Correlations beyond the horizon

It is a fundamental feature of quantum field theory that correlations between observable quantities occur over all spacetime regions. In particular, in cosmological models with horizons, such correlations will be present in regions which lie outside of each other's horizon. Such correlations may play an important role in processes occurring in the early universe.This essay received the first award from the Gravity Research Foundation, 1992—Ed.     

Orthostructures from sesquilinear forms. A primer

We make a linkage with the ultimate generalization of Hilbert space, anR-module with an orthogonality relation, and certain constructs due to Foulis and Randall and other related structures suggested by Cattaneo, Franco, and Marino.     

Time decay for nonlinear wave equations in two space dimensions

The Cauchy Problem for the equation u_tt–u+|u|^p–1u=0 (x², t>0, >1) is studied. Smooth Cauchy data is prescribed, and no smallness condition is imposed. For >5, it is shown that the maximum amplitude of such a wave decays at the expected rate t^–1/2 as t. For 1+8<5, the maximum amplitude still decays, but at a slower rate. These results are then used to demonstrate the existence of the scattering operator when >_o, where _o is the root of the cubic equation ³-2²-7-8=0; thus _o4.15.Alfred P. Sloan Research Fellow     

Recurrence vs. transience for spatially inhomogeneous birth and death in a random environment

Summary We consider birth and death in a random environment, having probabilitiesp(,x) andq(,x) of a step to the right or left, respectively, from statex in environment. Under several sets of conditions involving the existence of limp(,x) and limq(,x) asx, we give conditions for certain extinction or escape to when 0 is absorbing, corresponding to recurrence or transience when 0 is reflecting. The environmental sequence is assumed to be stationary ergodic, and for some results stronger assumptions are required.     

Polymerization and polymers of silicic acid

Linear relationships among molecular weight, polymerization time, and gelation for the condensation of any monomer, including those of unknown size and functionality, are developed and applied to data on soluble silicic acids generated from tetraethyl silicate and from sodium silicate. The results suggest the formation of monomers containing ca. 12–15 ? OSi units with functionality of ca. 2.05 that condense with a rate constant of ca. 10^?4 liter/mole sec and an activation energy of 40–70 kJ/mole. One model compatible with these characteristics and the stoichiometry involved is a ladder polymer ca. 3 ? SiO units wide. Polymer isolation was achieved by replacing residual ? OH with (CH₃)₃Sio? , as well as by freezing of of aqueous solutions, which yielded fibers under special conditions. Solutions of the uncapped and capped polymers and melts of the latter had low viscosity even for fractions with M?_n ～100,000. This implies a coiled or globular nature for the polymers, which is supported by their limited propensity for film and fiber formation. Attemps to improve this situation by copolymerization, the use of other capping agents, and by the polymerization of precapped monomers were unsuccessful.     

Structure, 31P and 13C chemical shift anisotrophy of (CH3)3P, (CH3)3PO, (CH3)3PS and (CH3)3PSe as determined by liquid crystal NMR spectroscopy

The ¹³P and ¹³C spectra of the triply ¹³C labelled molecules (CH₃)₃P, (CH₃)₃PO, (CH₃)₃PS and (CH₃)₃PSe oriented in a nematic phase are reported. The CPC bond angles have been measured. The ¹³P chemical shift tensor shows a large anisotropy except in the case of (CH₃)₃P. The abnormal large value observed for the PSe bond length suggests a large anisotropy of the ¹J(PSe) spin coupling.     

Synthesis of 1,4-annulated cyclooctatetraenophanes based on a novel cubane building block approach

A general synthetic approach to strained 1,4-annulated cyclooctatetraene-based cyclophanes is described. A key feature in this approach is exploitation of the cubane core as a masked cyclooctatetraene synthon. Thus, 1,4-disubstituted cubanes 3 and 4 used as precursors to cyclooctatetraenophanes have been prepared in four steps from the readily available 1,4-cubanedicarboxaldehyde (5). The synthesis of 3 was effected by palladium/copper-mediated coupling of 1,4-bis[(Z,Z)-2-iodovinyl]cubane (6) and 1,4-bis[(Z,Z)-but-1-en-3-ynyl]cubane (8). For the synthesis of 4, on the other hand, modified Eglington-Glaser coupling was applied for the macrocyclization step. The general characteristic of Rh(I) to induce [2 + 2] cycloreversion of the cubane core to syn-tricyclo[4.2.0.0(2,5)]octa-3,7-diene followed by thermal rearrangement to cyclooctatetraene was applied as a key structural transformation toward targeted cyclooctatetraenophanes 1 and 2.     

Determination of trace metals in industrial boron carbide by solid sampling optical emission spectrometry. Optimization of DC arc excitation (current, atmosphere and chemical modifier)

Graphite arc emission spectrometry has become possible as a result of the invention of novel types of optical spectrometers with Echelle-optics and semiconductor array detectors, and by the application of electronically controlled, high current arc generators. An optimization of the excitation parameters to boron carbide analysis is reported here, measuring background corrected line intensities that were integrated for the time of total evaporation of 5 mg boron carbide sample with or without added chemical modifiers. The following set of experimental conditions were compared with respect of analytical sensitivity and precision: (A) no modifier, Ar + O₂ (20%), 16 A; (B) sample + graphite powder (1 + 1), Ar + O₂ (20%), 16 A; (C) sample + CaF₂ (1 + 1), Ar, 25 A; (D) sample + CaF₂ + graphite powder (1 + 1 + 1), Ar, 25 A. The graphite powder modifier resulted in improved precision in general, and the CaF₂ was effective as a plasma ionization buffer and fluorinating agent. The best compromise was found under conditions B, when oxygen was present in the discharge atmosphere. This is likely due to the stepwise conversion of the boron carbide matrix to the more volatile boron oxide. Under conditions B, detection limits in the ranges of 0.3–9 μg g⁻¹ for Al, Ca, Cr, Cu, Fe, Mg, Mn and Si and that of 18–38 μg g⁻¹ for Ti, W, and Zr were attained. Average RSDs of 10.2 and 9.7% were found, respectively, without and with internal referencing to boron.     

New Dolabellane Derivatives from the Brown Alga Dictyota pardalis

Reinvestigation of the brown alga Dictyota pardalis f. pseudohamata CRIBB led to the crystallization of 1 and to the isolation of the two new dolabellane derivatives 2 and 3 . X-Ray analysis of 1 and 2 , together with detailed 1D-and 2D-NMR studies on 2 and 3 , allowed their structures to be elucidated as (1R*,3S*,7S*,11R*,4Z)-dolabella-4,8(17), 12(18)-triene-3,7-diol ( 1 ), (1R*,3S*,4S*,7S*,8S*,11R*,14R*,12E)-3,4:7,8-diepoxydolabe11-12-ene-14, 18-diol ( 2 ), and (1R*,3S*,4S*,7S*,8S*,11R*,14R*)-3,4:7,8-diepoxy-l,4,8,12,12-pentamethylbicyclo[9. 3. 0]tetra-decan-14-ol( 3 ).