Dynamical Vacuum in Quantum Cosmology

By regarding the vacuum as a perfect fluid with equation of state p = -, de Sitter's cosmological model is quantized. Our treatment differs from previous ones in that it endows the vacuum with dynamical degrees of freedom, following modern ideas that the cosmological term is a manifestation of the vacuum energy. Instead of being postulated from the start, the cosmological constant arises from the degrees of freedom of the vacuum regarded as a dynamical entity, and a time variable can be naturally introduced. Taking the scale factor as the sole degree of freedom of the gravitational field, stationary and wave-packet solutions to the Wheeler-DeWitt equation are found, whose properties are studied. It is found that states of the Universe with a definite value of the cosmological constant do not exist. For the wave packets investigated, quantum effects are noticeable only for small values of the scale factor, a classical regime being attained at asymptotically large times.     

Characterization of two minor saponins from Cordia piauhiensis by 1H and 13C NMR spectroscopy

A careful NMR analysis with full assignment of the 1H and 13C spectral data for two minor saponins isolated from stems of Cordia piauhiensis is reported. These saponins were isolated by high-performance liquid chromatography and characterized as 3beta-O-[alpha-L-rhamnopyranosyl-(1 --> 2)-beta-D-glucopyranosyl]pomolic acid 28-O-[beta-D-glucopyranosyl-(1 --> 6)-beta-D-glucopyranosyl] ester (1) and 3beta-O-[alpha-L-rhamnopyranosyl-(1 --> 2)-beta-D-glucopyranosyl]oleanolic acid 28-O-[beta-D-xylopyranosyl-(1 --> 2)-beta-D-glucopyranosyl-(1 --> 6)-beta-D-glucopyranosyl] ester (2). Their structures were established using a combination of 1D and 2D (1H, 1H-COSY, TOCSY, NOESY, gs-HMQC and gs-HMBC) NMR techniques, electrospray ionization mass spectrometry and chemical evidence.     

A new functionalized resin and its application in preconcentration system with multivariate optimization for nickel determination in food samples

In this work, Amberlite XAD-2 resin functionalized with 4,5-dihydroxy-1,3-benzenedisulfonic acid was synthesized, characterized and applied as a new packing material for an on-line system to nickel preconcentration. The method is based on the sorption of Ni(II) ions in a minicolumn containing the synthesized resin, posterior desorption using an acid solution and measurement of the nickel by spectrophotometry (PAR method). The optimization of the system was performed using factorial design and Doehlert matrix considering five variables: eluent concentration, PAR solution pH, sample flow rate, PAR solution concentration and sample pH. Signals were measured as peak height by using an instrument software. Using the experimental conditions defined in the optimization, the method allowed nickel determination with achieved sampling rate of 25 samples per hour, detection limit (3 s) of 2 μg l⁻¹ and precision (assessed as the relative standard deviation) of 8.2-2.6%, for nickel solutions of 10.0-200.0 μg l⁻¹ concentration, respectively. The experimental enrichment factor of the proposed system was 46, for 120 s preconcentration time. The proposed procedure was applied for nickel determination in food samples. Recoveries of spike additions (5 or 10 μg g⁻¹) to food samples were quantitative (94-110%).     

Darstellung und Kristallstrukturen von neutralen und kationischen Kupfer(I)-Gemischtligandkomplexen mit Derivaten des Biimidazols und Triphenylphosphan

Preparation and Crystal Structures of Neutral and Cationic Copper(I) Mixed Ligand Complexes with Triphenylphosphane and Derivatives of Biimidazole Eight triphenylphosphanecopper(I) complexes with bibenzimidazole, tetramethylbiimidazole or tetrahydrobiimidazole were prepared and characterized so far as possible by elemental analysis, IR, ¹H-NMR and ³¹P-NMR spectra. The crystal structures of two complexes with bibenzimidazole were determined. [Cu(bbimH₂)(PPh₃)₂]Cl · CH₂Cl₂: Reaction of CuCl with bibenzimidazole in fused triphenylphosphane or [CuCl(PPh₃)₃] with bibenzimidazole in CH₂Cl₂. Space group P 1, Z = 2, 6440 observed independent reflections, R = 0.064 for refletions with I > 2σ(I). Lattice parameters at 203 K: a = 983.6; b = 1348.9; c = 1805.5 pm; α = 77.24; β = 80.90; γ = 85.81°. The crystal structure is built up by monomeric molecules with distorted tetrahedral coordination of the copper atom (CuN₂P₂) and bibenzimidazole as bidentate ligand. The chloride ion is linked by H-bonds with the NH groups of the bibenzimidazole. [{Cu(PPh₃)₂}₂(μ-bbim)] · 2 CH₂Cl₂: Reaction of [CuCl(PPh₃)₃] with the dipotassium salt of bibenzimidazole in CH₃OH/CH₂Cl₂. Space group P 1, Z = 1, 7192 observed independent reflections, R = 0.057 for reflections with I > 2σ(I). Lattice parameters at 203 K: a = 1334.1; b = 1386.8; c = 1443.7 pm; α = 107.51; β = 103.35; γ = 113.74°. The crystal structure is built up by centrosymmetric molecules with distorted tetrahedral coordination of the copper atoms (CuN₂P₂) and bibenzimidazolate(2–) as tetradentate bridging ligand.     

