Related papers: On Visibility and Blockers
It is conjectured that if a finite set of points in the plane contains many collinear triples then there is some structure in the set. We are going to show that under some combinatorial conditions such pointsets contain special…
We review some basic results of convex analysis and geometry in $\mathbb{R}^n$ in the context of formulating a differential equation to track the distance between an observer flying outside a convex set $K$ and $K$ itself.
A brief overview of jets and their central drivers is presented, with a focus on accreting black hole systems. In particular, scaling relations that elucidate some basic properties of the engines are derived, and the implications for the…
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…
In this article we explore some of the combinatorial consequences of recent results relating the isospectral commuting variety and the Hilbert scheme of points in the plane.
We consider the number of visible lattice points under the assumption of the Extended Lindel\"{o}f Hypothesis. We get a relation between visible lattice points and the Extended Lindel\"{o}f Hypothesis. And we also get a relation between…
We study some natural operators acting on configurations of points and lines in the plane and remark that many interesting configurations are fixed points for these operators. We review ancient and recent results on line or point…
This is a study of a problem in geodesy with methods from complex algebraic geometry: for a fixed number of measure points and target points at unknown position in the Euclidean plane, we study the problem of determining their relative…
Several results about the union-closed sets conjecture are presented.
These lecture notes give an introduction to the Brauer-Manin obstruction to the existence of rational points, focusing on the interplay between theory and computation.
In this paper, we have stated some results about this concept. Furthermore, we introduce the notion of controlled $E$-frames and we characterize all controlled $E$-duals associated with a given controlled $E$-frame.
The main purpose of this paper is to study the vector groupoids. This is an algebraic structure which combines the concepts of Brandt groupoid and vector space such that these are compatible.
This article has two interpenetrating motifs. One is an exposition of some major ideas and techniques behind the use of block matrices, and especially their positivity properties. This is done by focussing on one major problem:…
I discuss some compelling suggestions about particles which could be the dark matter in the universe, with special attention to experimental searches for them.
Possible explanations of solar neutrino and atmospheric neutrino anomalies are summarized and future tests discussed.
This paper presents an offering of some of the myriad connections between Combinatorics and Probability, directed in particular toward combinatorialists. The choice of material was dictated by the author's own interests, tastes and…
A review of muon colliders is presented. Basic features of the accelerator and detector are outlined, and the very exciting physics prospects are reviewed.
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.
Outstanding questions in the study of relativistic jets in their various astrophysical settings are discussed in the context of a general dynamical model.
I discuss recent developments in the field of relativistic jets in AGNs. After a brief review of our current knowledge of emission from Blazars, I discuss some consequences of the recent detection made by {\it Chandra} of X-ray emission…