相关论文: The Elliptical Envelope

The ellipses model is a continuum percolation process in which ellipses with random orientation and eccentricity are placed in the plane according to a Poisson point process. A parameter $\alpha$ controls the tail distribution of the major…

We investigate the existence of elliptic islands for a special family of periodic orbits of a two-parameter family of maps corresponding to the billiard problem on the elliptical stadium. The hyperbolic or elliptical character of these…

Soit l un entier et E_{c,l} la famille de Kubert des courbes elliptiques definies sur Q munies d'un point rationnel A d'ordre l. On note F_{c,l} la courbe elliptique quotient de E_{c,l} par le groupe engendre' par A, et f_l l'isogenie de…

A little known property of free-fall motion is the elliptic locus of the maximum heights attained by coplanar projectiles launched from a single point in different directions with the same initial speed. Another, less known and perhaps…

It is well known that among all closed bounded curves in the plane with the given perimeter, the circle encloses the maximum area. There are many proofs in the literature. In this article we have given a new proof using some ideas of Demar.

The paper is devoted to the description of family of scalene triangles for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles. We call them Sharygin triangles. It turns out that they are…

We investigate a one-parameter family of Coulomb gases in two dimensions, which are confined to an ellipse, due to a hard wall constraint, and are subject to an additional external potential. At inverse temperature $\beta=2$ we can use the…

Consider a family of graphs having a fixed girth and a large size. We give an optimal lower asymptotic bound on the number of even cycles of any constant length, as the order of the graphs tends to infinity.

Let $\mathcal{F}\subseteq \binom{[n]}{r}$ be an intersecting family of sets and let $\Delta(\mathcal{F})$ be the maximum degree in $\mathcal{F}$, i.e., the maximum number of edges of $\mathcal{F}$ containing a fixed vertex. The…

Translate the positive-integer lattice points in the first quadrant by some amount in the horizontal and vertical directions. Take a decreasing concave (or convex) curve in the first quadrant and construct a family of curves by rescaling in…

In this paper we consider the problem of packing a fixed number of identical circles inside the unit circle container, where the packing is complicated by the presence of fixed size circular prohibited areas. Here the objective is to…

We obtain two parametric solutions of the diophantine equation $\phi(x_1, x_2, x_3)=\phi(y_1, y_2, y_3)$ where $\phi(x_1, x_2, x_3)$ is the octic form defined by $\phi(x_1, x_2, x_3)=x_1^8+ x_2^8 + x_3^8 - 2x_1^4x_2^4 - 2x_1^4x_3^4 -…

We give a pattern avoidance criterion to classify the orbits of Sp(p,C) x Sp(q,C) (resp. GL(n,C)) on the flag variety of type C_{p+q} (resp. D_n) with rationally smooth closure. We show that all such orbit closures fiber (with smooth fiber)…

Given two semistable, non potentially isotrivial elliptic surfaces over a curve $C$ defined over a field of characteristic zero or finitely generated over its prime field, we show that any compatible family of effective isometries of the…

The family of Euclidean triangles having some fixed perimeter and area can be identified with a subset of points on a nonsingular cubic plane curve, i.e., an elliptic curve; furthermore, if the perimeter and the square of the area are…

We develop two-scale methods for computing the convex envelope of a continuous function over a convex domain in any dimension.This hinges on a fully nonlinear obstacle formulation [A. M. Oberman, "The convex envelope is the solution of a…

This paper explores equi-centro-affine extremal hypersurfaces in an ellipsoid. By analyzing the evolution of invariant submanifold flows under centro-affine unimodular transformations, we derive the first and second variational formulas for…

We describe four special families of ellipse-inscribed Poncelet triangles about the incircle which maintain certain triangle centers stationary and which also display interesting conservations.

The aim of this paper is to study the singular solutions to fractional elliptic equations with absorption $$ \left\{\arraycolsep=1pt \begin{array}{lll} (-\Delta)^\alpha u+|u|^{p-1}u=0,\quad & \rm{in}\quad\Omega\setminus\{0\},\\[2mm]…

The hamiltonian circuit polytope is the convex hull of feasible solutions for the circuit constraint, which provides a succinct formulation of the traveling salesman and other sequencing problems. We study the polytope by establishing its…