Related papers: Regulating the $P^+ = 0$ Singularity
The principles behind the sharp, singular structures in a crumpled sheet are well understood. Here we discuss more general ways of exploiting such sharp structures to control the shape of a sheet by deforming or forcing it elsewhere. Often,…
Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities,…
This is a survey article on $F$-singularities and their applications.
A mixed Dirichlet-Neumann problem is regularized with a family of singularly perturbed Neumann-Robin boundary problems, parametrized by $\varepsilon > 0$. Using an asymptotic development by Gamma-convergence, the asymptotic behavior of the…
Many properties of current \emph{ab initio} approaches to the quantum many-body problem, both perturbational or otherwise, are related to the singularity structure of Rayleigh--Schr\"odinger perturbation theory. A numerical procedure is…
This paper addresses the fundamental question of determining the minimum number of distinct control laws required for global controllability of nonlinear systems that exhibit singularities in their feedback linearising controllers. We…
This Living Review updates a previous version which its itself an update of a review article. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic…
Spectral singularities are certain points of the continuous spectrum of generic complex scattering potentials. We review the recent developments leading to the discovery of their physical meaning, consequences, and generalizations. In…
We present an abstract result on removing regularization for singular potentials which are not semibounded from below. The relation between ``right'' regularizations and ``right'' self-adjoint extensions of the perturbed Schr\"odinger…
We review the current status of the singularity problem in string theory for non-experts. After the problem is discussed from the point of view of supergravity, we discuss classic examples and recent examples of singularity resolution in…
We consider systems of parabolic equations coupled in zero order terms in a star-like or a tree-like shape, with an internal control acting in only one of the equations. We obtain local exact controllability to the stationary solutions of…
We make comments on the letter by Barrow [{\it Class. Quantum Grav.} {\bf 21} (2004) L79] since we cannot observe a singularity for $p(t)$ as $t\to t_s$. Instead, there might be a singularity for $\rho(t)$ for $t\sim 0$ case.
This paper is concerned with the constrained approximate null controllability of heat equation coupled by a real matrix $P$, where the controls are impulsive and periodically acted into the system through a series of real matrices…
A nonlinear scattering transform is studied for the two-dimensional Schrodinger equation at zero energy with a radial potential. First explicit examples are presented, both theoretically and computationally, of potentials with nontrivial…
The natural duality between "topological" and "regular," both considered as convergence space properties, extends naturally to p-regular convergence spaces, resulting in the new concept of a p-topological convergence space. Taking advantage…
In this paper, we present a control problem related to a semilinear differential equation with a moving singularity, i.e., the singular point depends on a parameter. The particularity of the controllability condition resides in the fact…
We characterize the spectrum (and its parts) of operators which can be represented as G=A+BC for a simpler operator A and a structured perturbation BC. The interest in this kind of perturbations is motivated, e.g., by perturbations of the…
This work studies the null controllability of a system of coupled parabolic PDEs. In particular, our work specializes to an important subclass of these control problems which are coupled by first and zero-order couplings and are,…
This paper is devoted to a study of the null controllability problems for one-dimensional linear degenerate wave equations through a boundary controller. First, the well-posedness of linear degenerate wave equations is discussed. Then the…
Though Mahler equations have been introduced nearly one century ago, the study of their solutions is still a fruitful topic for research. In particular, the Galois theory of Mahler equations has been the subject of many recent papers.…