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A graph G is a diameter graph in R-d if its vertex set is a finite subset in R-d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in R-4 contains the complete subgraph K on five vertices, then any ...
Modifying the moduli of supporting convexity and supporting smoothness, we introduce new moduli for Banach spaces which occur, for example, as lengths of catheti of right-angled triangles (defined via so-called quasiorthogonality). These triangles have two ...
We prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent: 1.On marked simplicial sets (due to Lurie [31]), 2.On bisimplicial spaces (due to deBrito [12]), 3.On bisimplicial sets, 4.On m ...
We present a methodology to simulate the mechanics of knots in elastic rods using geometrically nonlinear, full three-dimensional (3D) finite element analysis. We focus on the mechanical behavior of knots in tight configurations, for which the full 3D defo ...
A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, ex ...
We extend the quasiparticle self-consistent approach beyond the GW approximation by using a range separated vertex function. The developed approach yields band gaps, dielectric constants, and band positions with an accuracy similar to highest-level electro ...
In previous research, microsaccades have been suggested as psychophysiological indicators of task load. So far, it is still under debate how different types of task demands are influencing microsaccade rate. This piece of research examines the relation bet ...
Cao and Yuan obtained a Blichfeldt-type result for the vertex set of the edge-to-edge tiling of the plane by regular hexagons. Observing that the vertex set of every Archimedean tiling is the union of translates of a fixed lattice, we take a more general v ...
