Obituary Gilbert Grynberg (1948-2003)

We mourn the death of Professor Dr. Gilbert Grynberg, April 17, 1948 - January 27, 2003. We have lost an excellent and highly esteemed scientist, an outstanding character and a good friend. He has been a very active colleague in the merger of Zeitschrift für Physik and Journal de Physique in the early days. As one of the Co-Editors-in-Chief of The European Physical Journal D, from its start, he has formed the scienti.c standards of EPJ. Untiringly he has served our Journal with greatest dedication. We are grateful that he has been with us. The editorial board and o.ce of EPJ B Siegfried Grossmann, Denis Jérome, Antonio Paoletti     

The vertex-cover polynomial of a graph

In this paper we define the vertex-cover polynomial Ψ(G,τ) for a graph G. The coefficient of τ^r in this polynomial is the number of vertex covers V′ of G with |V′|=r. We develop a method to calculate Ψ(G,τ). Motivated by a problem in biological systematics, we also consider the mappings f from {1, 2,…,m} into the vertex set V(G) of a graph G, subject to f⁻¹(x)f⁻¹(y)≠ for every edge xy in G. Let F(G,m) be the number of such mappings f. We show that F(G,m) can be determined from Ψ(G,τ).     

A tight upper bound for the number of intersections between two rectangular paths

The problem of finding the number of intersections between two geometric figures in the plane has been studied extensively in literature. In this paper, the geometric figure comprising a continuous rectilinear path (called rectangular path) is considered, and a tight (least) upper bound onI(P, Q), the number of intersections between two rectangular pathsP andQ, is given.Editors' Note: One of our referees has reported that the main result of this paper has recently been given independently by a Chinese researcher at the University of Science and Technology, Hefei, P. R. of China. His paper is under publication in the Chinese Science Bulletin. However, since this journal may not be easily accessible to our readers, and further the two papers are obviously independent of each other, theBIT Editors have decided to accept the present paper.     

Packing two graphs of ordern having total size at most 2n − 2

Two graphsG andH of the same order are packable ifG can be embedded in the complement ofH. In this paper we give a complete characterization of two graphs of ordern having total size at most 2n – 2 which are packable. This result extends an earlier result of B. Bollobás and S.E. Eldridge.     

Crystallinity of ethylene oxide oligomers

Nonaethylene glycol and pentadecaethylene glycol and their dimethyl ethers have been prepared and characterized, with respect to crystallinity by wide- and small-angle X-ray scattering, Raman scattering, i.r. spectroscopy and differential scanning calorimetry. Wide-angle X-ray scattering is similar to that from high molecular weight poly(ethylene oxide). The crystal habit is lamella. The lamellae are highly crystalline and the surface layers are ordered. Comparison with crystalline poly(ethylene oxide) prepared conventionally, and having a distribution of chain lengths, shows that such samples crystallize into lamellae with disordered surface layers.     

Synthesis and Structure of [DB24C8)Na][Cd(SCN)3. Formation of a novel linear Cd...Cd...Cd chain with a mer-CdN3S3 coordination confirmation and new coiled [(DB24C8)Na]+ cation

We report herein a novel coordination solid, [(DB24C8)Na][Cd(SCN)3] (6) (DB24C8 denotes dibenzo-24-crown-8), which exhibits a new type of [Cd(SCN)3-]infinity chain with two unusual stereochemical characteristics: (1) a mer-CdN3S3 coordination and (2) a linear Cd chain with a Cd...Cd...Cd angle of 180 degrees. In addition, the [(DB24C8)Na]+ monocation adopts a new structural type-a coiled structure-for the combination of crown ether DB24C8 and alkali metal Na+. The title compound crystallizes in a monoclinic unit cell of C2/c space group symmetry with lattice parameters a = 16.110(8) A, b = 20.380(5) A, c = 11.01(1) A, beta = 119.87(3) degrees, and Z = 4. The arrangement of the [Cd(SCN)3-](infinity) chains in the crystal lattice in the title compound is approximately hexagonal, creating triangular channels which are filled with [(DB24C8)Na]+ monocations. It was previously reasoned by us that the coiled [(DB24C8)Na]+ monocation, which lacks inversion or mirror symmetries, should enhance the tendency for the formation of the noncentrosymmetric space group of the title crystal, making it a potential second-order nonlinear optical crystal. Interestingly, however, the title compound crystallizes in a centrosymmetric space group (C2/c) and gives rise to no second harmonic generation (SHG). Previously known [Cd(SCN)3-](infinity) chains adopt fac-CdN3S3 coordination and a zigzag Cd chain configuration with a Cd...Cd...Cd angle of 165 degrees. The zigzag chains can align in either parallel or antiparallel fashion, resulting in efficient or no SHG effects, respectively. The linear Cd.Cd.Cd chain configuration observed in the title compound, on the other hand, makes it indistinguishable between parallel and antiparallel alignments. It is concluded that, to ensure the formation of noncentrosymmetric space groups, it is necessary to employ optically pure chiral cations as spacers and/or controllers. Furthermore, to enhance the nonlinear optical responses, [Cd(SCN)3-]infinity chains with fac-CdN3S3 coordination and parallel alignments of the zigzag Cd chains should be used.     

Determination of average degree of polymerisation and distribution of oligosaccharides in a partially acid-hydrolysed homopolysaccharide: a comparison of four experimental methods applied to mannuronan

The average degree of polymerisation (DP) and distribution of oligosaccharides in partially acid hydrolysed mannuronans were quantitatively evaluated by 1H NMR, electrospray ionisation mass spectrometry (ESI-MS), micellar electrokinetic capillary chromatography with UV detection (MEKC-UV), and high-pressure anion-exchange chromatography with pulsed amperometric detection (HPAEC-PAD). Our investigation shows that 1H NMR, MEKC-UV and, in particular, HPAEC-PAD can be used as quantitative tools to aid the investigation of polysaccharide structure, function and synthesis. For the latter two techniques, especially, this represents a significant new development as it enables calculation of the quantity of individual oligomers of nominal DP by direct analysis of a defined oligomer mixture. Appropriate statistical averages of number and weight distributions were also calculated and found to fit very well to predicted Kuhn distributions that assume random depolymerisation.     

Synthesis of new tren-based tris-macrocycles. Anion cluster assembling inside the cavity generated by a bowl-shaped receptor

The synthesis of three new tris-macrocycles, containing three [12]aneN(4) (L1), [12]aneN(3)O (L2), or [14]aneN(4) (L3) moieties appended to a tren unit, is reported. The crystal structure of the [(Na(ClO(4))(6)) subset L1(2)H(13)]Na(6)Cl(2)(ClO(4))(12) compound shows the anionic cluster [Na(ClO(4))(6)](5)(-) assembled inside the cavity defined by two bowl-shaped polyammonium receptors, held by multiple charge-charge and hydrogen bond interactions.     

Catalytic enantioselective allylation of aldehydes via a moisture-tolerant chiral BINOL-In(III) complex

A moisture-tolerant chiral indium complex has been developed to effect good enantioselectivities in the addition of allyltributylstannanes to aldehydes. The allylation of a variety of aromatic, α,β-unsaturated and aliphatic aldehydes resulted in both moderate to good yields and high enantioselectivities (up to 86% ee).