A Mass for ALF Manifolds

We prove a positive mass theorem on ALF manifolds, i.e. complete noncompact manifolds that are asymptotic to a circle fibration over a Euclidean base, with fibers of asymptotically constant length.     

Dynamic Ion Speciation during the Hydrolysis of Aryltrifluoroborates**

Organotrifluoroborates serve as coupling partners during transmetalation in the Suzuki–Miyaura reaction but require hydrolysis prior to the coupling reaction. Their anionic nature allows study of their hydrolysis by electrospray ionization mass spectrometry (ESI-MS) through real-time monitoring, complemented by pH analysis. The induction period varied according to the borates employed, and a dynamic series of equilibria for numerous ions was observed during hydrolysis. We found that the induction periods and reaction rates were sensitive to the R group of the borates, the shape of the reaction vessel, and stir rate.     

Carbon Materials for Lithium Sulfur Batteries—Ten Critical Questions

Lithium–sulfur batteries are among the most promising electrochemical energy storage devices of the near future. Especially the low price and abundant availability of sulfur as the cathode material and the high theoretical capacity in comparison to state‐of‐the art lithium‐ion technologies are attractive features. Despite significant research achievements that have been made over the last years, fundamental (electro‐) chemical questions still remain unanswered. This review addresses ten crucial questions associated with lithium–sulfur batteries and critically evaluates current research with respect to them. The sulfur–carbon composite cathode is a particular focus, but its complex interplay with other hardware components in the cell, such as the electrolyte and the anode, necessitates a critical discussion of other cell components. Modern in situ characterisation methods are ideally suited to illuminate the role of each component. This article does not pretend to summarise all recently published data, but instead is a critical overview over lithium–sulfur batteries based on recent research findings.     

A note on records in a random sequence

In an infinite sequence of independent identically distributed continuous random variables we study the number of strings of two subsequent records interrupted by a given number of non-records. By embedding in a marked Poisson process we prove that these counts are independent and Poisson distributed. Also the distribution of the number of uninterrupted strings of records is considered.     

Pairs of oblique duals in spaces of periodic functions

We construct non-tight frames in finite-dimensional spaces consisting of periodic functions. In order for these frames to be useful in practice one needs to calculate a dual frame; while the canonical dual frame might be cumbersome to work with, the setup presented here enables us to obtain explicit constructions of some particularly convenient oblique duals. We also provide explicit oblique duals belonging to prescribed spaces different from the space where we obtain the expansion. In particular this leads to oblique duals that are trigonometric polynomials.     

Positivity preserving finite element approximation

We consider finite element operators defined on ``rough' functions in a bounded polyhedron in . Insisting on preserving positivity in the approximations, we discover an intriguing and basic difference between approximating functions which vanish on the boundary of and approximating general functions which do not. We give impossibility results for approximation of general functions to more than first order accuracy at extreme points of . We also give impossibility results about invariance of positive operators on finite element functions. This is in striking contrast to the well-studied case without positivity.

     

Taylor dispersion monitored by electrospray mass spectrometry: a novel approach for studying diffusion in solution

This work describes a novel approach for monitoring analyte diffusion in solution that is based on electrospray ionization mass spectrometry (ESI-MS). A mass spectrometer at the end of a laminar flow tube is used to measure the Taylor dispersion of an initially sharp boundary between two solutions of different analyte concentration. This boundary is dispersed by the laminar flow profile in the tube. However, this effect is diminished by analyte diffusion that continuously changes the radial position, and hence the flow velocity of individual analyte molecules. The steepness of the resulting dispersion profile therefore increases with increasing diffusion coefficient of the analyte. A theoretical framework is developed to adapt the equations governing the dispersion process to the case of mass spectrometric detection. This novel technique is applied to determine the diffusion coefficients of choline and cytochrome c. The measured diffusion coefficients, (11.9 +/- 1.0) x 10(-10) m(2) s(-1) and (1.35 +/- 0.08) x 10(-10) m(2) s(-1), respectively, are in agreement with the results of control experiments where the Taylor dispersion of these two analytes was monitored optically. Due to the inherent selectivity and sensitivity of ESI-MS, it appears that the approach described in this work could become a valuable alternative to existing methods for studying diffusion processes, especially for experiments on multicomponent systems.