We construct a family of in…nite Markov systems on [ 1; 1] with the property that the rational functions from these systems are not dense in C[ 1; 1]. This gives counterexamples to a long standing conjecture of D.J. Newman. Key Words: Markov Systems, Rational Approximation, Muntz Polynomials Classi…cation Numbers: 41A20, 41A50 Peter B. Borwein1 Department of Mathematics, Statistics and Computin...

Muntz and Coffman proposed an algorithm to solve the problem of scheduling preemptable tasks either with arbitrary precedences on two processors, or tasks with tree-like precedences on an arbitrary number of processors, for the schedule length criterion. In this work, we demonstrate that this well-known algorithm has interesting features which extend its application to many other scheduling pro...

A strong visually determined white preference has been demonstrated for many Anura when they are given a choice of going toward stimuli of different intensity, or of turning toward or away from a light source (Pearse, 1910; Muntz, 19626). This preference is probably mediated by a system of 'on' fibres projecting to the diencephalon (Muntz, 1962 a, b) and dependent on the development of the gree...

Under suitable experimental conditions (Boycott, Mrosovsky & Muntz, 1964) frogs jump towards the light (Pearse, 1910; Muntz, 19626). This response, which is released most readily by blue light, appears to be a function of the retinal projection to the diencephalon (Muntz, 1962 a, b). The responsiveness to blue is very marked, and is largely independent of the intensity and saturation of the sti...

The classical Mu'ntz theorem and the so-called Jackson-Muntz theorems concern uniform approximation on [0,1 ] by polynomials whose exponents are taken from an increasing sequence of positive real numbers A. Under mild restrictions on the exponents, the degree of approximation for A-poly nomials with real coefficients is compared with the corresponding degree of approximation when the coefficien...