We discuss free subsemigroups in solvable and elementary amenable groups improving earlier results of Milnor-Wolf, Rosenblatt, Alperin and Osin about uniform exponential growth for these groups.

We consider the inverse scattering problem on the energy interval in three dimensions. We are focused on stability and instability questions for this problem. In particular, we prove an exponential instability estimate which shows optimality of the logarithmic stability result of [Stefanov, 1990] (up to the value of the exponent). 1. Introdution We consider the Schrödinger equation −∆ψ + v(x)ψ ...

In this paper a class of singularly perturbed system of conservation laws is considered. The partial differential equations are equipped with boundary conditions which may be studied to derive the exponential stability. Lyapunov stability technique is used to derive sufficient conditions for the exponential stability of this system. A Lyapunov function in H-norm for a singularly perturbed syste...

We consider a class of viscous damped vibrating systems. We prove that, under the assumption that the damping term ensures the exponential decay for the corresponding inviscid system, then the exponential decay rate is uniform for the viscous one, regardless what the value of the viscosity parameter is. Our method is mainly based on a decoupling argument of low and high frequencies. Low frequen...

This is an exposition of examples and classes of finitely-generated groups which have uniform exponential growth. The main examples are non-Abelian free groups, semi-direct products of free Abelian groups with automorphisms having an eigenvalue of modulus distinct from 1, and Golod–Shafarevich infinite finitely-generated p-groups. The classes include groups which virtually have non-Abelian free...

We consider a rectangular grid induced by the south-west records from the planar Poisson point process in R+. A random symmetry property of the matrix whose entries are the areas of tiles of the grid implies cute multivariate distributional identities for certain rational functions of independent exponential and uniform random variables.

In this article, some new sufficient conditions for the exponential stability of nonlinear time-varying delay differential equations are given. An extension classical asymptotical theorem in terms a Lyapunov–Razumikhin function is obtained. The condition non-positivity time derivative Razumikhin weakened. Additionally, resulting asymptotic allow us to guarantee uniform and evaluate convergence ...

We discuss the relation between exponential stabilization and asymptotic controllability of nonlinear control systems with constrained control range at singular points. Using a discounted optimal control approach, we construct discrete feedback laws minimizing the Lyapunov exponent of the linearization. Thus we obtain an equivalence result between uniform exponential controllability and uniform...