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61.
Necessary conditions for existence of a (v,k,λ) perfect Mendelsohn design (or PMD) are v k and λv(v − 1) ≡ 0 mod k. When k = 7, this condition is satisfied if v ≡ 0 or 1 mod 7 and v 7 when λ 0 mod 7 and for all v 7 when λ ≡ 0 mod 7. Bennett, Yin and Zhu have investigated the existence problem for k = 7, λ = 1 and λ even; here we provide several improvements on their results and also investigate the situation for λ odd. We reduce the total number of unknown (v,7,λ)-PMDs to 36,31 for λ = 1 and 5 for λ > 1. In particular, v = 294 is the largest unknown case for λ = 1, and the only unknown cases for λ > 1 are for v = 42, λ [2,3,5,9] and v = 18, λ = 7. 相似文献
62.
If and are positive integers with and , then the equation of the title possesses at most one solution in positive integers and , with the possible exceptions of satisfying , and . The proof of this result relies on a variety of diophantine approximation techniques including those of rational approximation to hypergeometric functions, the theory of linear forms in logarithms and recent computational methods related to lattice-basis reduction. Additionally, we compare and contrast a number of these last mentioned techniques.
63.
In this article we give some new constructions of self-conjugate self-orthogonal diagonal Latin squares (SCSODLS). As an application of such constructions, we give a conclusive result regarding the existence of SCSODLS and show that there exists an SCSODLS of order n if and only if n ≡ 0, 1 (mod 4), except for n = 5. This result completely disproves a conjecture of Danhof, Phillips, and Wallis about SCSODLS in Danhof, Philips, and Wallis, JCMCC, 8 (1990), 3–8. © 1998 John Wiley & Sons, Inc. J Combin Designs 6:51–62, 1998 相似文献
64.
Kenneth S. Berenhaut Bennett J. Stancil Jonathan H. Newman 《Journal of Difference Equations and Applications》2013,19(7):729-733
This paper studies solutions of some piecewise-linear difference equations. In two particular cases, a descent argument is used to show that all solutions are periodic with either prime period 3(2 k ? 1) or 6(2 k ? 1) for some k ≥ 1. The existence of solutions with such periods is also considered. 相似文献
65.
Let M = {m1, m2, …, mh} and X be a v-set (of points). A holey perfect Mendelsohn designs (briefly (v, k, λ) - HPMD), is a triple (X, H, B), where H is a collection of subsets of X (called holes) with sizes M and which partition X, and B is a collection of cyclic k-tuples of X (called blocks) such that no block meets a hole in more than one point and every ordered pair of points not contained in a hole appears t-apart in exactly λ blocks, for 1 ≤ t ≤ k − 1. The vector (m1, m2, …, mh) is called the type of the HPMD. If m1 = m2 = … = mh = m, we write briefly mh for the type. In this article, it is shown that the necessary condition for the existence of a (v, 4, λ) - HPMD of type mh, namely, is also sufficient with the exception of types 24 and 18 with λ = 1, and type m4 for odd m with odd λ. © 1997 John Wiley & Sons, Inc. J Combin Designs 5: 203–213, 1997 相似文献
66.
Bennett RG Zhelev N Smith EN Pollanen J Halperin WP Parpia JM 《Physical review letters》2011,107(23):235504
Motivated by the recent prediction that uniaxially compressed aerogel can stabilize the anisotropic A phase over the isotropic B phase, we measure the pressure dependent superfluid fraction of (3)He entrained in 10% axially compressed, 98% porous aerogel. We observe that a broad region of the temperature-pressure phase diagram is occupied by the metastable A phase. The reappearance of the A phase on warming from the B phase, before superfluidity is extinguished at T(c), is in contrast to its absence in uncompressed aerogel. The phase diagram is modified from that of pure (3)He, with the disappearance of the polycritical point (PCP) and the appearance of a region of A phase extending below the PCP of bulk (3)He, even in zero applied magnetic field. The expected alignment of the A phase texture by compression is not observed. 相似文献
67.
Phase locking and supermode selection in multicore photonic crystal fiber lasers with a large doped area 总被引:6,自引:0,他引:6
Michaille L Bennett CR Taylor DM Shepherd TJ Broeng J Simonsen HR Petersson A 《Optics letters》2005,30(13):1668-1670
We report on the laser properties of multicore photonic crystal fiber lasers. A stable phase locking of six- and seven-core structures through evanescent coupling is observed. Effective supermode selection is obtained by using both diffraction losses and the Talbot effect. A pure in-phase supermode is obtained (1.1 times diffraction limited). The laser operating in this mode has a slope efficiency of 70% with up to 44 W of output power. The modal area of the in-phase supermode multicore fiber is 1150 microm2, which makes it, to our knowledge, the single-mode fiber laser with the largest mode field area. In-phase laser action is stable when the fiber is bent. 相似文献
68.
Adare A Adler SS Afanasiev S Aidala C Ajitanand NN Akiba Y Al-Bataineh H Alexander J Al-Jamel A Aoki K Aphecetche L Armendariz R Aronson SH Asai J Atomssa ET Averbeck R Awes TC Azmoun B Babintsev V Baksay G Baksay L Baldisseri A Barish KN Barnes PD Bassalleck B Bathe S Batsouli S Baublis V Bauer F Bazilevsky A Belikov S Bennett R Berdnikov Y Bickley AA Bjorndal MT Boissevain JG Borel H Boyle K Brooks ML Brown DS Bruner N Bucher D Buesching H Bumazhnov V Bunce G Burward-Hoy JM Butsyk S Camard X 《Physical review letters》2007,98(23):232302
We present azimuthal angle correlations of intermediate transverse momentum (1-4 GeV/c) hadrons from dijets in Cu+Cu and Au+Au collisions at square root sNN=62.4 and 200 GeV. The away-side dijet induced azimuthal correlation is broadened, non-Gaussian, and peaked away from Delta phi=pi in central and semicentral collisions in all the systems. The broadening and peak location are found to depend upon the number of participants in the collision, but not on the collision energy or beam nuclei. These results are consistent with sound or shock wave models, but pose challenges to Cherenkov gluon radiation models. 相似文献
69.
Bennett GR Cuneo ME Vesey RA Porter JL Adams RG Aragon RA Caird JA Landen OL Rambo PK Rovang DC Ruggles LE Simpson WW Smith IC Wenger DF 《Physical review letters》2002,89(24):245002
An inertial-confinement-fusion (ICF) concept using two 60-MA Z pinches to drive a cylindrical hohlraum to 220 eV has been recently proposed. The first capsule implosions relevant to this concept have been performed at the same physical scale with a lower 20-MA current, yielding a 70+/-5 eV capsule drive. The capsule shell shape implies a polar radiation symmetry, the first high-accuracy measurement of this type in a pulsed-power-driven ICF configuration, within a factor of 1.6-4 of that required for scaling to ignition. The convergence ratio of 14-21 is to date the highest in any pulsed-power ICF system. 相似文献
70.
In the interaction of molecules with light endowed with orbital angular momentum, an exchange of orbital angular momentum in an electric dipole transition occurs only between the light and the center of mass motion; i.e., internal "electronic-type" motion does not participate in any exchange of orbital angular momentum in a dipole transition. A quadrupole transition is the lowest electric multipolar process in which an exchange of orbital angular momentum can occur between the light, the internal motion, and the center of mass motion. This rules out experiments seeking to observe exchange of orbital angular momentum between light beams and the internal motion in electric dipole transitions. 相似文献