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作者：Fusco, G.; Gronchi, G. F.; Negrini, P.
作者单位：University of Pisa; University of L'Aquila; Sapienza University Rome
摘要：We prove the existence of a number of smooth periodic motions u(*) of the classical Newtonian N-body problem which, up to a relabeling of the N particles, are invariant under the rotation group R of one of the five Platonic polyhedra. The number N coincides with the order vertical bar R vertical bar of R and the particles have all the same mass. Our approach is variational and u(*) is a minimizer of the Lagrangian action A on a suitable subset K of the H-1 T-periodic maps u : R -> R-3N. The se...
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作者：Gurjar, R. V.; Paul, S.; Purnaprajna, B. P.
作者单位：Tata Institute of Fundamental Research (TIFR); University of Kansas
摘要：We prove that for a hyperelliptic fibration on a surface of general type with irreducible fibers over a (possibly) non-complete curve, the image of the fundamental group of a general fiber in the fundamental group of the surface is finite. Examples show that the result is optimal. As a corollary of this result we prove two conjectures; the Shafarevich conjecture on holomorphic convexity for the universal cover of these surfaces, and a conjecture of Nori on the finiteness of the fundamental gro...
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作者：Diaconis, Persi; Lebeau, Gilles; Michel, Laurent
作者单位：Universite Cote d'Azur; Stanford University; Stanford University
摘要：This paper gives geometric tools: comparison, Nash and Sobolev inequalities for pieces of the relevant Markov operators, that give useful bounds on rates of convergence for the Metropolis algorithm. As an example, we treat the random placement of N hard discs in the unit square, the original application of the Metropolis algorithm.
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作者：Cheng, Shun-Jen; Lam, Ngau; Wang, Weiqiang
作者单位：University of Virginia; Academia Sinica - Taiwan; National Cheng Kung University
摘要：We formulate and establish a super duality which connects parabolic categories O for the ortho-symplectic Lie superalgebras and classical Lie algebras of BCD types. This provides a complete and conceptual solution of the irreducible character problem for the ortho-symplectic Lie superalgebras in a parabolic category O, which includes all finite dimensional irreducible modules, in terms of classical Kazhdan-Lusztig polynomials.
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作者：Bonk, Mario
作者单位：University of California System; University of California Los Angeles
摘要：Let S-i, i is an element of I, be a countable collection of Jordan curves in the extended complex plane (C) over cap that bound pairwise disjoint closed Jordan regions. If the Jordan curves are uniform quasicircles and are uniformly relatively separated, then there exists a quasiconformal map f : (C) over cap -> (C) over cap such that f (S-i) is a round circle for all i is an element of I. This implies that every Sierpinski carpet in (C) over cap whose peripheral circles are uniformly relative...
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作者：Cheung, Yitwah; Hubert, Pascal; Masur, Howard
作者单位：California State University System; San Francisco State University; Aix-Marseille Universite; University of Chicago
摘要：Given an irrational 0 < lambda < 1, we consider billiards in the table P-lambda formed by a 1/2 x 1 rectangle with a horizontal barrier of length 1-lambda/2 with one end touching at the midpoint of a vertical side. Let NE(P-lambda) be the set of theta such that the flow on P-lambda in direction theta is not ergodic. We show that the Hausdorff dimension of NE(P-lambda) can only take on the values 0 and 1/2, depending on the summability of the series Sigma(k) log log(qk+1)/q(k) where {q(k)} is t...
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作者：Chierchia, Luigi; Pinzari, Gabriella
作者单位：Roma Tre University; University of Naples Federico II
摘要：The 6n-dimensional phase space of the planetary (1 + n)-body problem (after the classical reduction of the total linear momentum) is shown to be foliated by symplectic leaves of dimension (6n - 2) invariant for the planetary Hamiltonian H. Such foliation is described by means of a new global set of Darboux coordinates related to a symplectic (partial) reduction of rotations. On each symplectic leaf H has the same form and it is shown to preserve classical symmetries. Further sets of Darboux co...
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作者：Varagnolo, M.; Vasserot, E.
作者单位：Universite Paris Cite; CY Cergy Paris Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We prove a series of conjectures of Enomoto and Kashiwara on canonical bases and branching rules of affine Hecke algebras of type B. The main ingredient of the proof is a new graded Ext-algebra associated with quiver with involutions that we compute explicitly.
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作者：Klingler, B.
作者单位：Sorbonne Universite; Universite Paris Cite; Institute for Advanced Study - USA
摘要：We prove general local rigidity results for cocompact complex hyperbolic lattices using Hodge theory.
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作者：Roques, Julien
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：This paper deals with regular singular generalized q-hypergeometric equations with either large or small Galois groups. In particular, we consider the fundamental problem of finding appropriate Galoisian substitutes for the usual notion of local monodromy.
