Lame Function and Its Application to Some Nonlinear Evolution Equations

In this paper, based on the Lame function and Jacobi elliptic function, the perturbation method is appliedto some nonlinear evolution equations to derive their multi-order solutions.     

Choquet-type Integral Representation of Invariant Functions for some Product Semigroups

We show that functions which are invariant for suitable product semigroups (one of which is a quasi-Poisson semigroup on a general state space) decompose into a singular eigen-function and a mixture of products of minimal eigen-functions.     

Complex Geometry of the Universal Teichmuller Space

We prove that all invariant distances on the universal Teichmuller space agree and are determined by the Grunsky coefficients of the naturally related conformal maps. This fact yields various important consequences; in particular, we obtain solutions of certain well-known geometric problems in complex analysis and related fields.     

Block transitive Steiner systems with more than one point orbit

For all ‘reasonable’ finite t, k, and s, we construct a t‐(?₀, k, 1) design and a group of automorphisms which is transitive on blocks and has s orbits on points. In particular, there is a 2‐(?0, 4, 1) design with a block‐transitive group of automorphisms having two point orbits. This answers a question of P. J. Cameron and C. E. Praeger. The construction is presented in a purely combinatorial way, but is a by‐product of a new way of looking at a model‐theoretic construction of E. Hrushovski. © 2004 Wiley Periodicals, Inc.     

Evaluation formulas for Tornheim's type of alternating double series

In this paper, we give some evaluation formulas for Tornheim's type of alternating series by an elementary and combinatorial calculation of the uniformly convergent series. Indeed, we list several formulas for them by means of Riemann's zeta values at positive integers.

     

Essential domains and two conjectures in dimension theory

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings in the context of (locally) essential domains.

     

Wave function mapping of self-assembled quantum dots by capacitance spectroscopy

We use frequency-dependent capacitance–voltage spectroscopy to study the dynamic charging of self-assembled InAs quantum dots. With increasing frequency, the AC charging becomes suppressed, beginning with the low-energy states. By applying an in-plane magnetic field, we generate an additional magnetic confinement that alters the tunneling barrier and hence the charging dynamics. In traveling through the potential barrier, the electrons acquire an additional momentum k₀, proportional to the magnetic field B. As the tunneling is enhanced, when k₀ matches the maximum of the electronic wave function Ψ (in momentum representation), we are able to map out the shape of Ψ by varying B.     

An Alternative Approach to the Extraction of Structure Functions in Deep Inelastic e-p Scattering at 5 to 20 GeV

Two structure functions W1(x,Q2) and W2(x,Q2) are determined by using the cross sections measured in the deep inelastic electron-proton scattering experiments at Stanford Linac in the energy range of 5 to 20 GeV. In this paper an alternative mathematical approach have been used in such determination, resulting in a larger number of points in the graphs of the structure functions.     

Bush连续不可微函数的分形性质

本文对用递推关系确定的Bush连续不可微函数,找出了迭代函数系(IFS),从而得到它的级数表达式和所具有的自仿射分形的有关性质.最后还计算出函数图象的Hausdorff 维数的准确值.