The number of ramified covering of a Riemann surface by Riemann surface

Interpreting the number of ramified covering of a Riemann surface by Riemann surfaces as the relative Gromov-Witten invariants and applying a gluing formula, we derive a recursive formula for the number of ramified covering of a Riemann surface by Riemann surface with elementary branch points and prescribed ramification type over a special point.Comment: LaTex, 14 page

A Recursive Method for Determining the One-Dimensional Submodules of Laurent-Ore Modules

We present a method for determining the one-dimensional submodules of a Laurent-Ore module. The method is based on a correspondence between hyperexponential solutions of associated systems and one-dimensional submodules. The hyperexponential solutions are computed recursively by solving a sequence of first-order ordinary matrix equations. As the recursion proceeds, the matrix equations will have constant coefficients with respect to the operators that have been considered.Comment: To appear in the Proceedings of ISSAC 200

Market Stability Switches in a Continuous-Time Financial Market with Heterogeneous Beliefs

By considering a financial market of fundamentalists and trend followers in which the price trend of the trend followers is formed as a weighted average of historical prices, we establish a continuous-time financial market model with time delay and examines the impact of time delay on market price dynamics. Conditions for the stability of the fundamental price in terms of agents' behavior parameters and time delay are obtained. In particular, it is found that an increase in time delay can not only destabilize the market price but also stabilize an otherwise unstable market price, leading to stability switching as delay increases. This interesting phenomena shed new light in understanding of mechanism on the market stability. When the fundamental price becomes unstable through Hopf bifurcations, suffcient conditions on the stability and global existence of the periodic solution are obtained.asset price; fundamentalists; trend followers; delay differential equations; stability; bifurcations

Microstructure Control and Performance Evolution of Aluminum Alloy 7075 by Nano-Treating.

Nano-treating is a novel concept wherein a low percentage of nanoparticles is used for microstructural control and property tuning in metals and alloys. The nano-treating of AA7075 was investigated to control its microstructure and improve its structural stability for high performance. After treatment with TiC nanoparticles, the grains were significantly refined from coarse dendrites of hundreds of micrometers to fine equiaxial ones smaller than 20 μm. After T6 heat treatment, the grains, with an average size of 18.5 μm, remained almost unchanged, demonstrating an excellent thermal stability. It was found that besides of growth restriction factor by pinning behavior on grain boundries, TiC nanoparticles served as both an effective nucleation agent for primary grains and an effective secondary phase modifier in AA7075. Furthermore, the mechanical properties of nano-treated AA7075 were improved over those of the pure alloy. Thus, nano-treating provides a new method to enhance the performance of aluminum alloys for numerous applications