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)).     

von Neumann代数中套子代数上的Lie同构

本文给出因子von Neumann代数中的幂等算子在广义Lie积下的一个刻画; 得到因子von Neumann代数中套子代数的幂等算子在Lie积下的一个特征．作为应用, 研究了因子von Neumann代数中套子代数上的Lie同构,并证明因子von Neumann 代数中套子代数之间的Lie同构,要么是同构与广义迹之和,要么是负反同构与广义迹之和．     

Tree-edges deletion problems with bounded diameter obstruction sets

We study the following problem: given a tree G and a finite set of trees H, find a subset O of the edges of G such that G-O does not contain a subtree isomorphic to a tree from H, and O has minimum cardinality. We give sharp boundaries on the tractability of this problem: the problem is polynomial when all the trees in H have diameter at most 5, while it is NP-hard when all the trees in H have diameter at most 6. We also show that the problem is polynomial when every tree in H has at most one vertex with degree more than 2, while it is NP-hard when the trees in H can have two such vertices.The polynomial-time algorithms use a variation of a known technique for solving graph problems. While the standard technique is based on defining an equivalence relation on graphs, we define a quasiorder. This new variation might be useful for giving more efficient algorithm for other graph problems.     

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，     

(4S)-4-羧基杂氮硅三环的合成

利用L-N,N-双(β-羟乙基)丝氨酸及L-N,N-双(β-羟乙基)苏氨酸与三乙氧基硅烷或氯烷基三乙氧基硅烷反应合成了具有手性的(4S)-4-羧基杂氮硅三环(1～5),并运用IR、~1HNMR、EI-MS等手段表征了结构。证据显示存在着贯穿笼状结构的N→Si配键。     

钍-铬天青S的极谱吸附波

在0.12moL/L乙酸铵-0.05%磺基水杨酸-0.15%乙醇,pH5.8～6.0的条件下,钍与铬天青S在-0.45W(vs SCE)有一良好的导数极谱波。钍浓度在0～0.4μg/mL范围内与波高呈直线关系。