Define a (pre)order on /3co as follows: p • q iff there is a finite to one function f c woo such that/3f(cl) = p. Let ,•{ denote he Rudin-Keisler order on Ow. We show that here are points p,qCw* such that Px•q, but p and q are •<-incomparable. 0. Introduction. In [5], M. E. Rudin showed that if there are points p,q G co* Such that for any finite to one function f G cow we have that 13f(p) 4:13f...

Abstract. Because of their potential for offering a computational speed-up when used on certain multiprocessor computers, implicit Runge-Kutta methods with a stability function having distinct poles are analyzed. These are called multiply implicit (MIRK) methods, and because of the so-called order reduction phenomenon, their poles are required to be real, i.e., only real MIRK’s are considered. ...

The Q-state Potts model in two dimensions is very fertile ground for the investigation of phase transitions and critical phenomena. For Q = 2 and 3 there is a second order phase transition between Q ferromagnetic ordered states and a disordered state. For Q = 4 the transition is also second order, but the usual critical behavior is modified by strong logarithmic corrections. For Q > 4 the trans...