to the correct marginals. However, on the QMR network, the loopy be liefs oscillated and had no obvious relation ship to the correct posteriors. We present some initial investigations into the cause of these oscillations, and show that some sim ple methods of preventing them lead to the wrong results

A hybrid system is a dynamical system whose behavior exhibits both discrete and continuous change. A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete change with differential equations for capturing

-type theorem (i.e., which permits, in some cases, replacing a sequence by its "two-scale " limit, up to a strongly convergent remainder in L2(12)) is also established. These results are especially useful for the homogenization of partial differential equations with periodically oscillating

the former is the quadratic mean of the latter. The spot process S is then governed by the following stochastic differential equation: dS �rt () dt��() t dW

is defined in terms of the Painlevé II differential equation and can be numerically evaluated and tabulated in software. Simulations showthe approximation to be informative for n and p as small as 5. The limit is derived via a corresponding result for complex Wishart matrices using methods from random matrix

are solved, where either f(x) or g(x) is specified in certain intervals in the range 0 ^ x < oo, with up to four intervals. r(f) may be different for different intervals. It is shown that the solution is closely allied to that of a type of Fourier-Bessel series with mixed boundary values so

to be developed in order to allow an efficient solution of even larger problems. This paper gives a review of the first hierarchical and purely matrix-based approach, algebraic multigrid (AMG). AMG can directly be applied, for instance, to efficiently solve various types of elliptic partial differential equations

A time-spectral method for solution of initial value partial differential equations is outlined. Multivariate Chebyshev series are used to represent all temporal, spatial and physical parameter domains in this generalized weighted residual method (GWRM). The approximate solutions obtained are thus

equations solvable by the inverse scattering method, such as the KdV, nonlinear Schrödinger (NLS), and Boussinesq equations, etc., and also to “integrable ” ordinary differential equations such as the Painlevé transcendents. As described, for example, in [IN] or [BC], the inverse scattering method

Abstract. MD5 is one of the most widely used cryptographic hash functions nowadays. It was designed in 1992 as an improvement of MD4, and its security was widely studied since then by several authors. The best known result so far was a semi free-start collision, in which the initial value