Regular principal factors in free objects in varieties in the interval [B 2 ,NB 2 ∨G n ]

The author has shown previously how to associate a completely 0-simple semigroup with a connected bipartite graph containing labelled edges and how to describe the regular principal factors in the free objects in the Rees-Sushkevich varieties RS _n generated by all completely 0-simple semigroups over groups from the Burnside variety G _n of groups of exponent dividing a positive integer n by employing this graphical construction. Here we consider the analogous problem for varieties containing the variety B ₂ , generated by the five element Brandt semigroup B ₂, and contained in the variety NB ₂ ∨G _n where NB ₂ is the variety generated by all left and right zero semigroups together with B ₂. The interval [NB ₂ ,NB ₂ ∨G _n ] is of particular interest as it is an important interval, consisting entirely of varieties generated by completely 0-simple semigroups, in the lattice of subvarieties of RS _n .     

Thermodynamic properties and rheology of sterically stabilized colloidal dispersions

A procedure for predicting thermodynamic, dynamic, and rheological properties of polymerically stabilized colloidal dispersions in good solvents by mapping onto an effective hard sphere dispersion is investigated and evaluated for its range of applicability. Configurational pressures and energies, calculted by Monte Carlo simulations, are used to assess the model's accuracy for predicting thermodynamic data. Similarly, long-time self-diffusivities, calculated by equilibrium Brownian Dynamic simulations, are used to assess the model's feasibility for predicting dynamic properties. Finally, zero shear viscosities are calculated by the method of hydrodynamic preaveraging and compared to rheological measurements. The various testing methods demonstrate the effectiveness of the procedure and suggest the model's range of applicability. Received: 13 March 2000 Accepted: 28 June 2000     

Systematic evaluation of acetone and acetonitrile for use in hydrophilic interaction liquid chromatography coupled with electrospray ionization mass spectrometry of basic small molecules

Sub‐2‐µm particle size hydrophilic interaction liquid chromatography [HILIC] combined with mass spectrometry has been increasing in popularity as a complementary technique to reversed‐phase LC for the analysis of polar analytes. The organic‐rich mobile phase associated with HILIC techniques provides increases in compound ionization, due to increased desolvation efficiency during electrospray ionisation mass spectrometric (ESI‐MS) analysis. Although recent publications illustrated selectivity and response comparisons between reversed‐phase LC/MS and HILIC LC/MS, there are limited discussions evaluating the optimisation of the mass spectrometry parameters regarding analytes and alternative mobile phases. The use of acetone as an alternative organic modifier in HILIC has been investigated with respect to signal‐to‐noise in ESI‐MS for a variety of polar analytes. Analyte reponses were measured based on a variety of cone and capillary voltages at low and high pH in both acetone and acetonitrile. In order to visualise compound behaviour in the ESI source, surface plots were constructed to assist in interpreting the observed results. The use of acetone in ESI is complicated at low m/z due to the formation of condensation products. Favourable responses were observed for certain analytes and we envisage offering an insight into the use of acetone as an alternative to acetonitrile under certain analytical conditions for particular compound classifications for small molecule analysis. We also highlight the importance of optimising source voltages in order to obtain the maximum signal stability and sensitivity, which are invariably, highly solvent composition dependent parameters. Copyright © 2011 John Wiley & Sons, Ltd.     

A Class of Operator Equations in Nonlinear Mechanics

A nonlinear evolution equation in Hilbert space is introduced and is shown to govern a broad class of problems of nonlinear solid mechanics. The simplest oscillations of this equation are described by a “generalized Liénard equation.”

AMS(MOS) Classification Nos: 73D35, 73F15, 58D25, 35L35, 34G20, 34C15.     

Preservice Teachers' Use of Multiple Representations In Solving Arithmetic Mean Problems

The development of preservice teachers' views of various mathematical concepts involves building a repertoire of flexible representations of the concepts they teach. In this study, science and mathematics preservice teachers (n = 19) were asked to solve graphical and numerical problems involving the arithmetic mean and to provide two different solutions for each problem. Background information about the preservice teachers was obtained, including subject area specialty, type of statistics courses previously taken, type of science laboratory courses previously taken, and prior experience with real data outside the classroom. In solving the problems, some participants presented two different methods: algorithmic computation and balancing deviations about the mean. A significant difference was found between science and mathematics preservice teachers in the use of balancing deviations to solve the problems but not in the use of the computational algorithm.     

A Comparison of Expert System and Human Operator Performance for Cement Kiln Operation

Using an observational study of the operation of a cement kiln and a set of operational rules published by Peray and Waddell, five knowledge-based advisory systems have been developed encapsulating the supervisory expertise of the process operators. The advisory systems were developed in the logic language PROLOG. Each expert adviser was applied to a set of plant data previously logged from the kiln, and the advice offered was compared with the actions taken by the operators. Statistical tests have been applied to the outcome of the comparisons in order to determine which expert adviser emulated the operator performance most successfully. The results demonstrate the value of such tests in quantitatively validating expert systems. In addition, the supervisory techniques that the operators were using in practice were identified.     

On the dimension of the algebra generated by a boolean matrix

We investigate the subspace of the space of all n × n Boolean (0,1)-matrices, spanned by the powers of an arbitrary matrix. We estimate the maximum dimension of such spaces as a function of n and show that their bases consists of consecutive integer powers of the matrix, starting at I. We also determine the maximum dimension of the space spanned by the powers of as symmetric matrix and characterise the matrices achieving that maximum.