Normal families and uniqueness theorems for entire functions

There exists a set S with 3 elements such that if f is a non-constant entire function satisfying E(S,f)=E(S,f′), then f≡f′. The number 3 is best possible. The proof uses the theory of normal families in an essential way.     

What is the Rees algebra of a module?

In this paper we show that the Rees algebra can be made into a functor on modules over a ring in a way that extends its classical definition for ideals. The Rees algebra of a module may be computed in terms of a ``maximal' map from to a free module as the image of the map induced by on symmetric algebras. We show that the analytic spread and reductions of can be determined from any embedding of into a free module, and in characteristic 0--but not in positive characteristic!--the Rees algebra itself can be computed from any such embedding.

     

Gas-phase and catalytic combustion in heat-recirculating burners

An experimental study of a spiral counterflow “Swiss roll” burner was conducted, with emphasis on the determination of extinction limits and comparison of results with and without bare-metal Pt catalyst. A wide range of Reynolds numbers (Re) were tested using propane–air mixtures. Both lean and rich extinction limits were extended with the catalyst, though rich limits were extended much further. With the catalyst, combustion could be sustained at Re as low as 1.2 with peak temperatures as low as 350 K. A heat transfer parameter characterizing the thermal performance of both gas-phase and catalytic combustion at all Re was identified. At low Re, the “lean” extinction limit was actually rich of stoichiometric, and rich-limit had equivalence ratios exceeded 40 in some cases. No corresponding behavior was observed without the catalyst. Gas-phase combustion, in general, occurred in a “flameless” mode near the burner center. With or without catalyst, for sufficiently robust conditions (high Re, near-stoichiometric) not requiring heat recirculation, a visible flame would propagate out of the center, but this flame could only be re-centered if the catalyst were present. Gas chromatography indicated that at low Re, even in extremely rich mixtures, CO and non-propane hydrocarbons did not form. For higher Re, where both gas-phase and catalytic combustion could occur, catalytic limits were slightly broader but had much lower limit temperatures. At sufficiently high Re, catalytic and gas-phase limits merged. It is concluded that combustion at low Re in heat-recirculating burners greatly benefits from catalytic combustion with the proper choice of mixtures that are different from those preferred for gas-phase combustion. In particular, the importance of providing a reducing environment for the catalyst to enhance O₂ desorption, especially at low Re where heat losses are severe thus peak temperatures are low, is noted.     

Stochastic coupling and thermodynamic inequalities

Let ₁ and ₂ be thermodynamic Gibbs measures on ^m and ⁿ , respectively. Diffusions are constructed having ₁, and ₂ as invariant measures. These diffusions are then coupled; inequalities between expectations of certain random variables on the two spaces result.Partially supported by NSF-MCS 74-07313-A03     

Measurement of traffic noise shielding provided by buildings

This paper presents a comparison between some current prediction methods for traffic noise shielding provided by buildings and the actual measured attenuations in typical residential areas. Generally, it was found that the method developed by the Department of Environment in the UK gives a reasonably accurate prediction of attenuation by shielding in fairly simple situations. In more complex situations, and particularly where a receiving position is close to a significant shielding structure, such as building, the attenuation obtained is underpredicted by the DOE method, thus the design facade levels for the rear of a building are overpredicted; however, in some other situations, the DOE method overpredicts the attenuation obtained. The attenuations measured for individual noise events under nominally identical conditions are shown to have large variations in attenuation.     

