A new continuum model has been proposed by Singh, Ceder, and Bazant for the ion intercalation dynamics in a single crystal of rechargeable-battery electrode materials. It is based on the Cahn-Hilliard equation coupled to ...

We define a new family of open Gromov-Witten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian ...

We introduce new, readily computable invariants of Legendrian knots and links in standard contact three-space, allowing us to answer many previously open questions in contact knot theory. The origin of these invariants is ...

The criterion of h-positivity corresponds to the criterion that a polynomial representation of the general linear group of V is a sum of tensor products of symmetric powers of V. Expanding the iterated exponential function ...

In the first part of this work, we study a long standing open problem on the mixing time of Kac's random walk on SO(n, R) by random rotations. We obtain an upper bound mix = O (n2.5 log n) for the weak convergence which ...

In recent years there has been a great deal of new activity at the interface of biology and computation. This has largely been driven by the massive in flux of data from new experimental technologies, particularly ...