Mathematical attitudes and semantic differentials

The semantic differential—one approach to attitude measurement— basically records a combination of a person's associations with a particular concept with a scaling procedure. This paper considers the implications of such a device for teachers of mathematics.     

BMO‐Type Norms Related to the Perimeter of Sets

In this paper we consider an isotropic variant of the BMO‐type norm recently introduced (Bourgain, Brezis, and Mironescu, 2015). We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.© 2016 Wiley Periodicals, Inc.     

Indirect UV detection of carbohydrates in capillary zone electrophoresis

Summary A new system for the rapid and sensitive analysis of underivatized carbohydrates has been established using capillary zone electrophoresis with indirect UV detection. At an applied potential of 28 kV, sugars and sugar acids could be separated by the combined effects of electroendosmosis and electrophoresis within 20 minutes in a fused silica capillary of 50 m internal diameter and an effective length of 100 cm using 6mM sorbic acid, pH 12.1, as both carrier electrolytie and chromophore. The alkaline pH ensured ionization of the sugars and, hence, their detection by means of charge displacement. Furthermore, the chosen concentration of sorbic acid allowed the smallest fractional change in the background signal to be measured. While the electrophoretic mobilities of the sugars were found to increase within a pH range of 11.9 to 12.3, those of the sugar acids were not affected. Due to the increasing competition of hydroxide ions in the displacement of the chromophore with rising pH, a significant loss of sensitivity is observed at pH values higher than 12.1 and this pH was found to provide sufficient resolution, optimum sensitivity, and a acceptably short analysis time. Under these conditions, a lower detection limit of 2 pmol was obtained for glucose.     

Screened hydrodynamic interaction in a narrow channel

We study experimentally and theoretically the hydrodynamic coupling between Brownian colloidal particles diffusing along a linear channel. The quasi-one-dimensional confinement, unlike other constrained geometries, leads to a sharply screened interaction. Consequently, particles move in concert only when their mutual distance is smaller than the channel width, and two-body interactions remain dominant up to high particle densities. The coupling in a cylindrical channel is predicted to reverse sign at a certain distance, yet this unusual effect is too small to be currently detectable.     

On the convergence rate of Fourier series

The rate of convergence of a Fourier‐series representation of a given function depends on the nature of the function and of its derivatives. This is shown by using the graphical outputs of a desk computer for different cases. For full‐range series, the effects of continuity and discontinuity of the function and its first derivatives are shown first. The advantage of half‐range formulae due to the free choice of function in the second half‐range are demonstrated next, along with the importance of choice of sine and cosine series according to the function being represented. Finally, a method is given of modifying the given function in a simple manner whereby a dramatic increase in the rate of convergence of the Fourier series is obtained. Examples of the Gibbs overshoot and its elimination are included.