相关论文: Nonlinear Accelerator Problems via Wavelets: 6. Re…

We propose a nonlinear, wavelet based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multi-reference alignment problem and generalizations thereof, we analyze the…

Global pointwise estimates are obtained for quasilinear Lane-Emden-type systems involving measures in the "sublinear growth" rate. We give necessary and sufficient conditions for existence expressed in terms of Wolff's potential. Our…

For describing the probability distribution of the positions and times of particles performing anomalous motion, fractional PDEs are derived from the continuous time random walk models with waiting time distribution having divergent first…

A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine…

We propose a trajectory-based quasiclassical method for approximating dynamics in condensed phase systems. Building upon the previously developed Optimized Mean Trajectory (OMT) approximation that has been used to compute linear and…

We propose a method of solving partial differential equations on the $n$-dimen\-sional unit sphere with methods based on the continuous wavelet transform derived from approximate identities.

The quasilinearization method (QLM) of solving nonlinear differential equations is applied to the quantum mechanics by casting the Schr\"{o}dinger equation in the nonlinear Riccati form. The method, whose mathematical basis in physics was…

We consider an approach to the analysis of nonstationary processes based on the application of wavelet basis sets constructed using segments of the analyzed time series. The proposed method is applied to the analysis of time series…

Relation of ultrametric analysis, wavelet theory and cascade models of turbulence is discussed. We construct the explicit solutions for the nonlinear ultrametric integral equation with quadratic nonlinearity. These solutions are built by…

The relativistic semi-classical approximation for a free massive particle is studied using the Wigner-Weyl formalism. A non-covariant Wigner function is proposed using the Newton-Wigner position operator. The perturbative solution for the…

Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the…

A class of non-linear eigenvalue problems defined in the form of operator polynomials is investigated. The problems are related to wave equations which appear in a relativistic quantum field theory. Spectral asymptotics for this class are…

Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation,…

By parametrizing input and state trajectories with basis functions different approximations to the constrained linear quadratic regulator problem are obtained. These notes present and discuss technical results that are intended to…

We present a systematic expansion of all constraint equations in canonical quantum gravity up to the order of the inverse Planck mass squared. It is demonstrated that this method generates the conventional Feynman diagrammatic technique…

In this paper, we study an adaptive finite element method for a class of a nonlinear eigenvalue problems that may be of nonconvex energy functional and consider its applications to quantum chemistry. We prove the convergence of adaptive…

This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…

The embodied intelligence bridges the physical world and information space. As its typical physical embodiment, humanoid robots have shown great promise through robot learning algorithms in recent years. In this study, a hardware platform,…

Spatial Fourier transforms of quasipatterns observed in Faraday wave experiments suggest that the patterns are well represented by the sum of 8, 10 or 12 Fourier modes with wavevectors equally spaced around a circle. This representation has…

We study a class of fourth-order quasilinear degenerate parabolic equations under both time-and space-dependent and time-and space-independent forces, modeling non-Newtonian thin-film flow over a solid surface in the "complete wetting"…