The Kuo condition and the second are known as criteria for an r-jet to be V-sufficient in Cr mappings Cr+1 mappings, respectively. In [2] we considered notions of V-sufficiency jets these conditions relative case a given closed set ?, showed that is criterion ?-V-sufficient sufficient mappings. this paper discuss several equivalent or condition.

Recently we proposed a model in which when a scientist writes a manuscript, he picks up several random papers, cites them and also copies a fraction of their references (cond-mat/0305150). The model was stimulated by our discovery that a majority of scientific citations are copied from the lists of references used in other papers (cond-mat/0212043). It accounted quantitatively for several prope...

3 4 Cassie Wilson, Mark A. King and Maurice R. Yeadon 5 6 1 Department for Health, University of Bath, Bath, BA2 7AY, UK. 7 2 School of Sport, Exercise and Health Sciences, Loughborough University, 8 Loughborough LE11 3TU, UK. 9 10 11 12

abstract Parallel programs are frequently non-deterministic, meaning they can give diierent results when provided the same input. These diierent results arise because variations in the timing of the multiple threads cause the threads to access shared resources in diierent orders. The phenomena that cause the non-deterministic behavior have been (and continue to be) variously referred to as acce...

In recent years much progress has been made in applying field-theoretic renormalization-group methods to models of diffusion-limited chemical reactions. One such example was a study by the present authors of the A + B--* ~ annihilation reaction with random initial conditions and equal particle densities. III Our purpose here is to correct a mistake contained in this worked and to revise the con...

Let Z t,z be a R -valued jump diffusion controlled by ν with initial condition Z t,z(t) = z. The aim of this paper is to characterize the set V (t) of initial conditions z such that Z t,z can be driven into a given target at a given time by proving that the function u(, z) = 1 − 1V (t) satisfies, in the viscosity sense, the equation (2) below. As an application, we study the problem of hedging ...

Given an attracting periodic orbit of a system of ordinary differential equations, one can assign an asymptotic phase to any initial condition that approaches such a periodic orbit. All initial conditions with the same asymptotic phase lie on what is known as an isochron. Isochrons foliate the basin of attraction, and may have intriguing geometric properties. We present here two cases of a plan...