Infinite loop space structure(s) on the stable mapping class group

Tillmann introduced two infinite loop space structures on the plus construction of the classifying space of the stable mapping class group, each with different computational advantages (Invent. Math. 130 (1997) 257; Math. Ann. 317 (2000) 613). The first one uses disjoint union on a suitable cobordism category, whereas the second uses an operad which extends the pair of pants multiplication (i.e. the double loop space structure introduced by Miller, J. Differential Geom. 24 (1986) 1). She conjectured that these two infinite loop space structures were equivalent, and managed to prove that the first delooping are the same. In this paper, we resolve the conjecture by proving that the two structures are indeed equivalent, exhibiting an explicit geometric map.     

L-Fuzzy映射的刻画

在文献 [6]中 ,史福贵借助于 L -fuzzy关系定义了 L -fuzzy集间的 L -fuzzy映射并借助于它们的水平截集给出了其若干刻画。在这篇文章中 ,我们将借助于另外的截集给出 L -fuzzy映射的一种新刻画。从而我们也得到了 L -fuzzy单射和 L -fuzzy满射的新刻画。     

L—模糊关系

Ｌ—模糊集与模糊集相比，在值域上使用的是更为一般的代数系统，本文以Ｌ—集合套为工具，对Ｌ—模糊映射，Ｌ—模糊变换，Ｌ—模糊关系以及它们之间的关系作了详尽的研究，得到了一些有意义的结果，这些结论可望得到广泛的应用。     

On the mapping class group action on the cohomology of the representation space of a surface

The mapping class group of a -pointed Riemann surface has a natural action on any moduli space of parabolic bundles with the marked points as the parabolic points. We prove that under some numerical conditions on the parabolic data, the induced action of the mapping class group on the cohomology algebra of the moduli space of parabolic bundles factors through the natural epimorphism of the mapping class group onto the symplectic group.

     

An extension of Tarski's fixed point theorem and its application to isotone complementarity problems

Tarski's fixed point theorem is extended to the case of set-valued mappings, and is applied to a class of complementarity problems defined by isotone set-valued operators in a complete vector lattice.     

Matching arc complexes: Connectedness and hyperbolicity

Addressing a question of Zaremsky, we give conditions on a finite simplicial graph which guarantee that the associated matching arc complex is connected and hyperbolic.     

Exact calculation of the flow of a staggered tandem cascade with moving second blade row

Summary  The plane flow around a tandem cascade of flat plates is calculated by means of conformal mapping. The blades of the two rows are perpendicular to each other. The first row is stationary, the second row moves with constant velocity. The conformal mapping will be constructed by a “mapping flow”. The blades of one row are stream lines and those of the other row are potential lines of the flow. By conformal mapping, the physical flow around the tandem cascade of the physical ζ-plane is converted into a flow between infinitely long straight walls in the z-plane, each wall corresponding to one of the blades. The conditions far upstream and far downstream of the cascade are represented by source-vortices. In the z-plane, the boundary conditions may be easily fulfilled by reflection and repetition of the source-vortices, and the flow may be calculated by well-known methods. The physical flow searched for is then obtained by inverse mapping. Received 24 July 2000; accepted for publication 6 December 2000     

半广义连续映射

这篇文章, 我们定义半广义连续映射, 研究它的一些性质, 给出它的等价刻画.     

Affine Configurations and Pure Braids

We show that the fundamental group of ordered affine-equivalent configurations with at least five points in the real plane is isomorphic to the pure braid group in as many strands, modulo its centre. In the case of four points, this fundamental group is free with 11 generators. This work was carried out at the Instituto de Matemáticas, UNAM and partially funded by the Sistema Nacional de Investigadores and a doctoral fellowship from CONACyT México.