Functorial methods in the theory of group representations I

We introduce a candidate for the group algebra of a Hausdorff group which plays the same role as the group algebra of a finite group. It allows to define a natural bijection betweenk-continuous representations of the group in a Hilbert space and continuous representations of the group algebra. Such bijections are known, but to our knowledge only for locally compact groups. We can establish such a bijection for more general groups, namely Hausdorff groups, because we replace integration techniques by functorial methods, i.e., by using a duality functor which lives in certain categories of topological Banach balls (resp., unit balls of Saks spaces).This paper was written while the authors were supported by the Swiss National Science Foundation under grant 21-33644.92.     

ρ混合、φ混合、ψ混合线性模型M估计的强相合性

研究了 ρ混合、φ混合、ψ混合样本线性模型中回归参数M估计的强相合性 ,在条件不变的情况下 ,获得与独立情形一样的M估计是强相合的充分条件 ,推广了文 [1 ]定理 2 .     

The Möbius distribution on the disc

A simple new family of distributions is proposed which has support the unit disc in two dimensions. The density functions of the family are unimodal, monotonic or uniantimodal. The bivariate symmetric beta distributions, which include the uniform distribution, are special cases, but many members of the family are skew. The distributions have three parameters, one controlling orientation, one controlling degree of concentration and the third controlling skewness, or more precisely off-centredness. Importantly, these parameters are globally orthogonal. An illustrative example of fitting the model to data is given. Conditional and marginal distributions are considered. The new distributions are compared favourably with an earlier suggestion of the same author.     

Modélisation du champ des vitesses de l'urine dans un bolus urétéralModelling of urine flow in an ureteral bolus

Urine transport is made from the kidney to the bladder through the ureter by isolated pockets called bolus. To determine the urine flow in a bolus, we use an adherence condition on the interface urine/wall. It gives us an infinite linear system verified by a set of parameters. An iterative and convergent algorithm allows us to solve this system and to determine analytically the components of the velocity vector in the bolus. To cite this article: A. Vogel et al., C. R. Mecanique 332 (2004).     

Synthesis, morphology and random laser action of ZnO nanostructures

Three-dimensional (3-D) ZnO random-wall nanostructures and one-dimensional (1-D) ZnO nanorods were prepared on silicon substrates by a simple solid-vapour phase thermal sublimation technique. Optical pumped random lasing has been observed in the ZnO random-wall arrays with a threshold intensity of 0.38 MW/cm² in the emission wavelength from 380 to 395 nm. The optical gain was attributed to the closed-loop scattering and light amplification of the ZnO random-wall. The experimental result suggests that the morphology of nanostructure is the key factor to effect random lasing.     

Dynamic frictionless contact with adhesion

A model for the dynamic, adhesive, frictionless contact between a viscoelastic body and a deformable foundation is described. The adhesion process is modeled by a bonding field on the contact surface. The contact is described by a modified normal compliance condition. The tangential shear due to the bonding field is included. The problem is formulated as a coupled system of a variational equality for the displacements and a differential equation for the bonding field. The existence of a unique weak solution for the problem is established, together with a partial regularity result. The existence proof proceeds by construction of an appropriate mapping which is shown to be a contraction on a Hilbert space.     

Bundles, Handcuffs, and Local Freedom

We answer a question of J. Anderson's by producing infinitely many commensurability classes of fibered hyperbolic 3-manifolds whose fundamental groups contain subgroups that are locally free and not free. These manifolds are obtained by performing 0–surgery on a collection of knots with the same properties.     

Tangent circle bundles admit positive open book decompositions along arbitrary links

In the present paper we generalize the divide lying in the unit disk, introduced by A'Campo, to compact, oriented, smooth surfaces, and prove a fibration theorem for generalized divides. As a consequence, we will show that, for any link L in the tangent circle bundle Y to the compact surface, there exists an additional knot K such that the link L∪K is the binding of a “positive” open book decomposition of Y.     

Zero-divisor graphs, von Neumann regular rings, and Boolean algebras

For a commutative ring R with set of zero-divisors Z(R), the zero-divisor graph of R is Γ(R)=Z(R)−{0}, with distinct vertices x and y adjacent if and only if xy=0. In this paper, we show that Γ(T(R)) and Γ(R) are isomorphic as graphs, where T(R) is the total quotient ring of R, and that Γ(R) is uniquely complemented if and only if either T(R) is von Neumann regular or Γ(R) is a star graph. We also investigate which cardinal numbers can arise as orders of equivalence classes (related to annihilator conditions) in a von Neumann regular ring.