Non-trivial simple poles at negative integers and mass concentration at singularity

Let (X,0) be the germ of a normal space of dimension n+1 and let f be the germ at 0 of a holomorphic function on X. Assume both X and f have an isolated singularity at 0. Denote by J the image of the restriction map , where F is the Milnor fibre of f at 0. We prove that the canonical Hermitian form on , given by poles of order at in the meromorphic extension of , passes to the quotient by J and is non-degenerate on . We show that any non-zero element in J produces a “mass concentration” at the singularity which is related to a simple pole concentrated at for (in a non-na?ve sense). We conclude with an application to the asymptotic expansion of oscillatory integrals , for , when . Received: 28 May 2001 / Published online: 26 April 2002     

Finite Abelian actions on surfaces

Edmonds showed that two free orientation preserving smooth actions φ₁ and φ₂ of a finite Abelian group G on a closed connected oriented smooth surface M are equivalent by an equivariant orientation preserving diffeomorphism iff they have the same bordism class [M,φ₁]=[M,φ₂] in the oriented bordism group Ω₂(G) of the group G. In this paper, we compute the bordism class [M,φ] for any such action of G on M and we determine for a given M, the bordism classes in Ω₂(G) that are representable by such actions of G on M. This will enable us to obtain a formula for the number of inequivalent such actions of G on M. We also determine the “weak” equivalence classes of such actions of G on M when all the p-Sylow subgroups of G are homocyclic (i.e. of the form n(Z/pαZ)).     

Quadratic transformations of the sixth Painlevé equation with application to algebraic solutions

In 1991, one of the authors showed the existence of quadratic transformations between the Painlevé VI equations with local monodromy differences (1/2, a, b, ±1/2) and (a, a, b, b). In the present paper we give concise forms of these transformations. They are related to the quadratic transformations obtained by Manin and Ramani–Grammaticos–Tamizhmani via Okamoto transformations. To avoid cumbersome expressions with differentiation, we use contiguous relations instead of the Okamoto transformations. The 1991 transformation is particularly important as it can be realized as a quadratic‐pull back transformation of isomonodromic Fuchsian equations. The new formulas are illustrated by derivation of explicit expressions for several complicated algebraic Painlevé VI functions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

美国初中级教育中对自然科学教师的培养及职业标准

对自然科学教师的培养及职业标准的研究是当代世界各国教育改革的焦点之一。本文试就美国对初中级教育中对自然科学教师的职业准备及其培养标准加以介绍和描述,特别是对美国七十年代以来对自然科学教育由重视到不重视再到重视的具体过程分析,以此为我国自然科学教师的培养提供借鉴作用。     

One-pot synthesis of an ionic half-sandwich complex of neodymium. Application to isoprene polymerisation catalysis

The reaction of one equivalent of Nd(BH₄)₃(THF)₃ with an half equivalent of dialkylmagnesium in the presence of a stoichiometric amount of pentamethylcyclopentadiene cleanly affords a new kind of half-sandwich of neodymium that is stable toward comproportionation. This strategy can be advantageously applied to generate in situ catalysts allowing the controlled polymerisation of isoprene.     

First Total Synthesis of 12-Hydroxy-13-methylpodocarpa-9, 11, 13-trien-3-one

12-Hydroxy-13-methylpodocarpa-9, 11, 13-trien-3-one 9 was isolated from the twigs ofCroton salutaris1. Many diterpenes exhibit significant bioactivities, such as antibac-terial and antitumour and 9 has a rare structure. In order to study the relationshipb…     

Proof of semialgebraic covering mapping cylinder conjecture with semialgebraic covering homotopy theorem

In this paper we prove the semialgebraic version of Palais' covering homotopy theorem, and use this to prove Bredon's covering mapping cylinder conjecture positively in the semialgebraic category. Bredon's conjecture was originally stated in the topological category, and a topological version of our semialgebraic proof of the conjecture answers the original topological conjecture for topological G-spaces over “simplicial” mapping cylinders.     

A procedure for measuring the flexibility of single wood-pulp fibres

A way of determining the flexibility of wood-pulp fibres is developed, which involves i) a precise measurement of the topology of single-fibres by using a confocal laser scanning microscope and ii) the measurement of the elastic modulus of the fibres by using a single-fibre fatigue cell. Reported in this paper are the initial results of tests carried out on black spruce fibres, which have been subjected to three different levels of mechanical refining energy, namely ∼1100, 2300, and 3500 kWh/t. It is found that the fibre flexibility rises significantly between the first and second energy levels, but it does not change to the same degree between the second and third ones. The described procedure of measuring the flexibility of fibres may be used to establish the appropriate refiner energy necessary for the production of a specific grade of paper. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 115–128, January–February, 2006.     

Direct ion beam deposition of polymeric styrene films and in situ characterization by electron spectroscopy

Polymeric styrene films with thicknesses ranging from about one nm up to a few m have been deposited by means of a direct ion beam deposition (IBD) technique. The deposition energy, which can be chosen independently of the parameters which govern the plasma conditions, has been varied between few eV and 1000 eV. The correlation between the deposition parameters and the resulting film properties in terms of the electronic structure is discussed. The in situ characterization by electron spectroscopy has proved to be a very useful characterization method and ultraviolet photoelectron spectroscopy in particular revealed an extremely high sensitivity to structural differences in the deposited films. The polymeric films have also been characterized by scanning electron microscopy and optical spectroscopy. These techniques have also served to compare films prepared by the direct IBD technique with films obtained by standard rf plasma polymerization (RFPP) in a tubular reactor. Significant differences have been found which are dependent on the deposition parameters; these are discussed in detail.Department of Chemical Engineering, Beijing Institute of Technology, P.O. Box 327 Beijing, 100081 Beijing, P.R. China     

晶化温度对中孔分子筛（M41S）结构转变的影响

在低表面活性剂浓度及低表面活性剂与氧化硅比的条件下，研究了十六烷基三甲基溴化铵－硅酸钠体系中晶化温度对中孔分子筛Ｍ４１Ｓ材料结构转变的影响。结果有，晶化温度提高至１３５℃改变了原六方晶相ＭＣＭ－４１的结构，晶化温度提高到１５０℃后，中孔结构六方ＭＣＭ－４１晶格转变为变不稳定的层状相，