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作者：Lee, Choongbum
摘要：A graph is d-degenerate if all its subgraphs have a vertex of degree at most d. We prove that there exists a constant c such that for all natural numbers d and r, every d-degenerate graph H of chromatic number r with |V(H)| >= 2(d22cr) has Ramsey number at most 2(d22cr) |V(H)|. This solves a conjecture of Burr and Erdos from 1973.
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作者：Guo, Yan; Ionescu, Alexandru D.; Pausader, Benoit
摘要：The fundamental two-fluid model for describing plasma dynamics is given by the Euler Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. We prove global stability of a constant neutral background, in the sense that irrotational, smooth and localized perturbations of a constant background with small amplitude lead to global smooth solutions in three space dimensions for the Euler Maxwell system. Our construction is robust ...
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作者：Harpaz, Yonatan; Wittenberg, Olivier
摘要：Conjectures on the existence of zero-cycles on arbitrary smooth projective varieties over number fields were proposed by Colliot-Thelene, Sansuc, Kato and Saito in the 1980's. We prove that these conjectures are compatible with fibrations, for fibrations into rationally connected varieties over a curve. In particular, they hold for the total space of families of homogeneous spaces of linear groups with connected geometric stabilisers. We prove the analogous result for rational points, conditio...
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作者：Liu, Gang
摘要：We study the uniformization conjecture of Yau by using the Gromov-Hausdorff convergence. As a consequence, we confirm Yau's finite generation conjecture. More precisely, on a complete noncompact Kahler manifold with nonnegative bisectional curvature, the ring of polynomial growth holomorphic functions is finitely generated. During the course of the proof, we prove if M-n is a complete noncompact Kahler manifold with nonnegative bisectional curvature and maximal volume growth, then M is biholom...
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作者：Bakker, Benjamin; Tsimerman, Jacob
摘要：Given a complex quasiprojective curve B and a nonisotrivial family epsilon of elliptic curves over B, the p-torsion epsilon[p] yields a monodromy representation p epsilon[p] : pi(1)(B) -> GL(2)(F-p). We prove that if p epsilon[p] congruent to p epsilon'[p], then epsilon and epsilon' are isogenous, provided p is larger than a constant depending only on the gonality of B. This can be viewed as a function field analog of the Frey-Mazur conjecture, which states that an elliptic curve over Q is det...
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作者：Fasel, Jean
摘要：For an ideal I in a noetherian ring R, let mu(I) be the minimal number of generators of I. It is well known that there is a sequence of inequalities mu(I/I-2)<=mu(I)<=mu(I/I-2)+1 that are strict in general. However, Murthy conjectured in 1975 that mu(I/I-2 = mu(I) for ideals in polynomial rings whose height equals mu(I/I-2) = mu(I) for ideals in polynomial rings whose height equals mu(I/I-2). The purpose of this article is to prove a stronger form of the conjecture in case the base field is in...
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作者：Ionel, Eleny-Nicoleta; Parker, Thomas H.
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作者：Schacht, Mathias
摘要：We study thresholds for extremal properties of random discrete structures. We determine the threshold for Szemeredi's theorem on arithmetic progressions in random subsets of the integers and its multidimensional extensions, and we determine the threshold for Turan-type problems for random graphs and hypergraphs. In particular, we verify a conjecture of Kohayakawa, Luczak, and Rodl for Turan-type problems in random graphs. Similar results were obtained independently by Conlon and Gowers.
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作者：Hill, M. A.; Hopkins, M. J.; Ravenel, D. C.
摘要：We show that Kervaire invariant one elements theta(j) is an element of pi S-2j+1-2(0) exist only for j <= 6. By Browder's Theorem, this means that smooth framed manifolds of Kervaire invariant one exist only in dimensions 2, 6, 14, 30, 62, and possibly 126. Except for dimension 126 this resolves a longstanding problem in algebraic topology
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作者：Jeffres, Thalia; Mazzeo, Rafe; Rubinstein, Yanir A.
摘要：This article considers the existence and regularity of Kahler Einstein metrics on a compact Kahler manifold M with edge singularities with cone angle 2 pi beta along a smooth divisor D. We prove existence of such metrics with negative, zero and some positive cases for all cone angles 2 pi beta <= 2 pi. The results in the positive case parallel those in the smooth case. We also establish that solutions of this problem are polyhomogeneous, i.e., have a complete asymptotic expansion with smooth c...
