Related papers: Heronian friezes
A classic result of Conway and Coxeter on frieze patterns has been generalized to a bijection between $p$-angulations of regular polygons and frieze patterns of type $\Lambda_p$. One of the features of Conway-Coxeter theory is a…
We prove coherence of relatively quasi-free algebras over noetherian rings. Chase criterion for coherence is used.
Inspired by the concept of coherent frozen waves, this paper introduces one possible theoretical framework of its partially coherent version, a frozen spatial coherence, in which a desired two-point correlation structure of an optical field…
We give a complete solution to the Mandelbrot-Kahane problem for the microcanonical cascade measures by determing their exact Fourier dimensions. We also discuss the Frostman regularity as well as the bi-H\"older continuity of the…
This article, based on joint work with Gabriel Carroll, Andy Itsara, Ian Le, Gregg Musiker, Gregory Price, Dylan Thurston, and Rui Viana, presents a combinatorial model based on perfect matchings that explains the symmetries of the…
Poisson plane and sphere --- homogeneous spaces of Poisson groups E(2) and SU(2) (resp.) --- have phase spaces (corresponding symplectic groupoids), in which a free Hamiltonian is naturally defined. We solve the equations of motion and…
A fibration of a Riemannian manifold is fiberwise homogeneous if there are isometries of the manifold onto itself, taking any given fiber to any other one, and preserving fibers. Examples are fibrations of Euclidean n-space by parallel…
One of the important theorems in homotopy theory is the Hilton splitting. In this paper we will construct all the Hilton homomorphisms by geometrical means and prove a family of sharper symmetry relations of linking coefficients which…
The emergence of statistical complexity in frictional systems, manifested in broad distributions of various observables, is not yet understood. We study this problem in velocity-driven, homogeneous (no quenched disorder) unstable frictional…
Coxeter defined the notion of frieze pattern, and Conway and Coxeter proved that triangulations of polygons are in bijection with integral frieze patterns. We show a $p$-angulated generalisation involving non-integral frieze patterns. We…
In this paper we consider the effect of symmetry on the rigidity of bar-joint frameworks, spherical frameworks and point-hyperplane frameworks in $\mathbb{R}^d$. In particular we show that, under forced or incidental symmetry, infinitesimal…
We study the asymptotic consistency properties of $\alpha$-R\'enyi approximate posteriors, a class of variational Bayesian methods that approximate an intractable Bayesian posterior with a member of a tractable family of distributions, the…
We give explicit formulae for fringe lengths of the Calegari-Walker Ziggurats -- i.e. graphs of extremal rotation numbers associated to positive words in free groups. These formulae reveal (partial) integral projective self-similarity in…
We use proof mining techniques to obtain a uniform rate of asymptotic regularity for the instance of the parallel algorithm used by L\'opez-Acedo and Xu to find common fixed points of finite families of $k$-strict pseudocontractive…
We show that the eigenvalues of any polarized endomorphism acting on the $\ell$-adic \'etale cohomology of a smooth projective variety satisfy certain parity and symmetry properties, as predicted by the standard conjectures. These…
The properties common to the Lorenz and Chen attractors, as well as their fundamental differences, have been studied for many years in a vast number of works and remain a topic far from a rigorous and complete description. In this paper we…
We study the structure of the Mather and Aubry sets for the family of lagrangians given by the kinetic energy associated to a riemannian metric $ g$ on a closed manifold $ M$. In this case the Euler-Lagrange flow is the geodesic flow of…
By Tits' deformation argument, a generic Iwahori--Hecke algebra $H$ associated to a finite Coxeter group $W$ is abstractly isomorphic to the group algebra of $W$. Lusztig has shown how one can construct an explicit isomorphism, provided…
It is well known in general relativity that trajectories of Hamiltonian systems lift to geodesics of pp-wave spacetimes, an example of a more general phenomenon known as the "Eisenhart lift." We review and expand upon the benefits of this…
We use Moser's normal forms to study chaotic motion in two-degree hamiltonian systems near a saddle point. Besides being convergent, they provide a suitable description of the cylindrical topology of the chaotic flow in that vicinity. Both…