Related papers: Spectral Theory and Nonlinear PDE: a Survey

This article gives a brief survey of the theory and applications of anomalies.

In a recent paper, Vink et al. analyzed some spectropolarimetry data of O-type stars. Here we comment on our disagreement with some points presented in this paper, with the hope of helping to fully grasp the scientific implication of these…

The paper "A General Theory of IR Evaluation Measures" develops a formal framework to determine whether IR evaluation measures are interval scales. This comment shows some limitations about its conclusions.

This paper has been withdrawn by the author because it has been substantially modified.

Spectroscopic measurements can show distorted spectral shapes arising from a mixture of absorbing and scattering contributions. These distortions (or baselines) often manifest themselves as non-constant offsets or low-frequency…

A refinement of the energy method is introduced for dispersive PDE with derivative nonlinearity posed on tori. Key ingredient is a shorttime bilinear Strichartz estimate, which is used in a known combination of perturbative and energy…

Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…

A perturbation theory for the Nonlinear Schroedinger Equation (NLSE) in 1D on a lattice was developed. The small parameter is the strength of the nonlinearity. For this purpose secular terms were removed and a probabilistic bound on small…

This is a short survey of amenable equivalence relations.

I present a brief survey of surveys, and their results and implications, intended to set the context for the ensuing discussion.

Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…

Observational constraints on standard CDM spectra and perturbation spectra with broken scale invariance are discussed.

The Comments are devoted to the paper ``Solutions of Multitime Reaction-Diffusion PDE'' (Mathematics, vol. 10 (2022), 3623), in which main results are misleading and can be derived in a simple way from those obtained earlier. Moreover, it…

The present paper presents two new approaches to Fourier series and spectral analysis of singular measures.

We review some of the recent advances in nonlinear pulsation theory, but also insist on some of the major extant shortcomings.

This is a survey of current and recent works on deformation quantization and index theorems.

A spatial point pattern is called anisotropic if its spatial structure depends on direction. Several methods for anisotropy analysis have been introduced in the literature. In this paper, we give an overview of nonparametric methods for…

This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…

This is a survey talk on the study of Gel'fand-Dorfman bialgebras.

This paper has been withdrawn by the author, since now all four parts of the review are available as a single file 0804.1639. I also made some revision of the text in order to avoid misprints and some inaccurate expressions.