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101.
In 2001, Borwein, Choi, and Yazdani looked at an extremal property of a class of polynomial with ±1 coefficients. Their key result was:
Theorem.
(See Borwein, Choi, Yazdani, 2001.) Letf(z)=±z±z2±?±zN−1, and ζ a primitive Nth root of unity. If N is an odd positive integer then
102.
Dana Pomykal Franz Nicole L. Thompson Bob Fuller R. Dwight Hare Nicole C. Miller Jacob Walker 《School science and mathematics》2010,110(6):298-308
Looping, a school structure where students remain with one group of teachers for two or more school years, is used by middle schools to meet the diverse needs of young adolescents. However, little research exists on how looping effects the academic performance of students. This study was designed to determine if looping influenced middle school students' mathematical academic achievement. Student scores on the Mississippi Curriculum Test (MCT) were compared between sixth and eighth grade years for 69 students who looped during the seventh and eighth grades with a group of 137 students who did not loop. Looping students achieved statistically significantly greater growth on the MCT than their nonlooping counterparts between sixth and eighth grades. Further, the data were disaggregated by gender, ethnicity, and socioeconomic status. Findings indicate that looping may academically reengage students during the middle school years. Advantages and disadvantages of looping at the middle grades are discussed. 相似文献
103.
Advances in technology for the manufacturing of integrated circuits have resulted in extremely large, and time consuming,
problems on how to lay out components for optimal circuit performance. These problems can be written as mixed integer programs
which are easily relaxed to linear programs with a very high number of variables and constraints. The relaxed programs can
often be solved by applying state-of-the-art linear programming software, however these solutions come at the expense of long
solution time. In this paper we show that, by considering the structure inherent in VLSI problems, one can specialize classical
preprocessing algorithms to take into account the standard form of the constraint matrix for VLSI problems, thereby achieving
improved preprocessing results with relatively little effort. We provide analysis showing our preprocessing techniques are
accurate and provide some numerical testing demonstrating the increased efficiency. The numerical tests also demonstrate that
using our preprocessing in conjunction with internal preprocessing methods that come with many linear program solvers, can
improve the overall performance of the linear program solver and its preprocessor. 相似文献
104.
Locating proximal points is a component of numerous minimization algorithms. This work focuses on developing a method to find the proximal point of a convex function at a point, given an inexact oracle. Our method assumes that exact function values are at hand, but exact subgradients are either not available or not useful. We use approximate subgradients to build a model of the objective function, and prove that the method converges to the true prox-point within acceptable tolerance. The subgradient g k used at each step k is such that the distance from g k to the true subdifferential of the objective function at the current iteration point is bounded by some fixed ε > 0. The algorithm includes a novel tilt-correct step applied to the approximate subgradient. 相似文献
105.
Borwein Peter; Hare Kevin G.; Mossinghoff Michael J. 《Bulletin London Mathematical Society》2004,36(3):332-338
The minimum value of the Mahler measure of a nonreciprocal polynomialwhose coefficients are all odd integers is proved here to bethe golden ratio. The smallest measures of reciprocal polynomialswith ±1 coefficients and degree at most 72 are also determined.2000 Mathematics Subject Classification 11R09 (primary), 11C08,11Y40 (secondary). 相似文献
106.
Kevin G. Hare. 《Mathematics of Computation》2005,74(250):1003-1008
Let denote the sum of the positive divisors of . We say that is perfect if . Currently there are no known odd perfect numbers. It is known that if an odd perfect number exists, then it must be of the form , where are distinct primes and . Define the total number of prime factors of as . Sayers showed that . This was later extended by Iannucci and Sorli to show that . This paper extends these results to show that .
107.
Brown HN Bunce G Carey RM Cushman P Danby GT Debevec PT Deile M Deng H Deninger W Dhawan SK Druzhinin VP Duong L Efstathiadis E Farley FJ Fedotovich GV Giron S Gray F Grigoriev D Grosse-Perdekamp M Grossmann A Hare MF Hertzog DW Hughes VW Iwasaki M Jungmann K Kawall D Kawamura M Khazin BI Kindem J Krienen F Kronkvist I Larsen R Lee YY Logashenko I McNabb R Meng W Mi J Miller JP Morse WM Nikas D Onderwater CJ Orlov Y Ozben CS Paley JM Polly C Pretz J Prigl R zu Putlitz G Redin SI Rind O 《Physical review letters》2001,86(11):2227-2231
A precise measurement of the anomalous g value, a(mu) = (g-2)/2, for the positive muon has been made at the Brookhaven Alternating Gradient Synchrotron. The result a(mu+) = 11 659 202(14) (6) x 10(-10) (1.3 ppm) is in good agreement with previous measurements and has an error one third that of the combined previous data. The current theoretical value from the standard model is a(mu)(SM) = 11 659 159.6(6.7) x 10(-10) (0.57 ppm) and a(mu)(exp) - a(mu)(SM) = 43(16) x 10(-10) in which a(mu)(exp) is the world average experimental value. 相似文献
108.
109.
We determine the maximum k such that the k-fold sum of some nontrivial,
adjoint orbit in the Lie algebra of a classical, compact Lie
group has measure zero. The orbits of minimal dimension are seen to
be the extreme examples. We show that for this choice of k there is a
central, continuous measure on the group such that
k
is singular to L
1.
For Lie groups other than type B
n or C
3 this result is sharp. 相似文献
110.
It is proved in this note that the Grundy number, Γ(G), and the ochromatic number, χ0(G), are the same for any graph G. 相似文献