The geometric Langlands correspondence for function fields over finite fields has been proved by Frenkel, Gaitsgory, Vilonen in [FGV]. The aim of this article is to write translation for curves over C and prove the correspondence in some special cases and some new cases, outside the frame of the usual geometric Langlands correspondence. 1 The geometric version of Langlands conjecture We start b...

We present the first rigorous derivation of a number of universal relations for a class of models with continuously varying indices (among which are interacting planar Ising models, quantum spin chains and 1D Fermi systems), for which an exact solution is not known, except in a few special cases. Most of these formulas were conjectured by Luther and Peschel, Kadanoff, and Haldane, but only chec...

We present and discuss a short and simple derivation of orbital epicyclic frequencies for circular geodesic orbits in stationary and axially symmetric spacetimes. Such spacetimes include as special cases analytically known black hole Kerr and Schwarzschild spacetimes, as well as the analytic Hartle-Thorne spacetime and all numerically constructed spacetimes relevant for rotating neutron stars. ...

Classical” optimization problems depending on a probability measure (and corresponding to many applications) belong mostly to a class of nonlinear deterministic optimization problems that are (from the numerical point of view) relatively complicated. On the other hand, these problems fulfill very often “suitable” mathematical properties guaranteing the stability (w.r.t probability measure) and ...

purpose: mesh technique is the standard for inguinal hernia repair because of less recurrence,   but it is inferior or equal to sutured technique in case of other post-operative complications   such as chronic pain. this clinical trial set out to compare these two techniques.   materials and methods: a total number of 322 cases of unilateral inguinal hernia in participants   older than 18 years...