Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics. Their ...

Transactions of the American Mathematical Society, Vol. 358, No. 8 (Aug., 2006), pp. 3363-3383 (21 pages) We investigate microlocal properties of partial differential operators with generalized ...

We consider the Heston model as an example of a parameterized parabolic partial differential equation. A space-time variational formulation is derived that allows for parameters in the coefficients ...

Mammalian cells have three types of endoplasmic reticulum (ER) stress-sensing molecules: ATF6, IRE1, and PERK. Among these, ATF6 is unique in that it is processed in an ER-stress-specific manner and ...

Machine learning and artificial intelligence methods are often referred to as “black boxes” when compared with traditional regression-based approaches. However, both traditional and machine learning ...