5 Area of Intersecting Ellipses 5 5.1 No Intersection Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5.2 One Intersection Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.3 Two Intersection Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.4 Three Intersection Points . . . ....

let $g$ be a finite group with the identity $e$‎. ‎the subgroup intersection graph $gamma_{si}(g)$ of $g$ is the graph with vertex set $v(gamma_{si}(g)) = g-e$ and two distinct vertices $x$ and $y$ are adjacent in $gamma_{si}(g)$ if and only if $|leftlangle xrightrangle capleftlangle yrightrangle|>1$‎, ‎where $leftlangle xrightrangle $ is the cyclic subgroup of $g$ generated by $xin g$‎. ‎in th...

Cet article traite du processus ponctuel d’intersection d’un d’hyperplans de Poisson stationnaire et isotrope dans Rd d’intensité t>0, où seuls les hyperplans qui intersectent une boule centrée rayon R>0 sont considérés. En prenant R=t−dd+1, on montre que ce converge en distribution, lorsque t→∞, vers un Rd∖{0} dont la mesure a densité proportionnelle à ‖x‖−(d+1) par rapport Lebesgue. Une borne...

We present a novel algorithm to compute intersections of two point clouds. It can be used to detect collisions between implicit surfaces defined by two point sets, or to construct their intersection curves. Our approach utilizes a proximity graph that allows for quick interpolation search of a common zero of the two implicit functions. First, pairs of points from one point set are constructed, ...

The Bentley Ottmann sweep line algorithm is a standard tool to compute the arrangement of algebraic curves in the plane. If degenerate positions are not excluded from the input, variants of this algorithm must, among other things, handle k ≥ 2 curves intersecting simultaneously in a single intersection point. In that situation, the algorithm knows the order of the curves immediately left of the...