2013

最新文章

• Uniqueness of non-linear ground states for fractional Laplacians in AI翻译
  作者：Frank, Rupert L.; Lenzmann, Enno
  作者单位：Princeton University; University of Copenhagen
  摘要：We prove uniqueness of ground state solutions Q = Q(vertical bar x vertical bar) >= 0 of the non-linear equation (-Delta)(s)Q+Q-Q(alpha+1)=0 in R, (-Delta) s Q + Q - Q alpha + 1 = 0 in R, where 0 < s < 1 and 0 < alpha < 4s/(1-2s) for s<1/2 s<1 2 and 0 < alpha < infinity for s >= 1/2 s >= 1 2. Here (-Delta)(s) denotes the fractional Laplacian in one dimension. In particular, we answer affirmatively an open question recently raised by Kenig-Martel-Robbiano and we generalize (by completely differ...
• Invariant Peano curves of expanding Thurston maps AI翻译
  作者：Meyer, Daniel
  作者单位：Constructor University
  摘要：We consider Thurston maps, i.e., branched covering maps f:S (2) -> S (2) that are post-critically finite. In addition, we assume that f is expanding in a suitable sense. It is shown that each sufficiently high iterate F = f (n) of f is semi-conjugate to z (d) :S (1) -> S (1), where d = deg F. More precisely, for such an F we construct a Peano curve gamma:S (1) -> S (2) (onto), such that Fa similar to gamma(z) = gamma(z (d) ) (for all zaS (1)).
• The Brownian map is the scaling limit of uniform random plane quadrangulations AI翻译
  作者：Miermont, Gregory
  作者单位：Ecole Normale Superieure de Lyon (ENS de LYON)
  摘要：We prove that uniform random quadrangulations of the sphere with n faces, endowed with the usual graph distance and renormalized by n (-1/4), converge as n -> a in distribution for the Gromov-Hausdorff topology to a limiting metric space. We validate a conjecture by Le Gall, by showing that the limit is (up to a scale constant) the so-called Brownian map, which was introduced by Marckert-Mokkadem and Le Gall as the most natural candidate for the scaling limit of many models of random plane map...
• Proof of the BMV conjecture AI翻译
  作者：Stahl, Herbert R.
  摘要：We prove the BMV (Bessis, Moussa, Villani, [1]) conjecture, which states that the function , , is the Laplace transform of a positive measure on [0,a) if A and B are Hermitian matrices and B is positive semidefinite. A semi-explicit representation for this measure is given.
• On divisors of Lucas and Lehmer numbers AI翻译
  作者：Stewart, Cameron L.
  作者单位：University of Waterloo
  摘要：Let u (n) be the nth term of a Lucas sequence or a Lehmer sequence. In this article we shall establish an estimate from below for the greatest prime factor of u (n) which is of the form n exp(log n/104 log log n). In doing so, we are able to resolve a question of Schinzel from 1962 and a conjecture of ErdAs from 1965. In addition we are able to give the first general improvement on results of Bang from 1886 and Carmichael from 1912.
• Isotropy of unitary involutions AI翻译
  作者：Karpenko, Nikita; Zhykhovich, Maksim
  作者单位：University of Alberta; Johannes Gutenberg University of Mainz
  摘要：We prove the so-called unitary isotropy theorem, a result on isotropy of a unitary involution. The analogous previously known results on isotropy of orthogonal and symplectic involutions as well as on hyperbolicity of orthogonal, symplectic, and unitary involutions are formal consequences of this theorem. A component of the proof is a detailed study of the quasi-split unitary grassmannians.