相关论文: A Parametrix Construction for the Wave Equation wi…

In many signal processing problems, it may be fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability…

Asymptotic representations for large values of the hyperradius are constructed for the scattering wave function of a system of $ N $ particles considered as a generalized function of angular variable coordinates. The coefficients of the…

The paper presents a statistical model which reproduces the results of Monte Carlo simulations to estimate the parameters of the gravitational wave signal from a coalesing binary system. The model however is quite general and would be…

It is shown that evolution of an open quantum system can be exactly described in terms of wave function which obeys Schrodinger equation with randomly varying parameters whose statistics is universally determined by separate dynamics of the…

Given a neighborhood graph representation of a finite set of points $x_i\in\mathbb{R}^d,i=1,\ldots,n,$ we construct a frame (redundant dictionary) for the space of real-valued functions defined on the graph. This frame is adapted to the…

This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…

We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth disorder. The conjecture of Gaussian fluctuations of wave functions put forward by Berry and generalized by…

The Random Particle Mesh (RPM) method used to simulate turbulence-induced broadband noise in several aeroacoustic applications is extended to realise isotropic turbulence spectra. With this method turbulent fluctuations are synthesised by…

We present a general theory of three-dimensional nonparaxial spatially-accelerating waves of the Maxwell equations. These waves constitute a two-dimensional structure exhibiting shape-invariant propagation along semicircular trajectories.…

We utilize a three-dimensional manifold to solve Riemann Problems that arise from a system of two conservation laws with quadratic flux functions. Points in this manifold represent potential shock waves, hence its name wave manifold. This…

We study stochastic wave equations in the sense of Walsh defined by fractal Laplacians on Cantor-like sets. For this purpose, we give an improved estimate on the uniform norm of eigenfunctions and approximate the wave propagator using the…

Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…

Gabardo and Nashed have studied nonuniform wavelets based on the theory of spectral pairs for which the associated translation set $\Lambda =\left\{ 0,r/N\right\}+2\,\mathbb Z$ is no longer a discrete subgroup of $\mathbb R$ but a spectrum…

We establish sharp pointwise kernel estimates and dispersive properties for the wave equation on noncompact symmetric spaces of general rank. This is achieved by combining the stationary phase method and the Hadamard parametrix, and in…

Under suitable conditions on the range of the Gauss map of a complete submanifold of Euclidean space with parallel mean curvature, we construct a strongly subharmonic function and derive a-priori estimates for the harmonic Gauss map. The…

A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in $L^2(\mathbb R)$ was considered by Gabardo and Nashed (J Funct. Anal. 158:209-241, 1998). In this setting, the associated…

Paraxial diffraction of monochromatic Gaussian beams by arbitrarily shaped polygonal apertures is analytically explored within the boundary diffraction wave theory framework. Exact closed-form expressions of the diffracted wavefield are…

We prove a structure theorem for multiplicative functions on the Gaussian integers, showing that every bounded multiplicative function on the Gaussian integers can be decomposed into a term which is approximately periodic and another which…

Via Gauge theory, we give a new proof of partial regularity for harmonic maps in dimension m>2 into arbitrary targets. This proof avoids the use of adapted frames and permits to consider targets of "minimal" C^2 regularity. The proof we…

This is the last of a sequence of four papers \cite{param1}, \cite{param2}, \cite{param3}, \cite{param4} dedicated to the construction and the control of a parametrix to the homogeneous wave equation $\square_{\bf g} \phi=0$, where ${\bf…