Related papers: To collide, or not to collide, that is the questio…
In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved
This paper has a double goal, the first one is to make a slight survey of some theoretical results about the existence of positively invariant curves that allow to describe important properties of the set of bounded orbits and its boundary…
We survey some results on toric topology.
The goal of the paper is twofold: it aims to give an extensive set of tools and bibliography towards Nowicki's conjecture both in an associative setting; it establishes a new result about Nowicki's conjecture for the free metabelian Poisson…
Free boundary problems are those described by PDEs that exhibit a priori unknown (free) interfaces or boundaries. These problems appear in Physics, Probability, Biology, Finance, or Industry, and the study of solutions and free boundaries…
We survey some old and new results about acyclic (affine) complex surfaces, also called homology planes. We ask several questions and leave open directions for future research.
Tackling the many open questions in particle physics will require the construction of new colliders. This short note includes a few considerations that seem to be brought up rarely.
A particle is thrown tangentially on a surface. It is shown that for some surfaces and for special initial velocities the thrown particle leaves immediately the surface, and for special conditions it never leaves the surface. The conditions…
For a wide class of two-body interactions, including standard examples like gravitational or Coulomb fields, we show that collision orbits in $n$-body systems are of Liouville measure zero for all energies. We use techniques from symplectic…
The close-limit method has given approximations in excellent agreement with those of numerical relativity for collisions of equal mass black holes. We consider here colliding holes with unequal mass, for which numerical relativity results…
We present a review of the literature on the subject of a possible collision between the Earthand a meteorite or comet. We emphasize the global effects when sufficient energy is involved.We propose several types of human actions adapted to…
We present a framework that allows an observer to determine occluded portions of a structure by finding the maximum-likelihood estimate of those occluded portions consistent with visible image evidence and a consistency model. Doing this…
We will look for stable structures in four situations and discuss what is known and unknown.
We discuss the possibility of making the {\it initial} definitions of mutually different (possibly interacting, or even entangled) systems in the context of decoherence theory. We point out relativity of the concept of elementary physical…
The main result of the paper is a boundedness for $n$-complements on algebraic surfaces. In addition, applications of this theorem to a classification of log Del Pezzo surfaces and of birational contractions for 3-folds are formulated.
The aim of this paper is to study a free boundary problem for a uniformly elliptic fully non-linear operator. Under certain assumptions we show that free and fixed boundaries meet tangentially at contact points.
Cross-match spatially clusters and organizes several astronomical point-source measurements from one or more surveys. Ideally, each object would be found in each survey. Unfortunately, the observation conditions and the objects themselves…
We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann's theorem to the complex case by proving that complex…
We propose a fluid-rigid body interaction benchmark problem, consisting of a solid spherical obstacle in a Newtonian fluid, whose centre of mass is fixed but is free to rotate. A number of different problems are defined for both two and…
Whether torsion plays or not a role in the description of the gravitational interaction is a problem that can only be solved by experiment. This is, however, a difficult task: since there are different possible interpretations for torsion,…