Asymmetric invariants for a class of strictly hyperbolic systems including the Timoshenko beam

We introduce a set of conserved quantities of energy‐type for a strictly hyperbolic system of two coupled wave equations in one space dimension. The system is subject to mechanical boundary conditions. Some of these invariants are asymmetric in the sense that their defining quadratic form contains second order derivatives in only one of the unknowns. We study their independence with respect to the usual energies and characterize their sign. In many cases, our results provide sharp well‐posedness and stability results. Finally, we apply some of our conservation laws to the study of a singular perturbation problem previously considered by J. Lagnese and J. L. Lions. Copyright © 2007 John Wiley & Sons, Ltd.     

Investigation on the Interaction of Bendazac with β-, Hydroxypropyl-β-, and γ-, yclodextrins

The interactions of Bendazac, a topical non-steroidal anti-inflammatory drug, with-cyclodextrin, hydroxypropyl--cyclodextrin and -cyclodextrinwere investigated to evaluate possibilities to improve the drug's poor water solubilityand eventually to enhance the topical delivery of Bendazac. Phase solubility studiesdemonstrated the ability of the selected cyclodextrins to complex with Bendazac andincrease drug solubility. The amount of solubilized Bendazac increased linearly withthe addition of each cyclodextrin according toA_L type plots. ¹³C-NMR studiesshowed that the Bendazac A-ring was included in the cavity of the three cyclodextrins.The -cyclodextrin was also able to include the B-ring of Bendazac, forminga complex where one drug molecule fitted into two cyclodextrin molecules. Equimolarsolid systems of the drug with each cyclodextrin carrier were prepared using varioustechniques (physical mixing, spray-drying and freeze-drying). The results of differential scanning calorimetry and Fourier transform infrared analysis, performed on the solid systems, demonstrated that freeze-dried and spray-dried products had a high degree of amorphization and agreed with the hypothesis of the existence of drug–cyclodextrin interaction in the solid state. The cyclodextrins tested were able to improve the dissolution of Bendazac. The dissolution profile of the drug was also affected by the physico-chemical properties of each solid system, the freeze-dried products being the most rapidly dissolving forms.     

Site‐Specific Investigation of the Steady‐State Kinetics and Dynamics of the Multistep Binding of Bile Acid Molecules to a Lipid Carrier Protein

The investigation of multi‐site ligand–protein binding and multi‐step mechanisms is highly demanding. In this work, advanced NMR methodologies such as 2D ¹H–¹⁵N line‐shape analysis, which allows a reliable investigation of ligand binding occurring on micro‐ to millisecond timescales, have been extended to model a two‐step binding mechanism. The molecular recognition and complex uptake mechanism of two bile salt molecules by lipid carriers is an interesting example that shows that protein dynamics has the potential to modulate the macromolecule–ligand encounter. Kinetic analysis supports a conformational selection model as the initial recognition process in which the dynamics observed in the apo form is essential for ligand uptake, leading to conformations with improved access to the binding cavity. Subsequent multi‐step events could be modelled, for several residues, with a two‐step binding mechanism. The protein in the ligand‐bound state still exhibits a conformational rearrangement that occurs on a very slow timescale, as observed for other proteins of the family. A global mechanism suggesting how bile acids access the macromolecular cavity is thus proposed.     

Synchronization and decomposability for a family of codes: Part 2

This paper is the second part of a work dealing with two Schützenberger's conjectures on variable-length codes. It contains the detailed proofs of the characterization that we obtained for the degree and the decomposability of finite maximal codes over the alphabet {a, b} with at most 3 occurrences of the letter b in each word.     

Methoxy and Methyl Group Rotation: Solid‐State NMR 1H Spin‐Lattice Relaxation,Electronic Structure Calculations,X‐ray Diffractometry,and Scanning Electron Microscopy

We report solid‐state ¹H nuclear magnetic resonance (NMR) spin‐lattice relaxation experiments, X‐ray diffractometry, field‐emission scanning electron microscopy, and both single‐molecule and cluster ab initio electronic structure calculations on 1‐methoxyphenanthrene ( 1 ) and 3‐methoxyphenanthrene ( 2 ) to investigate the rotation of the methoxy groups and their constituent methyl groups. The electronic structure calculations and the ¹H NMR relaxation measurements can be used together to determine barriers for the rotation of a methoxy group and its constituent methyl group and to develop models for the two coupled motions.     

Methyl reorientation in solid 3-ethylchrysene and 3-isopropylchrysene

We have measured the proton spin-lattice relaxation rate as a function of temperature in polycrystalline 3-ethylchrysene at nuclear magnetic resonance Larmor frequencies of 53.0 and 22.5 MHz and in polycrystalline 3-isopropylchrysene at 53.0, 22.5 and 8.50 MHz. The syntheses of these new compounds are presented. The relatively large chrysene backbone creates an ideal and unique environment for the alkyl groups such that methyl group rotation is the only motion on the nuclear magnetic resonance Larmor frequency timescale over a large temperature range. The relaxation rate data are interpreted in terms of the simplest possible dynamical model; that of random hopping for the methyl group(s), all of which are equivalent in the solid state. The barriers of 11–12 kJ mol⁻¹ are typical for methyl groups in ‘isolated' ethyl and isopropyl groups.     

Probing the internal environment of PVP networks generated by irradiation with different sources

Poly(N-vinyl-2-pyrrolidone) (PVP) hydrogels have been synthesised from the aqueous solutions of the same linear polymer by two different radiation sources: electron beams and UV rays. The present investigation couples conventional hydrogel characterisation techniques with the study of the partition equilibria, fluorescence behaviour and release of two different molecular probes, 1-anilino-8-naphthalene sulphonate (ANS) and Thioflavin T (ThT). The two probes have comparable molecular weight and different structural and optical properties. The ‘chemical’ networks produced upon irradiation in different experimental conditions presented quite distinctive mechanical spectra, yielded to different porous solids upon freeze-drying and showed specific rehydration ratios when ‘equilibrated’ in water. More interestingly, they offered ‘hydrophobic pockets’ to host the ANS molecules in a way that the probe is completely occluded from water, making it fluoresce. Conversely, the generated PVP networks did not show any specific affinity towards the hydrophilic ThT that was only barely untaken.     

Smart hydrogels for Novel Optical Functions

Nanocomposites of inherently conductive polyaniline (PANI) within a highly hydrophilic polyvinyl alcohol (PVA) based hydrogel have been produced by coupling a conventional dispersion chemical oxidative polymerization to a subsequent high energy irradiation step, in order to convert the polymer stabilizing the aqueous dispersion, namely the PVA, into a highly water swollen hydrogel incorporating the PANI particles. The incorporation of the electroactive and “pH-sensitive” polymer into a transparent and highly permeable hydrogel matrix has been pursued as a route to the development of a novel class of potentially biocompatible, smart hydrogels that can respond to changes of the surrounding environment with measurable changes in their optical properties. Absorption spectra show that the optical absorption bands typical of PANI, known to be reversibly affected by changes of the polymer oxidation state or pH or both, are well preserved in the PVA hydrogels. Even more interestingly, fluorescence is observed from the nanoparticles of PANI in its inherently conductive form, whose intensity is strongly affected by changes of pH. This has enhanced the importance of this material to a large extent from both a scientific and a practical point of view.