Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves

Denote the set of 21 non-isomorphic cubic graphs of order 10 by L. We first determine precisely which L is an element of L occur as the leave of a partial Steiner triple system, thus settling the existence problem for partial Steiner triple systems of order 10 with cubic leaves. Then we settle the embedding problem for partial Steiner triple systems with leaves L is an element of L. This second result is obtained as a corollary of a more general result which gives, for each integer v greater than or equal to 10 and each L is an element of L, necessary and sufficient conditions for the existence of a partial Steiner triple system of order v with leave consisting of the complement of L and v - 10 isolated vertices. (C) 2004 Elsevier B.V. All rights reserved.

Bounds on integrals of the Wigner function: The hyperbolic case

Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of phase space. We investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary Wigner function over noncompact subregions of the phase plane with hyperbolic boundaries. We show using symmetry techniques that this problem reduces to computing the bounds on the spectrum associated with an exactly solvable eigenvalue problem and that the bounds differ from those on classical Liouville distributions. In particular, we show that the total "quasiprobability" on such a region can be greater than 1 or less than zero. (C) 2005 American Institute of Physics.

Synthesis and characterization of Pd(II) and Pt(II) complexes with triazolopyrimidine derivatives: The crystal structure of [Pd2L2Cl4] where L=5,7-dimethyl-1,2,4-triazolo[1,5-a]pyrimidine

The Pd(II) and Pt(II) complexes with triazolopyrimidine C-nucleosides L-1 (5,7-dimethyl-3-(2',3',5'-tri-O-benzoyl-beta-D-ribofuranosyl-s-triazolo)[4,3-a]pyrimidine), L-2 (5,7-dimethyl-3-beta-D-ribofuranosyl-s-triazolo [4,3-a]pyrimidine) and L-3 (5,7-dimethyl[1,5-a]-s-triazolopyrimidine), [Pd(en)(L-1)](NO3)(2), (Pd(bpy)(L-1)](NO3)(2), cis-Pd(L-3)(2)Cl-2, [Pd-2(L-3)(2)Cl-4]center dot H2O, cis-Pd(L-2)(2)Cl-2 and [Pt-3(L-1)(2)Cl-6] were synthesized and characterized by elemental analysis and NMR spectroscopy. The structure of the [Pd-2(L-3)(2)Cl-4]center dot H2O complex was established by Xray crystallography. The two L-3 ligands are found in a head to tail orientation, with a (PdPd)-Pd-... distance of 3.1254(17) angstrom.L-1 coordinates to Pd(II) through N8 and N1 forming polymeric structures. L-2 coordinates to Pd(II) through N8 in acidic solutions (0.1 M HCl) forming complexes of cis-geometry. The Pd(II) coordination to L-2 does not affect the sugar conformation probably due to the high stability of the C-C glycoside bond. (c) 2006 Elsevier B.V. All rights reserved.