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作者：Hairer, Martin; Mattingly, Jonathan C.
摘要：The stochastic 2D Navier-Stokes equations on the torus driven by degenerate noise are studied. We characterize the smallest closed invariant subspace for this model and show that the dynamics restricted to that subspace is ergodic. In particular, our results yield a purely geometric characterization of a class of noises for which the equation is ergodic in L-0(2)(T-2). Unlike previous works, this class is independent of the viscosity and the strength of the noise. The two main tools of our ana...
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作者：Vakil, Ravi
摘要：We describe a geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties into the union of Schubert varieties. There are no restrictions on the base field, and all multiplicities arising are 1; this is important for applications. This rule should be seen as a generalization of Pieri's rule to arbitrary Schubert classes, by way of explicit homotopies. It has straightforward bijections to other Littlewood-Richardson rules, such as tableaux, and Knut...
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作者：Prasanna, Kartik
摘要：We prove integrality of the ratio < f, f >/(g, g) (outside an explicit finite set of primes), where g is an arithmetically normalized holomorphic newform on a Shimura curve, f is a normalized Hecke eigenform on GL(2) with the same Hecke eigenvalues as g and <,> denotes the Petersson inner product. The primes dividing this ratio are shown to be closely related to certain level-lowering congruences satisfied by f and to the central values of a family of Rankin-Selberg L-functions. Finally we giv...
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作者：Shen, Weixiao
摘要：We prove that a nonrenormalizable smooth unimodal interval map with critical order between 1 and 2 displays decay of geometry, by an elementary and purely real argument. This completes a real approach to Milnor's attractor problem for smooth unimodal maps with critical order not greater than 2.
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作者：Buff, Xavier; Cheritiat, Arnaud
摘要：If a is an irrational number, Yoccoz defined the Brjuno function Phi by Phi(alpha) = Sigma(n >= 0) alpha(0)alpha(1)...alpha(n-1)log 1/alpha(n), where alpha(0) is the fractional part of alpha and alpha(n+1) is the fractional part of 1/alpha(n). The numbers alpha such that Phi(alpha) < +infinity are called the Brjuno numbers. The quadratic polynomial P-alpha : z negated right arrow e(2i pi alpha)z + z(2) has an indifferent fixed point at the origin. If P-alpha is linearizable, we let r(alpha) be...
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作者：Etingof, P; Nikshych, D; Ostrik, V
摘要：Using a variety of methods developed in the literature (in particular, the theory of weak Hopf algebras), we prove a number of general results about fusion categories in characteristic zero. We show that the global dimension of a fusion category is always positive, and that the S-matrix of any (not necessarily hermitian) modular category is unitary. We also show that the category of module functors between two module categories over a fusion category is semisimple, and that fusion categories a...
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作者：Achlioptas, D; Naor, A
摘要：Given d epsilon (0, infinity) let k(d) be the smallest integer k such that d < 2k log k. We prove that the chromatic number of a random graph G(n, d/n) is either kd or k(d) + 1 almost surely.
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作者：Gómez, T; Sols, I
摘要：Let G be a connected reductive group. The late Ramanathan gave a notion of (semi)stable principal G-bundle on a Riemann surface and constructed a projective moduli space of such objects. We generalize Ramanathan's notion and construction to higher dimension, allowing also objects which we call semistable principal G-sheaves, in order to obtain a projective moduli space: a principal G-sheaf on a projective variety X is a triple (P, E, psi), where E is a torsion free sheaf on X, P is a principal...
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作者：Fefferman, CL
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作者：Zung, NT
摘要：We show that any analytically integrable Hamiltonian system near an equilibrium point admits a convergent Birkhoff normalization. The proof is based on a new, geometric approach to the topic.
