The number of Hamiltonian decompositions of regular graphs

A Hamilton cycle in a graph Γ is a cycle passing through every vertex of Γ. A Hamiltonian decomposition of Γ is a partition of its edge set into disjoint Hamilton cycles. One of the oldest results in graph theory is Walecki’s theorem from the 19th century, showing that a complete graph K _n on an odd number of vertices n has a Hamiltonian decomposition. This result was recently greatly extended by Kühn and Osthus. They proved that every r-regular n-vertex graph Γ with even degree r = cn for some fixed c > 1/2 has a Hamiltonian decomposition, provided n = n(c) is sufficiently large. In this paper we address the natural question of estimating H(Γ), the number of such decompositions of Γ. Our main result is that H(Γ) = r ^(1+o(1))nr/2. In particular, the number of Hamiltonian decompositions of K _n is \({n^{\left( {1 + o\left( 1 \right)} \right){n^2}/2}}\).     

Der Effekt der Viscosit?t eines Peaks in der gas-chromatographischen S?ule auf die quantitative Analyse

Ohne Zusammenfassung     

5. Toxikologische Analyse

Ohne Zusammenfassung     

Crystal growth of novel osmium-containing triple perovskites

Single crystals of two new osmium-containing triple perovskites, Ba(3)LiOs(2)O(9) and Ba(3)NaOs(2)O(9), were grown from reactive molten hydroxide fluxes in sealed silver tubes. They crystallize in the space group P6(3)/mmc with lattice parameters of a = 5.8025(1) A, c = 14.1468(4) A for Ba(3)LiOs(2)O(9) and a = 5.8858(1) A, c = 14.3451(5) A for Ba(3)NaOs(2)O(9). The magnetic susceptibility of these osmates indicates significant Os-Os coupling within the octahedra pair.     

Double quantum modulation NMR spectroscopy on spins with I = 1 in solids

NMR experiments with amplitude modulated rf pulses are introduced for the detection of double quantum coherences from spin I = 1 nuclei with large quadrupolar frequencies v_Q in solids. rf pulses of intensity v₁ and with modulation frequency v_m create effective irradiation fields of intensity $\text{1}\text{4}$v²₁/(v_Q-v_m) on the double quantum transition when v₁<¦v_Q-v_m¦?v_Q+v_m. ²D-NMR measurements on an oriented single crystal of deuterated malonic acid are presented.     

A three-dimensional, noninterpenetrating metal--organic framework with the moganite topology: a simple (4(2)x6(2)x8(2))(4x6(4)x8)(2) net containing two kinds of topologically nonequivalent points

Self assembly of Cu(2+) with the multifunctional ligand 2-(4-pyridyl)thiazole-4-carboxylic acid (Pytac) affords the neutral 3D coordination polymer [Cu(3)(Pytac)(6)](H(2)O)(14) (hereafter, SZL-1), which has the rare moganite topology. The mineral moganite has a topology that is closely related to the well-known quartz topology, but the two topologies are differentiated by the number of topologically inequivalent nodes. Whereas only one kind of node is present in quartz, two types of topologically inequivalent nodes are present in moganite. The title compound, which has three vertices in its repeat unit, has two types of topologically inequivalent nodes with the overall vertex symbol (4(2)x6(2)x8(2))(4x6(4)x8)(2) corresponding to the moganite net. Prior to this report, few metal-organic framework materials (MOFs) have been found to contain more than one type of node, and SZL-1 is the first MOF with the moganite topology.     

Contribution a la determination potentiometrique des constantes de stabilite des complexes 1:2 avec les acides aminopolyacetiques MeHnY2

An extension of the potentiometric method based on pH measurement is applied to the determination of the stability constants of addition complexes. On the one hand, the polybasic chelating agent H_nY, and on the other hand the same acid in presence of an equimolar concentration of the entity to be complexed, are titrated with standard sodium hydroxide in a medium of constant ionic strength. By means of a least-square computer program, the stepwise stability contants of the addition complexes are obtained. This method is applied to the 1:2 complexes formed between several trivalent lanthanides and hydroxyethylethylenediaminotriacetic acid (HEDTA).     

Supertropical matrix algebra II: Solving tropical equations

We continue the study of matrices over a supertropical algebra, proving the existence of a tangible adjoint of A, which provides the unique right (resp. left) quasi-inverse maximal with respect to the right (resp. left) quasi-identity matrix corresponding to A; this provides a unique maximal (tangible) solution to supertropical vector equations, via a version of Cramer’s rule. We also describe various properties of this tangible adjoint, and use it to compute supertropical eigenvectors, thereby producing an example in which an n × n matrix has n distinct supertropical eigenvalues but their supertropical eigenvectors are tropically dependent.