Related papers: Extreme Points on Circumconics Induced by Isogonal…
We compute the number of triangulations of a convex $k$-gon each of whose sides is subdivided by $r-1$ points. We find explicit formulas and generating functions, and we determine the asymptotic behaviour of these numbers as $k$ and/or $r$…
In this survey, we consider the sharp Sobolev inequality in convex cones. We also prove it by using the optimal transport technique. Then we present some results related to the Euler-Lagrange equation of the Sobolev inequality: the…
The intersection matrix of a simplicial complex has entries equal to the rank of the intersection of its facets. In [1] the authors prove the intersection matrix is enough to determine a triangulation of a surface up to isomorphism. In this…
We count the number of conics through two general points in complete intersections when this number is finite and give an application in terms of quasi-lines.
We report the existence of exceptional points for the hydrogen atom in crossed magnetic and electric fields in numerical calculations. The resonances of the system are investigated and it is shown how exceptional points can be found by…
The collision of a fixed point with a switching manifold (or border) in a piecewise-smooth map can create many different types of invariant sets. This paper explores two techniques that, combined, establish a chaotic attractor is created in…
If we label the vertices of a triangle with 1, 2 and 4, and the orthocentre with 7, then any of the four numbers 1, 2, 4, 7 is the nim-sum of the other three and is their orthocentre. Regard the triangle as an orthocentric quadrangle.…
Given a triangulation of a closed topological cube, we show that (under some technical condition) there is an essentially unique tiling of a rectangular parallelepiped by cubes, indexed by the vertices of the triangulation. Moreover, i -…
We develop a rigidity theory for frameworks in $\mathbb{R}^3$ which have two coincident points but are otherwise generic and only infinitesimal motions which are tangential to a family of cylinders induced by the realisation are considered.…
A simple consequence of a theorem of Franks says that whenever a continuous map, $g$, is homotopic to angle doubling on the circle it is semiconjugate to it. We show that when this semiconjugacy has one disconnected point inverse, then the…
Across natural and human-made systems, transition points mark sudden changes of order and are thus key to understanding overarching system features. Motivated by recent experimental observations, we here uncover an intriguing class of…
Max cones are max-algebraic analogs of convex cones. In the present paper we develop a theory of generating sets and extremals of max cones in ${{\mathbb R}}_+^n$. This theory is based on the observation that extremals are minimal elements…
The paper is devoted to some extremal problems for convex curves and polygons in the Euclidean plane referring to the relative Chebyshev radius. In particular, we determine the relative Chebyshev radius for an arbitrary triangle. Moreover,…
In this note, we examine the arrangements of lines and configurations of points that emerge from Fermat (von Dyck) and Komiya-Kuribayashi quartics. These quartics are characterized by having the maximum number of lines of maximal tangency,…
We present a survey of some aspects and new results on configurations, i.e. disjoint unions of constellations of infinitely near points, local and global theory, with some applications and results on generalized Enriques diagrams, singular…
We study the double homology associated to triangulated spheres and present two results. First, we explicitly compute the double homology for minimum degree sphere triangulations. Using a spectral sequence argument, we compute the effect of…
We formulate a relationship between finite-order rondle invariants with respect to triple-point modifications and the lower central series of subgroups of a pure twin group. Using our formulation, we construct infinitely many infinite…
Exceptional points are singularities of eigenvalues and eigenvectors for complex values of, say, an interaction parameter. They occur universally and are square root branch point singularities of the eigenvalues in the vicinity of level…
If one erects regular hexagons upon the sides of a triangle $T$, several surprising properties emerge, including: (i) the triangles which flank said hexagons have an isodynamic point common with $T$, (ii) the construction can be extended…
We consider the problem of characterizing the extreme points of the set of analytic functions f on the bidisk with positive real part and f(0)=1. If one restricts to those f whose Cayley transform is a rational inner function, one gets a…