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.     

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.     

Le Groupe Quantique Compact Libre U(n)

The free analogues of U(n) in Woronowicz' theory [Wo2] are the compact matrix quantum groups introduced by Wang and Van Daele. We classify here their irreducible representations. Their fusion rules turn to be related to the combinatorics of Voiculescu's circular variable. If we find an embedding , where A _o (F) is the deformation of SU(2) studied in [B2]. We use the representation theory and Powers' method for showing that the reduced algebras A _u (F) _red are simple, with at most one trace. Received: 1 March 1996 / Accepted: 4 April 1997     

Measurement of the sign and the magnitude of heteronuclear coupling constants from spin-state-edited J-cross-polarization NMR experiments

New spin-state-selective (S3) NMR pulse sequences exclusively applying cross-polarization schemes to achieve optimum homonuclear and heteronuclear 1H-X coherence transfer are reported for the simple and accurate measurement of the magnitude and sign of heteronuclear coupling constants for samples at natural abundance. The proposed spin-edited HCP-TOCSY experiments are based on clean heteronuclear S3 excitation, generated by simultaneous co-addition of two independent in-phase and anti-phase components created during the mixing heteronuclear J-cross-polarization (HCP) step, which is finally transferred to other protons by a conventional homonuclear TOCSY mechanism. Selective 1D and non-selective 2D approaches for the easy determination of long-range proton-carbon and proton-nitrogen coupling constants on any protonated and non-protonated heteronuclei are presented and discussed for several organic molecules.     

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.     

(+)- and (-)-2-aminocyclobutane-1-carboxylic acids and their incorporation into highly rigid beta-peptides: stereoselective synthesis and a structural study

[Chemical reaction: See text] Several derivatives of (+)- and (-)-2-aminocyclobutane-1-carboxylic acid, 1, have been prepared through enantiodivergent synthetic sequences. The stereoselective synthesis of free amino acid (+)-1 has been achieved, and this product has been fully characterized for the first time. Stereocontrolled alternative synthetic methodologies have been developed for the preparation of bis(cyclobutane) beta-dipeptides in high yields. Among them, enantio and diastereomers have been synthesized. beta,beta- and beta,delta-Dimers resulting from the coupling of a cyclobutane residue and a linear amino acid have also been prepared. The ability of the cyclobutane ring as a structure-promoting unit both in the monomers and in the dimers has been manifested. The NMR structural study and DFT theoretical calculations evidence the formation of strong intramolecular hydrogen bonds giving rise to cis-fused [4.2.0]octane structural units that confer high rigidity on these molecules both in solution and in the gas phase. The contribution of a cis-trans conformational equilibrium derived from the rotation around the carbamate N-C(O) bond has also been observed, the trans form being the major conformer. In the solid state, this equilibrium does not exist, and moreover, intermolecular hydrogen bonds are present.     

Simultaneous recording of spin-state-selective NMR spectra for different InS spin systems

Heteronuclear magnetization transfer occurring during heteronuclear cross-polarization mixing processes in liquid-state NMR experiments can be easily monitored as a function of the involved in-phase, antiphase, and multiple-quantum magnetization components. The theoretical background on the simultaneous detection of E.COSY-type, TROSY-type, or spin-edited multiplet patterns for different IS and I(2)S spin systems in the same solution-state NMR spectrum is described. The proposed pulse scheme preserves high sensitivity levels and shows good tolerance to the presence of undesired cross-talk artifacts for both NH and NH(2) multiplicities providing an interesting NMR tool for biomolecular applications.     

Stability-Indication LC Determination of Entacapone in Tablets

A rapid and sensitive RP-HPLC method with UV detection at 305 nm for routine quality control of entacapone in tablets was developed. The procedure was validated by specificity, robustness, linearity, accuracy, repeatability and intermediate precision. Experimental design was used during validation to calculate method robustness. The method employs an Ace RP-18 (250 × 4.6 mm i.d., particle size 5 μm), with a mobile phase consisting of water pH 3.0: acetonitrile (65:35, v/v). Entacapone solutions were exposed to direct UV radiation (254 nm), alkaline hydrolysis, acid hydrolysis and effect of oxidation by hydrogen peroxide to evaluate method stability-indication and peak purity tool was utilized to verify the peak purity. The results confirm that the method is highly suitable for its intended purpose.     

Transition metal-mediated intramolecular [2+2+2] cycloisomerizations of cyclic triynes and enediynes

[reaction: see text] Nitrogen-containing 15-membered triacetylenic macrocycles known as 1,6,11-tris(arylsulfonyl)-1,6,11-triazacyclopentadeca-3,8,13-triynes (1) and enediynic macrocycles called 1,6,11-tris(arylsulfonyl)-1,6,11-triazacyclopentadeca-3-ene-8,13-diynes (4 and 5) were satisfactorily prepared. [2+2+2] cycloisomerization processes catalyzed by transition metals were tested in the above-mentioned macrocycles. Readily available and familiar cyclotrimerization precatalysts were examined for efficiency. Among them, the RhCl(CO)(PPh(3))(2) complex was found to catalyze the cycloisomerization reaction giving the desired cycloadducts in high yields.     

Interdisciplinary study on pottery experimentally impregnated with wine

Experimentally developed ceramic pots, with two different sizes of grain, were half-filled with wine and subjected to thermal alteration at constant elevated temperature ((60 ± 2)°C) in darkness for 12 weeks. This work sought to characterise the samples thereby obtained from chemical and mineralogical perspectives using scanning electron microscopy and an energy-dispersive X-ray microanalysis system (SEM-EDX), Fourier transform infrared spectroscopy (FTIR) and capillary electrophoresis (CE) with UV detection as an alternative to chromatographic methods, due to its good resolution, automation, simplicity, high speed, low consumption of chemicals and short time required for sample preparation. The capillary electrophoresis method was used for the detection of five wine biomarkers: succinic acid, malic acid, tartaric acid, citric acid and lactic acid. In general, it was noted that the fine-grained ceramic assortment retained the organic material better than the coarser-grained ceramics. An interesting observation derived from this study was that not only could tartaric acid be considered as a biomarker for wine residues in archaeological pottery, but malic acid could also act similarly for white wine and lactic acid for red wine.