Myers-Type Theorems and Some Related Oscillation Results

In this paper we study the behavior of solutions of a second-order differential equation. The existence of a zero and its localization allow us to get some compactness results. In particular we obtain a Myers-type theorem even in the presence of an amount of negative curvature. The technique we use also applies to the study of spectral properties of Schr?dinger operators on complete manifolds.     

The BIOREMA project—part 3: International interlaboratory comparison for bio-ethanol test methods

The main objective of the reference materials for biofuel specifications (BIOREMA) project is the development of two test materials (one bio-ethanol material and one biodiesel material) with well-established reference values. Of a series of three papers, this part describes the material preparation, homogeneity study, stability study, and characterisation of the bio-ethanol material. The test material thus obtained was used in an interlaboratory comparison (ILC) to assess current practices and comparability amongst laboratories providing bio-ethanol testing services. Only 13 participants provided data, resulting in a small dataset for evaluation. Further, it appeared that for a number of laboratories, there was not sufficient material for the determination of all requested parameters. In most cases, as far as the data permit, it can be concluded that the consensus values (based on participant’s results) are in good agreement with the reference or the BIOREMA values (obtained by NMIs participating in the project). For three parameters, namely ethanol content, water content, and density, there is good agreement between the reference and consensus values. For these parameters, the reproducibility standard deviation is close to, or even smaller than, the expanded uncertainty associated with the reference value. A number of parameters show very poor reproducibility, for example, pH_e, electrolytic conductivity, and acidity. The same applies to sodium and copper content, which are very low and therefore challenging parameters to measure accurately. The results of the ILC underpin the need for certified reference materials and demonstrate the requirement for more robust quality control to improve the precision and trueness of the results from testing laboratories.     

Conservative numerical methods for the Full von Kármán plate equations

This article is concerned with the numerical solution of the full dynamical von Kármán plate equations for geometrically nonlinear (large‐amplitude) vibration in the simple case of a rectangular plate under periodic boundary conditions. This system is composed of three equations describing the time evolution of the transverse displacement field, as well as the two longitudinal displacements. Particular emphasis is put on developing a family of numerical schemes which, when losses are absent, are exactly energy conserving. The methodology thus extends previous work on the simple von Kármán system, for which longitudinal inertia effects are neglected, resulting in a set of two equations for the transverse displacement and an Airy stress function. Both the semidiscrete (in time) and fully discrete schemes are developed. From the numerical energy conservation property, it is possible to arrive at sufficient conditions for numerical stability, under strongly nonlinear conditions. Simulation results are presented, illustrating various features of plate vibration at high amplitudes, as well as the numerical energy conservation property, using both simple finite difference as well as Fourier spectral discretizations. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1948–1970, 2015