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1. INTRODUCTION. In the seventeenth century, Fermat defined the sequence of numbers F n = 2 2 n + 1 for n ≥ 0, now known as Fermat numbers. If F n happens to be prime, F n is called a Fermat prime. Fermat showed that F n is prime for each n ≤ 4, and he conjectured that F n is prime for all n (see Brown [1] or Burton [2, p. 271]). Almost one hundred years(More)
B. Abbott, R. Abbott, R. Adhikari, A. Ageev, J. Agresti, P. Ajith, B. Allen, J. Allen, R. Amin, S. B. Anderson, W. G. Anderson, M. Araya, H. Armandula, M. Ashley, F. Asiri, P. Aufmuth, C. Aulbert, S. Babak, R. Balasubramanian, S. Ballmer, B. C. Barish, C. Barker, D. Barker, M. Barnes, B. Barr, M. A. Barton, K. Bayer, R. Beausoleil, K. Belczynski, R.(More)
B. Abbott, R. Abbott, R. Adhikari, A. Ageev, J. Agresti, B. Allen, J. Allen, R. Amin, S. B. Anderson, W. G. Anderson, M. Araya, H. Armandula, M. Ashley, F. Asiri, P. Aufmuth, C. Aulbert, S. Babak, R. Balasubramanian, S. Ballmer, B. C. Barish, C. Barker, D. Barker, M. Barnes, B. Barr, M. A. Barton, K. Bayer, R. Beausoleil, K. Belczynski, R. Bennett, S. J.(More)
The Beijing Spectrometer (BES) p ex eriment has observed purely leptonic decays of the D, meson in the reaction e+e+ D$D; at a c.m. energy of 4.03 GeV. Three events are observed in which one D, decays hadronically to +r, li*“K, or K”li, and the other decays leptonically to ova or l-v,. With the assumption of p-r universality, values of the branching(More)
In 1849, Alphonse de Polignac conjectured that every odd positive integer can be written in the form 2n + p, for some integer n ≥ 0 and some prime p. In 1950, Erdős constructed infinitely many counterexamples to Polignac’s conjecture. In this article, we show that there exist infinitely many positive integers that cannot be written in either of the forms Fn(More)
A unit x in a commutative ring R with identity is called exceptional if 1−x is also a unit in R. For any integer n ≥ 2, define φe(n) to be the number of exceptional units in the ring of integers modulo n. Following work of Shapiro, Mills, Catlin and Noe on iterations of Euler’s φ-function, we develop analogous results on iterations of the function φe, when(More)
The effect of grazing by large herbivores on the microbial community and the ecosystem functions they provide are relatively unknown in grassland systems. In this study, the impact of grazing upon the size, composition and activity of the soil microbial community was measured in field experiments in two coastal ecosystems: one salt marsh and one sand dune(More)
B. Abbott, R. Abbott, R. Adhikari, A. Ageev, B. Allen, R. Amin, S. B. Anderson, W. G. Anderson, M. Araya, H. Armandula, M. Ashley, F. Asiri, P. Aufmuth, C. Aulbert, S. Babak, R. Balasubramanian, S. Ballmer, B. C. Barish, C. Barker, D. Barker, M. Barnes, B. Barr, M. A. Barton, K. Bayer, R. Beausoleil, K. Belczynski, R. Bennett, S. J. Berukoff, J. Betzwieser,(More)
B. Abbott, R. Abbott, R. Adhikari, A. Ageev, B. Allen, R. Amin, S. B. Anderson, W. G. Anderson, M. Araya, H. Armandula, F. Asiri, P. Aufmuth, C. Aulbert, S. Babak, R. Balasubramanian, S. Ballmer, B. C. Barish, D. Barker, C. Barker-Patton, M. Barnes, B. Barr, M. A. Barton, K. Bayer, R. Beausoleil, K. Belczynski, R. Bennett, S. J. Berukoff, J. Betzwieser, B.(More)
To meet the overall isolation and alignment requirements for the optics in Advanced LIGO, the planned upgrade to LIGO, the US laser interferometric gravitational wave observatory, we are developing three sub-systems: a hydraulic external pre-isolator for low frequency alignment and control, a two-stage active isolation platform designed to give a factor of(More)