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In this paper, assuming a certain set-theoretic hypothesis, a positive answer is given to a question of H. Kraljevi, namely it is shown that there exists a Lebesgue measurable subsetA of the real line such that the set {c R: A + cA contains an interval} is nonmeasurable. Here the setA + cA = {a + ca: a, a A}. Two other results about sets of the formA + cA are presented. 相似文献
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14.
Ammar R Ball RC Banerjee S Bhat PC Bosetti P Bromberg C Canough GE Coffin T Dershem TO Dixon RL Fenker HC Ganguli SN Gensch U Girtler P Goshaw AT Grard F Gurtu A Hamilton C Henri VP Hernandez JJ Hrubec J Iori M Jones LW Kuhn D Knauss D Leedom ID Legros P Lemonne J Leutz H Liu X Malhotra PK Marraffino JM Mendez GE Miller R Naumann T Nguyen A Nowak H Pilette P Poirier J Poppleton A Raghavan R Rasner K Reucroft S Robertson WJ Roe BP Roth A Senko M Struczinski W Subramanian A Touboul MC Vonck B 《Physical review letters》1988,61(19):2185-2188
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Stochastic modeling of a billiard in a gravitational field: Power law behavior of Lyapunov exponents
We consider the motion of a point particle (billiard) in a uniform gravitational field constrained to move in a symmetric wedge-shaped region. The billiard is reflected at the wedge boundary. The phase space of the system naturally divides itself into two regions in which the tangent maps are respectively parabolic and hyperbolic. It is known that the system is integrable for two values of the wedge half-angle
1 and
2 and chaotic for
1<<
2. We study the system at three levels of approximation: first, where the deterministic dynamics is replaced by a random evolution; second, where, in addition, the tangent map in each region is, replaced by its average; and third, where the tangent map is replaced by a single global average. We show that at all three levels the Lyapunov exponent exhibits power law behavior near
1 and
2 with exponents 1/2 and 1, respectively. We indicate the origin of the exponent 1, which has not been observed in unaccelerated billiards. 相似文献
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The variational calculation of Siegert eigenvalues has previously been shown to provide reliable positions and widths for atomic resonances. This approach is herein extended to molecular problems, and the first such calculations for a molecular autoionizing system, He(21,3S)+H→ He+H++e?, are reported. 相似文献
20.
Serber Z Ledwidge R Miller SM Dötsch V 《Journal of the American Chemical Society》2001,123(37):8895-8901
Our recently developed in-cell NMR procedure now enables one to observe protein conformations inside living cells. Optimization of the technique demonstrates that distinguishing the signals produced by a single protein species depends critically on protein overexpression levels and the correlation time in the cytoplasm. Less relevant is the selective incorporation of (15)N. Poorly expressed proteins, insoluble proteins, and proteins that cannot tumble freely due to associations within the cell cannot yet be observed. We show in-cell NMR spectra of bacterial NmerA and human calmodulin and discuss limitations of the technique as well as prospects for future applications. 相似文献