The Loewner differential equation, introduced by Charles Loewner in 1923, describes the time evolution of a family of conformal (angle-preserving) functions defined on subsets of the complex plane.

Moreover, research into elliptic differential-difference equations in the half-space has further illustrated how integral representations, such as Poisson-type formulae, can be used to establish ...

Jozef Dodziuk, Difference Equations, Isoperimetric Inequality and Transience of Certain Random Walks, Transactions of the American Mathematical Society, Vol. 284, No. 2 (Aug., 1984), pp. 787-794 ...

G. A. Edgar, J. M. Rosenblatt, Difference Equations Over Locally Compact Abelian Groups, Transactions of the American Mathematical Society, Vol. 253 (Sep., 1979), pp ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. Partial ...