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Bruck nets,codes, and characters of loops 总被引:1,自引:1,他引:0
G. Eric Moorhouse 《Designs, Codes and Cryptography》1991,1(1):7-29
Numerous computational examples suggest that if
k-1
k
are (k- 1)- and k-nets of order n, then rank
p
k
- rank
p
k-1 n - k + 1 for any prime p dividing n at most once. We conjecture that this inequality always holds. Using characters of loops, we verify the conjecture in case k = 3, proving in fact that if p
e n, then rank
p
3 3n - 2 - e, where equality holds if and only if the loop G coordinatizing 3 has a normal subloop K such that G/K is an elementary abelian group of order p
e
. Furthermore if n is squarefree, then rank
p
= 3n - 3 for every prime p ¦ n, if and only if 3 is cyclic (i.e., 3 is coordinated by a cyclic group of order n).The validity of our conjectured lower bound would imply that any projective plane of squarefree order, or of order n 2 mod 4, is in fact desarguesian of prime order. 相似文献
4.
RITVA LINDBERG GORAN SUNDHOLM JOHAN SJö BLOM PETRI AHONEN ESKO I. KAUPPINEN 《Journal of Dispersion Science and Technology》2013,34(1-2):715-722
The zeta-potentials of silica, copper, platinum and gold particles have been measured as a function of pH. The isoelectric points were found to be at pH 3.0, 5.8, 3.0 and 3.5, respectively. In the pH range 3.0 to 5.8 copper and silica particles are oppositely charged and accordingly the coating of silica with copper particles could be demonstrated. In the case of gold and platinum the sign of the charge is such that direct adhesion to silica particles cannot be expected and this was also demonstrated in the case of platinum. 相似文献
5.
van Enk SJ 《Physical review letters》2000,84(4):789; author reply 790
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An intersection representation of a graph is a function gf mapping vertices to sets such that for any u ≠ v, u is adjacent to v iff gf(u) ∩ gf(v) ≠ . The intersection class defined by a set of sets ∑ is the set of all graphs having an intersection representation using sets from ∑. Interval graphs and chordal graphs are well-studied examples of intersection classes.
This paper introduces the notion of completeness for intersection classes. That is, determining precisely what restrictions can be made on the allowable sets without losing the power to represent any graph in the intersection class. The solution to this problem is presented for the chordal graphs. 相似文献
8.
Williams GR Moorhouse SJ Prior TJ Fogg AM Rees NH O'Hare D 《Dalton transactions (Cambridge, England : 2003)》2011,40(22):6012-6022
This paper reports a number of recent developments in the intercalation chemistry of Al(OH)(3). From Rietveld refinement and solid-state NMR, it has been possible to develop a structural model for the recently reported [M(II)Al(4)(OH)(12)](NO(3))(2)·yH(2)O family of layered double hydroxides (LDHs). The M(2+) cations occupy half of the octahedral holes in the Al(OH)(3) layers, and it is thought that there is complete ordering of the metal ions while the interlayer nitrate anions are highly disordered. Filling the remainder of the octahedral holes in the layers proved impossible. While the intercalation of Li salts into Al(OH)(3) is facile, it was found that the intercalation of M(II) salts is much more capricious. Only with Co, Ni, Cu, and Zn nitrates and Zn sulfate were phase-pure LDHs produced. In other cases, there is either no reaction or a phase believed to be an LDH forms concomitantly with impurity phases. Reacting Al(OH)(3) with mixtures of M(II) salts can lead to the production of three-metal M(II)-M(II)'-Al LDHs, but it is necessary to control precisely the starting ratios of the two M(II) salts in the reaction gel because Al(OH)(3) displays selective intercalation of M nitrate (Li > Ni > Co ≈ Zn). The three-metal M(II)-M(II)'-Al LDHs exhibit facile ion exchange intercalation, which has been investigated in the first energy dispersive X-ray diffraction study of a chemical reaction system performed on Beamline I12 of the Diamond Light Source. 相似文献
9.
A new family of distance-regular graphs is constructed. They are antipodal 22t–1-fold covers of the complete graph on 22t
vertices. The automorphism groups are determined, and the extended Preparata codes are reconstructed using walks on these graphs.There are connections to other interesting structures: the graphs are equivalent to certain generalized Hadamard matrices; and their underlying 3-class association scheme is formally dual to the scheme of a system of linked symmetric designs obtained from Kerdock sets of skew matrices in characteristic two. 相似文献
10.
We show the extension of the Forgacs-Manton Killing symmetry for gauge theories, to solutions, extended to superspace, of the d = 11 supergravity theory. 相似文献