The old classical problems of theoretical physics are revisited from the point view nonlocal physics. Nonlocal leads to very complicated mathematical apparatus. Here, we explain main principles using transparent considerations and animations.

This thesis deals with the reconstruction of images where the measured data are corrupted by Poisson noise and a specific signal-dependent speckle noise, which occurs e.g. in medical ultrasound images. Since both noise types fundamentally differ from the frequently studied additive Gaussian noise in mathematical image processing, adapted variational models are required to handle these types of ...

Reduced nonlocal matrix integrable modified Korteweg–de Vries (mKdV) hierarchies are presented via taking two transpose-type group reductions in the Ablowitz–Kaup–Newell–Segur (AKNS) spectral problems. One reduction is local, which replaces parameter ? with its complex conjugate ??, and other one nonlocal, negative ???. Riemann–Hilbert problems thus inverse scattering transforms formulated from...

on the basis of a reproducing kernel space, an iterative algorithm for solving the inverse problem for heat equation with a nonlocal boundary condition is presented. the analytical solution in the reproducing kernel space is shown in a series form and the approximate solution vn is constructed by truncating the series to n terms. the convergence of vn to the analytical solution is also proved. ...