Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...

Complex Hessian equations extend the classical framework of the complex Monge–Ampère equation by involving the m-th elementary symmetric function of the eigenvalues of the complex Hessian. This ...

Boundary value problems and integro-differential equations lie at the heart of modern applied mathematics, providing robust frameworks to model phenomena across physics, engineering and beyond. These ...

The team has improved the capabilities of physics-informed neural networks (PINNs), a type of artificial intelligence that incorporates physical laws into the learning process. Researchers from the ...

Trigonometric identities are powerful tools for simplifying complex equations in math and science. Three core groups—reciprocal, quotient, and Pythagorean—form the foundation. Effective strategies ...

In a recent study, mathematicians from Freie Universität Berlin have demonstrated that planar tiling, or tessellation, is much more than a way to create a pretty pattern. Consisting of a surface ...