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Obstacles $K$ and $L$ in $R^d$ ($dgeq 2$) are considered that are finite disjoint unions of strictly convex domains with $C^3$ boundaries. We show that if $K$ and $L$ have (almost) the same scattering length spectrum, or (almost) the same traveling times, then $K = L$.
It was proved in cite{NS1} that obstacles $K$ in $R^d$ that are finite disjoint unions of strictly convex domains with $C^3$ boundaries are uniquely determined by the travelling times of billiard trajectories in their exteriors and also by their so c
The purpose of this article is to study the eigenvalues $u_1^{, t}=e^{ittheta_1},dots,u_N^{,t}=e^{ittheta_N}$ of $U^t$ where $U$ is a large $Ntimes N$ random unitary matrix and $t>0$. In particular we are interested in the typical times $t$ for which
In this paper we consider compact, Riemannian manifolds $M_1, M_2$ each equipped with a one-parameter family of metrics $g_1(t), g_2(t)$ satisfying the Ricci flow equation. Motivated by a characterization of the super Ricci flow developed by McCann-T
The paper deals with some problems related to recovering information about an obstacle in an Euclidean space from certain measurements of lengths of generalized geodesics in the exterior of the obstacle. The main result is that if two obstacles satis
In this paper we investigate the existence of closed billiard trajectories in not necessarily smooth convex bodies. In particular, we show that if a body $Ksubset mathbb{R}^d$ has the property that the tangent cone of every non-smooth point $qin part