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作者：Haagerup, U; Thorbjornsen, S
摘要：In the process of developing the theory of free probability and free entropy, Voiculescu introduced in 1991 a random matrix model for a free semicircular system. Since then, random matrices have played a key role in von Neumann algebra theory (cf. [V8], [V9]). The main result of this paper is the following extension of Voiculescu's random matrix result: Let (X-1((n)),..., X-r((n))) be a system of r stochastically independent n x n Gaussian self-adjoint random matrices as in Voiculescu's random...
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作者：Maz'ya, V; Shubin, M
摘要：We provide a class of necessary and sufficient conditions for the discreteness of spectrum of Schrodinger operators with scalar potentials which are semibounded below. The classical discreteness of spectrum criterion by A. M. Molchanov (1953) uses a notion of negligible set in a cube as a set whose Wiener capacity is less than a small constant times the capacity of the cube. We prove that this constant can be taken arbitrarily between 0 and 1. This solves a problem formulated by I. M. Gelfand ...
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作者：Merle, F; Raphael, P
摘要：We consider the critical nonlinear Schrodinger equation iut = -Delta u-vertical bar u vertical bar(4)/(n)u with initial condition u(0, x) = u(0) in dimension N = 1. For u(0) (E H-1, local existence in the time of solutions on an interval [0, T) is known, and there exist finite time blow-up solutions, that is, u(0) such as that lim(t up arrow T <+infinity)vertical bar ux(t)vertical bar L2=+infinity. is the smallest power in the nonlinearity for which blow-up occurs, and is critical in this sens...
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作者：Bhargava, M
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作者：Kohn, JJ
摘要：Let {X-1,..., X-p} be complex-valued vector fields in R-n and assume that they satisfy the bracket condition (i.e. that their Lie algebra spans all vector fields). Our object is to study the operator E = Sigma X-i*X-i, where X-i* is the L-2 adjoint of X-i. A result of Hormander is that when the X-i are real then E is hypoelliptic and furthemore it is subelliptic (the restriction of a destribution u to an open set U is smoother then the restriction of Eu to U). When the X-i are complex-valued i...
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作者：Lindblad, H
摘要：We study the motion of an incompressible perfect liquid body in vacuum. This can be thought of as a model for the motion of the ocean or a star. The free surface moves with the velocity of the liquid and the pressure vanishes on the free surface. This leads to a free boundary problem for Euler's equations, where the regularity of the boundary enters to highest order. We prove local existence in Sobolev spaces assuming a physical condition, related to the fact that the pressure of a fluid has t...
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作者：Borisov, L; Libgober, A
摘要：We establish a correspondence between orbifold and singular elliptic genera of a global quotient. While the former is defined in terms of the fixed point set of the action, the latter is defined in terms of the resolution of singularities. As a byproduct, the second quantization formula of Dijkgraaf, Moore, Verlinde and Verlinde is extended to arbitrary Kawamata log-terminal pairs.
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作者：Epstein, DBA; Markovic, V
摘要：Given a nonempty compact connected subset X subset of S-2 with complement a simply-connected open subset Omega subset of S-2, let Dome (Omega) be the boundary of the hyperbolic convex hull in H-3 of X. We show that if X is a certain logarithmic spiral, then we obtain a counterexample to the conjecture of Thurston and Sullivan that there is a 2-quasiconformal homeomorphism Omega -> Dome (Omega) which extends to the identity map on their common boundary in S-2. This leads to related counterexamp...
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作者：Host, B; Kra, B
摘要：We study the L-2-convergence of two types of ergodic averages. The first is the average of a product of functions evaluated at return times along arithmetic progressions, such as the expressions appearing in Furstenberg's proof of Szemeredi's theorem. The second average is taken along cubes whose sizes tend to +infinity. For each average, we show that it is sufficient to prove the convergence for special systems, the characteristic factors. We build these factors in a general way, independent ...
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作者：Oort, F
