Recent changes in A-level Mathematics: is the availability and uptake of mechanics declining yet more?

In the past 6 years changes have occurred in GCE A-levels. Inparticular, there have been several major changes in A-levelMathematics courses. As engineering students are usually requiredto have studied A-level Mathematics, or its equivalent, thesechanges have had an effect on their prior mathematical knowledge.Moreover, engineering students traditionally obtained a goodgrounding in mechanics as part of their A-level Mathematicsqualification. However, mechanics, which was once included inthe core syllabus, is now optional. This article investigatesthe current availability and uptake of mechanics modules withinA-level Mathematics courses in schools. Comparisons are drawnbetween these results and results of a survey of schools in2004 and surveys of first year engineering students conductedin 2004 and 2005. It is found that there is a decline in theavailability of mechanics modules and the uptake of more thanone mechanics module has also decreased. The implications ofthese findings for engineering educators are discussed.     

Studies on calcium‐containing poly(urethane ether)s

The calcium salt of mono(hydroxyethoxyethyl)phthalate [Ca(HEEP)₂] was synthesized by the reaction of diethylene glycol, phthalic anhydride, and calcium acetate. Calcium‐containing poly(urethane ether)s (PUEs) were synthesized by the reaction of hexamethylene diisocyanate (HMDI) or tolylene 2,4‐diisocyanate (TDI) with a mixture of Ca(HEEP)₂ and poly(ethylene glycol) (PEG₃₀₀ or PEG₄₀₀) with di‐n‐butyltin dilaurate as a catalyst. A series of calcium‐containing PUEs of different compositions were synthesized with Ca(HEEP)₂/PEG₃₀₀ (or PEG₄₀₀)/diisocyanate (HMDI or TDI) molar ratios of 2:2:4, 3:1:4, and 1:3:4 so that the coating properties of the PUEs could be studied. Blank PUEs without calcium‐containing ionic diols were also prepared by the reaction of PEG₃₀₀ or PEG₄₀₀ with HMDI or TDI. The PUEs were well characterized by Fourier transform infrared, ¹H and ¹³C NMR, solid‐state cross‐polarity/magic‐angle‐spinning ¹³C NMR, viscosity, solubility, and X‐ray diffraction studies. The thermal properties of the polymers were also studied with thermogravimetric analysis and differential scanning calorimetry. The PUEs were applied as top coats on acrylic‐coated leather, and their physicomechanical properties were also studied. The coating properties of PUEs, such as the tensile strength, elongation at break, tear strength, water vapor permeability, flexing endurance, cold crack resistance, abrasion resistance, color fastness, and adhesive strength, were better than the standard values. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2865–2878, 2003     

Isotone relations revisited

We propose a new approach towards proving that the fixed point property for ordered sets is preserved by products. This approach uses a characterization of fixed points in products via isotone relations. First explorations of classes of isotone relations are presented. These first explorations give us hope that this approach could lead to advances on the Product Problem.     

On testing the divisibility of lacunary polynomials by cyclotomic polynomials

An algorithm is described that determines whether a given polynomial with integer coefficients has a cyclotomic factor. The algorithm is intended to be used for sparse polynomials given as a sequence of coefficient-exponent pairs. A running analysis shows that, for a fixed number of nonzero terms, the algorithm runs in polynomial time.

     

SASEGASA: A New Generic Parallel Evolutionary Algorithm for Achieving Highest Quality Results

This paper presents a new generic Evolutionary Algorithm (EA) for retarding the unwanted effects of premature convergence. This is accomplished by a combination of interacting generic methods. These generalizations of a Genetic Algorithm (GA) are inspired by population genetics and take advantage of the interactions between genetic drift and migration. In this regard a new selection scheme is introduced, which is designed to directedly control genetic drift within the population by advantageous self-adaptive selection pressure steering. Additionally this new selection model enables a quite intuitive heuristics to detect premature convergence. Based upon this newly postulated basic principle the new selection mechanism is combined with the already proposed Segregative Genetic Algorithm (SEGA), an advanced Genetic Algorithm (GA) that introduces parallelism mainly to improve global solution quality. As a whole, a new generic evolutionary algorithm (SASEGASA) is introduced. The performance of the algorithm is evaluated on a set of characteristic benchmark problems. Computational results show that the new method is capable of producing highest quality solutions without any problem-specific additions.     

A Multisensor Deconvolution Problem

Meisters and Peterson gave an equivalent condition under which the multisensor deconvolution problem has a solution when there are two convolvers, each the characteristic function of an interval. In this article we find additional conditions under which the deconvolution problem for multiple characteristic functions is solvable. We extend the result to the space of Gevrey distributions and prove that every linear operator S, fromthe space of Gevrey functions with compact support onto itself, which commutes with translations can be represented as convolution with a unique Gevrey distribution T of compact support. Finally, we find explicit formula for deconvolvers when the convolvers satisfy weaker conditions than the equivalence conditions using nonperiodic sampling method.     

Determination of carbamazepine by chemiluminescence detection using chemically prepared tris(2,2'-bipyridine)ruthenium(III) as oxidant.

A new chemiluminescence method for the determination of carbamazepine (CBZ) has been developed. The method is based on the chemiluminescence produced in the reaction of tris(2,2'-bipyridine)ruthenium(III) and CBZ in an acidic medium. The chemiluminescence intensity was enhanced by organic solvents in the reaction system. Under the optimum experimental conditions, the calibration curve was linear over the range 4.0 x 10(-3)-8.6 x 10(-7) mol/L for CBZ. The detection limit (S/N = 3) was 2.5 x 10(-7) mol/L and the relative standard deviation of six replicate measurements was 2.6% for 4.0 x 10(-4) mol/L of CBZ. The possible reaction mechanism were also discussed. The chemiluminescence method was successfully applied to assay the CBZ contents in pharmaceutical tablets.     

A Variable Neighborhood Search for the Multi Depot Vehicle Routing Problem with Time Windows

The aim of this paper is to propose an algorithm based on the philosophy of the Variable Neighborhood Search (VNS) to solve Multi Depot Vehicle Routing Problems with Time Windows. The paper has two main contributions. First, from a technical point of view, it presents the first application of a VNS for this problem and several design issues of VNS algorithms are discussed. Second, from a problem oriented point of view the computational results show that the approach is competitive with an existing Tabu Search algorithm with respect to both solution quality and computation times.     

Capacity Constrained Transit Assignment with Common Lines

This paper proposes the use of absorbing Markov chains to solve the capacity constrained transit network loading problem taking common lines into account. The approach handles congested transit networks, where some passengers will not be able to board because of the absence of sufficient space. The model also handles the common lines problem, where choice of route depends on frequency of arrivals. The mathematical formulation of the problem is presented together with a numerical example. This revised version was published online in July 2006 with corrections to the Cover Date.