Polynomial Dehn Functions and the Length of Asynchronously Automatic Structures

We extend the range of observed behaviour among length functionsof optimal asynchronously automatic structures. We do so bymeans of a construction that yields asynchronously automaticgroups with finite aspherical presentations where the Dehn functionof the group is polynomial of arbitrary degree. Many of thesegroups can be embedded in the automorphism group of a free group.Moreover, the fact that the groups have aspherical presentationsmakes them useful tools in the search to determine the spectrumof exponents for second order Dehn functions. We contributeto this search by giving the first exact calculations of groupswith quadratic and superquadratic exponents. 2000 Mathematical Subject Classification: 20F06, 20F65, 20F69.     

Robust Optimal Service Analysis of Single-Server Re-Entrant Queues

We generalize the analysis of J.A. Ball, M.V. Day, and P. Kachroo (Mathematics of Control, Signals, and Systems, vol. 12, pp. 307–345, 1999) to a fluid model of a single server re-entrant queue. The approach is to solve the Hamilton-Jacobi-Isaacs equation associated with optimal robust control of the system. The method of staged characteristics is generalized from Ball et al. (1999) to construct the solution explicitly. Formulas are developed allowing explicit calculations for the Skorokhod problem involved in the system equations. Such formulas are particularly important for numerical verification of conditions on the boundary of the nonnegative orthant. The optimal control (server) strategy is shown to be of linear-index type. Dai-type stability properties are discussed. A modification of the model in which new customers are allowed only at a specified entry queue is considered in 2 dimensions. The same optimal strategy is found in that case as well.     

Relative Asymptotic Efficiency of the Maximum Pseudolikelihood Estimate for Gauss–Markov Random Fields

A general version of the maximum pseudolikelihood estimate of parameters within the class of Gauss–Markov random fields is stated in a rigorous way. Its asymptotic properties, namely the consistency, the asymptotic normality, and the relative asymptotic efficiency are studied. Explicit formulas for the asymptotic covariance matrix are given, and a decrease of efficiency is proved. A numerical example is added to show that the efficiency can be improved by enlarging the range of the conditional distribution used in the estimator. This revised version was published online in June 2006 with corrections to the Cover Date.     

The AE-XA1 System of CaOCH3

We have recorded laser excitation spectra of the CaOCH₃ free radical in a laser ablation molecular beam apparatus, at a spectral resolution of about 0.010 cm⁻¹ and a rotational temperature estimated at 15 K. The two spin-orbit components of the A²E-X²A₁ 0₀⁰ origin band between 625 and 630 nm have been analyzed. Five main subbands were revealed, with ΔK=+1 and K″=0,±1,±2. There was clear evidence of lambda-doubling in the A²E_1/2-X²A₁ 0₀⁰ (F′₁) K′=+1←K″=0 component. A nonlinear least-squares fitting program based on the model developed by Endo et al. [Y. Endo, S. Saito, and E. Hirota, J. Chem. Phys.81, 122-135 (1984)] fit the experimental data (514 A-X lines, N″≤37) with a root mean square deviation of 0.003 cm⁻¹, using known molecular constants of the ground state. The main vibronic (T₀=15 925.1232(5) cm⁻¹), spin-orbit (aζ_ed=66.974 48(51) cm⁻¹), Coriolis (Aζ_t=5.437 30(24)) cm⁻¹, rotational (A=5.439 97(24) cm⁻¹, B=0.117 884(2) cm⁻¹), and fine structure constants (ε₁=−8.208(14)×10⁻³ cm⁻¹, h₁=1.50(12)×10⁻⁴ cm⁻¹, ε_aa=3.58(89)×10⁻³ cm⁻¹, ε_bc=3.20(76)×10⁻³ cm⁻¹) for the excited state have been obtained.     

