Thermal Characterization of Polybutadiyne

Butadiyne was thermally polymerized from the vapor phase onto substrate polyethylene, poly(vinylidene fluoride), polytetrafluoro-ethylene, and fluorinated ethylene propylene films at 20°C. The reaction is characterized as an initial absorption of monomer into the film followed by polymerization in the condensed state. A postpolymerization thermal reaction of the polybutadiyne pendant ethynyl groups was conducted over a 120 to 470°C temperature range with a subsequent surface electrical resistivity decrease to 7 × 10¹¹ ohm/square. The reaction of the pendant acetylenic groups was monitored by DSC and IR spectroscopy and found to be more complex than an intramolecular conversion of an acetylenic polyene to a polyacene structure.     

Subdirect products of hereditary congruence lattices

A congruence lattice L of an algebra A is called power-hereditary if every 0-1 sublattice of Lⁿ is the congruence lattice of an algebra on Aⁿ for all positive integers n. Let A and B be finite algebras. We prove

Compact complex homogeneous manifolds with large automorphism groups

Let X be a compact complex homogeneous manifold and let Aut(X) be the complex Lie group of holomorphic automorphisms of X. It is well-known that the dimension of Aut(X) is bounded by an integer that depends only on n=dim X. Moreover, if X is K?hler then dimAut (X)≤n(n+2) with equality only when X is complex projective space. In this article examples of non-K?hler compact complex homogeneous manifolds X are given that demonstrate dimAut(X) can depend exponentially on n. Let X be a connected compact complex manifold of dimension n. The group of holomorphic automorphisms of X, Aut(X), is a complex Lie group [3]. For a fixed n>1, the dimension of Aut(X) can be arbitrarily large compared to n. Simple examples are provided by the Hirzebruch surfaces F _m , m∈N, for which dimAut(F _m )=m+5, see, e.g. [2, Example 2.4.2]. If X is homogeneous, that is, any point of X can be mapped to any other point of X under a holomorphic automorphism, then the dimension of the automorphism group of X is bounded by an integer that depends only on n, see [1, 2, 6]. The estimate given in [2, Theorem 3.8.2] is roughly dimAut(X)≤(n+2) ⁿ . For many classes of manifolds, however, the dimension of the automorphism group never exceeds n(n+2). For example, it follows directly from the classification given by Borel and Remmert [4], that if X is a compact homogeneous K?hler manifold, then dimAut(X)≤n(n+2) with equality only when X is complex projective space P ⁿ . It is an old question raised by Remmert, see [2, p. 99], [6], whether this same bound applies to all compact complex homogeneous manifolds. In this note we show that this is not the case by constructing non-K?hler compact complex homogeneous manifolds whose automorphism group has a dimension that depends exponentially on n. The simplest case among these examples has n=3m+1 and dimAut(X)=3m+3 ^m , so the above conjectured bound is exceeded when n≥19. These manifolds have the structure of non-trivial fiber bundles over products of flag manifolds with parallelizable fibers given as the quotient of a solvable group by a discrete subgroup. They are constructed using the original ideas of Otte [6, 7] and are surprisingly similar to examples found there. Generally, a product of manifolds does not result in an automorphism group with a large dimension relative to n. Nevertheless, products are used in an essential way in the construction given here, and it is perhaps this feature that caused such examples to be previously overlooked. Oblatum 13-X-97 & 24-X-1997     

Cluster chemistry: XXXVIII. Reactions between M(C2R)(PR′3 (M = Cu,Ag, Au; R = Ph,C6F5; R′ = Me Ph) and H2Os3(CO)10: X-ray structures of Os3Au(μ-CHCHR)(CO)10(PPh3) (R = Ph and C6F5)

