Proper generating trees and their internal path length

We find the generating function counting the total internal path length of any proper generating tree. This function is expressed in terms of the functions (d(t),h(t)) defining the associated proper Riordan array. This result is important in the theory of Riordan arrays and has several combinatorial interpretations.     

Viscoelastic properties of durum wheat and common wheat dough of different strengths

Linear viscoelastic properties (LVP) were determined for five durum wheat doughs and five common wheat doughs (representing four different classes of Canadian common wheat) of different strength using creep testing. A creep time of 10,000 s was sufficient to reach a state of steady state flow for all of the doughs. Creep compliances were analyzed in terms of a Burgers model. For the durum doughs, the entire elastic compliance curve was shifted to higher values as the strength of the dough (as measured by extensigraph) decreased, while the steady state viscosity increased with strength. For common wheat doughs, the elastic compliance curves were steeper and the steady state viscosities were lower than for durum doughs of comparable extensigraph strength. The retardation strengths associated with a maximum in the retardation spectra were lower for the stronger durum doughs than for common wheat doughs of comparable strength. Differences in the LVP between durum and common wheat doughs of similar extensigraph strength were interpreted in the context of physical gels with crosslinks and entanglements, whose contributions to material properties are difficult to distinguish in short-time creep or dynamic measurements. The increased extensibility of common wheat doughs relative to durum doughs of comparable extensigraph strength was attributed to a higher molecular weight fraction in the polypeptide chains, similar in some respects to end-linked bimodal polymer networks. The idea of considering these doughs as physical gels was supported by their stress relaxation behavior. Received: 6 February 2000 Accepted: 22 August 2000     

Structural Analysis of a Helical Peptide Unfolding Pathway

The analysis of the folding mechanism in peptides adopting well‐defined secondary structure is fundamental to understand protein folding. Herein, we describe the thermal unfolding of a 15‐mer vascular endothelial growth factor mimicking α‐helical peptide (QK_L10A) through the combination of spectroscopic and computational analyses. In particular, on the basis of the temperature dependencies of QK_L10A H_α chemical shifts we show that the first phase of the thermal helix unfolding, ending at around 320 K, involves mainly the terminal regions. A second phase of the transition, ending at around 333 K, comprises the central helical region of the peptide. The determination of high‐resolution QK_L10A conformational preferences in water at 313 K allowed us to identify, at atomic resolution, one intermediate of the folding–unfolding pathway. Molecular dynamics simulations corroborate experimental observations detecting a stable central helical turn, which represents the most probable site for the helix nucleation in the folding direction. The data presented herein allows us to draw a folding–unfolding picture for the small peptide QK_L10A compatible with the nucleation–propagation model. This study, besides contributing to the basic field of peptide helix folding, is useful to gain an insight into the design of stable helical peptides, which could find applications as molecular scaffolds to target protein–protein interactions.     

DNA damage induced by organotins on ­trout‐nucleated erythrocytes

The effect of tributyltin‐chloride (TBTC), dibutyltin‐chloride (DBTC) and monobutyltin‐chloride (MBTC) on rainbow trout (Salmo irideus) nuclear DNA, was investigated by means of single cell gel electrophoresis (‘comet’ assay). Our data show that TBTC presents a marked genotoxic effect, whereas the genotoxic effect is less pronounced for DBTC and it is completely absent for MBTC. These results could be important in evaluating the environmental risks deriving from the use of these molecules as a antifouling agents in marine paints and as agricultural biocides. Copyright © 2001 John Wiley & Sons, Ltd.

Abbreviations:

TBTC,

tributyltin‐chloride;

DBTC,

dibutyltin‐chloride;

MBTC,

monobutyltin‐chloride;

Hb,

hemoglobin.

     

A parallel domain reduction method

We relate a particular version of a parallel multigrid method to a domain decomposition method, showing that the parallel multigrid method reduces computation to a small portion of the domain and then extends the solution to the entire domain using the correct reflections to get the exact solution. We extend a particular example to double the parallelism in a nonobvious manner. While the techniques of this paper are applied to twodimensional problems, they can be applied to higher dimensional problems in an obvious manner.     

Analytical methods to determine Po and Pb in marine samples

This paper describes the methods of sampling, preconcentration, chemical separation and final count of ²¹⁰Po and ²¹⁰Pb present in different marine matrices to determine their background levels in a marine ecosystem. Complex, time consuming and selective radioanalytical methods have been used to prepare final clear sources for alpha spectrometry and beta count; in fact, gamma spectrometry, a method direct and non destructive, cannot be taken into account because the ²¹⁰Pb activity is very low which does not allow to carry out sufficiently accurate measurements and ²¹⁰Po is not a gamma emitter but it emits only alpha particle at 5.40 MeV. The results of ²¹⁰Po and ²¹⁰Pb activity concentrations obtained in different marine samples collected in the first two campaigns are still very few to discuss about the ²¹⁰Po and ²¹⁰Pb behavior in marine environment.     

