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1.
A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight , in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable . Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that . We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, that with the modified hard edge scaling , the rate of convergence to the limiting distribution is , which is optimal. In the case , general the explicit functional form of the distribution of the smallest eigenvalue at this order can be computed, as it can for and general . An iterative scheme is presented to numerically approximate the functional form for general . 相似文献
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Lynn C. Hart 《School science and mathematics》2004,104(2):79-88
Results from an earlier study ( Hart, 2002 ) suggested that a group of 14 teachers participating in an alternative preparation program for elementary teachers had developed beliefs that were consistent with current thinking in mathematics education. The current study follows 8 of those teachers into their first year of teaching in an urban classroom. Qualitative data were collected from three sources: reflection logs, mathematics case discussions, and field notes made during classroom observations. This provided a triangulation of perspectives: the teachers' views of themselves, the teachers' views of others, and the university faculty member's view of them. Also, teachers completed the Standards Belief Instrument (Zollman & Mason, 1996) at the end of Phase I and at the end of Phase II. Results from the instrument and the qualitative analysis suggest that the teachers maintained a strong reform perspective in their beliefs, but they were unable to consistently implement pedagogy that was consistent with those beliefs. 相似文献
4.
Jalal M. Nawash Brendan Twamley Kelvin G. Lynn 《Acta Crystallographica. Section C, Structural Chemistry》2007,63(8):i66-i68
Our investigations into the ZnO–TeO2 system have produced a new phase, zinc(II) hexatellurium(IV) tridecaoxide, ZnTe6O13, with trigonal (R) symmetry, synthesized by repeated heating and cooling to a maximum temperature of 1053 K. The asymmetric unit consists of a Zn atom coordinated in a distorted octahedral fashion by two unique tellurium(IV) oxide units that form trigonal–bipyramidal TeO4 and TeO3+1 corner‐ and edge‐shared polyhedra. Except for the Zn and an O atom, which occupy 6c positions, all atoms occupy 18f general positions. 相似文献
5.
Using lower-cost lasers, 30% savings are possible for 10-Gb/s uncompensated metro transmission over NZDF, compared to G.652 fiber. We present WDM transmission results for a mixed plant of NZDF rings interconnected to G.652.C-fiber access laterals. 相似文献
6.
Cordula Grüttner Knut Müller Joachim Teller Fritz Westphal Allan Foreman Robert Ivkov 《Journal of magnetism and magnetic materials》2007
Bionized nanoferrite (BNF) particles with high specific power absorption rates were synthesized in the size range of 20–100 nm by high-pressure homogenization for targeted cancer therapy with alternating magnetic fields. Several strategies were used to conjugate antibodies to the BNF particles. These strategies were compared using an immunoassay to find optimal conditions to reach a high immunoreactivity of the final antibody–particle conjugate. 相似文献
7.
L. Erbe A. Peterson S.H. Saker 《Journal of Mathematical Analysis and Applications》2007,329(1):112-131
In this paper, we extend the oscillation criteria that have been established by Hille [E. Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948) 234-252] and Nehari [Z. Nehari, Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957) 428-445] for second-order differential equations to third-order dynamic equations on an arbitrary time scale T, which is unbounded above. Our results are essentially new even for third-order differential and difference equations, i.e., when T=R and T=N. We consider several examples to illustrate our results. 相似文献
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Louis Block James Keesling Shihai Li Kevin Peterson 《Journal of statistical physics》1989,55(5-6):929-939
A new algorithm is presented for computing the topological entropy of a unimodal map of the interval. The accuracy of the algorithm is discussed and some graphs of the topological entropy which are obtained using the algorithm are displayed. 相似文献