The reactions of Os₃(μ-H)₂(CO)₁₀ with a series of Group IB metal acetylide-tertiary phosphine complexes are described. Whereas the compounds M(C₂C₆F₅)(PPh₃) (M = Cu, Ag, Au) afforded the complexes MOs₃(μ-CHCHC₆F₅)(CO)₁₀(PPh₃) cleanly and in high yield, complex mixtures of products were obtained from reactions of the analogous phenylacetylides. The complexes MOs₃(μ-CHCHPh)(CO)₁₀(PPh₃), MOs₃(μ-CHCHPh)(CO)₉(PPh₃)₂ and MOs₃(μ-H)(CO)₁₀(PPh₃) (of known structure), and MOs₃(μ-CHCHPh)(CO)₉(PPh₃)₂ and HMOs₃(CHCPh)(CO)₈ (of unknown structure) were characterised; Au(C₂Ph)(PMe₃) afforded similar derivatives. The reactions proceed by oxidative-addition and hydrogen migration steps; MP bond cleavage reactions also occur to a small extent. The molecular structures of AuOs₃(μ-CHCHC₆R₅)(CO)₁₀(PPh₃) (R = F or H) were determined by X-ray analyses. For R = F, crystals are triclinic, space group P$\text{1}$ with a 9.081(2), b 13.291(2), c 17.419(2) Å, α 84.49(1), β 76.20(2), γ 75.81(2)° and Z = 2; 4622 observed data [I > 2.5σ(I)] were refined to R = 0.027, R_W = 0.031. For R = H, crystals are triclinic, space group P$\text{1}$, with a 9.403(4), b 13.448(3), c 13.774(4) Å, α 83.34(2), β 88.66(3), γ 70.21(3)°, and Z = 2; 4405 observed data [I > 2.5σ(I)] were refined to R = 0.030, R_W = 0.033. The two molecules differ in the orientation of the Ph rings of the PPh₃ groups, but are otherwise similar to Os₃(μ-H)(μ-CHCHBu^t)(CO)₁₀ with the μ-H ligand replaced by the isolobal μ-Au(PPh₃) group.     

Generation and reactivity of bis(2,6-diethylphenyl)germanium(II)

The title intermediate ($\text{3a}$) is produced on photolysis of hexakis(2,6-diethyl-phenyl)cyclotrigermane ($\text{1}$) or bis(2,6-diethylphenyl)bis(trimethylsilyl)germane ($\text{4}$) as evidenced by trapping experiments, and thermally dimerizes to tetrakis(2,6-diethyl-phenyl)digermene ($\text{2a}$). Diarylgermylenes such as $\text{3a}$ do not form stable triethylamine adducts (e.g. $\text{5a}$) as has been previously reported.     

Exact solution of Maxwell's equations for optical interactions with a macroscopic random medium

We report what we believe to be the first rigorous numerical solution of the two-dimensional Maxwell equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. Our solution is based on the pseudospectral time-domain technique, which provides essentially exact results for electromagnetic field spatial modes sampled at the Nyquist rate or better. The results point toward the emerging feasibility of direct, exact Maxwell equations modeling of light propagation through many millimeters of biological tissues. More generally, our results have a wider implication: Namely, the study of electromagnetic wave propagation within random media is moving toward exact rather than approximate solutions of Maxwell's equations.     

Using path sampling to build better Markovian state models: predicting the folding rate and mechanism of a tryptophan zipper beta hairpin

We propose an efficient method for the prediction of protein folding rate constants and mechanisms. We use molecular dynamics simulation data to build Markovian state models (MSMs), discrete representations of the pathways sampled. Using these MSMs, we can quickly calculate the folding probability (P(fold)) and mean first passage time of all the sampled points. In addition, we provide techniques for evaluating these values under perturbed conditions without expensive recomputations. To demonstrate this method on a challenging system, we apply these techniques to a two-dimensional model energy landscape and the folding of a tryptophan zipper beta hairpin.     

Cross section for b-Jet production in &pmacr;p collisions at radicals = 1.8 TeV

Bottom-quark production in &pmacr;p collisions at sqrt[s] = 1.8 TeV is studied with 5 pb(-1) of data collected in 1995 by the D0 detector at the Fermilab Tevatron Collider. The differential production cross section for b jets in the central rapidity region ( | y(b)|<1) as a function of jet transverse energy is extracted from a muon-tagged jet sample. Within experimental and theoretical uncertainties, D0 results are found to be higher than, but compatible with, next-to-leading-order QCD predictions.