Related papers: Spherical harmonic analysis for multivariate stabl…
The connection between spherical harmonics and symmetric tensors is explored. For each spherical harmonic, a corresponding traceless symmetric tensor is constructed. These tensors are then extended to include nonzero traces, providing an…
In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of…
In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization. Based on the obtained spherical design point sets, we…
Reflection of particles from a disordered or chaotic medium is characterized by a scattering matrix that can be represented as a superposition of resonances. Each resonance corresponds to an eigenstate inside the medium and has a width…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
A class of multivariate spectral representations for real-valued nonstationary random variables is introduced, which is characterised by a general complex Gaussian distribution. In this way, the temporal signal properties -- harmonicity,…
The problem of calculating the probability density and distribution function of a strictly stable law is considered at $x\to0$. The expansions of these values into power series were obtained to solve this problem. It was shown that in the…
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…
This work is devoted to the stability/resolution analysis of several imaging functionals in complex environments. We consider both linear functionals in the wavefield as well as quadratic functionals based on wavefield correlations. Using…
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
This paper considers the estimation of Shannon entropy for discrete distributions with countably infinite support. While minimax rates for finite-support distributions are established, infinite-support distributions present distinct…
We discuss stability of spherically symmetric static solutions in Newtonian limit of Jordan, Brans-Dicke field equations. The behavior of the stable equilibrium solutions for the spherically symmetric configurations considered here, it…
We consider the class of stationary-increment harmonizable stable processes with infinite control measure, which most notably includes real harmonizable fractional stable motions. We give conditions for the integrability of the paths of…
We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered…
We give an introduction to basic harmonic analysis and representation theory for homogeneous spaces $Z=G/H$ attached to a real reductive Lie group $G$. A special emphasis is made to the case where $Z$ is real spherical.
A method is described for predicting statistical properties of turbulence. Collections of Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics of the full dynamics can be…
We determine sufficient and necessary conditions for a spherically symmetric initial data set to satisfy the dynamical horizon conditions in the spacetime development. The constraint equations reduce to a single second order linear master…
The stability analysis of elastic rings subjected to various loading conditions is examined, focusing on stable and unstable configurations. The harmonic balance method is employed to investigate the stability range under different loading…
We have performed a series of high resolution N-body experiments on a Connection Machine CM-5 in order to study the stability of collisionless self-gravitating spherical systems. We interpret our results in the framework of symplectic…