the inverse magnetisation problem is considered. It is assumed that the support of a magnetic sample (a source term in the Poisson equation in $\mathbb{R}^3$) is contained in a bounded planar set parallel to the…

We develop a robust method to extract the pole configuration of a given partial-wave amplitude. In our approach, a deep neural network is constructed where the statistical errors of the experimental data are taken into account. The teaching…

Starting from the orthogonal polynomial expansion of a function $F$ corresponding to a finite positive Borel measure with infinite compact support, we study the asymptotic behavior of certain associated rational functions…

Let M be a smooth compact oriented manifold without boundary, imbedded in a euclidean space E and let f be a smooth map of M into a Riemannian manifold N. An unknown state x in M is observed via X=x+su where s>0 is a small parameter and u…

In cosmological perturbation theory a first major step consists in the decomposition of the various perturbation amplitudes into scalar, vector and tensor perturbations, which mutually decouple. In performing this decomposition one uses --…

Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…

Nuclear lattice effective field theory (NLEFT) provides an efficient ab initio framework for computing low-lying states via imaginary-time projection. However, the extraction of unstable resonances, especially those with broad widths,…

We present a method able to recover location and residue of poles of functions meromorphic in a half--plane from samples of the function on the real positive semi-axis. The function is assumed to satisfy appropriate asymptotic conditions…

Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-forming instability in a wide variety of experiments and mathematical models. However, there is currently no mathematical theory to explain this…

Branching ratios for the decay of hadrons with large width or near thresholds depend on their definition. We test different definitions and show that rather different branching ratios can be obtained. For wide resonances and for sequential…

Let $X_1,X_2, \ldots $ be independent random uniform points in a bounded domain $A \subset \mathbb{R}^d$ with smooth boundary. Define the coverage threshold $R_n$ to be the smallest $r$ such that $A$ is covered by the balls of radius $r$…

The higher-dimensional generalization of Randall-Sundrum approach with additional positive curvature $n$-dimensional and Ricci-flat $m$-dimensional compuct subspaces is considered in pure gravity theory with metric of space-time and…

We present a PDE-based approach for the multidimensional extrapolation of smooth scalar quantities across interfaces with kinks and regions of high curvature. Unlike the commonly used method of [2] in which normal derivatives are…

We discuss the pole mass and the width of the $\Delta(1232)$ resonance to third order in chiral effective field theory. In our calculation we choose the complex-mass renormalization scheme (CMS) and show that the CMS provides a consistent…

Man-made environments such as households, offices, or factory floors are typically composed of linear structures. Accordingly, polylines are a natural way to accurately represent their geometry. In this paper, we propose a novel…

The van der Pauw method for two-dimensional samples of arbitrary shape with an isolated hole is considered. Correlations between extreme values of the resistances allow one to determine the specific resistivity of the sample and the…

A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specified value is sought. A simple method to evaluate the probability density is…

We report on our recent progress in the generation of resonant behavior in unitarized meson-meson scattering amplitudes obtained from Chiral Perturbation Theory. These amplitudes provide simultaneously a remarkable description of the…

Tensors decompositions are a class of tools for analysing datasets of high dimensionality and variety in a natural manner, with the Canonical Polyadic Decomposition (CPD) being a main pillar. While the notion of CPD is closely intertwined…

We obtain extensions of the Poincar\'e and Perron theorems for higher order recurrence relations and apply them to obtain an inverse type theorem for row sequences of (type II) Hermite-Pad\'e approximation of a vector of formal power…