Topologically conjugate Kleinian groups

Two Kleinian groups and are said to be topologically conjugate when there is a homeomorphism such that . It is conjectured that if two Kleinian groups and are topologically conjugate, one is a quasi-conformal deformation of the other. In this paper generalizing Minsky's result, we shall prove that this conjecture is true when is finitely generated and freely indecomposable, and the injectivity radii of all points of and are bounded below by a positive constant.

     

On representations of affine Kac-Moody groups and related loop groups

We demonstrate a one to one correspondence between the irreducible projective representations of an affine Kac-Moody group and those of the related loop group, which leads to the results that every non-trivial representation of an affine Kac-Moody group must have its degree greater than or equal to the rank of the group and that the equivalence appears if and only if the group is of type for some . Moreover the characteristics of the base fields for the non-trivial representations are found being always zero.

     

Algebraic surfaces with log canonical singularities and the fundamental groups of their smooth parts

Let be a log surface with at worst log canonical singularities and reduced boundary such that is nef and big. We shall prove that either has finite fundamental group or is affine-ruled. Moreover, and the structure of are determined in some sense when .

     

Orientation-reversing involutions on handlebodies

The observation that the quotient orbifold of an orientation- reversing involution on a 3-dimensional handlebody has the structure of a compression body leads to a strong classification theorem, and general structure theorems. The structure theorems decompose the action along invariant discs into actions on handlebodies which preserve the -fibers of some -bundle structure. As applications, various results of R. Nelson are proved without restrictive hypotheses.

     

Realization of fixed point sets

Letf:XX be a selfmap of a compact connected polyhedron, andA a nonempty closed subset ofX. In this paper, we shall deal with the question whether or not there is a mapg:XX homotopic tof such that the fixed point set Fixg ofg equalsA. We introduce a necessary condition for the existence of such a mapg. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.Partially supported by the Natural Science Foundation of Liaoning University.     

Oxidation of aromatic hydrocarbons with oxygen in a radiofrequency plasma

The reactions of three aromatic hydrocarbons, benzene, toluene, and styrene, with oxygen in a radiofrequency (r) plasma were investigated. Benzene was oxidized to yield phenol as a single volatile organic product. Similarly, toluene gave the ring oxidation products, cresols, as well as considerable amounts of methyl oxidation products, consisting mainly of benzaldehyde and benzyl alcohol. In contrast, the oxidation of styrene took place predominantly on the olefinic double bond to produce styrene oxide On basis of the products and effects of reaction variables, r power and flow rates of hydrocarbons and oxygen, on the reaction rate, the oxidation mechanism was discussed, particularly focusing on the intermediate species responsible for the formation of major products.     

Derivative of the exponential mapping for infinite dimensional lie groups

It is proved that for infinite dimensional Lie groups in the sense of the differential calculus of Frölicher and Kriegl the derivative of the exponential mappings is given by the formula d(exp)(X)Y=d_exp(X)(e) ₀ ¹ Ad_exp(–tX) Y dt, where stands for the left translation ande is the neutral element.This work was supported by the Alexander von Humboldt-Stiftung.     

Cocycle d'Euler etK2

In this paper we construct a canonical 2-cocycle on the groupP SL(2,k) with values in the Witt groupW(k) of the fieldk. This allows us to produce anatural homomorphism :H ₂(SL(2,k); Z)I ²(k), whereI ²(k) is the square of the fundamental ideal. We prove that this homomorphism is in fact a lift of Milnor's symbol.

     

Two-Arc Transitive Graphs and Twisted Wreath Products

The paper addresses a part of the problem of classifying all 2-arc transitive graphs: namely, that of finding all groups acting 2-arc transitively on finite connected graphs such that there exists a minimal normal subgroup that is nonabelian and regular on vertices. A construction is given for such groups, together with the associated graphs, in terms of the following ingredients: a nonabelian simple group T, a permutation group P acting 2-transitively on a set , and a map F : Tsuch that x = x ^–1 for all x F() and such that Tis generated by F(). Conversely we show that all such groups and graphs arise in this way. Necessary and sufficient conditions are found for the construction to yield groups that are permutation equivalent in their action on the vertices of the associated graphs (which are consequently isomorphic). The different types of groups arising are discussed and various examples given.     

Lattice and continuum wavelets and the block renormalization group

We obtain a resolution of the identity operator, for functions on a latticeZ ^d, which is derived from the block renormalization group. We use eigenfunctions of the terms of the decomposition to form a basis forl ₂(Z^d) and show how the basis is generated from lattice wavelets. The lattice spacing is taken to zero and continuum wavelets are obtained.