For a simple Lie algebra $\mathfrak{g}$, we derive algorithm for computing logarithmic derivatives of tau-functions Drinfeld--Sokolov hierarchy $\mathfrak{g}$-type in terms $\mathfrak{g}$-valued resolvents. We show, the topological solution to lowest-weight-gauge $\mathfrak{g}$-type, resolvents evaluated at zero satisfy $\textit{topological ODE}$.

In this article, we will show how to use Zamolodchikov's higher equations of motion in Liouville field theory explicitly calculate N-point correlation numbers minimal gravity for N>4. We find the explicit expression 5-point and compare it with calculations one-matrix models.

This paper extends our previous study of the breaking probability of dominant deep water gravity surface waves into the finite water depth environment. It reports a unified behavior of the mean breaking statistics once the effects of finite water depth are taken into account. The shallow water wave data that form the basis of this study were acquired at a field experiment site at Lake George, N...

Point-to-point correlation functions of hadron currents in the QCD vacuum are calculated on a lattice and analyzed using dispersion relations, providing physical information down to small spatial separations. Qualitative agreement with phenomenological results is obtained in channels for which experimental data are available, and these correlation functions are shown to be useful in exploring a...