Abstract: In this article, a mathematical formulation for describing and designing activation functions in deep neural networks is provided. The methodology is based on a precise characterization of ...

Mathematicians have broken through a long-standing barrier in the study of “minimizing surfaces,” which play an important role in both math and physics. In the mid-19th century, the Belgian physicist ...

We study the classical linear partial differential equations: Poisson's equation and the heat equation. We learn about representation formulas for solutions, maximum principles, and energy estimates.

The course gives an introduction to analytical techniques for partial differential equations, in particular to separation of variables. In addition the course treats qualititative properties of ...

Abstract: This brief deals with a control framework for manufacturing flow lines. For this framework, a continuous approximation model of the manufacturing system is required, which is computationally ...

An illustration of a magnifying glass. An illustration of a magnifying glass.