A Look at Examinations

This paper discusses various aspects of mathematics examinations and gives the results of some experiments which highlight the discrepancies that arise between the marks obtained in two equivalent mathematics examination papers.     

A Look at Project AIMS

Project AIMS (Activities that Integrate Mathematics and Science) began in 1981 as a National Science Foundation grant. Twelve years later it is a flourishing program which relies on materials developed and written by teachers, and one which uses inexpensive, easily acquired equipment and materials. It is particularly noteworthy that the focus of AIMS-integration through hands-on mathematics and science-supports such recent initiatives as the NCTM Standards and Project 2061 of the AAAS, even though it predates both of them.     

A New Look at the Burnside-Schur Theorem

The famous Burnside–Schur theorem states that every primitivefinite permutation group containing a regular cyclic subgroupis either 2-transitive or isomorphic to a subgroup of a 1-dimensionalaffine group of prime degree. It is known that this theoremcan be expressed as a statement on Schur rings over a finitecyclic group. Generalizing the latter, Schur rings are introducedover a finite commutative ring, and an analogue of this statementis proved for them. Also, the finite local commutative ringsare characterized in permutation group terms. 2000 MathematicsSubject Classification 20B10, 20B15, 05E99.     

A 2-groupoid Characterisation of the Cubical Homotopy Pushout

We give a 2-track-theoretical characterisation of the homotopy pushout of a 3-corner by recognising the mapping 2-simplex as an initial object in a coherent homotopy category of Hausdorff spaces under a 3-corner with morphisms expressed in terms of the 1-morphisms and 2-morphisms of a homotopy 2-groupoid.     

A Constructive Look at Generalised Cauchy Reals

We investigate how nonstandard reals can be established constructively as arbitrary infinite sequences of rationals, following the classical approach due to Schmieden and Laugwitz. In particular, a total standard part map into Richman's generalised Dedekind reals is constructed without countable choice.     

A Constructive Look at Functions of Bounded Variation

Functions with bounded variation and with a (total) variationare examined within Bishop's constructive mathematics. It isshown that the property of having a variation is hereditarydownward on compact intervals, and hence that a real-valuedfunction f with a variation on a compact interval can be expressedas a difference of two increasing functions. Moreover, if fis sequentially continuous, then the corresponding variationfunction, and hence f itself, is uniformly continuous. 1991Mathematics Subject Classification 26A45.     

A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

Engineering sciences and applications of mathematics show unambiguously that positive semidefiniteness of matrices is the most important generalization of non-negative real numbers. This notion of non-negativity for matrices has been well-studied in the literature; it has been the subject of review papers and entire chapters of books.     

A New Look at Mourre’s Commutator Theory

Mourre’s commutator theory is a powerful tool to study the continuous spectrum of self-adjoint operators and to develop scattering theory. We propose a new approach of its main result, namely the derivation of the limiting absorption principle (LAP) from a so called Mourre estimate. We provide a new interpretation of this result. Received: September 20, 2006. Revised: February 1, 2007.     

再论中国股票市场的弱有效性

本文利用检验鞅差序列的非参数统计量来检验中国股票市场的弱有效性问题,本文给出的方法不同于文献中已有的方法,实证分析表明本文使用的检验股票市场弱有效的方法比文献中的大多数方法更有效。实证结果显示,中国的股市在发展过程中,表现山渐进有效的态势;中国A股市场比B股市场更有效率:沪市比深市更趋于有效。文中的有些结论是以前的实证研究所没有的。另外,本文比较了中国股市和境外成熟股市之间有效性程度的差异,并得出香港市场对深市影响显著的结论。     

Multiple Categories: The Equivalence of a Globular and a Cubical Approach

We show the equivalence of two kinds of strict multiple category, namely the well-known globular ω-categories, and the cubical ω-categories with connections.     

Designing a Parliamentary Briefing System: an OR Look at the Commons

A recent project aimed to find ways of improving the effectiveness of the House of Commons in scrutinizing government policy, and hence holding Ministers to account. The study identified some interlocking obstacles to effective scrutiny, and made a set of proposals for overcoming them, involving both the provision of information and analysis to MPs and reform of procedures. It was influenced by lessons from within OR about the effective provision and use of analysis, and this paper reflects further on what an OR perspective can offer in this area, and on developments subsequent to the original study.