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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.
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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.
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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.
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作者：Bigelow, Stephen; Morrison, Scott; Peters, Emily; Snyder, Noah
作者单位：University of California System; University of California Santa Barbara; Australian National University; Massachusetts Institute of Technology (MIT); Indiana University System; Indiana University Bloomington
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作者：Gerard-Varet, David; Masmoudi, Nader
作者单位：Universite Paris Cite; Sorbonne Universite; New York University
摘要：This paper deals with the homogenization of elliptic systems with a Dirichlet boundary condition, when the coefficients of both the system and the boundary data are epsilon-periodic. We show that, as epsilon -> 0, the solutions converge in L-2 with a power rate in epsilon, and identify the homogenized limit system. Due to a boundary layer phenomenon, this homogenized system depends in a non-trivial way on the boundary. Our analysis answers a longstanding open problem, raised for instance in [6...
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作者：Colding, Tobias Holck
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We prove three new monotonicity formulas for manifolds with a lower Ricci curvature bound and show that they are connected to rate of convergence to tangent cones. In fact, we show that the derivative of each of these three monotone quantities is bounded from below in terms of the Gromov-Hausdorff distance to the nearest cone. The monotonicity formulas are related to the classical Bishop-Gromov volume comparison theorem and Perelman's celebrated monotonicity formula for the Ricci flow. We will...
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作者：Namazi, Hossein; Souto, Juan
作者单位：University of Texas System; University of Texas Austin; University of British Columbia
摘要：We give a complete proof of the Bers-Sullivan-Thurston density conjecture. In the light of the ending lamination theorem, it suffices to prove that any collection of possible ending invariants is realized by some algebraic limit of geometrically finite hyperbolic manifolds. The ending invariants are either Riemann surfaces or filling laminations supporting Masur domain measured laminations and satisfying some mild additional conditions. With any set of ending invariants we associate a sequence...
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作者：Bainbridge, Matt; Moeller, Martin
作者单位：Indiana University System; Indiana University Bloomington; Goethe University Frankfurt
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作者：Poltoratski, Alexei
作者单位：Texas A&M University System; Texas A&M University College Station
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作者：Matui, Hiroki; Sato, Yasuhiko
作者单位：Chiba University; Kyoto University
摘要：For any unital separable simple infinite-dimensional nuclear C (au)-algebra with finitely many extremal traces, we prove that -absorption, strict comparison and property (SI) are equivalent. We also show that any unital separable simple nuclear C (au)-algebra with tracial rank zero is approximately divisible, and hence is -absorbing.
