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Arc length

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Optimal Fair Computation

Rachid Guerraoui, Junxiong Wang

A computation scheme among n parties is fair if no party obtains the computation result unless all other n-1 parties obtain the same result. A fair computation scheme is optimistic if n honest parties can obtain the computation result without resorting to ...

2016

Understanding the mixing process in 3D microfluidic nozzle/diffuser systems: simulations and experiments

Martinus Gijs, Abdeljalil Sayah

We characterise computationally and experimentally a three-dimensional (3D) microfluidic passive mixer for various Reynolds numbers ranging from 1 to 100, corresponding to primary flow rates of 10-870 mu l min(-1). The 3D mixing channel is composed of mult ...

Iop Publishing Ltd2016

Goodwillie calculus and Whitehead products

Jérôme Scherer

We prove that iterated Whitehead products of length. (n+1) vanish in any value of an n-excisive functor in the sense of Goodwillie. We compare then different notions of homotopy nilpotency, from the Berstein-Ganea definition to the Biedermann-Dwyer one. Th ...

Walter de Gruyter2015

Free Edge Lengths in Plane Graphs

Radoslav Fulek, Filip Moric

We study the impact of metric constraints on the realizability of planar graphs. Let G be a subgraph of a planar graph H (where H is the "host" of G). The graph G is free in H if for every choice of positive lengths for the edges of G, the host H has a pla ...

Springer2015

Similarity-Based Shape Priors for 2D Spline Snakes

Michaël Unser, Daniel Andreas Schmitter

We present a new formulation of a shape space containing all continuously defined 2D spline curves up to a similarity transform of a reference shape. We are able to measure a distance between an arbitrary curve and the shape space itself. Our contribution ...

IEEE2015

Empty Triangles in Complete Topological Graphs

Andres Jacinto Ruiz Vargas

A simple topological graph is a graph drawn in the plane so that its edges are represented by continuous arcs with the property that any two of them meet at most once. Let be a complete simple topological graph on vertices. The three edges induced by any t ...

Springer2015

Air concentration distribution in deflector-jets

Michael Pfister, Sebastian Schwindt

As an alternative to ski jumps, deflectors can be implemented on spillways to generate free jets. They guide, up to a certain limit, the jet to an achieved location onto the plunge pool surface, and furthermore enhance the process of jet disintegration. Th ...

The University of Queensland2014

Large global solutions for energy supercritical nonlinear wave equations on $\R^{3+1}$

Joachim Krieger

For the radial energy-supercritical nonlinear wave equation

\Box u = -u_{tt} + \triangle u = \pm u^7

\R^{3+1}

, we prove the existence of a class of global in forward time

C^\infty

-smooth solutions with infinite critical Sobolev norm $\dot{H}^{\f ...

Springer Verlag2014

Constructing reparameterization invariant metrics on spaces of plane curves

Martins Bruveris, Martin Bauer

Metrics on shape spaces are used to describe deformations that take one shape to another, and to define a distance between shapes. We study a family of metrics on the space of curves, which includes several recently proposed metrics, for which the metrics ...

Elsevier2014

The visible perimeter of an arrangement of disks

János Pach, Gábor Tardos, Gabriel Nivasch

Given a collection of n opaque unit disks in the plane, we want to find a stacking order for them that maximizes their visible perimeter, the total length of all pieces of their boundaries visible from above. We prove that if the centers of the disks form ...

Elsevier Science Bv2014