A Mass for ALF Manifolds

We prove a positive mass theorem on ALF manifolds, i.e. complete noncompact manifolds that are asymptotic to a circle fibration over a Euclidean base, with fibers of asymptotically constant length.     

Evolution of the structure of near-surface ultrahigh molecular weight polyethylene nanolayers during orientational drawing

A comparative investigation of the surface structure of ultrahigh molecular weight polyethylene film filaments obtained with different draw ratios from xerogels prepared from 1.5 wt % polymer solutions in decaline and mineral oil has been performed using a SUPRA-55V scanning electron microscope and a nanoluminograph for recording thermoluminescence of ultrathin near-surface layers of solids. It has been found that, with an increase in the draw ratio, the luminescence intensity decreases, and the peaks responsible for the segmental mobility are shifted toward higher temperatures. It has been assumed that this is associated with the improvement of the structure of near-surface layers of the polymer (with a decrease in the number of microcavities and segments of molecules with a high degree of coiling). It has also been revealed that the peaks observed in glow curves of the oriented gel samples from polymer solutions in decaline are shifted more significantly than those of the gel samples from polymer solutions in mineral oil, and the extremely oriented films are characterized by a large discretization of kinetic units of motion.     

Novel ligands based on bromosubstituted hydroxycarbonyl [2.2]paracyclophane derivatives: synthesis and application in asymmetric catalysis

New planar-chiral hydroxycarbonyl [2.2]paracyclophane derivatives, 4-acetyl-13-bromo-5-hydroxy[2.2]paracyclophane (Br-АНРС, 63%) and 4-benzoyl-13-bromo-5-hydroxy[2.2]paracyclophane (Br-BHPC, 53%), were synthesized and reacted with the enantiomers of α-phenylethylamine to form corresponding Schiff bases, 12-bromo-4-hydroxy-5[1-(1-phenyl-ethylimino)-ethyl]-[2.2]paracyclophane and 12-bromo-4-hydroxy-5[1-(1-phenyl-ethylimino)-(phenyl)methylen-[2.2]paracyclophane. The diastereomers of the imines were resolved and their absolute configurations and consequently the corresponding configurations of the enantiomers of Br-АНРС were determined by X-ray diffraction. Enantiomerically pure Schiff bases were applied as ligands to form catalysts for the enantioselective addition reaction of diethylzinc with benzaldehyde where 1-phenylpropanol was obtained with 77–91% ee.     

On the model of non-holonomic billiard

In this paper we develop a new model of non-holonomic billiard that accounts for the intrinsic rotation of the billiard ball. This model is a limit case of the problem of rolling without slipping of a ball without slipping over a quadric surface. The billiards between two parallel walls and inside a circle are studied in detail. Using the three-dimensional-point-map technique, the non-integrability of the non-holonomic billiard within an ellipse is shown.     

Integrated Density of States for Ergodic Random Schrödinger Operators on Manifolds

We consider the Riemannian universal covering of a compact manifold M = X/ and assume that is amenable. We show the existence of a (nonrandom) integrated density of states for an ergodic random family of Schrödinger operators on X.     

Aromatization of 1,6,7,7a-tetrahydro-2H-indol-2-ones by a novel process. Preparation of key-intermediate methyl 1-benzyl-5-methoxy-1H-indole-3-acetate and the syntheses of serotonin, melatonin, and bufotenin

Imine 7 of 1,4-cyclohexanedione mono-ethylene ketal 6 was reacted with maleic anhydride, affording the cyclized adduct 8. Methyl esterification of 8, accompanied by transacetalization, led to the dihydrooxindole derivative 10. Aromatization of 10 was then accomplished with POCl(3), leading directly to the key-intermediate title compound 11 in 74% yield from ketone 6. Serotonin, melatonin, and bufotenin were then obtained by standard reactions.     

Nitration of 2-substituted pyrimidine-4,6-diones,structure and reactivity of 5,5-gem-dinitropyrimidine-4,6-diones

Nitration of some 2-substituted pyrimidine-4,6-diones in sulfuric acid was studied, which afforded previously unknown 5,5-gem-dinitropyrimidine-4,6-diones in high yields. The gem-dinitro products were easily attacked by nucleophiles with concomitant formation of gem-dinitroacetyl derivatives, which in turn could be further hydrolyzed to salts of dinitromethane and triureas.     

Determination of arsenic at a gold-plated carbon paste electrode using constant current stripping analysis

A new stripping method for the determination of arsenic in water samples with a gold film-plated carbon paste electrode has been developed for the use in constant current stripping analysis (CCSA). In the novelized procedure, differentiation between As(III) and chemically pre-reduced As(V), the effect of Cu(II) on the response of arsenic, and the stability of sample solutions were studied in detail. Compared to the voltammetric approach, the method utilizing CCSA offers a more rapid procedure with improved analytical characteristics such as reproducibility, selectivity over the Cu(II) ions, or lower detection limit (3 ppb for As(III) and 0.5 ppb for As(V), respectively). The possibilities of the optimized method are demonstrated by determinations of As(III), As(V), and total arsenic in samples of polluted river water.