We present a new dispersive analysis of the isospin breaking decay η → 3π. The resulting representation of the decay amplitude allows us to determine the quark mass double ratio Q and we find as a preliminary result Q = 22.3 ± 0.4. Finally, we discuss a number of improvements that we intend to implement in the future.

The purpose of the present paper is to establish the local energy decay estimates and dispersive estimates for 3-dimensional wave equation with a potential to the initial-boundary value problem on exterior domains. The geometrical assumptions on domains are rather general, for example non-trapping condition is not imposed in the local energy decay result. As a by-product, Strichartz estimates i...

We give mappings between hierarchies having nonisospectral scattering problems and hierarchies having isospectral scattering problems. Special cases of these changes of variables involve similarity variables, and similarity solutions of a hierarchy are seen to correspond to time-independent solutions of an equivalent hierarchy. We thus explain why the use of nonisospectral scattering problems a...

We consider the pricing of volatility products and especially volatility and variance swaps. Under risk-neutral valuation we provide closed form formulae for volatility-average and variance swaps. Also we provide a general partial differential equation for derivatives that have an extra dependence on an average of the volatility. We give approximate solutions of this equation for volatility pro...

It is well known that difference schemes for hyperbolic equations display dispersion of waves. For a general dissipative difference scheme, we present a dispersive wave equation and show that the dispersions are essentially the same when the initial data is a step function.

We consider the class of viscous-dispersive and higher-order conservation laws. We generalize the work of Kawashima and Shizuta, and others, by extending to higher-order the notions of symmetrizability, strict dissipativity, and genuine coupling. We prove, for symmetrizable systems, that strict dissipativity is equivalent to both (i) genuine coupling and (ii) the existence of a skew-symmetric c...