Dynamics of the modified Michaelis-Menten system

The theory of cooperative and competitive systems is used to study the dynamical behaviour of the modified Michaelis-Menten system. Conditions for convergence to equilibria and existence of stable closed orbits are given, improving previous results obtained in [R.A. Smith, Some modified Michaelis-Menten equations having stable closed orbits, Proc. Roy. Soc. Edinburgh Sect. A 109 (1988) 341-359].     

Relaxations during the postcure of unsaturated polyester networks by ultrasonic wave propagation,dynamic mechanical analysis,and dielectric analysis

Ultrasonic wave propagation, dynamic mechanical analysis, and dielectric analysis were used to monitor relaxation phenomena during the nonisothermal postcure of unsaturated polyester networks. The measurements covered 6 decades of frequency. As a result, the residual reactive groups, immobilized in the glassy state by vitrification during an isothermal cure step, gained molecular mobility, which promoted the formation of additional crosslinks. After the postcure, the reaction was complete, and the maximum achievable glass‐transition temperature was reached. Moreover, the frequency and temperature dependence of the two relaxations, one related to the glass‐transition temperature of the partially cured sample and the other to the glass transition of the fully cured sample, was evaluated. The Williams–Landel–Ferry equation was used to model the frequency dependence of the main α‐relaxation data obtained with the different techniques. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 596–602, 2005     

Procyanidin size and composition by thiolysis with cysteamine hydrochloride and chromatography

Summary Cysteamine hydrochloride is shown to be an alternative thiol reagent to toluene-α-thiol for the estimation of structural parameters (mean size, galloylation) of plant polymeric procyanidins. Acid depolymerization in the presence of the thiol yields mixtures which may be directly analysed by RPHPLC. Alternatively, the terminal units of the polymer may be separated from the extension units by cation-exchange chromatography previous to RPHPLC. High reaction-recovery yields (ca. 90% thiolysis and RPHPLC, ca. 69% thiolysis, cation exchange and RPHPLC) are obtained and both procedures are precise.     

Rigid Motions in the Presence of a Magnetic Field

It is shown that, in the standard framework of non-relativistic quantum mechanics, the presence of a magnetic field implies that there are no operators representing those translations or rotations that do not leave invariant the magnetic field, and the corresponding components of the linear or angular momentum are undefined. Pacs: 03.65.-w. 02.20.-a     

A functorial construction of moduli of sheaves

We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical aspects of existing constructions and yields new simpler definitions of theta functions, about which more complete results can be proved. Dedicated to the memory of Joseph Le Potier.     

Rejection of the Light Quantum: The Dark Side of Niels Bohr

Evidence is recalled of the strong opposition of Niels Bohr, at the time of the Old Quantum Theory 1913–1925, to the Lichtquanten hypothesis of Einstein. Some episodes with H. A. Kramers, J. C. Slater, and W. Heisenberg are recollected; Bohr's changing point of view is traced back to some philosophical antecedents and to his endeavor to deduce quantum results from the Correspondence Principle. Some consequences for the future interpretation of Quantum Mechanics, specially to the Complementarity Principle, are considered.     

Paradoxical vocal fold movement: A case report

We present a case of one patient with respiratory stridor that was resolved by speech therapy. Paradoxical vocal fold movements were observed by flexible fiberoptic videolaryngoscopy in this patient during episodes of wheezing and dyspnea. Otherwise, normal vocal fold movement was observed in normal conditions of breathing (out of the crisis) and during phonation. Many different terms have been used to describe this entity in the literature, and it is crucial that clinicians recognize the subtle signs of functional stridor. Paradoxical vocal fold motion has to be considered as an important cause of respiratory disease. Its recognition and treatment are discussed in this report.     

On the probability distribution of data at points in real complete intersection varieties

We show several estimates on the probability distribution of some data at points in real complete intersection varieties: norms of real affine solutions, condition number of real solution of real systems of multi-variate polynomial equations and convergence radius of Newton's operator for under-determined system of multi-variate polynomial equations.     

Self-Assembly of Supramolecular Architectures Using Chlorotetra(Pyrrole-2-Carboxylato)Diruthenium Molecules as Building Blocks

Two new complexes, based on the unit Ru₂Cl(μ-O₂CC₄H₄N)₄ (1) (O₂CC₄H₄N = pyrrole-2-carboxylate), Ru₂Cl(μ-O₂CC₄H₄N)₄(H₂O)·4H₂O [1(H ₂ O)·4H ₂ O], and Ru₂Cl(μ-O₂CC₄H₄N)₄(Me₂CO) [1(Me ₂ CO)], are synthesized and structurally characterized. The physical properties of these complexes are studied and compared with those previously reported for Ru₂Cl(μ-O₂CC₄H₄N)₄(thf)·thf·H₂O [1(thf)·thf·H ₂ O]. The nature of the solvent molecule bonded to the axial position of the dimetallic unit determines the supramolecular interactions leading to different arrangements in the solid state. The presence of NH groups in the pyrrolic rings favours the existence of hydrogen bond interactions that are present in the three complexes. In addition, complex 1(Me ₂ CO) shows π–π stacking interactions through pyrrolic rings of different dimetallic units. Dedicated to the memory of Prof. F. Albert Cotton.     

A Multivalued Approach to the Planar Isosceles Three Body Problem

The isosceles three body problem consists of three point masses located on the vertices of an isosceles triangle on the plane. The two masses on the asymmetric edge are equal. This problem has been extensively studied but not as a perturbation of the Kepler problem. In this case we arrive at a differential inclusion as a natural formulation when we regularize the problem. We also derive an extension of the vectorfield that allows us to consider orbits across singular sets.