The geometry of Hamilton spaces - An introduction

A short introduction of Hamilton, Cartan and Generalized Hamilton spaces is provided. The Hamilton--Jacobi equations are deduced by variational calculus.     

Vector potential theory on nonsmooth domains in R<Superscript>3</Superscript> and applications to electromagnetic scattering

We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space. The main goal is to develop the corresponding theory for L^p-integrable bounday data for optimal values of p's. We also discuss a number of relevant applications in electromagnetic scattering.     

The geometry of Ingarden spaces

The Randers spaces RFⁿ were introduced by R. S. Ingarden. They are considered as Finsler spaces Fⁿ = (M, α + β) equipped with the Cartan nonlinear connection. In the present paper we define and study what we call the Ingarden spaces, I Fⁿ, as Finsler spaces I Fⁿ = (M, α + β) equipped with the Lorentz nonlinear connection. The spaces R Fⁿ and I Fⁿ are completely different. For I Fⁿ we discuss: the variational problem, Lorentz nonlinear connection, canonical N-metrical connection and its structure equations, the Cartan 1-form ω, the electromagnetic 2-form tF and the almost symplectic 2-form 0. The formula dω = F+θ is established. It has as a consequence the generalized Maxwell equations. Finally, the almost Hermitian model of I Fⁿ is constructed.     

On the Besov regularity of conformal maps and layer potentials on nonsmooth domains

We study the Besov regularity of conformal mappings for domains with rough boundary based on the well-posedness for the Dirichlet problem with Besov data. Also, sharp invertibility results for the classical layer potential operators on Sobolev-Besov spaces on the boundary of curvilinear polygons are obtained.     

A general converse theorem for mean‐value theorems in linear elasticity

We prove a rather general mean‐value formula in the theory of elasticity, which expresses the value of the displacement at the centre of a sphere in terms of certain combinations of integral averages over the sphere itself of the traction and the displacement. We also establish the corresponding converse to this mean‐value formula under minimal smoothness assumptions on the displacement. Copyright © 2006 John Wiley & Sons, Ltd.     

Conductance in homomorphous solvents: Tetrabutylammonium salts and alkali picrates in butyrolactone-sulfolane mixtures

Conductance measurements are reported for LiPi, NaPi, KPi, RbPi, CsPi, Bu₄NPi, Bu₄NBr, Bu₄NClO₄, Bu₄NNO₃, and Bu₄NBBu₄ at 25°C in -butyrolactone-sulfolane mixtures. In these mixtures of solvents that are practically homomorphous, isodielectic and with comparable dipole moments, the ion pair association and ionic mobilities of large ions conform to the expectations of the primitive model. Electrolytes containing lithium or sodium ions show anomalies indicating that other factors besides shape, dipole moment, and polarizability of the solvent molecules are involved in the association and transport processes of these ions.     

Activation of trisacryl gels with chloroformates and their use for affinity chromatography and protein immobilization

In this study we describe the activation with chloroformates of Trisacryl-GF-2000, a new synthetic gel support that is stable, hydrophilic, and contains large amounts of hydroxyl groups available for activation. Of all the reagents tested, the activation withN-hydroxysuccinimide-chloroformate andp-nitrophenylchloroformate in organic solvents provides the best activation yield and subsequent coupling. When Trisacryl was activated in acetone with the chloroformates in the presence of 4-dimethylaminopyridine as base and catalyst, up to 30% of the hydroxyl groups, (i.e., 1/repeating unit) could be activated. Amino-containing ligands and proteins could be coupled to these carriers at pH 8 or higher. For better results in affinitychromatographic applications, spacers of ε-amino caproic acid or diaminohexane were introduced. The efficacy of these columns was demonstrated by purification of enzymes, antibodies, and antigens. The performance of these new columns were compared with that of Sepharose columns activated in various ways. In every case, the properties of the Trisacryl support proved superior with particular reference to the purity of the product obtained.     

Bridged peptide macrocycles as ligands for PDZ domain proteins

[reaction: see text] Conformationally constrained side chain-bridged cyclic peptides were prepared using bis-carboxylic acid ring spacers. These macrocyles were designed to inhibit protein-protein interactions mediated by the third PDZ domain (PDZ3) of a mammalian neuronal protein, PSD-95. Isothermal titration calorimetry (ITC) experiments measured dissociation constants in the low micromolar range. For each compound, the change in entropy (TdeltaS) of binding either is comparable in magnitude to the enthalpy change (deltaH) or is the predominant driving force for association.     

Molecular interactions in 1-pentanol +2-methyl-2-butanol mixtures: Static dielectric constant,viscosity and refractive index investigations at 5, 25 and 45°C

Static dielectric constants, refractive indices and viscosities of 1-pentanol +2-methyl-2-butanol mixtures were measured at 5, 25 and 45°C. The results show that the mixing of the two isomers modifies the polarizability and the resistence of viscous flow of the system depending on the composition and temperature. Short range intermolecular interactions producing hetero-alcohol open dimers are considered.     

Synthesis and evaluation of stereopure α-trifluoromethyl-malic hydroxamates as inhibitors of matrix metalloproteinases

The total synthesis of trifluoromethyl (Tfm) analogs of known nanomolar matrix metalloproteinases (MMPs) inhibitors has been performed. The synthetic protocol is based on a moderately stereoselective aldol reaction of trifluoropyruvate with an N-acyl-oxazolidin-2-thione for the construction of the core α-Tfm-malic unit. Both the diastereomeric forms of the target α-Tfm-malic hydroxamates showed micromolar inhibitory potency toward MMP-2 and 9, with a substantial drop with respect to the parent unfluorinated compounds.