Frequency-Dependent Streaming Potentials

An experimental apparatus and data acquisition system was constructed to measure the streaming potential coupling coefficients as a function of frequency. The purpose of the experiments was to measure, for the first time, the real and imaginary portion of streaming potentials. In addition, the measured frequency range was extended beyond any previous measurements. Frequency-dependent streaming potential experiments were conducted on one glass capillary and two porous glass filters. The sample pore diameters ranged from 1 mm to 34 μm. Two frequency-dependent models (Packard and Pride) were compared to the data. Both Pride's and Packard's models have a good fit to the experimental data in the low- and intermediate-frequency regime. In the high-frequency regime, the data fit the theory after being corrected for capacitance effects of the experimental setup. Pride's generalized model appears to have the ability to more accurately estimate pore sizes in the porous medium samples. Packard's model has one unknown model parameter while Pride's model has four unknown model parameters, two of which can be independently determined experimentally. Pride's additional parameters may allow for a determination of permeability. Copyright 2001 Academic Press.     

The investigation of an equilibrium dependent reaction for the formation of enamines in a microchemical system

The paper describes the equilibrium dependant reaction for the formation of enamines in a microchemical system utilising electroosmotic flow (EOF) for fluid mobilisation. The authors have shown that the reaction can be carried out without the presence of a Lewis acid catalyst, in addition the enamine intermediate was synthesised at room temperature using mild solvent conditions. A 42% conversion of cyclohexanone into the enamine has been achieved to date.     

High-performance liquid chromatographic method to resolve and determine lipopolysaccharide sub-groups of Escherichia coli endotoxin in isolated perfused rat liver perfusate.

A high-performance liquid chromatographic method was developed for resolving heterogeneous preparations of fluorescently labelled endotoxin derived from Escherichia coli (Serotype 0111:B4) into separate lipopolysaccharide sub-groups. The endotoxin was chromatographed on an analytical gel permeation column using a mobile phase of acetonitrile (20%, v/v) and 100 mM phosphate buffer (pH 7.75). Four fluorescent peaks were resolved, representing sub-groups of markedly different molecular sizes. Three of the four sub-groups contained the core polysaccharide 2-keto-3-deoxyoctonate, confirming that they contained lipopolysaccharide. Fluorescein isothiocyanate (FITC)-labelled endotoxins derived from Vibrio cholerae and Salmonella minnesota chromatographed using the same system eluted with distinctly different patterns of peaks from each other and from E. coli. Extraction of E. coli FITC-endotoxin from a buffer solution using a phenol-diethyl ether method and subsequent chromatography allowed the determination of three of the four fluorescent sub-groups over the concentration range 1-15 micrograms/ml.     

A theoretical approximation scheme for Stackelberg problems

We consider the Stackelberg problem corresponding to a two-player game in which one of the two players has the leadership in playing the game. We present a general approach for approximating the considered hierarchical programming problem by a sequence of two-level optimization problems. From a practical point of view, we also give some results for asymptotically Stackelberg approximating sequences and for problems with perturbed constraints.This paper is based upon results first presented at Journées Fermat: Mathematics for Optimization, Toulouse, France, May 1985.     

Simultaneous local exact controllability of 1D bilinear Schrödinger equations

We consider N independent quantum particles, in an infinite square potential well coupled to an external laser field. These particles are modelled by a system of linear Schrödinger equations on a bounded interval. This is a bilinear control system in which the state is the N  -tuple of wave functions. The control is the real amplitude of the laser field. For N=1$N=1$, Beauchard and Laurent proved local exact controllability around the ground state in arbitrary time. We prove, under an extra generic assumption, that their result does not hold in small time if N?2$N?2$. Still, for N=2$N=2$, we prove that local controllability holds either in arbitrary time up to a global phase or exactly up to a global delay. This is proved using Coron's return method. We also prove that for N?3$N?3$, local controllability does not hold in small time even up to a global phase. Finally, for N=3$N=3$, we prove that local controllability holds up to a global phase and a global delay.     

A linear algorithm for a core of a tree

A core of a graph G is a path P in G that is central with respect to the property of minimizing d(P) = Σ_υ?V(G)d(υ, P), where d(υ, P) is the distance from vertex υ to path P. We present a linear algorithm for finding a core of a tree. Since the core of a graph is not necessarily unique, we also output a list of all the vertices which are in some core.     

The standard double bubble is the unique stable double bubble in

We prove that the only equilibrium double bubble in which is stable for fixed areas is the standard double bubble. This uniqueness result also holds for small stable double bubbles in surfaces, where it is new even for perimeter-minimizing double bubbles.

     

Corrigendum to “Maximal linear groups induced on the Frattini quotient of a p-group” [J. Pure Appl. Algebra 222 (10) (2018) 2931–2951]

We give a correction to Fig. 1 and supporting text published in the paper: ‘Maximal linear groups induced on the Frattini quotient of a p-group’, J. Pure Appl. Algebra 222 (10) (2018) 2931–2951.     

To what extent are students expected to participate in specialised mathematical discourse? Change over time in school mathematics in England

ABSTRACT

From a discursive perspective, differences in the language in which mathematics questions are posed change the nature of the mathematics with which students are expected to engage. The project The Evolution of the Discourse of School Mathematics (EDSM) analysed the discourse of mathematics examination papers set in the UK between 1980 and 2011. In this article we address the issue of how students over this period have been expected to engage with the specialised discourse of school mathematics. We explain our analytic methods and present some outcomes of the analysis. We identify changes in engagement with algebraic manipulation, proving, relating mathematics to non-mathematical contexts and making connections between specialised mathematical objects. These changes are discussed in the light of public and policy domain debates about ‘standards’ of examinations.