The electrochemistry of arylated anthraquinones in room temperature ionic liquids

Arylated anthraquinone derivatives of different sizes and different π‐basicities have been prepared, and the electrochemical behaviour of these substances has been studied on screen printed graphite electrodes in the three room temperature ionic liquids (RTILs), 1‐butyl‐3‐methylimidazolium hexafluorophosphate ([C₄MIM][PF₆]), 1‐hexyl‐3‐methylimidazolium hexafluorophosphate ([C₆MIM][PF₆]) and 1‐octyl‐3‐methylimidazolium hexafluorophosphate ([C₈MIM][PF₆]). Half redox potentials for the first and second one electron reduction waves were identified, and the diffusion coefficient values were estimated from cyclic voltammetry measurements. The influence of the nature of the RTIL and of the substitution pattern of the anthraquinone on the solvodynamic radii were studied. A correlation of the reductive potentials with the corresponding Hammett constants of the substituents was tested. Copyright © 2013 John Wiley & Sons, Ltd.     

Synthesis of Fluorinated Graphene Oxide and its Amphiphobic Properties

The richly functionalized basal plane bonded to polar organic moieties makes graphene oxide (GO) innately hydrophilic. Here, a methodology to synthesize fluorinated graphene oxide by oxidizing the basal plane of fluorinated graphite, allowing for tunable hydrophobicity of GO, is reported. Fluorine exists as tertiary alkyl fluorides covalently bonded to graphitic carbons, and using magic‐angle spinning (MAS) ¹³C NMR as a primary tool chemical structures for the two types of synthesized fluorinated graphene oxides (FGOs) with significantly different fluorine contents are proposed. The low surface energy of the C–F bond drastically affects GO's wetting behavior, leading to amphiphobicity in its highly fluorinated form. Ease of solution processing enables the fabrication of inks that are spray‐painted on various porous/non‐porous substrates. These coatings maintain amphiphobicity for solvents with surface tensions down to 59 dyn/cm, thus bypassing existing lithographic means to create similar surfaces. The approach towards fluorinating GO and fabricating graphene‐based surfaces with tunable wettability opens the path towards unique, accessible, carbon‐based amphiphobic coatings.     

Initial applications of the molecular model to compute defect vibrations of oxygen in silicon

Abstract

We have employed the molecular model introduced first by Jaswal to compute the vibrational spectra of oxygen bearing defects in a silicon crystal. This was done in the context of a silicon molecular cluster with outer valencies terminated by hydrogen. We employ the MINDO/3 semi-empirical electronic structure method to compute the total energy of the molecular cluster. We examine the conditions in applications of the molecular model required for accurate predictions of oxygen local-mode vibrational frequencies. We find that the oxygen atom and its nearest neighbor silicon atoms must be allowed to vibrate. The nearest-neighbor and next nearest-neighbor shells of silicon atoms must be allowed to relax from their lattice positions. The outermost relaxed shell of silicon atoms should be bonded to silicon atoms in their lattice positions. We apply the molecular model to three defects of crystalline silicon; interstitial oxygen, oxygen in a vacancy (the A-center), and two oxygen atoms in a vacancy. Comparison of our computed local-mode oxygen vibration frequencies with experiment shows the computed oxygen local-mode frequencies to be almost uniformly 10% greater than those observed. Isotope shifts fit experiment equally well. We conclude that the molecular model represents an accurate and efficient approach for the computation of defect local mode vibrational frequencies for oxygen and other defects in crystalline silicon.     

Molecular vacancies in herringbone crystals

We have found evidence of molecular vacancies in the herringbone molecular crystals pentacene and hexabenzo[bc,?ef,?hi,?kl,?no,?qr]coronene using electron diffraction. Experimental electron diffraction patterns taken parallel to the long molecular axis from these crystals exhibited streaking in two characteristic directions, and the streaking approximately followed the molecular herringbone directions. Molecular dynamics simulations of vacancies in pentacene showed that the streaks can be explained by anisotropic lattice relaxations near the defects. Simulated electron diffraction patterns from the crystal–vacancy models at finite temperatures showed streaking similar to the experimental data. The energy of formation of vacancies in pentacene was calculated to be 1.7?eV. The vacancy entropy in pentacene was simulated to be approximately 40 times the Boltzmann constant. We expect these molecular vacancies to influence charge transport and mechanical properties.