Growth order for the size of smallest hamiltonian chain saturated uniform hypergraphs

We say that a hypergraph H$H$ is hamiltonian chain saturated if H$H$ does not contain a hamiltonian chain but by adding any new edge we create a hamiltonian chain in H$H$. In this paper, for each k≥3$k\ge 3$, we establish the right order of magnitude n^k−1$n^{k-1}$ for the size of the smallest k$k$-uniform hamiltonian chain saturated hypergraph. This solves an open problem of G.Y. Katona.     

Scaling laws of complex band random matrices

We study a model of complex band random matrices capable of describing the transitions between three different ensembles of Hermitian matrices: Gaussian orthogonal, Gaussian unitary and Poissonian. Analyzing numerical data we observe new scaling relations based on the generalized localization length of eigenvectors. We show that during transitions between canonical ensembles of random matrices the changes of statistical properties of eigenvalues and eigenvectors are correlated.     

Über Biegungsinvarianten

Ohne Zusammenfassung     

Pseudorapidity distributions of charged particles from Au + Au collisions at the maximum RHIC energy,square root[s(NN)] = 200 GeV

We present charged-particle multiplicities as a function of pseudorapidity and collision centrality for the 197Au+197Au reaction at square root[s(NN)] = 200 GeV. For the 5% most central events we obtain dN(ch)/deta/(eta = 0) = 625+/-55 and N(ch)/(-4.7< or =eta < or =4.7) = 4630 +/- 370, i.e., 14% and 21% increases, respectively, relative to square root[s(NN)] = 130 GeV collisions. Charged-particle production per pair of participant nucleons is found to increase from peripheral to central collisions around midrapidity. These results constrain current models of particle production at the highest RHIC energy.     

On the completeness of a metric related to the Bergman metric

We study the completeness of a metric which is related to the Bergman metric of a bounded domain (sometimes called the Burbea metric or Fuks metric). We provide a criterion for its completeness in the spirit of the Kobayashi criterion for the completeness of the Bergman metric. In particular we prove that in hyperconvex domains our metric is complete.     

Application of the TPR method for the studies of Ni(II) in Chrysoprase

TPR method was used to elucidate the status of nickel ions in chrysoprase. Temperature profiles of chrysoprase samples were interpreted by comparing them with TPR curves of references. Two kinds of nickel species were identified in the studied samples. The first one is nickel in 2:1 layer silicates while the other is nickel in the extra-framework positions. Apparent activation energies (85±3 and 20±5 kJ mol⁻¹) which were obtained from TPR data support the above attribution. This revised version was published online in July 2006 with corrections to the Cover Date.     

On completely nonmeasurable unions

Assume that there is no quasi-measurable cardinal not greater than 2^ω . We show that for a c. c. c. σ -ideal 𝕀 with a Borel base of subsets of an uncountable Polish space, if 𝒜 is a point-finite family of subsets from 𝕀, then there is a subfamily of 𝒜 whose union is completely nonmeasurable, i.e. its intersection with every non-small Borel set does not belong to the σ -field generated by Borel sets and the ideal 𝕀. This result is a generalization of the Four Poles Theorem (see [1]) and a result from [3]. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonrelativistic phase-space and octonions

The octonion algebra seems to constitute the natural underlying algebra of nonrelativistic phase-space. A correspondence between the imaginary unit of quantum mechanics and the seventh imaginary unit of octonion algebra is proposed. Conjectures as to the possible physical meaning of some particular transformations from the automorphism group of octonions are presented.     

(Liquid + liquid) equilibria of binary systems containing hyperbranched polymer Boltorn® H2004 – Experimental study and modelling in terms of lattice-cluster theory

(Liquid + liquid) phase equilibria (LLE) of binary mixtures containing hyperbranched polymer Boltorn® H2004 and n-alkanes (n-hexane, n-heptane, n-octane, and n-decane) were studied over the temperature range from about (260 up to 360) K. The polymer is partially miscible with n-alkanes and the solubility decreases with an increase of the chain length of the solvent. Corresponding LLE phase diagrams including spinodal and binodal (liquid + liquid) coexistence curves were calculated in terms of the statistical mechanics – based on the lattice-cluster theory, based only on the upper critical solution temperature, and the polymer chain architecture. The results show semi-qualitative agreement of predicted and experimental equilibrium compositions and temperatures. Boltorn® H2004 reveals complete miscibility in the liquid phase with alcohols (C₁–C₈), aromatic hydrocarbons (benzene, toluene, and thiophene), and ethers (methyl tetra-butyl ether, ethyl tetra-butyl ether, and tetrahydrofurane).