相关论文: To collide, or not to collide, that is the questio…
I discuss two techniques that can be used in the investigation of the properties of ``colliding" and ``non-colliding" anyons.
In this paper we survey many of the known results about Morse boundaries and stability.
We discuss a methodology that could be gainfully exploited using easily measurable experimental quantities to ascertain if the ``no-slip" boundary condition is appropriate for the flows of fluids past a solid boundary.
We consider a bounded domain $\Omega\subset\mathbb R^3$ and a rigid body $\mathcal{S}(t)\subset\Omega$ moving inside a viscous compressible Newtonian fluid. We exploit the roughness of the body to show that the solid collides its container…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
This is a survey on coarse geometry with an emphasis on coarse homology theories.
We present an approach to analyzing the safety of asynchronous, independent, non-deterministic, turn-to-bearing horizontal maneuvers for two vehicles. Future turn rates, final bearings, and continuously varying ground speeds throughout the…
We study of the shape of a compact singular minimal surface in terms of the geometry of its boundary, asking what type of {\it a priori} information can be obtained on the surface from the knowledge of its boundary. We derive estimates of…
This is a survey of results on random group presentations, and on random subgroups of certain fixed groups. Being a survey, this paper does not contain new results, but it offers a synthetic view of a part of this very active field of…
The no-slip boundary condition at a solid-liquid interface is at the center of our understanding of fluid mechanics. However, this condition is an assumption that cannot be derived from first principles and could, in theory, be violated. We…
We consider a body in a parallel flow of non-interacting particles. One can imagine that the flow is highly rarefied or consists of light rays. The interaction of particles with the body is perfectly elastic. We introduce the notions of a…
The purpose of this note is twofold. First, we survey results on the construction of large class groups of number fields by specialization of finite covers of curves. Then we give examples of applications of these techniques.
We consider a body in a parallel flow of non-interacting particles. The interaction of particles with the body is perfectly elastic. We introduce the notions of a body of zero resistance, a body that leaves no trace, and an invisible body,…
A complete treatment of the intersections of two geodesics on the surface of an ellipsoid of revolution is given. With a suitable metric for the distances between intersections, bounds are placed on their spacing. This leads to fast and…
In this work we present a general introduction to the Signorini problem (or thin obstacle problem). It is a self-contained survey that aims to cover the main currently known results regarding the thin obstacle problem. We present the theory…
In this paper, we address the problem of predicting collision for objects moving on the surface of a spherical manifold. Toward this end, we develop the notion of a collision triangle on such manifolds. We use this to determine analytical…
A major goal in robotics is to enable intelligent mobile robots to operate smoothly in shared human-robot environments. One of the most fundamental capabilities in service of this goal is competent navigation in this ``social" context. As a…
This is survey of some recent results connecting random matrices, non-colliding processes and queues.
We answer an open question proposed by P\'{o}lik and Terlaky in 2007 that: {\it how we can decide whether two quadratic surfaces intersect without actually computing the intersections?}
Convex geometry and complex geometry have long had fascinating interactions. This survey offers a tour of a few.