A note on entropy inequalities and error estimates for higher-order accurate finite volume schemes on irregular families of grids

Recently, Cockburn, Coquel and LeFloch proved convergence and error estimates for higher-order finite volume schemes. Their result is based on entropy inequalities which are derived under restrictive assumptions on either the flux function or the numerical fluxes. Moreover, they assume that the spatial grid satisfies a standard regularity assumption. Using instead entropy inequalities derived in previous work by Kröner, Noelle and Rokyta and a weaker condition on the grid, we can generalize and simplify the error estimates.

     

Usage of systematic multi-body equations of motion for the design of a nonlinear vehicle dynamics controller

In this article the authors outline how systematic multi-body equations can efficiently be used to derive a model for the design of a nonlinear vehicle dynamics controller for truck-semitrailer combinations, steering the last trailer axle. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental and Numerical Study of Polypropylene/Polyethylene Thin Foil in Biaxial Tension

The material under consideration is a thermoplastic copolymer blend of polypropylene and polyethylene (PP/PE), constituting the core layer of a steel/polymer/steel composite material. A biaxial loading machine was developed for studying the behavior of the copolymer subjected to in-plane complex stress states. A study on the shape of the specimen by means of numerical finite element simulations and preliminary experimental tests are carried out, in order to obtain a maximization of the strain distribution in the middle region of the cruciform specimen. Afterwards, the sensitivity of the mechanical response under both equibiaxial and non-equibiaxial conditions is addressed. All the experiments are monitored by means of a digital image correlation (DIC) system, providing full-field measurements of the displacements, and, consequently, of the strain distribution. The presented experimental results will be used for validating the material model developed for the PP/PE layer material. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Red-blue covering problems and the consecutive ones property

Set Cover problems are of core importance in many applications. In recent research, the “red-blue variants” where blue elements all need to be covered whereas red elements add further constraints on the optimality of a covering have received considerable interest. Application scenarios range from data mining to interference reduction in cellular networks. As a rule, these problem variants are computationally at least as hard as the original set cover problem. In this work we investigate whether and how the well-known consecutive ones property, restricting the structure of the input sets, makes the red-blue covering problems feasible. We explore a sharp border between polynomial-time solvability and NP-hardness for these problems.     

A skew normal dilation on the numerical range of an operator

Simple facts about the Poincaré-Neumann double layer potential are used in the construction of a normal dilation, on the numerical range of an arbitrary Hilbert space operator. Recent and old ideas in the theory of the numerical range are unified by this framework. A couple of mapping results for the numerical range are derived.Revised version: 15 July 2002First author partially supported by the National Science Foundation Grant DMS 0100367, Second author supported by STINT, The Swedish Foundation for International Cooperation in Research and Higher Education.     

Postoptimal analysis in multicriteria linear programming

The aim of the paper is to present the postoptimal analysis of a chosen extreme efficient point in multicriteria linear programming. There are three cases considered: one objective function coefficient change, objective function addition and objective function removal. The proven theorems allow us to create methods based on the analysis of a simplex tableau.     

Harnack inequalities on weighted graphs and some applications to the random conductance model

We establish elliptic and parabolic Harnack inequalities on graphs with unbounded weights. As an application we prove a local limit theorem for a continuous time random walk \(X\) in an environment of ergodic random conductances taking values in \((0, \infty )\) satisfying some moment conditions.     

Virtual boundaries of Hadamard spaces with admissible actions of higher rank

In this paper, we prove that every conformal minimal immersion of an open Riemann surface into \({\mathbb {R}}^n\) for \(n\ge 5\) can be approximated uniformly on compacts by conformal minimal embeddings (see Theorem 1.1). Furthermore, we show that every open Riemann surface carries a proper conformal minimal embedding into \({\mathbb {R}}^5\) (see Theorem 1.2). One of our main tools is a Mergelyan approximation theorem for conformal minimal immersions to \({\mathbb {R}}^n\) for any \(n\ge 3\) which is also proved in the paper (see Theorem 5.3).     

On the Majorana condition for nonlinear Dirac systems

For arbitrarily large initial data in an open set defined by an approximate Majorana condition, global existence and scattering results for solutions to the Dirac equation with Soler-type nonlinearity and the Dirac–Klein–Gordon system in critical spaces in spatial dimension three are established.     

The Schur–Potapov Algorithm for Sequences of Complex p × q Matrices. II

This is the second and final part of a paper which appeared in a preceding issue of this journal. Herein the methods developed in the earlier sections of this paper are used first to develop a number of applications. A central theme of this paper is to study the interplay between functions from and their sequence of SP-parameters. In particular, we describe how certain summability properties of the SP-parameters are expressed in terms of the associated functions from . As a byproduct of our investigations on the interplay between the SP-algorithm for p × q Schur functions and the SP-algorithm for sequences of complex p × q matrices we present a new approach to the nondegenerate matricial Schur problem. Our method complies with the basic strategy in Schur’s classical paper [138] because it does not make use of any tools outside of the theory of Schur functions and Schur sequences. A closer look at the behaviour of distinguished subclasses of with respect to the SP-algorithm enables us to handle the corresponding versions of the matricial Schur problem restricted to these subclasses. Submitted: August 17, 2006. Accepted: September 13, 2006.