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].     

Direct observation of charge-carrier capture in an array of self-assembled InAs/GaAs quantum dots

In this work, charge-carrier capture by an array of self-assembled InAs/GaAs quantum dots was directly observed for the first time by capacitance recharge. It is proposed to process the obtained transient-capture data by a similar method to that used for emission, by the box-car method. The capture activation energies are determined and compared with the emission activation energies.     

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.