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.     

Thermal decomposition of Cu(II) Malonate

The isothermal decomposition of anhydrous Cu(II) malonate of uniform particle size has been studied at 170, 180 and 190°. Decomposition to cupric oxide takes place via the intermediate formation of 2CuCO₃.Cu(OH)₂. X-ray diffraction has been employed to identify the decomposition products. The experimental kinetic data for Cu(II) malonate decomposition are best fitted by two stages: (i) a linear process and (ii) a first-order expression. The activation energies for the two kinetic stages have been found to be 45.7 and 57.2 kcal/mole, respectively. A DTA study of Cu(II) malonate decomposition has also been made. Activation energies have been determined via analysis of the DTA curve using the Borchardt and Piloyan equations.

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Zusammenfassung Die isotherme Zersetzung von wasserfreiem Cu(II)-malonat einheitlicher Partikelgröße wurde bei Temperaturen von 170°, 180° und 190° untersucht. Die Zersetzung von Cu(II)-malonat zu Kupfer(II)-oxid erfolgt über die intermediäre Bildung von 2CuCO₃.Cu(OH)₂. Die Röntgendiffraktionstechnik wurde zur Identifizierung der Zersetzungsprodukte eingesetzt. Die Versuchsergebnisse von Cu(II)-malonat können am besten zwei kinetischen Zuständen angepaßt werden: (1) einem linearen Prozeß und (2) einem Ausdruck erster Ordnung. Die entsprechenden Aktivierungsenergien für die zwei kinetischen Zustände waren 45.7 Kcal/Mol bzw. 57.2 Kcal/Mol. Eine DTA-Untersuchung von Cu(II)-malonat wurde ebenfalls durchgeführt. Die Aktivierungsenergien wurden aus der Analyse der DTA-Kurve mittels der Gleichungen von Borchardt und Piloyan bestimmt.

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Résumé On a étudié la décomposition thermique du malonate de cuivre(II) anhydre à 170, 180 et 190°. La décomposition du malonate en CuO se produit avec formation intermédiaire de 2CuCO₃.Cu(OH)₂. Les produits de décomposition ont été identifiés par diffraction des rayons X. Les données expérimentales correspondent à deux étapes de cinétique différente: (i) un processus linéaire et (ii) une expression du premier ordre. Les énergies d'activation respectives des deux étapes cinétiques s'élèvent à 45.7 et 57.2 kcal.mol^/s-1. Le malonate de cuivre(II) a aussi été étudié par ATD. Les énergies d'activation ont été déterminées à partir de la courbe ATD en appliquant les équations de Borchardt et de Piloyan.

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(II) 170°, 180° 190°. (II) 2CuCO₃. Cu(H)₂. . (II) : (1) (2) . , , , 45,7 / 57,2 /. (II). , , .

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One of the authors (P.C.K.) is grateful to the University Grants Comission, New Delhi, for the award of a junior research fellowship. The authors are grateful to Dr. K. N. Goswami of the Physics Department, University of Jammu, for his help in the X-ray studies of the products.     

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.