F eb 1 99 6 Complex dynamics in several variables

. C O ] 9 F eb 1 99 5 Operator Expansion in the Derivative and Multiplication by x

We generalize to several variables Kurbanov and Maksimov’s result that all linear polynomial operators can be expressed as a formal sum ∑∞ k=0 ak(X) D k in terms of the derivative D (or any degree reducing operator) and multiplication by x. In contrast, we characterize those linear operators that can be expressed as ∑∞ k=0 fk(D) X k and give several examples. Generalizations to several variable...

Some inequalities in connection to relative orders of entire functions of several complex variables

Let f, g and h be all entire functions of several complex variables. In this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given.

al g - ge om / 9 60 20 19 27 F eb 1 99 6 FORMULAS FOR LAGRANGIAN ANDORTHOGONAL DEGENERACY LOCI ; The eQ - Polynomials Approach 1

F eb 1 99 9 A geometric parametrization for the virtual Euler characteristics of the moduli spaces of real and complex algebraic curves ∗

F eb 1 99 6 Soluble Infinite - Range Model of Kinetic Roughening

A modified Kardar-Parisi-Zhang (KPZ) equation is introduced, and solved exactly in the infinite-range limit. In the low-noise limit the system exhibits a weak-to-strong coupling transition, rounded for non-zero noise, as a function of the KPZ non-linearity. The strong-coupling regime is characterised by a double-peaked height distribution in the stationary state. The nonstationary dynamics is q...