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作者：Miao, Shuang; Yu, Pin
作者单位：University of Michigan System; University of Michigan; Tsinghua University
摘要：The paper is devoted to the study of shock formation of the 3-dimensional quasilinear wave equation -(1 + 3G ''(0)(partial derivative(t)phi)(2))partial derivative(2)(t)phi + Delta phi = 0, where is a non-zero constant. We will exhibit a family of smooth initial data and show that the foliation of the incoming characteristic hypersurfaces collapses. Similar to 1-dimensional conservational laws, we refer this specific type breakdown of smooth solutions as shock formation. Since satisfies the cla...
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作者：Le, Nam Q.; Savin, Ovidiu
作者单位：Indiana University System; Indiana University Bloomington; Columbia University
摘要：We obtain estimates up to the boundary for solutions to degenerate Monge-AmpSre equations of the type det D(2)u = f in Omega, f similar to dist(alpha)(., partial derivative Omega) near partial derivative Omega, alpha > 0. As a consequence we obtain global estimates up to the boundary for the eigenfunctions of the Monge-AmpSre operator on smooth, bounded, uniformly convex domains in R-n.
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作者：Radu, Nicolas
作者单位：Universite Catholique Louvain
摘要：Let T be a locally finite tree all of whose vertices have valency at least 6. We classify, up to isomorphism, the closed subgroups of acting 2-transitively on the set of ends of T and whose local action at each vertex contains the alternating group. The outcome of the classification for a fixed tree T is a countable family of groups, all containing two remarkable subgroups: a simple subgroup of index and (the semiregular analog of) the universal locally alternating group of Burger-Mozes (with ...
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作者：Christiansen, Jacob S.; Simon, Barry; Zinchenko, Maxim
作者单位：Lund University; California Institute of Technology; California Institute of Technology; University of New Mexico
摘要：We consider Chebyshev polynomials, T-n(z), for infinite, compact sets e subset of R (that is, the monic polynomials minimizing the sup-norm,parallel to T-n parallel to(e), on ). We resolve a 45+ year old conjecture of Widom that for finite gap subsets of R , his conjectured asymptotics (which we call Szego-Widom asymptotics) holds. We also prove the first upper bounds of the form parallel to T-n parallel to(e) <= QC(e)(n) (where C (e) is the logarithmic capacity of e) for a class of e's with a...
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作者：Baraud, Y.; Birge, L.; Sart, M.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：The aim of this paper is to present a new estimation procedure that can be applied in various statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density estimation, they asymptotically coincide with the celebrated maximum likelihood estimators at least when the statistical model is regular enough and contains the true density to estimate. For very general models of densities, including non-compact ones, these es...
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作者：Bertola, Marco; Korotkin, Dmitry; Norton, Chaya
作者单位：Concordia University - Canada; Universite de Montreal; International School for Advanced Studies (SISSA)
摘要：We study the symplectic geometry of the space of linear differential equations with holomorphic coefficients of the form on Riemann surfaces of genus g. This space coincides with the moduli space of projective connections which is an affine bundle modelled on the cotangent bundle . We show that for several choices of the origin, or base, holomorphic projective connection (such as Bergman, Wirtinger or Schottky) the canonical Poisson structure on induces the Goldman bracket on the monodromy cha...
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作者：Tolman, Susan
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：We construct a non-Hamiltonian symplectic circle action on a closed, connected, six-dimensional symplectic manifold with exactly 32 fixed points.
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作者：Le Boudec, Adrien
作者单位：Universite Paris Saclay; Universite Catholique Louvain
摘要：A countable group is -simple if its reduced -algebra is simple. It is well-known that -simplicity implies that the amenable radical of the group must be trivial. We show that the converse does not hold by constructing explicit counter-examples. We additionally prove that every countable group embeds into a countable group with trivial amenable radical and that is not C*-simple.
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作者：Liu, Yi
摘要：For an irreducible orientable compact 3-manifold N with empty or incompressible toral boundary, the full -Alexander torsion associated to any real first cohomology class of N is represented by a function of a positive real variable t. The paper shows that is continuous, everywhere positive, and asymptotically monomial in both ends. Moreover, the degree of equals the Thurston norm of . The result confirms a conjecture of J. Dubois, S. Friedl, and W. Luck and addresses a question of W. Li and W....
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作者：Walther, Uli
作者单位：Purdue University System; Purdue University
摘要：For a germ f on a complex manifold X, we introduce a complex derived from the Liouville form acting on logarithmic differential forms, and give an exactness criterion. We use this Liouville complex to connect properties of the D-module generated by to homological data of the Jacobian ideal; specifically we show that for a large class of germs the annihilator of is generated by derivations. Through local cohomology, we connect the cohomology of the Milnor fiber to the Jacobian module via logari...
