相关论文: Resonances and lower resolvent bounds

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…

Lower bounds for some explicit decision problems over the complex numbers are given.

A correspondence between the sextic anharmonic oscillator and a pair of third-order ordinary differential equations is used to investigate the phenomenon of quasi-exact solvability for eigenvalue problems involving differential operators…

We show that deciding simulation equivalence and simulation preorder have quadratic lower bounds assuming that the Strong Exponential Time Hypothesis holds. This is in line with the best know quadratic upper bounds of simulation…

We consider resonances for third order ordinary differential operator with compactly supported coefficients on the real line. Resonance are defined as zeros of a Fredholm determinant on a non-physical sheet of three sheeted Riemann surface.…

This paper continues the authors' previous study (SIAM J. Math. Anal., 2016) of the trend toward equilibrium of the Becker-D\"oring equations with subcritical mass, by characterizing certain fine properties of solutions to the linearized…

Resolution over linear equations is a natural extension of the popular resolution refutation system, augmented with the ability to carry out basic counting. Denoted Res(lin_R), this refutation system operates with disjunctions of linear…

The temporal response of open systems is marked by damped oscillations. These oscillations, often referred to as ringings, are the signature of the decay of quasinormal modes (QNMs). A major research objective across various fields is to…

In this short note we review some known results on the structure and regularity of spaces with lower Ricci curvature bounds. We present some known and new open questions about next steps.

The propagation of radio emission in pulsar magnetospheres is discussed. We follow a kinematics model in order to derive dispersion relations for electromagnetic oscillations and transversal waves, propagating in a cold moving plasma. We…

This paper deals with an improvement of the "a-priori stability bounds" on the variation of the action variables and on the stability time obtained from a given Birkhoff normal form around the elliptic equilibrium point of an Hamiltonian…

When high-frequency sound waves travel through media with anomalous diffusion, such as biological tissues, their motion can be described by nonlinear wave equations of fractional higher order. These can be understood as nonlocal…

The possibility of the resonance reflection (100 % at maximum) is revealed. The corresponding exactly solvable models with the controllable numbers of resonances, their positions and widths are presented.

We discuss the composite nature of hadrons appearing near the s-wave two-hadron threshold. Generalizing the Weinberg's weak-binding relation for stable bound states, we show that the compositeness of near-threshold resonances and…

Lyapunov equations with low-rank right-hand sides often have solutions whose singular values decay rapidly, enabling iterative methods that produce low-rank approximate solutions. All previously known bounds on this decay involve quantities…

We obtain positive lower bounds on the Hausdorff dimension of sets of real numbers given by expressions of the form $\sum_{n=1}^\infty \frac{1}{a_n b_n}$, where $b_n$ satisfies some growth condition and $a_n$ lies in some set, possibly…

We prove sharp upper bounds for the number of resonances in boxes of size 1 at high frequency for the Laplacian on finite volume surfaces with hyperbolic cusps. As a corollary, we obtain a Weyl asymptotic for the number of resonances in…

Bound, antibound and resonance states are associated to poles in the on-shell partial wave amplitudes. We show here that from the residues of the pole a rank 1 projection operator associated with any of these states can be extracted, in…

We prove that there exists a dense set of analytic expanding maps of the circle for which the Ruelle eigenvalues enjoy exponential lower bounds. The proof combines potential theoretic techniques and explicit calculations for the spectrum of…

This note is about variations on a theorem of Bers about short pants decompositions of surfaces. It contains a version for surfaces with boundary but also a slight improvement on the best known bound for closed surfaces.