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作者：Mavlyutov, AR
作者单位：Indiana University System; Indiana University Bloomington
摘要：One can deform the complex structure of Calabi-Yau hypersurfaces in toric varieties by changing the coefficients of the defining polynomial. However, there must also exist non-polynomial deformations of the Calabi-Yau hypersurfaces which cannot be realized inside the ambient toric variety. In this paper, we have constructed the missing non-polynomial deformations, which are induced by an automorphism on the open part of the ambient toric variety.
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作者：Daskalopoulos, P; Lee, KA
作者单位：Columbia University; Seoul National University (SNU)
摘要：We study the all time regularity of the free-boundary problem associated to the deformation of a compact weakly convex surface Sigma in R-3, with a flat side, by its Gaussian Curvature. We show that under certain necessary regularity and non-degeneracy initial conditions the interface separating the flat from the strictly convex side, remains smooth on 0
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作者：Kerov, S; Olshanski, G; Vershik, A
作者单位：Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：The infinite symmetric group S(infinity), whose elements are finite permutations of {1,2,3,...}, is a model example of a big group. By virtue of an old result of Murray-von Neumann, the one-sided regular representation of S(infinity) in the Hilbert space l(2)(S(infinity)) generates a type II1 von Neumann factor while the two-sided regular representation is irreducible. This shows that the conventional scheme of harmonic analysis is not applicable to S(infinity): for the former representation, ...
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作者：Boyle, M; Downarowicz, T
作者单位：University System of Maryland; University of Maryland College Park; Wroclaw University of Science & Technology
摘要：Fix a topological system (X, T), with its space K(X, T) of T-Invariant Borel probabilities. If (Y, S) is a symbolic system (subshift) and phi : (Y, S) (X, T) is a topological extension (factor map), then the function h(ext)(phi) on K(X, T) which assigns to each mu the maximal entropy of a measure nu on Y mapping to mu is called the extension entropy function of phi. The infimum of such functions over all symbolic extensions is called the symbolic extension entropy function and is denoted by h(...
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作者：Kostant, B
作者单位：Massachusetts Institute of Technology (MIT)
摘要：If g is a complex simple Lie algebra, and k does not exceed the dual Coxeter number of g, then the absolute value of the k(th) coefficient of the dim g power of the Euler product may be given by the dimension of a subspace of boolean AND(k) g defined by all abelian subalgebras of g of dimension k. This has implications for all the coefficients of all the powers of the Euler product. Involved in the main results are Dale Peterson's 2(rank) theorem on the number of abelian ideals in a Borel suba...
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作者：Buff, X; Chéritat, A
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：If alpha is an irrational number, we let {p(n)/q(n)}(ngreater than or equal to0), be the approximants given by its continued fraction expansion. The Bruno series B(alpha) is defined as [GRAPHICS] The quadratic polynomial P-alpha : z \--> l(2ipipialpha) z + z(2) has an indifferent fixed point at the origin. If P-alpha is linearizable, we let r(alpha) be the conformal radius of the Siegel disk and we set r(alpha) = 0 otherwise. Yoccoz proved that if B(alpha) = infinity, then r(alpha) = 0 and P-a...