On size, circumference and circuit removal in 3-connected matroids

This paper proves several extremal results for 3-connected matroids. In particular, it is shown that, for such a matroid M, (i) if the rank r(M) of M is at least six, then the circumference c(M) of M is at least six and, provided |E(M)|4r(M)−5, there is a circuit whose deletion from M leaves a 3-connected matroid; (ii) if r(M)4 and M has a basis B such that Me is not 3-connected for all e in E(M)−B, then |E(M)|3r(M)−4; and (iii) if M is minimally 3-connected but not hamiltonian, then |E(M)|3r(M)−c(M).     

On the 3-Connected Matroids That are Minimal Having a Fixed Restriction

 Let N be a restriction of a 3-connected matroid M and let M ^′ be a 3-connected minor of M that is minimal having N as a restriction. This paper gives a best-possible upper bound on |E(M ^′)−E(N)|. Received: July 17, 1998 Revised: March 15, 1999     

The thermal behaviour of nickel, copper and zinc complexes with the Schiff bases cis- and trans-N,N′-bis(salicylidene)-1,2-ciclohexadiamine (Salcn)

The Schiff base complexes were prepared and characterised by UV, IR and NMR (¹H and ¹³C) spectroscopy, elemental analysis and X-ray powder diffractometry. Free ligands and some new complexes were submitted to thermal analysis (TG and DSC) under dynamic air atmosphere. The differences in the decomposition profiles were related to the structure of isomers and decomposition intermediates were characterised according to their X-ray diffraction pattern.     

Synthesis and structural characterization of cadmium(II) complexes with chelating keto-hydroxy compounds: The X-ray molecular structure of [Cd2(nq)4(H2O)4]·3H2O (nqH = 2-hydroxynaphthoquinone)

The reaction of cadmium(II) acetate dehydrate with the complexing agents tropolone (tropH), 2-hydroxynaphthoquinone (nqH), 1,2-dihydroxyanthraquinone (alizH₂), and 1,8-dihydroxyanthraquinone (chryzH₂), afforded the complexes [Cd(trop)₂] 1, [Cd₂(nq)₄(H₂O)₄]·3H₂O 2·3H₂O, [Cd(alizH)₂(H₂O)₃] 3, and [Cd(chryzH)₂(H₂O)₂] 4, respectively. The X-ray molecular structure of the dinuclear complex 2·3H₂O reveals that each cadmium(II) atom is seven-coordinated. The nature of water molecules (lattice or coordinated) was discerned by thermogravimetric studies. The ¹¹³Cd NMR spectra were discussed in light of the chemical exchange.     

Influence of feeding strategies of mixed microbial cultures on the chemical composition and microstructure of copolyesters P(3HB‐co‐3HV) analyzed by NMR and statistical analysis

NMR spectroscopy was applied for quantitative and qualitative characterization of the chemical composition and microstructure of a series of poly(3‐hydroxybutyrate‐co‐3‐hydoxyvalerate) copolymers, P(3HB‐co‐3HV), synthesized by mixed microbial cultures at several different feeding strategies. The monomer sequence distribution of the bacterially synthesized P(3HB‐co‐3HV) was defined by analysis of their high‐resolution 1D ¹³C NMR and 2D ¹H/¹³C HSQC and ¹H/¹³C HMBC NMR spectra. The results were verified by employment of statistical methods and suggest a block copolymer microstructure of the P(3HB‐co‐3HV) copolymers studied. Definitive distinction between block copolymers or a mixture of random copolymers could not be achieved. NMR spectral analysis indicates that the chemical composition and microstructure of the copolymers can be tuned by choosing a correct feeding strategy. Copyright © 2009 John Wiley & Sons, Ltd.