Quantum Mayer Graphs for Coulomb Systems and the Analog of the Debye Potential

Within the Feynman–Kac path integral representation, the equilibrium quantities of a quantum plasma can be represented by Mayer graphs. The well known Coulomb divergencies that appear in these series are eliminated by partial resummations. In this paper, we propose a resummation scheme based on the introduction of a single effective potential that is the quantum analog of the Debye potential. A low density analysis of shows that it reduces, at short distances, to the bare Coulomb interaction between the charges (which is able to lead to bound states). At scale of the order of the Debye screening length ^–1 _D, approaches the classical Debye potential and, at large distances, it decays as a dipolar potential (this large distance behaviour is due to the quantum nature of the particles). The prototype graphs that result from the resummation obey the same diagrammatical rules as the classical graphs of the Abe–Meeron series. We give several applications that show the usefulness of to account for Coulombic effects at all distances in a coherent way.     

Synthesis,characterization, and bonding properties of polymeric fullerides AC70.nNH3 (A = Ca,Sr, Ba,Eu, Yb)

Reduction of C70 with alkaline earth and rare earth metals dissolved in liquid ammonia results in metal fulleride solvates AC70.nNH3 (A = Ca, Sr, Ba, Eu, Yb) containing linear polymeric, anionic chains infinity 1 [C70(2-)]. The compounds were characterised by means of Raman spectroscopy and single-crystal structure determination. The accurate crystal structure of [Sr(NH3)8]C70.3NH3, determined with atomic resolution, allowed for a comparison with results of quantum chemical calculations. The nature of the C-C bonds in the fulleride is analysed in detail leading to a model explaining the unexpected polymerisation of C70(2-).     

Network forming properties of various proteins adsorbed at the air/water interface in relation to foam stability

A series of proteins was studied with respect to their ability to form a network at the air/water interface and their suitability as foaming agents and foam stabilizers. Proteins were chosen with a range of structures from flexible to rigid/globular: beta-casein, beta-lactoglobulin, ovalbumin, and (soy) glycinin. Experiments were performed at neutral pH except for glycinin, which was studied at both pH 3 and pH 6.7. The adsorption process was followed with an automated drop tensiometer (ADT). Network forming properties were assessed in terms of surface dilational modulus (determined with the ADT), the critical falling film length (L(still)) and flow rate (Q(still)) below which a stagnant film exists (as measured with the overflowing cylinder technique), and the fracture stress and fracture strain measured in surface shear. It was found that glycinin (pH 3) can form an interfacial gel in a very short time, whereas beta-casein has very poor network-forming properties. Hardly any foam could be produced at the chosen conditions with glycinin (pH 6.7) and with ovalbumin, whereas beta-casein, beta-lactoglobulin, and glycinin (pH 3) were good foaming agents. It seems that adsorption and unfolding rate are most important for foam formation. Once the foam is formed, a rigid network might favor stabilizing the foam.     

In situ formation of allyl ketones via Hiyama-Nozaki reactions followed by a chromium-mediated Oppenauer oxidation

In Hiyama-Nozaki reactions of allylchromium with aldehydes the expected products are homoallylalcohols. However, oxidation products derived from these, predominantly allyl ketones, can be common side products. This can be explained by an Oppenauer-(Meerwein-Ponndorf-Verley)-type mechanism (OMPV-reaction). The amount of oxidation is strongly dependent on the substitution pattern of the reaction partners and the reaction conditions. An appropriate choice of these can lead to preferential formation of ketones instead of the alcohols. In addition to its synthetic usefulness, the oxidation-reduction equilibrium is of the utmost importance for the design of enantioselective Hiyama-Nozaki reactions because it is also a potential racemization pathway.     

A solid-phase synthetic route to unnatural amino acids with diverse side-chain substitutions

Reacting imine derivatives of resin-bound amino acids with alpha,omega-dihaloalkanes provides highly versatile intermediates to racemic alpha,alpha-disubstituted amino acids with a wide variety of side-chain functionality. Two strategies were developed to convert the intermediate omega-chloro or omega-bromo derivatives to the desired products. Together, they allow the creation of amino acids with diverse functionalities (omega-chlorides, nitriles, azides, acetates, thioacetates, thioethers, secondary and tertiary aliphatic amines, and anilines) placed at varying chain lengths (2-5) from the alpha-center of the amino acid.