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.     

Quantum dynamics of bosons in a double-well potential: Josephson oscillations,self-trapping and ultralong tunneling times

The dynamics of the population imbalance of bosons in a double-well potential is investigated from the point of view of many-body quantum mechanics in the framework of the two-mode model. For small initial population imbalances, coherent superpositions of almost equally spaced energy eigenstates lead to Josephson oscillations. The suppression of tunneling at population imbalances beyond a critical value is related to a high concentration of initial state population in the region of the energy spectrum with quasi-degenerate doublets. Negligible coherences among adjacent doublets result in imbalance oscillations with a very small amplitude. For unaccessible long times, however, the system recovers the regime of Josephson oscillations.     

Matching shape graphs

Graphs are important structures to model complex relationships such as chemical compounds, proteins, geometric or hierarchical parts, and XML documents. Given a query graph, indexing has become a necessity to retrieve similar graphs quickly from large databases. We propose a novel technique for indexing databases, whose entries can be represented as graph structures. Our method starts by representing the topological structure of a graph as well as that of its subgraphs as vectors in which the components correspond to the sorted laplacian eigenvalues of the graph or subgraphs. By doing a nearest neighbor search around the query spectra, similar but not necessarily isomorphic graphs are retrieved. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A study of the particle size effect on the pozzolanic activity of an equilibrium catalyst

A self-healing material for coating applications was synthesized using the Diels–Alder (DA) reaction as cross-linking reaction. The built-in reversibility allows local mobility and rearrangements in the polymeric network, which is composed of a furan functionalized epoxy-amine and a bismaleimide. The self-healing material was characterized by physical–chemical means using Fourier Transform Infrared spectroscopy, thermogravimetric analysis (TG) and rapid heat-cool differential scanning calorimetry. It has been shown that the reversibility, as a result of a change in DA/retro-DA equilibrium, occurs in a temperature window ranging from ca. 80 to 150 °C. The repeatability of the non-autonomous healing was checked by TG, showing no evaporation or degradation of the components involved in the temperature window of interest.     

Harada–Tsutsui gauge recovery procedure: From Abelian gauge anomalies to the Stueckelberg mechanism

Revisiting a path-integral procedure developed by Harada and Tsutsui for recovering gauge invariance from anomalous effective actions, it is shown that there are two ways to achieve gauge symmetry: one already presented by the authors, which is shown to preserve the anomaly in the sense of standard current conservation law, and another one which is anomaly-free, preserving current conservation. It is also shown that the application of the Harada–Tsutsui technique to other models which are not anomalous but do not exhibit gauge invariance allows the identification of the gauge invariant formulation of the Proca model, also done by the referred authors, with the Stueckelberg model, leading to the interpretation of the gauge invariant map as a generalization of the Stueckelberg mechanism.