stability relative to this special class. Moreover the problem can be extended, within the framework of our general method, by considering obstacles whose contours are composed of a finite number of analytic arcs with shock waves originating at their points of intersection. It is evident that instability at V, or local instability, is sufficient to insure instability in the large. Hence, the ab...

SIR — Far from being dominated by scepticism about science, as Harry Collins claims, mainstream philosophy of science opposes the relativism that Collins decries. We are both philosophers of biology, a field that analyses key biological concepts such as species and genes, dissects theoretical debates in biology and examines emerging fields such as systems biology. This work often involves criti...

We shall see that in these cases the spectra come from irreducible representations of G occurring in L2(Γ\G), and that the resulting integral transform of g has a kernel composed of Bessel functions of representations of G. It should be noted that (2) can readily be extended to any imaginary quadratic number field of class number one. Other examples that share the same structure and have been m...

We introduce a class of neural networks derived from probabilistic models in the form of Bayesian networks. By imposing additional assumptions about the nature of the probabilistic models represented in the networks, we derive neural networks with standard dynamics that require no training to determine the synaptic weights, that perform accurate calculation of the mean values of the random vari...

Abstract. We study the 2k-th power moment of Dirichlet L-functions L(s, χ) at the centre of the critical strip (s = 1/2), where the average is over all primitive characters χ (mod q). We extend to this case the hybrid Euler-Hadamard product results of Gonek, Hughes and Keating for the Riemann zeta-function. This allows us to recover conjectures for the moments based on random matrix models, inc...

In this article, a new proof of monotonicity for extended mean values is given.