On the Noncommutative Geometry of Twisted Spheres

We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres of Connes and Landi and of Connes and Dubois Violette, by using the differential and integral calculus on these spaces that is covariant under the action of their corresponding quantum symmetry groups. We start from multiparametric deformations of the orthogonal groups and related planes and spheres. We show that only in the twisted limit of these multiparametric deformations the covariant calculus on the plane gives, by a quotient procedure, a meaningful calculus on the sphere. In this calculus, the external algebra has the same dimension as the classical one. We develop the Haar functional on spheres and use it to define an integral of forms. In the twisted limit (differently from the general multiparametric case), the Haar functional is a trace and we thus obtain a cycle on the algebra. Moreover, we explicitly construct the *-Hodge operator on the space of forms on the plane and then by quotient on the sphere. We apply our results to even spheres and compute the Chern–Connes pairing between the character of this cycle, i.e. a cyclic 2n-cocycle, and the instanton projector defined in math.QA/0107070.     

A Gibbs variational principle in space-time for infinite-dimensional diffusions

 We show that the set of stationary weak solutions for a class of infinite dimensional stochastic differential equations coincides with the set of shift invariant, space-time Gibbs fields for a certain potential. The key step consists in proving the Gibbs variational principle for space-time Gibbs fields. Received: 20 May 1999 / Revised version: 14 May 2001 / Published online: 11 December 2001     

Damping of giant monopole resonances within a linearized Landau-Vlasov dynamics

Isoscalar monopole vibrations in spherical nuclei are studied within the Landau-Vlasov dynamics. Energy and strength of the giant monopole resonance (GMR) are well reproduced. The Landau damping of the monopole vibrations is analyzed. It is found that the local Fermi surface corresponding to the GMR is deformed. The collision integral is included within the relaxation time approximation. The found total width is too small to explain the observed one in heavy nuclei. Because the Landau damping is sensitive to the effective nuclear force the missing part of the width can be connected to certain properties of the latter.     

Synthesis of thiometallate complexes and catalytic hydration of acetonitrile

The bimetallic complexes [M(bipy)nS2M′X2], where M=FeII, RuII, NiII or CoII; bipy=2,2′-bipyridine; n=1 or 2; M′=MoVI or WVI and X=O or S, were synthesized using tetrathiometallates and dithiometallates as bidentate ligands. The characterization of the new bimetallic complexes was carried out by standard techniques. The complexes were tested as catalysts in acetonitrile hydrolysis. The reaction products are acetamide and acetic acid, formed by hydrolysis of acetamide. The most active catalysts in the acetonitrile hydrolysis are [Fe(bipy)2S2MoS2], [Ru(bipy)2S2MoS2] and [Co(bipy)2S2WS2], whereas the lowest activity is shown by the nickel complexes. However, the latter exhibit the highest selectivity in acetamide formation. ZINDO semi-empirical calculations were performed in order to explain some of the properties of the complexes. This revised version was published online in June 2006 with corrections to the Cover Date.     

Experimental determination of rheological properties of polydimethylsiloxane

A series of linear polydimethylsiloxane of different molecular weight and with reduced polydispersity were prepared by partial fractionation of commercial products. The rheological functions, i.e. zero shear viscosity (η₀), first and second normal stress coefficients (Ψ₁₀ and Ψ₂₀), of the materials were experimentally measured by conventional rotational rheometers and by a rotation rod apparatus. The relationships between molecular structure (molecular weight and polydispersity index) and rheological functions are presented and discussed on the basis of equations proposed in the literature. Zero shear viscosity data conform to the well-known dependence on a power 3.5 of molecular weight. However, a consistently stronger influence of molecular weight over Ψ₁₀ and Ψ₂₀ is found. The influence of polydispersity over Ψ₁₀ is also analyzed.     

类p-Laplace方程的无穷多解的存在性

本文研究了类p-Laplace方程,利用证明其对应的变分泛函满足Cerami条件,得到了无穷多个大能量解的存在性,推广并改进了已有结果.     

Constructive (2,3)-generation: A permutational approach

A groupG is said to be (2,3)-generated if it can be generated by two elements of respective orders 2 and 3. The class of these groups has recently received a lot of attention by several authors: a brief survey of the results in this area is given in the introduction. In this paper we show that, ifR is a ring generated by one element of finite multiplicative order, then the analogues of classical groups overR are (2,3)-generated, provided that their rank is sufficiently large. Our lower bound for the rank improves previous results.