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作者：Dolgopyat, Dmitry; Dong, Changguang; Kanigowski, Adam; Nandori, Peter
作者单位：University System of Maryland; University of Maryland College Park; Yeshiva University; Nankai University; Nankai University
摘要：We exhibit new classes of smooth systems which satisfy the Central Limit Theorem (CLT) and have (at least) one of the following properties: Zero entropy; Weak but not strong mixing; (Polynomial) mixing but not K; K but not Bernoulli and mixing at arbitrary fast polynomial rate. We also give an example of a system satisfying the CLT where the normalizing sequence is regularly varying with index 1. All these examples are C-infinity except for a zero entropy diffeomorphism satisfying the CLT whic...
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作者：Nicola, Fabio; Tilli, Paolo
作者单位：Polytechnic University of Turin
摘要：In this paper we solve an open problem concerning the characterization of those measurable sets Omega subset of R-2d that, among all sets having a prescribed Lebesgue measure, can trap the largest possible energy fraction in time-frequency space, where the energy density of a generic function f is an element of L-2(R-d) is defined in terms of its Short-time Fourier transform (STFT) nu f (x, omega), with Gaussian window. More precisely, given a measurable set Omega subset of R-2d having measure...
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作者：Chaidez, J.; Edtmair, O.
作者单位：University of California System; University of California Berkeley
摘要：Let X subset of R-4 be a convex domain with smooth boundary Y. We use a relation between the extrinsic curvature of Y and the Ruelle invariant of the Reeb flow on Y to prove that there are constants C > c > 0 independent of Y such that c <= ru(Y).sys(Y)(1/2) <= C Here sys(Y) is the systolic ratio of Y, i.e. the square of the minimal period of a closed Reeb orbit of Y divided by twice the volume of X, and ru(Y) is the volume-normalized Ruelle invariant. We then construct dynamically convex cont...
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作者：Li, Chao
作者单位：Stanford University
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作者：Balister, Paul; Bollobas, Bela; Morris, Robert; Sahasrabudhe, Julian; Tiba, Marius
作者单位：University of Oxford; University of Memphis; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：Since their introduction by Erdos in 1950, covering systems (that is, finite collections of arithmetic progressions that cover the integers) have been extensively studied, and numerous questions and conjectures have been posed regarding the existence of covering systems with various properties. In particular, Erdos asked if the moduli can be distinct and all arbitrarily large, Erdos and Selfridge asked if themoduli can be distinct and all odd, and Schinzel conjectured that in any covering syst...
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作者：Briggs, Benjamin
作者单位：Utah System of Higher Education; University of Utah
摘要：For any ideal I of finite projective dimension in a commutative noetherian local ring R, we prove that if the conormal module I/I-2 has finite projective dimension over R/I, then I must be generated by a regular sequence. This resolves a conjecture of Vasconcelos. We prove a similar result for the first Koszul homology module of I. When R is a localisation of a polynomial ring over a field K of characteristic zero, Vasconcelos conjectured that R/I is a reduced complete intersection if the modu...
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作者：Stokman, J., V; Reshetikhin, N.
作者单位：University of Amsterdam; Tsinghua University; Saint Petersburg State University
摘要：Let G be a split real connected Lie group with finite center. In the first part of the paper we define and study formal elementary spherical functions. They are formal power series analogues of elementary spherical functions on G in which the role of the quasi-simple admissible G-representations is replaced by Verma modules. For generic highest weight we express the formal elementary spherical functions in terms of Harish-Chandra series and integrate them to spherical functions on the regular ...
