The topics include a level set method for the numerical simulation of damage evolution, some nonlinear problems involving non-local diffusions, radar imaging, the multiscale analysis of density function theory, asymptotic solutions of Hamilton-Jacobi equations for large time and related topics, second-order partial differential equations and deterministic games, order-value optimization and new applications, visibility and invisibility, and the life and work of Leonhard Euler.

The Hamilton-Jacobi equation is derived for such motion and the effects of the curvature upon the quantization are analyzed, starting from a generalization of the Klein-Gordon equation in curved spaces.

Recall that the QCM general wave equation derived from the general relativistic Hamilton-Jacobi equation is approximated by a Schrodinger-like wave equation and that a QCM quantization state is completely determined by the system's total baryonic mass M and its total angular momentum [H.

It is then shown that the Schrodinger equation can be derived after using the Hamilton-Jacobi equation in conjunction with the continuity equation and where the "quantum force" arising from Bohm's quantum potential Q can be related to (or described by) the Weyl geometric properties of space.

Other topics include homogenization of stochastic Hamilton-Jacobi equations, general relative entropy in a nonlinear McKendrick model, pointwise Fourier inversion in analysis and geometry, and a class of one-dimensional Markov processes with continuous paths.