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Concept

Triangulation (topology)

Related publications (13)

Dual-Band Circularly Polarized Transmitarray Antenna for Satellite Communications at (20 to 30) GHz

Juan Ramon Mosig, Maria Garcia Vigueras, Santiago Capdevila Cascante, Joana Rita Alves dos Santos Silva, Hamed Hasani

A novel dual-band polarization-independent transmitarray is introduced in this paper for communication systems in Ka-band. Thanks to its unit-cell topology, the transmitarray antenna demonstrates almost complete independent performance at two design freque ...

2019

The hamburger theorem

Jan Kyncl

We generalize the ham sandwich theorem to d +1 measures on R-d as follows. Let mu(1), mu(2),..., mu(d+1) be absolutely continuous finite Borel measures on R-d. Let omega(i) = mu(i) (R-d) for i is an element of [d + 1], omega = min{omega(i) : i is an elemen ...

Elsevier Science Bv2018

Matching fields and lattice points of simplices

Georg Peter Loho

We show that the Chow covectors of a linkage matching field define a bijection of lattice points and we demonstrate how one can recover the linkage matching field from this bijection. This resolves two open questions from Sturmfels & Zelevinsky (1993) on l ...

2020

An improvement on the number of simplices in F-q(d)

Van Thang Pham

Let epsilon be a set of points in F-q(d). Bennett et al. (2016) proved that if \epsilon\ >> [GRAHICS] then epsilon determines a positive proportion of all k-simplices. In this paper, we give an improvement of this result in the case when epsilon is the Car ...

Elsevier Science Bv2017

High order discontinuous Galerkin methods on simplicial elements for the elastodynamics equation

Alfio Quarteroni

In this work we apply the discontinuous Galekin (dG) spectral element method on meshes made of simplicial elements for the approximation of the elastodynamics equation. Our approach combines the high accuracy of spectral methods, the geometrical flexibilit ...

Springer Verlag2016

Remarks on Schur's conjecture

János Pach, Filip Moric

Let P be a set of n > d points in for d >= 2. It was conjectured by Zvi Schur that the maximum number of (d-1)-dimensional regular simplices of edge length diam(P), whose every vertex belongs to P, is n. We prove this statement under the condition that any ...

Elsevier Science Bv2015

Bounds for Pach's Selection Theorem and for the Minimum Solid Angle in a Simplex

Jan Kyncl

We estimate the selection constant in the following geometric selection theorem by Pach: For every positive integer d, there is a constant such that whenever are n-element subsets of , we can find a point and subsets for every , each of size at least , suc ...

Springer2015

Extendability of Continuous Maps Is Undecidable

We consider two basic problems of algebraic topology: the extension problem and the computation of higher homotopy groups, from the point of view of computability and computational complexity. The extension problem is the following: Given topological space ...

Springer2014

Two and a half billion years of distance research

János Pach, Filip Moric

In a seminal paper published in 1946, Erd ̋os initiated the investigation of the distribution of distances generated by point sets in metric spaces. In spite of some spectacular par- tial successes and persistent attacks by generations of mathe- maticians, ...

2013

Weakly regular subdivisions

Lionel Pournin

It is shown that 2-dimensional subdivisions can be made regular by moving their vertices within parallel 1-dimensional spaces. As a consequence, any 2-dimensional subdivision is projected from the boundary complex of a 4-polytope. ...

Springer-Verlag2012

Overlap properties of geometric expanders

The overlap number of a finite (d + 1)-uniform hypergraph H is the largest constant c(H) is an element of (0, 1] such that no matter how we map the vertices of H into R-d, there is a point covered by at least a c(H)-fraction of the simplices induced by the ...

De Gruyter2011

The loop group and the cobar construction

Kathryn Hess Bellwald

We prove that for any 1-reduced simplicial set X, Adams' cobar construction, on the normalised chain complex of X is naturally a strong deformation retract of the normalised chains CGX on the Kan loop group GX, opening up the possibility of applying the to ...

American Mathematical Society (AMS)2010

Coalgèbres d'Alexander-Whitney : un modèle algébrique pour les espaces topologiques

The goal of this work is to study Alexander-Whitney coalgebras (first defined in [HPST06]) from a topological point of view. An Alexander-Whitney coalgebra is a coassociative chain coalgebra over Z with an extra algebraic structure : the comultiplication m ...

EPFL2009

Related publications (13)