Waves on vortex cores

Here we discuss the types of waves which can be supported on compact regions of vorticity. This is a subject first studied by Lord Kelvin for waves propagating along the vortex lines of the Rankine and hollow-core vorticity distributions. Kelvin's major interest was in the stability of vortex rings and the numerous resurgencies in interest have usually been driven by practically important phenomena, e.g., the observations of vortex breakdown and waves on tornado and aircraft vortices in the early 1960's and more recently in technologically and geophysically significant flows and on the quantised vortices of super fluid HeII.

The major wave-types of interest are of varicose, helicoidal and fluted form and represent a periodic swelling and contraction, a bending and a “krinkling” of the core, respectively. The first two propagate along and the third around the vortex lines. All have been studied theoretically, experimentally and numerically in the limit of small wave amplitude and their major characteristics are now clear. Of particular interest is the extension of these results to the non-linear regime in which case the two first types are known to exhibit solitary wave or soliton characteristics in certain parameter ranges. It is these non-linear waves which often dominate observations of vortex flows both in nature and in technological applications and which have caused much controversy in the interpretation of results found under complex circumstances of flow and apparatus geometry.     

Diols and anions can control the formation of an exciplex between a pyridinium boronic acid with an aryl group connected via a propylene linker

The exciplex formation between a pyridinium boronic acid and phenyl group connected via a propylene linker can be monitored using fluorescence. Addition of pinacol affords a cyclic boronate ester with enhanced Lewis acidity that increases the strength of its cation-π stacking interaction causing a four-fold fluorescence enhancement.     

Ultrasonication-assisted spray ionization mass spectrometry for on-line monitoring of organic reactions

A straightforward on-line monitoring of organic reactions by ultrasonication-assisted spray ionization mass spectrometry (UASI MS) is demonstrated in this work.     

MATHEMATICS,LANGUAGE AND DERRIDA

Abstract

Derrida's revolutionary work in the study of language has seriously challenged the way in which we see words being attached to meanings. This paper makes tentative steps towards examining how his work might assist us in understanding the way in which our attempts to describe or capture our mathematical experiences modify the experience itself. In doing this we draw on the work of Jacques Derrida and John Mason in locating possible frameworks through which to conceptualise the relationship between language and mathematical cognition. It concludes that mathematical meaning never stabilises since it is caught between the individual's ongoing experience and society's ongoing renewal of its conventions. That is, mathematics, language and the human performing them are always evolving in relation to each other.     

A stochastic expectation-maximization algorithm for the analysis of system lifetime data with known signature

Statistical estimation of the model parameters of component lifetime distribution based on system lifetime data with known system structure is discussed here. We propose the use of stochastic expectation-maximization (SEM) algorithm for obtaining the maximum likelihood estimates of model parameters based on complete and censored system lifetimes. Different ways of implementing the SEM algorithm are also studied. We have shown that the proposed methods are feasible and are easy to implement for various families of component lifetime distributions. The proposed methodologies are then illustrated with two popular lifetime models—the Weibull and Birnbaum-Saunders distributions. Monte Carlo simulation is then used to compare the performance of the proposed methods with the corresponding estimation by direct maximization. Finally, two illustrative examples are presented along with some concluding remarks.