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.     

Selective synthesis of isobutanol by means of the Guerbet reaction: Part 2. Reaction of methanol/ethanol and methanol/ethanol/n-propanol mixtures over copper based/MeONa catalytic systems

The synthesis of isobutanol via the Guerbet condensation between methanol and ethanol was studied by using sodium methoxide (MeONa) as soluble basic component and copper-based catalysts as heterogeneous dehydrogenating/hydrogenating metal species. The effect of the nature of the catalyst and the relative amount of its individual components with respect to the reacting alcohols as well as of temperature on productivity and selectivity of the process was investigated. The collected data indicated that the copper chromite/MeONa was more active than Cu-Raney/MeONa system. The reaction was shown to proceed with the formation only of n-propanol and isobutanol. Ethanol conversion up to 61% with selectivity to isobutanol up to 98.4% was obtained. The same catalytic systems were also employed in the reaction of the methanol/ethanol/n-propanol ternary mixture. Again copper chromite/MeONa resulted more active than the Cu-Raney/MeONa system. Finally, experiments were carried out on methanol/n-propanol mixtures in the presence of the copper chromite/MeONa catalytic system by recycling both the recovered solid copper component and the liquid reaction mixture for evidencing eventual copper leaching by MeONa. On the basis of the obtained results it was concluded that in the Guerbet reaction copper chromite works as heterogeneous catalyst.     

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.     

Sulle varieta' intersezioni complete

The online version of the original article can be found at     

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.     

Prodotti sghembi di insiemi e strutture di gruppo collegate

Riassunto Dati due insiemiG e Γ si considerano le coppie (a, α( cona∈G ed α ∈ Γ e per queste una legge di prodotto di tipo affatto generico. L'insieme dell (a, α) risulta allora un ?prodotto sghembo?G ⊗ Γ. Si dimostra che l'essereG ⊗ Γ un gruppo—con o senza l'aggiunta di ulteriori condizioni—porta all'esistenza di certi sottogruppi particolari inG⊗Γ; introduce delle strutture di gruppo inG e in Γ od in loro sottinsiemi; ed importa perG⊗Γ una scomposizione in prodotti di gruppi permutabili ed in ampliamenti di Schreier.

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Résumé étant donnés deux ensemblesG et Γ, on considère l'ensemble des couples (a, α) oùa∈G et α∈Γ et à propos de celles-ci une loi de produit, tout à fait générique. L'ensemble des (a, α) est alors un ?produit gauche?G⊗Γ. On démontre que, lorsqueG⊗Γ est un groupe (en ajoutant éventullement quelques autres hypothèses) on a les propriétés suivantes; enG⊗Γ existent certains sous-groupes; enG et en Γ, ou dans quelques luers sousensembles, on a des structures de groupe; le produit G⊗Γ peut être décomposé en produits de groupes permutables et en extensions de Schreier.