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作者：Rakhmanov, E. A.
摘要：Let E be the set of N equidistant points in (- 1, 1) and P-n, (E) be the set of all polynomials P of degree <= n with max {vertical bar P(zeta)vertical bar,zeta is an element of E} <= 1. We prove that [GRAPHICS] T where n < N and C is an absolute constant. The result is essentially sharp. Bounds for K-n,K-N(z), z E C, uniform for n < N, are also obtained. The method of proof of those results is a general one. It allows one to obtain sharp, or sharp up to a log N factor, bounds for K-n,K-N unde...
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作者：Madsen, Ib; Weiss, Michael
摘要：D. Mumford conjectured in [33] that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra generated by certain classes kappa(i) of dimension 2i. For the purpose of calculating rational cohomology, one may replace the stable moduli space of Riemann surfaces by B Gamma infinity, where Gamma infinity is the group of isotopy classes of automorphisms of a smooth oriented connected surface of large genus. Tillmann's theorem [44] that the plus construction mak...
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作者：Borwein, Peter; Dobrowolski, Edward; Mossinghoff, Michael J.
摘要：We prove that if f(x) = Sigma(n-1)(k=0)a(k)x(k) is a polynomial with no cyclotomic factors whose coefficients satisfy a(k) equivalent to 1 mod 2 for 0 <= k < n, then Mahler's measure of f satisfies log m(f) >= log 5/4 (1-1/n). This resolves a problem of D. H. Lehmer [12] for the class of polynomials with odd coefficients. We also prove that if f has odd coefficients, degree n - 1, and at least one noncyclotomic factor, then at least one root a of f satisfies vertical bar alpha vertical bar > 1...
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作者：Babson, Eric; Kozlov, Dmitry N.
摘要：To any two graphs G and H one can associate a cell complex Hom (G, H) by taking all graph multihomomorphisms from G to H as cells. In this paper we prove the Lovasz conjecture which states that if Hom (C2r+1, G) is k-connected, then chi(G) >= k + 4, where r, k epsilon Z, r >= 1, k >= -1, and C2r+1 denotes the cycle with 2r + I vertices. The proof requires analysis of the complexes Hom (C2r+l, K-n). For even n, the obstructions to graph colorings are provided by the presence of torsion in H* (H...
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作者：Granville, Andrew; Soundararajan, K.
摘要：Analytic number theorists usually seek to show that sequences which appear naturally in arithmetic are well-distributed in some appropriate sense. In various discrepancy problems, combinatorics researchers have analyzed limitations to equidistribution, as have Fourier analysts when working with the uncertainty principle. In this article we find that these ideas have a natural setting in the analysis of distributions of sequences in analytic number theory, formulating a general principle, and g...
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作者：Germinet, Francois; Klein, Abel; Schenker, Jeffrey H.
摘要：We prove the existence of dynamical delocalization for random Landau Hamiltonians near each Landau level. Since typically there is dynamical localization at the edges of each disordered-broadened Landau band, this implies the existence of at least one dynamical mobility edge at each Landau band, namely a boundary point between the localization and delocalization regimes, which we prove to converge to the corresponding Landau level as either the magnetic field goes to infinity or the disorder g...
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作者：Nikolov, Nikolay; Segal, Dan
摘要：We prove two results. (1) There is an absolute constant D such that for any finite quasisimple group S, given 2D arbitrary automorphisms of S, every element of S is equal to a product of D 'twisted commutators' defined by the given automorphisms. (2) Given a natural number q, there exist C = C(q) and M M(q) such that: if S is a finite quasisimple group with vertical bar S/ Z (S) vertical bar > C, beta j (j = 1,..., M) are any automorphisms of S, and q(j) (j = 1,..., M) are any divisors of q, t...
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作者：Bobenko, Alexander I.; Hoffmann, Tim; Springborn, Boris A.
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作者：Bierstone, Edward; Milman, Pierre D.; Pawlucki, Wieslaw
摘要：Whitney [W2] proved that a function defined on a closed subset of R is the restriction of a C-m function if the limiting values of all m(th) divided differences form a continuous function. We show that Fefferman's solution of Whitney's problem for R-n [F, Th. 1] is equivalent to a variant of our conjecture in [BMP2] giving a criterion for C-m extension in terms of iterated limits of finite differences.
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作者：Yoshida, Tomoyoshi
