Motivic Serre invariants of curves

In this article, we generalize the theory of motivic integration on formal schemes topologically of finite type and the notion of motivic Serre invariant, to a relative point of view. We compute the relative motivic Serre invariant for curves defined over the field of fractions of a complete discrete valuation ring R of equicharacteristic zero. One aim of this study is to understand the behavior of motivic Serre invariants under ramified extension of the ring R. Thanks to our constructions, we obtain, in particular, an expression for the generating power series, whose coefficients are the motivic Serre invariant associated to a curve, computed on a tower of ramified extensions of R. We give an interpretation of this series in terms of the motivic zeta function of Denef and Loeser.     

西门子PLC与计算机间的通讯程序设计

介绍了西门子（Siemens）公司生产的S7－200型PLC与计算机之间的通讯网络构成及主要通讯指令，说明了利用PLC进行通信的实质和设计步骤，给出了PLC与计算机通讯时上位机和下位机的相应程序。     

Growth and characterization of GaAs films deposited on Ge/Si composite substrates by metalorganic chemical vapor deposition

We report the results of studies which have been made on heteroepitaxial layers of GaAs and AlGaAs grown by metalorganic chemical vapor deposition on composite substrates that consist of four different types of heteroepitaxial layered structures of Ge and Ge-Si grown by molecular beam epitaxy on (100)-oriented Si substrates. It is found that of the four structures studied, the preferred composite substrate is a single layer of Ge ∼1 μm thick grown directly on a Si buffer layer. The double-crystal X-ray rocking curves of 2 μm thick GaAs films grown on such substrates have FWHM values as small as 168 arc sec. Transmission electron micrographs of these Ge/Si composite substrates has shown that the number of dislocations in the Ge heteroepitaxial layer can be greatly reduced by an anneal at about 750° C for 30 min which is simultaneously carried out during the growth of the GaAs layer. The quality of the GaAs layers grown on these composite substrates can be greatly improved by the use of a five-period GaAs-GaAsP strained-layer superlattice (SLS). Using the results of these studies, low-threshold optically pumped AlGaAs-GaAs DH laser structures have been grown by MOCVD on MBE Ge/Si composite substrates.     

Invariant measures for equicontinuous semigroups of continuous transformations of a compact Hausdorff space

Equicontinuous semigroups of transformations of a compact Hausdorff space and their sets of all invariant (Borel, regular and probabilistic) measures are studied. Conditions equivalent to the existence of at least one invariant measure are given. The (algebraic and topological) structure of the set of invariant measures is researched.     

Cohomological properties of the quantum shuffle product and application to the construction of quasi-Hopf algebras

For a commutative algebra the shuffle product is a morphism of complexes. We generalize this result to the quantum shuffle product, associated to a class of non-commutative algebras (for example all the Hopf algebras). As a first application we show that the Hochschild-Serre identity is the dual statement of our result. In particular, we extend this identity to Hopf algebras. Secondly, we clarify the construction of a class of quasi-Hopf algebras.     

Multiderivations of Coxeter arrangements

Let V be an ℓ-dimensional Euclidean space. Let G⊂O(V) be a finite irreducible orthogonal reflection group. Let ? be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For H∈? choose α _H ∈V ^* such that H=ker(α _H ). For each nonnegative integer m, define the derivation module D ^(m) (?)={θ∈Der _S |θ(α _H )∈Sα ^m _H }. The module is known to be a free S-module of rank ℓ by K. Saito (1975) for m=1 and L. Solomon-H. Terao (1998) for m=2. The main result of this paper is that this is the case for all m. Moreover we explicitly construct a basis for D ^(m) (?). Their degrees are all equal to mh/2 (when m is even) or are equal to ((m−1)h/2)+m _i (1≤i≤ℓ) (when m is odd). Here m ₁≤···≤m _ℓ are the exponents of G and h=m _ℓ+1 is the Coxeter number. The construction heavily uses the primitive derivation D which plays a central role in the theory of flat generators by K. Saito (or equivalently the Frobenius manifold structure for the orbit space of G). Some new results concerning the primitive derivation D are obtained in the course of proof of the main result. Oblatum 27-XI-2001 & 4-XII-2001?Published online: 18 February 2002     

On the Log-Laplace Equation for Nonlocal Operators Generating Sub-Markovian Semigroups

We consider the semilinear Cauchy problem for a class of pseudo-differential operators generating sub-Markovian semigroups. Solutions of such problems with negative definite nonlinearity play an important role in constructing branching measure-valued processes. We establish local existence and uniqueness of solutions in the context of the Dirichlet space associated to the problem. Comparison and global properties of solutions are also studied. Accepted 29 August 2001. Online publication 17 December 2001.     

Finite Groups Acting on Homology 3-Spheres: On a Result of M. Reni

 We give a list including all finite groups G which admit smooth orientation preserving actions on homology 3-spheres (arbitrary actions, i.e. possibly with fixed points; if the action is free then the group G has periodic cohomology and the classification of such groups is well known). The main work in this direction is due to M. Reni. In the present paper, we complete and extend his results for the case of nonsolvable groups G. Received 19 March 2001; in revised form 15 September 2001