Euler characteristics of general linear sections and polynomial Chern classes

We obtain a precise relation between the Chern–Schwartz–MacPherson class of a subvariety of projective space and the Euler characteristics of its general linear sections. In the case of a hypersurface, this leads to simple proofs of formulas of Dimca–Papadima and Huh for the degrees of the polar map of a homogeneous polynomial, extending these formula to any algebraically closed field of characteristic \(0\), and proving a conjecture of Dolgachev on ‘homaloidal’ polynomials in the same context. We generalize these formulas to subschemes of higher codimension in projective space. We also describe a simple approach to a theory of ‘polynomial Chern classes’ for varieties endowed with a morphism to projective space, recovering properties analogous to the Deligne–Grothendieck axioms from basic properties of the Euler characteristic. We prove that the polynomial Chern class defines homomorphisms from suitable relative Grothendieck rings of varieties to \(\mathbb{Z }[t]\).     

Die Kristallstruktur des l, 6-8, 13-Bis-oxido-[14]-annulens

Crystals of 1,6-8, 13-bis-oxido-[14]-annulene are monoclinic, a = 9,29, b = 9,74, c = 11,46 Å, β = 90,0°, space group P 2₁/c, with 4 molecules in the unit cell. The structure has been solved by direct methods and refined by full-matrix least-squares analysis of three-dimensional intensity data. The cis-configuration of the two oxygen bridges is confirmed, and the observed molecular parameters are in full accord with the aromatic properties of the molecule.     

5-vinylisoxazole

Cycloaddition of fulminic acid to 1-butyn-3-ol gave a mixture of 5-α-hydroxyethylisoxazole (I) and 4-α-hydroxyethylisoxazole (II) in the ratio 9:1. By the dehydration of 1, 5-vinylisoxazole (III) was obtained. Compound III has also been prepared by cyclization of 4-penten-2-ynal as well as its diethylacetal with hydroxylamine hydrochloride; in both instances no isomers have been obtained. Compound III spontaneously polymerizes even at room temperature yielding a polymer still containing isoxazole rings.     

Enantiomeric separation of acidic compounds of pharmaceutical interest by capillary electrochromatography employing glycopeptide antibiotic stationary phases

Enantiomeric separation of some selected acidic compounds of pharmaceutical interest belonging to the group of non-steroidal anti-inflammatory drugs were separated by capillary electrochromatography employing silica based glycopeptide antibiotic stationary phases, namely vancomycin or a teicoplanin derivatives (Hepta-Tyr). The vancomycin stationary phase allowed to achieve the chiral resolution of some racemic studied compounds only using mobile phases containing ammonium formate at a relatively low pH 2.5-3.5 and acetonitrile. Employing the teicoplanin derivative stationary phase, good enantiomeric resolution was achieved eluting with mobile phases containing sodium phosphate pH 6-acetonitrile. Enantiomers were moved to the detector because a relatively high reversed electroosmotic flow (due to the positive charge of the stationary phase) and to the electrophoretic mobility of analytes.     

On the biological importance of the hydrogen bond breaking potency of fluorocarbons

Fluorocarbons containing higher halogens have the potency of breaking certain hydrogen bonds in solutions. The relative strength of this potency varies in the series F < Cl < Br < I and the presence of hydrogen atoms in the fluorocarbon increases it. There is a striking parallelism between the hydrogen bond breaking and the anaesthetic potency of these molecules. It is suggested that the breaking of hydrogen bonds is an important step in the mechanism of anaesthesia.     

Enantioselective total synthesis of (−)-microcarpalide

The enantioselective total synthesis of the actin-targeting metabolite (−)-microcarpalide is described. Key steps include ring-closing metathesis (RCM) for the final construction of the 10-membered lactone framework and stereoselective homologation of boronic esters for the insertion of all stereocentres with the desired absolute configuration. In particular, the acidic fragment was prepared in seven steps from a suitable chiral bromomethane boronate by means of two sequential stereoselective homologations to install the two stereocentres with the correct final R stereochemistry, employing (−)-pinanediol as the chiral director. Subsequent elaboration to the required C₇ backbone entailed nucleophilic displacement with a vinyl Grignard reagent, oxidative cleavage of the boronic scaffold and protection-deprotection manipulations. Interestingly, when the tribenzyloxy diene ester resulting from DCC-mediated coupling of the two key synthons was subjected to RCM in the presence of Grubbs' catalyst, the reaction proceeded stereoselectively to yield the desired trans oxecin-2-one, albeit with poor conversion.     

Negative ion chemical ionization mass spectra of (η6-arene)Cr(CO)3

The negative ion chemical ionization mass spectra, with ammonia and methane as reagent gases, of the (η⁶-arene)Cr(CO)₃ complexes, where the arene is C₆H₅COCH₃, C₆H₅COC₂H₅, C₆H₅COC₃H₇, C₆H₅COC(CH₃)₃, 2-CH₃C₆H₄COC₃H₇, C₆H₅COOCH₃, C₆H₅CH₃, 1,3,5-(CH₃)₃C₆H₃ and C₆H₅CH₂COC₂H₅, are reported. Similar behaviour is observed with the two reagent gases, but ammonia shows a much higher abundance for the ions produced by reactions of [NH₂]^? with sample molecules. The compounds containing the C₆H₅CO group display an abundant [M]^{? ˙}, whereas the other compounds exhibit [M? H]^? as base peak, produced by ion/molecule reactions. A comparison of the negative ion chemical ionization mass spectra of the (η⁶-arene)Cr(CO)₃ complexes with those of the corresponding ligands shows the strong electron withdrawing power of the Cr(CO)₃ group in the gas phase.     

Transition metal-catalysed sequences of nucleophilic addition

Summary In presence of nickel or palladium catalysts, nucleophiles can attack vinylcyclopropanes with concomitant ring cleavage. With palladium catalysts in presence of appropriate substituents the terminal carbon atom of the resulting open chain is able to add to two molecules of a conjugated diene giving rise to long-chain unsaturated compounds.     

Simultaneous determination of concentration,diffusion coefficient and number of electrons for electroactive species by combining suitable electroanalytical measurements

The electroanalytical method described for the simultaneous determination of concentration, the number of electrons involved in the redox process and diffusion coefficient is based on evaluation of the ratios between the currents recorded for the analyte and for an easily standardized reference species dissolved in the same medium. Three different electroanalytical techniques are used in which the currents exhibit, for two techniques at least, different dependences on both the diffusion coefficient and electron number. The approach is applicable to diffusion-controlled processes, regardless of the degree of reversibility involved. Reliability tests with electroactive organic compounds dissolved in dimethyl sulphoxide show that both accuracy and precision are within 10% depending on the chosen combination of techniques.