Compatible relations on filters and stability of local topological properties under supremum and product

An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Fréchetness, strong Fréchetness, countable tightness and countable fan-tightness, some of which recover or refine classical results, some of which are new. The reader may find other applications as well.     

Globally Linked Pairs of Vertices in Equivalent Realizations of Graphs

A two-dimensional framework (G,p) is a graph G = (V,E) together with a map p: V → ℝ². We view (G,p) as a straight line realization of G in ℝ². Two realizations of G are equivalent if the corresponding edges in the two frameworks have the same length. A pair of vertices {u,v} is globally linked in G if %and for all equivalent frameworks (G,q), the distance between the points corresponding to u and v is the same in all pairs of equivalent generic realizations of G. The graph G is globally rigid if all of its pairs of vertices are globally linked. We extend the characterization of globally rigid graphs given by the first two authors [13] by characterizing globally linked pairs in M-connected graphs, an important family of rigid graphs. As a byproduct we simplify the proof of a result of Connelly [6] which is a key step in the characterization of globally rigid graphs. We also determine the number of distinct realizations of an M-connected graph, each of which is equivalent to a given generic realization. Bounds on this number for minimally rigid graphs were obtained by Borcea and Streinu in [3].     

On the finite-size scalling equation for the spherical model

The mean spherical model with an arbitrary interaction potential, the Fourier transform of which has a long-wavelength exponent , 0<2, is considered under periodic boundary conditions and fully finite geometry ind dimensions, when <d<2. A new form of the finite-size scaling equation for the spherical field in the critical region is derived, which relates the temperature shift to Madelung-type lattice constants. The method of derivation makes use of the Poisson summation formula and a Laplace transformation of the momentumspace correlation function.On leave of absence from Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria.     

Effect of film thickness and supercooling on the performance of cholesteryl cinnamate liquid crystal capillary columns

Improved separations of the isomers of olefinic aliphatic insect pheromones were obtained on cholesteryl cinnamate glass capillary columns by operating in the supercooled temperature range of the liquid crystal. Capillary columns were prepared with varying film thickness of the stationary phase; choice of the correct film thickness ensured optimum retention for a wide range of compounds within the most effective temperature range of the liquid crystal. The deactivation procedures described made the liquid crystal columns suitable for separation of the geometric isomers of polar and nonpolar compounds.     

Acrylonitrile polymerization by Cy3PCuMe and (Bipy)2FeEt2

Cy(3)PCuMe (1) undergoes reversible ligand redistribution at low temperature in solution to form the tight ion pair [Cu(PCy(3))(2)][CuMe(2)] (3). The structure of 3 was assigned on the basis of (i) the stoichiometry of the 1 = 3 equilibrium, (ii) the observation of a triplet for the PCy(3) C1 (13)C NMR resonance due to virtual coupling to two (31)P nuclei, and (iii) reverse synthesis of 1 by combining separately generated Cu(PCy(3))(2)(+) and CuMe(2)(-) ions. Complex 1 and [Cu(PCy(3))(2)][PF(6)] (5) coordinate additional PCy(3) to form (Cy(3)P)(2)CuMe and [Cu(PCy(3))(3)][PF(6)], respectively, while 3 does not. Complex 1, free PCy(3), and (bipy)(2)FeEt(2) (2) each initiate the polymerization of acrylonitrile. In each case, the polyacrylonitrile contains branches that are characteristic of an anionic polymerization mechanism. The major initiator in acrylonitrile polymerization by 1 is PCy(3), which is liberated from 1. A transient iron hydride complex is proposed to initiate acrylonitrile polymerization by 2.     

The use of Hückel theory charge densities and localization energies for the prediction of kinetic and thermodynamic factors involved in an assumed model for the hydrohalogenation of 1,3-butadiene,isoprene and chloroprene

It is assumed that the first step in the hydrohalogenation of a diene under conditions such that an ionic mechanism is operative involves the formation of a linear carbonium ion via attachment of a proton to the 1-position and that the second step involves addition of the halide ion to either the 2- or 4-positions. If it is also assumed that hyperconjugation plays some non-negligible role in the carbonium ion intermediate, then it turns out that the use of Hückel theory charge densities and localization energies predict (1) that the 1,2-product is kinetically favored in the cases of butadiene and isoprene, (2) that the 1,4-product is kinetically favored in the case of chloroprene, and (3) that the 1,4-product is thermodynamically favored in all of the above systems. All of these predictions appear to be in agreement with available experimental results.

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Zusammenfassung Bei der Addition von Halogenwasserstoffen an die hier untersuchten Diene wird im Reaktions-ablauf ein lineares Carbeniumion angenommen. Das Proton wird in 1-Stellung addiert und in einem zweiten Schritt wird das Halogenion in 2- oder 4-Stellung angelagert. Weiter wird angenommen, daß Hyperkonjugation beim intermediären Carbeniumion eine Rolle spielt. Aus den mit der Hückel-theorie ermittelten Ladungsverteilungen und Lokalisierungsenergien läßt sich dann voraussagen, daß (1) das 1,2-Produkt bei Butadien und Isopren, (2) das 1,4-Produkt bei Chloropren kinetisch und (3) das 1,4-Produkt in allen Fällen thermodynamisch bevorzugt ist. Diese Voraussagen scheinen mit den bekannten experimentellen Resultaten übereinzustimmen.

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Résumé On admet que l'hydrohalogénation d'un diène dans des conditions où prévaut un mécanisme ionique comporte comme première étape la formation d'un ion carbonium linéaire par addition d'un proton à la position 1 et comme seconde étape l'addition de l'ion halogène à l'une des positions 2 ou 4. Si l'on admet par ailleurs que l'hyperconjuguaison joue un rôle non négligeable dans l'intermédiaire carbonium, l'emploi de la théorie de Hückel permet de prédire à l'aide des densités de charge et des énergies de localisation (1) que le produit 1,2 est favorable du point de vue cinétique dans les cas du butadiène et de l'isoprène (2) que le produit 1,4 est favorable du point de vue cinétique dans le cas du chloroprène et (3) que le produit 1,4 est favorable du point de vue thermodynamique dans tous ces systèmes. Toutes ces prédictions sont apparemment en accord avec les résultats expérimentaux disponibles.

     

Native bromoperoxidases do not bind to nitrocellulose: use of DEAE-cellulose as an alternative in blotting

Bromoperoxidases were investigated by protein blotting after polyacrylamide gel electrophoresis. While the denatured proteins bound to nitrocellulose, the native enzymes did not. Instead, they could be transferred successfully to DEAE-cellulose. Procedures for immunostaining and glycoprotein detection with concanavalin A on DEAE-cellulose are described. The results indicate that binding of native proteins to nitrocellulose can not necessarily be assumed. DEAE-cellulose is suitable both to investigate this phenomenon or as a substitute for nitrocellulose in blotting of native proteins.