Structural flexibility and role of vicinal 2-thienyl rings in 2,3-dicyano-5,6-di(2-thienyl)-1,4-pyrazine, [(CN)2Th2Pyz], its palladium(II) complex [(CN)2Th2Pyz(PdCl2)2], and the related pentametallic pyrazinoporphyrazines [(PdCl2)4Th8TPyzPzM] (M = Mg(II)(H2O), Zn(II))

The solid state and solution structure of 2,3-dicyano-5,6-di(2-thienyl)-1,4-pyrazine, [(CN)(2)Th(2)Pyz], and its Pd(II) derivative, [(CN)(2)Th(2)Pyz(PdCl(2))(2)]·H(2)O, formed by reaction of [(CN)(2)Th(2)Pyz] with [(C(6)H(5)CN)(2)PdCl(2)] were characterized by X-ray, UV-visible, (1)H and (13)C NMR, and extended X-ray absorption fine structure (EXAFS) spectral measurements. The X-ray crystal structure of [(CN)(2)Th(2)Pyz] shows the presence of one thienyl ring positioned orthogonal to the rest of the molecule, with the two vicinal thienyl rings lying orthogonal to each other in a rare arrangement. NMR studies of [(CN)(2)Th(2)Pyz] in the solid state and in solutions of dimethylformamide or dimethyl sulfoxide confirm a nonequivalence of the thienyl rings in the solid state and also in solution. EXAFS results indicate that two distinct Pd(II) coordination sites are formed at the di(2-thienyl)pyrazino moiety of [(CN)(2)Th(2)Pyz(PdCl(2))(2)]·H(2)O, with identical Pd-N(pyz) (2.03(3) ?) and Pd-Cl (2.36(3) ?) bond lengths but with different Pd-S1 (2.25(4) ?) and Pd-S2 (3.21(5) ?) bond distances in an overall asymmetric molecular framework. Density functional theory (DFT) and time-dependent DFT (TDDFT) theoretical studies also provide information about the structure and spectral behavior of the precursor and its metalated Pd(II) derivative. (1)H/(13)C NMR and UV-visible spectral measurements were also carried out on two heteropentametallic porphyrazine macrocycles which were prepared by a reaction of PdCl(2) with [Th(8)TPyzPzM] where Th(8)TPyzPz = tetrakis-2,3-[5,6-di-(2-thienyl)-pyrazino]porphyrazinato dianion and M = Mg(II)(H(2)O) or Zn(II). Spectroscopic data on the newly synthesized [(PdCl(2))(4)Th(8)TPyzPzM] compounds suggest that the binding of PdCl(2) involves coordination sites of the type S(2(th))PdCl(2) with the two thienyl rings of each di(2-thienyl)pyrazino fragment bound to Pd(II) in an equivalent manner ("th-th" coordination). This is similar to what was found for the corresponding octapyridinated analogues ("py-py" coordination).     

Very long-distance magnetic coupling in a dicopper(II) metallacyclophane with extended π-conjugated diphenylethyne bridges

Self-assembly of the rigid rodlike ligand N,N'-4,4'-diphenylethynebis(oxamate) (dpeba) and Cu(2+) ions affords a novel dinuclear copper(II) metallacyclophane (nBu(4)N)(4)[Cu(2)(dpeba)(2)]·4MeOH·2Et(2)O (1) featuring a very long intermetallic distance (r = 15.0 ?). Magnetic susceptibility measurements for 1 reveal a moderately weak but nonnegligible intramolecular antiferromagnetic coupling between the two metal centers across the double para-substituted diphenylethynediamidate bridge (J = -3.9 cm(-1); H = -JS(1)S(2), where S(1) = S(2) = S(Cu) = (1)/(2)). Density functional electronic structure calculations on 1 support the occurrence of a spin polarization mechanism.     

A Multidimensional Model for the Combustion of Compressible Fluids

We consider a multidimensional model for the combustion of compressible reacting fluids. The flow is governed by the Navier–Stokes in Eulerian coordinates and the chemical reaction is irreversible and is governed by the Arrhenius kinetics. The existence of globally defined weak solutions is established by using weak convergence methods, compactness and interpolation arguments in the spirit of Feireisl [16] and P.L. Lions [24].