相关论文: Nonlinear asymptotic mean value characterizations …
We apply the nonlinear steepest descent method to a class of 3x3 Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix random model. The general case of two equilibrium measures supported on an arbitrary number of…
For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
The describing function method is a useful tool for the qualitative analysis of limit cycles in the stability analysis of nonlinear systems. This method is inherently approximate; therefore, it should be used for a fast qualitative analysis…
We present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations,…
A new method, called the method of self-similar approximants, and its recent developments are described. The method is based on the ideas of renormalization group theory and optimal control theory. It allows for the effective extrapolation…
The concept of square-mean almost automorphy for stochastic processes is introduced. The existence and uniqueness of square-mean almost automorphic solutions to some linear and non-linear stochastic differential equations are established…
Recently, symbolic regression (SR) has demonstrated its efficiency for discovering basic governing relations in physical systems. A major impact can be potentially achieved by coupling symbolic regression with asymptotic methodology. The…
We define an abstract nonlinear elliptic system, admitting a variational structure, and including the vortex equations for some Maxwell-Chern-Simons gauge theories as special cases. We analyze the asymptotic behavior of its solutions, and…
During the last years, asymptotic (or sequential) constraint qualifications, which postulate upper semicontinuity of certain set-valued mappings and provide a natural companion of asymptotic stationarity conditions, have been shown to be…
We deal with the large time behavior for a porous medium equation posed in nonhomogeneous media with singular critical density $$ |x|^{-2}\partial_tu(x,t)=\Delta u^m(x,t), \quad (x,t)\in \real^N\times(0,\infty), \ m\geq1, $$ posed in…
We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds…
We describe nonlinear quantum atom-light interfaces and nonlinear quantum metrology in the collective continuous variable formalism. We develop a nonlinear effective Hamiltonian in terms of spin and polarization collective variables and…
Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…
A heuristic method to find asymptotic solutions to a system of non-linear wave equations near null infinity is proposed. The non-linearities in this model, dubbed good-bad-ugly, are known to mimic the ones present in the Einstein field…
A novel type of trajectory on semiflows, called asymptotically unpredictable, was proposed by Fen and Tokmak Fen [15]. The presence of sensitivity, which is an indispensable feature of chaotic dynamics, is a crucial property that arises…
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…
Purely numerical methods do not always provide an accurate way to find all the global solutions to nonlinear ODE on infinite intervals. For example, finite-difference methods fail to capture the asymptotic behavior of solutions, which might…
In this paper we give a meaning to the nonlinear characteristic Cauchy problem for the Wave Equation in base form by replacing it by a family of non-characteristic problems in an appropriate algebra of generalized functions. We prove…