Coloring mixed hypertrees

A mixed hypergraph is a triple (V,C,D) where V is its vertex set and C and D are families of subsets of V, called C-edges and D-edges, respectively. For a proper coloring, we require that each C-edge contains two vertices with the same color and each D-edge contains two vertices with different colors. The feasible set of a mixed hypergraph is the set of all k's for which there exists a proper coloring using exactly k colors. A hypergraph is a hypertree if there exists a tree such that the edges of the hypergraph induce connected subgraphs of the tree.We prove that feasible sets of mixed hypertrees are gap-free, i.e., intervals of integers, and we show that this is not true for precolored mixed hypertrees. The problem to decide whether a mixed hypertree can be colored by k colors is NP-complete in general; we investigate complexity of various restrictions of this problem and we characterize their complexity in most of the cases.     

On Super-KMS functionals and entire cyclic cohomology

We formulate the super-KMS condition suggested by Connes and Kastler, in the context of entire cyclic cohomology of quantum algebras. We show that the Chern character of Jaffe, Lesniewski, and Osterwalder — associated by Kastler to a super-KMS functional — satisfies the entire growth condition. Hence, a super-KMS functional defines a cocycle for the entire cyclic cohomology of quantum algebras.Supported in part by the National Science Foundation.     

Ab initio study of the NMR shielding constants and spin-spin coupling constants in cyclopropene

Summary Ab initio calculations of parameters which characterize the NMR spectrum are presented for the cyclopropene molecule. The London orbitals CHF (or GIAO-CHF, Gauge-Independent Atomic Orbital Coupled Hartree-Fock) results for the shielding constants are in good agreement with the experimental data, accurately determined, and with otherab initio values. The calculations of the NMR spin-spin coupling constants have been performed using the Multiconfiguration Time-Dependent Hartree-Fock (MC TDHF) approach. Different basis sets and MC SCF wavefunctions were used to estimate the accuracy of the results. Good agreement is obtained with the coupling constants estimated using the available experimental data.Dedicated to Professor Werner Kutzelnigg on the occasion of his 60th birthday     

Prediction of adsorption of organic component and water vapour mixture onto activated carbon

A simple isotherm equation is derived for the adsorption of an organic component onto activated carbon in presence of water vapour. The theoretical results are compared with experimental data for toluene-water vapour-activated carbon, which were published byRipperger andGermerdonk [10].

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Vorhersage der Adsorption einer organischen Komponente und Wasserdampf an Aktivkohle

Zusammenfassung Es wird eine einfache Adsorptionsisotherme abgeleitet, welche die gleichzeitige Adsorption eines organischen Stoffes und Wasser an Aktivkohle beschreibt. Die theoretischen Ergebnisse werden mit experimentellen Resultaten vonRipperger undGermerdonk [10] für Toluol-Wasser-Aktivkohle verglichen.

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Symbols a _i adsorbate concentration in adsorbent, kg/kg of carbon - a _0i monolayer capacity, kg/kg of carbon - b _i kinetic parameter of theLangmuir equation - E _j adsorption energy in thej-th layer - i i-th component (1 — water vapour, 2 — organic compound) - j j-th layer - m number of layers - n number of adsorbed components - p partial pressure, Pa - p* saturation partial pressure, Pa - p _C water vapour partial pressure at begining of capillary condensation, Pa - surface coverage     

Effect of silica-type sol-gel carrier’s structure and morphology on a supported Ziegler-Natta catalyst for ethylene polymerization

Silica xerogels with different structures and morphology, synthesized using a sol-gel procedure, were used as a carrier of vanadium catalysts (VOCl₃/AlEt₂Cl) for ethylene polymerization. Two techniques of catalyst synthesis were applied: slurry impregnation and gas-phase adsorption and the relevant polymerization methods were then employed. The effect of the carrier structure and morphology on the vanadium loading in the catalysts, the catalyst’s activity and kinetic stability were investigated.     

Cumulative atomic multipole representation of the molecular charge distribution and its basis set dependence

A simple procedure to decompose the theoretical molecular charge distribution into cumulative atomic multipoles supplementing any population analysis scheme has been described and tested for a number of molecules in extended basis sets. This approach may be applied to describe local charge distributions in neutral as well as charged systems and also leads to a simplified point-charge model conserving the local anisotropy of the atomic charge distribution in molecules. Such an approach may be useful in estimating intermolecular interactions, representing the molecular environment in solvent effect or enzyme catalytic activity studies, evaluation of molecular electrostatic potentials or tracing the quality of basis set functions.     

X-ray structure and multinuclear NMR studies of platinum(II) and palladium(II) complexes with 5,7-ditertbutyl-1,2,4-triazolo[1,5-a]pyrimidine

Pt(II) and Pd(II) dichloride complexes with 5,7-ditertbutyl-1,2,4-triazolo[1,5-a]pyrimidine (dbtp) have been synthesized and characterized by infrared and ¹H, ¹³C NMR, ¹³C CPMAS spectroscopy. The structures of the cis-PtCl₂(dbtp)₂ · EtOH (1) and cis-PdCl₂(dbtp)(dmso) (2) has been determined by signal-crystal X-ray diffraction. In both complexes the X-ray crystal structures shows that heterocycle ligand (dbtp) binds the central atom monodentate via nitrogen atom N(3). In addition, compound (2) is interesting for its structural features, because it is the first report of mixed dichloride Pd(II) complexes with N-donor (triazolopyrimidine) and S-donor (dimethylsulfoxide) ligands. In this structure the Pd–Cl distances are: 2.302(1) and 2.281(1) Å, Pd–N 2.041(3) Å and Pd–S 2.245(1) Å. The ¹H, ¹³C NMR studies show clearly that these structures are retained in solution.     

Thermal properties of rare earth dodecaborides

We have measured heat capacity and thermal expansion of rare earth dodecaborides REB₁₂ (RE=Y, Tb-Tm, Lu). YB₁₂ and LuB₁₂ are diamagnetics whereas the other dodecaborides are ordered antiferromagnetically. The amplitude of the heat capacity discontinuity at the Néel temperature and the shape of the heat capacity variation in the critical region for all these antiferromagnetics are characteristics for amplitude-modulated magnetic structures. In the ordered state TbB₁₂ reveals two first-order phase transitions, most likely due to magnetic structure changes. The heat capacity of ErB₁₂ just below the Néel point shows an anomaly of unclear origin. From the Schottky contribution to the heat capacity we have determined crystal field parameters. They are completely different than that is estimated from Point Charge Model.     

Study of the influence of substituents on spectroscopic and photoelectric properties of zinc phthalocyanines

In this paper we describe conversion of light energy into electric energy in a photoelectrochemical cell containing zinc phthalocyanine (ZnPc) dyes. For all dyes investigated in liquid polyvinyl alcohol with dimethyl sulfoxide solution and located in the photoelectrochemical cell the following measurements have been done: absorption, fluorescence, photoacoustic spectra, photovoltaic spectra, kinetics of photocurrent and current–voltage characteristics. It has been shown that all dyes located in the photoelectrochemical cell are able to convert light into electric energy but with different effectiveness. The influence of substituted different peripheral groups to ZnPc core and the correlation between the molecular structure and effectiveness of solar to electric energy conversion were observed and described. The unique behavior of ZnPc substituted with fluorines was indicated.