On the Classification of Flag-Transitive c.c*- Geometries

Let ( G) be a flag-transitive c.c*-geometry whose point-stabilizer is not an affine group. We list all known examples and show that, if (, G) is a minimal unknown example, then G is an almost simple group and the commutator subgroup G is a simple group of Lie type.     

让世界跳跃的人--马克思*普朗克

回顾了普朗克在物理学上的贡献和对爱因斯坦的帮助，挖掘了他的物理思想，得到对他公正的认识．     

An experiment on program development

As a contribution to programming methodology, the paper contains a detailed, step-by-step account of the considerations leading to a program for solving the 8-queens problem. The experience is related to the method of stepwise refinement and to general problem solving techniques.     

Algebraic -actions of entropy rank one

We investigate algebraic -actions of entropy rank one, namely those for which each element has finite entropy. Such actions can be completely described in terms of diagonal actions on products of local fields using standard adelic machinery. This leads to numerous alternative characterizations of entropy rank one, both geometric and algebraic. We then compute the measure entropy of a class of skew products, where the fiber maps are elements from an algebraic -action of entropy rank one. This leads, via the relative variational principle, to a formula for the topological entropy of continuous skew products as the maximum of a finite number of topological pressures. We use this to settle a conjecture concerning the relational entropy of commuting toral automorphisms.

     

Asymptotics of the transition probabilities of the simple random walk on self-similar graphs

It is shown explicitly how self-similar graphs can be obtained as `blow-up' constructions of finite cell graphs . This yields a larger family of graphs than the graphs obtained by discretising continuous self-similar fractals.

For a class of symmetrically self-similar graphs we study the simple random walk on a cell graph , starting at a vertex of the boundary of . It is proved that the expected number of returns to before hitting another vertex in the boundary coincides with the resistance scaling factor.

Using techniques from complex rational iteration and singularity analysis for Green functions, we compute the asymptotic behaviour of the -step transition probabilities of the simple random walk on the whole graph. The results of Grabner and Woess for the Sierpinski graph are generalised to the class of symmetrically self-similar graphs, and at the same time the error term of the asymptotic expression is improved. Finally, we present a criterion for the occurrence of oscillating phenomena of the -step transition probabilities.

     

BERNOULLI CONVOLUTIONS ASSOCIATED WITH CERTAIN NON——PISOT NUMBERS

The Bernoulli convolution Vλ measure is shown to be absolutely continuous with L^2 density for almost all 1/2＜λ＜1, and singular if λ^-1 is a Pisot number. It is an open question whether the Pisot type Bernoulli conuolutions are the only singular ones. In this paper, we construct a family of non-Pisot type Bernoulli convo-lutions Vλ such that their density functions, if they exist, are not L^2. We also construct other Bernolulli convo-lutions whose density functions if they exist, behave rather badly.     

Poincaré duality in P.A. Smith theory

Let , or more generally be a finite -group, where is an odd prime. If acts on a space whose cohomology ring fulfills Poincaré duality (with appropriate coefficients ), we prove a mod congruence between the total Betti number of and a number which depends only on the -module structure of . This improves the well known mod congruences that hold for actions on general spaces.

     

of Hamiltonian manifolds

Let be a connected, compact symplectic manifold equipped with a Hamiltonian action. We prove that, as fundamental groups of topological spaces, , where is the symplectic quotient at any value in the image of the moment map .

     

Proper actions on cohomology manifolds

Essential results about actions of compact Lie groups on connected manifolds are generalized to proper actions of arbitrary groups on connected cohomology manifolds. Slices are replaced by certain fiber bundle structures on orbit neighborhoods. The group dimension is shown to be effectively finite. The orbits of maximal dimension form a dense open connected subset. If some orbit has codimension at most , then the group is effectively a Lie group.

     

Hyperbolic -spheres with conical singularities, accessory parameters and Kähler metrics on

We show that the real-valued function on the moduli space of pointed rational curves, defined as the critical value of the Liouville action functional on a hyperbolic -sphere with conical singularities of arbitrary orders , generates accessory parameters of the associated Fuchsian differential equation as their common antiderivative. We introduce a family of Kähler metrics on parameterized by the set of orders , explicitly relate accessory parameters to these metrics, and prove that the functions are their Kähler potentials.