Concept
Quadrilatère
Publications associées (17)
A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane
Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...
Electronic Journal Of Combinatorics2024Atomic-scale insights into the origin of rectangular lattice in nanographene probed by scanning tunneling microscopy
We conducted atomic-scale scanning tunneling microscopy of a graphene nanosheet on graphite. In addition to a rhombus lattice representing the (root 3x root 3)R30 degrees superstructure, we resolved another quadrangle lattice similar to a rectangle in the ...
AMER PHYSICAL SOC2021On Katznelson's Question for skew product systems
Katznelson's Question is a long-standing open question concerning recurrence in topological dynamics with strong historical and mathematical ties to open problems in combinatorics and harmonic analysis. In this article, we give a positive answer to Katznel ...
2021Twisted Bilayer Graphene Quantum Dots for Chiral Nanophotonics
Twisted bilayer graphene (TBG) is a two-dimensional chiral material whose optical activity is remarkably strong for its atomic thickness. While the chiral optical properties of TBG are currently well understood, the optical activity of quantum dots (QDs) m ...
2020Vase-Kite Equilibrium of Resorcin[4]arene Cavitands Investigated Using Molecular Dynamics Simulations with Ball-and-Stick Local Elevation Umbrella Sampling
A key feature of resorcin[4]arene cavitands is their ability to switch between a closed/contracted (Vase) and an open/expanded (Kite) conformation. The mechanism and dynamics of this interconversion remains, however, elusive. In the present study, the Vase ...
2019Bisector Energy and Few Distinct Distances
We define the bisector energy E(P) of a set P in R-2 to be the number of quadruples (a, b, c, d) is an element of P-4 such that a, b determine the same perpendicular bisector as c, d. Equivalently, E(P) is the number of isosceles trapezoids determined by P ...
Springer2016Mixed strain-displacement finite elements for landslide and avalanche release prediction
Determination of the initial detaching volume is one of the major challenges in snow avalanche and debris flow forecast. Soil liquefaction due to loss of cohesion results in landslides, whereas quasi-brittle failure triggers the release of snow avalanches. ...
2015Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity
This paper presents the application of a stabilized mixed strain/displacement finite element formulation for the solution of nonlinear solid mechanics problems involving compressible and incompressible plasticity. The variational multiscale stabilization i ...
Elsevier2015Upper bounds for the perimeter of plane convex bodies
We show that the maximum total perimeter of k plane convex bodies with disjoint interiors lying inside a given convex body C is equal to , in the case when C is a square or an arbitrary triangle. A weaker bound is obtained for general plane convex bodies. ...
Springer2014