Related papers: The virial theorem for nonlinear problems
We establish almost sure invariance principles, a strong form of approximation by Brownian motion, for non-stationary time-series arising as observations on dynamical systems. Our examples include observations on sequential expanding maps,…
We show how to reduce the problem of solving members of a certain family of nonlinear differential equations to that of solving some corresponding linear differential equations.
A Lagrange multiplier theorem is derived for the case of an imprecise objective function and a precise constraint. The proof uses methods of analysis which deal in a direct, algebraic way with imprecisions. They include imprecise…
Linear theory provides a reasonable description of the velocity correlations of biased tracers both perpendicular and parallel to the line of separation, provided one accounts for the fact that the measurement is almost always made using…
A method for solving a quasilinear nonelliptical equation of the second order is developed and we give classification and parametrization of simple elements of the equation.We find exact solutions of an equation for potential stationary…
To study the existence and uniqueness of solutions to Cauchy-type problems for fractional q-difference equations with the bi-ordinal Hilfer fractional q-derivative which is an extension of the Hilfer fractional q-derivative. An approach is…
In this paper we prove the existence of a nontrivial solution to the nonlinear Schrodinger-Maxwell equations in $\R^3,$ assuming on the nonlinearity the general hypotheses introduced by Berestycki & Lions.
Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We…
There is presented an approach to find an approximation polynomial of a function with two variables based on the two dimensional discrete Fourier transform. The approximation polynomial is expressed through Chebyshev polynomials. There is…
We construct the general theory of first-order relativistic hydrodynamics for a fluid exhibiting a chiral anomaly, including all possible viscous terms allowed by symmetry. Using standard techniques, we compute the necessary and sufficient…
An astonishingly simple analytical frequency approximation formula for a class of strongly nonlinear oscillators is derived and applied to various example systems yielding useful quick estimates.
We show that the equivalent linearization technique, when used properly, enables us to calculate frequency corrections of weakly nonlinear oscillators beyond the first order in nonlinearity. We illustrate the method by applying it to the…
In this article we study the estimation of bifurcation coefficients in nonlinear branching problems by means of Rayleigh-Ritz approximation to the eigenvectors of the corresponding linearized problem. It is essential that the approximations…
Liouville theorems for scaling invariant nonlinear parabolic problems in the whole space and/or the halfspace (saying that the problem does not posses positive bounded solutions defined for all times $t\in(-\infty,\infty)$) guarantee…
The nonlinear Vlasov equation contains the full nonlinear dynamics and collective effects of a given Hamiltonian system. The linearized approximation is not valid for a variety of interesting systems, nor is it simple to extend to higher…
Binomial Theorem for (N+n)^r is described with non-commuting variables N and n.
We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant…
We prove an existence result for solutions to a class of nonlinear degenerate-elliptic equations with measurable coefficients and zero Dirichlet boundary condition. The main term is given by a nonlinear operator in divergence form…
This paper introduces an elliptic quasi-variational inequality (QVI) problem class with fractional diffusion of order $s \in (0,1)$, studies existence and uniqueness of solutions and develops a solution algorithm. As the fractional…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…