(1.1) du/dt = 9u = a{x)uxx + b{x)ux + c{x)u in R x (0, T) where T ^ oo. Here a(x) ^ 0, c(x) S M, l/«(x), b(x)/a(x) and c(x)/a(x) are locally integrable in R, but otherwise the coefficients are unrestricted. The results below extend characterizations of Widder ([17], [18]) for positive solutions of the heat equation (see §1.1). In particular, we find that all positive solutions of (1.1) are of t...

SUMMARY The computation of the Love numbers (LNs) for a spherically symmetric self-gravitating viscoelastic Earth is classical problem in global geodynamics. Here we revisit numerical evaluation loading and tidal LNs static limit an incompressible planetary body, adopting Laplace inversion scheme based upon Post-Widder formula as alternative to traditional normal modes method. We also consider,...

In this paper, we will explain how to perfectly hedge under Heston’s stochastic volatility 17 model with jump-to-default, which is in itself a generalization of the Merton jump-todefault model and a special case of the Heston model with jumps. The hedging instru19 ments we use to build the hedge will be as usual the stock and the bond, but also the Variance Swap (VS) and a Credit Default Swap (...

We present new multiwavelet transforms for discrete signals. The transforms are implemented in two phases: 1. Pre (post)processing which transform the scalar signal into the vector one (and back). 2.Wavelet transforms of the vector signal. Both phases are performed in a lifting manner. We use the cubic interpolatory Hermite splines as a predicting aggregate in the vector wavelet transform. We p...