ar X iv : 0 90 7 . 20 23 v 1 [ m at h - ph ] 1 2 Ju l 2 00 9 Menelaus relation and Fay ’ s trisecant formula are associativity equations

ar X iv : 0 90 7 . 41 78 v 1 [ m at h . PR ] 2 3 Ju l 2 00 9 An Introduction to Stochastic PDEs

2 Some Motivating Examples 2 2.1 A model for a random string (polymer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 The stochastic Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 The stochastic heat equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 What have we learned? . . . . . . . . . . . . . . . . . . . . . ...

Menelaus Relation and Fay's Trisecant Formula Are Associativity Equations

It is shown that the celebrated Menelaus relation and Fay's trisecant formula similar to the WDVV equation are associativity conditions for structure constants of certain three-dimensional algebra.

ar X iv : m at h - ph / 0 30 90 05 v 4 1 7 Ju l 2 00 4 Lamé polynomials , hyperelliptic reductions and Lamé band structure

The band structure of the Lamé equation, viewed as a one-dimensional Schrödinger equation with a periodic potential, is studied. At integer values of the degree parameter l, the dispersion relation is reduced to the l = 1 dispersion relation, and a previously published l = 2 dispersion relation is shown to be partly incorrect. The Hermite–Krichever Ansatz, which expresses Lamé equation solution...

ar X iv : 0 90 7 . 29 64 v 1 [ m at h . FA ] 1 7 Ju l 2 00 9 THE NORM OF A TRUNCATED TOEPLITZ OPERATOR

We prove several lower bounds for the norm of a truncated Toeplitz operator and obtain a curious relationship between the H and H∞ norms of functions in model spaces.

ar X iv : 0 70 7 . 33 03 v 1 [ m at h . O A ] 2 3 Ju l 2 00 7 OPERATOR - VALUED FRAMES