Think of \begin{center} \( u_{tt} + 2au_t + Au = 0 \) \end{center} as a wave equation. Bounded solutions of this equation tend to solutions of the heat equation \begin{center} \( 2av_t + Av = 0. \) \e...
The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control–to–observable inverse problems. In this context, the EnKF is known as...
In this talk we describe the influence of the initial data and the forcing terms on the regularity of the solutions to a class of evolution equations including the heat equation, linear and semilinear...
Suppose that two nonlocal minimal surfaces are included one into the other and touch at a point. Then, they must coincide. But this is perhaps less obvious than what it seems at first glance. This se...
Abstract: Let C be a Riemann surface, x_1,...,x_n a set of points on C, and a_1,...,a_n integers adding up to 0. The theorem of Abel and Jacobi determines when C carries a meromorphic function wi...
Semi-Lagrangian schemes are characteristic-based methods for the numerical solution of hyperbolic partial differential equations (PDEs), which maintain stability under large Courant numbers.However, t...
Bryant’s Laplacian flow is an analogue of Ricci flow that seeks to flow an arbitrary initial closed G_2-structure on a 7-manifold toward a torsion-free one, to obtain a Ricci-flat metric with holonomy...
A numerical algorithm for the Mañé critical value approximation of eikonal Hamilton–Jacobi equations on networks is presented. The proposed method is based on the long time approximation of the corres...
Fano varieties are projective varieties with “positive curvature”. Examples of Fano varieties are projective spaces, products of projective spaces, Grassmannians and hypersurfaces in projective spaces...
Digital models (DMs) are designed to be replicas of systems and processes. At the core of a digital model (DM) is a physical/mathematical model that captures the behavior of the real system across tem...
Non-commutative Iwasawa theory has emerged as a powerful framework for understanding deep arithmetic properties over number fields contained in a p-adic Lie extension and their precise relationship to...
