The entropies of renewal systems

Renewal systems are symbolic dynamical systems originally introduced by Adler. IfW is a finite set of words over a finite alphabetA, then the renewal system generated byW is the subshiftX _W ⊂A ^Z formed by bi-infinite concatenations of words fromW. Motivated by Adler’s question of whether every irreducible shift of finite type is conjugate to a renewal system, we prove that for every shift of finite type there is a renewal system having the same entropy. We also show that every shift of finite type can be approximated from above by renewal systems, and that by placing finite-type constraints on possible concatenations, we obtain all sofic systems. The authors were supported in part by NFS grants DMS-8706284, DMS-8814159 and DMS-8820716.     

Atomic layer deposition in nanometer-level replication of cellulosic substances and preparation of photocatalytic TiO2/cellulose composites

TiO2 replicas of filter paper with nanometer-level accuracy were prepared by atomic layer deposition of thin conformal TiO2 coating, followed by a removal of the paper by air-anneal at 450 degrees C. Photocatalytic anatase TiO2/cellulose composites were also made by leaving the paper intact. The TiO2 films were deposited from Ti(OMe)4 and H2O at 150-250 degrees C. The photocatalytic activity of the TiO2/cellulose composite was verified by photocatalytic reduction of Ag(I) from an aqueous solution to Ag nanoparticles on the TiO2 surface. The TiO2/cellulose composites are mechanically more stable than the free-standing TiO2 replicas and are therefore potentially suitable as lightweight, high surface area photocatalysts.     

Seeding and the Non-Hydrolytic Sol-Gel Synthesis of ZrW2O8 and ZrMo2O8

The unseeded non-hydrolytic sol-gel synthesis of ZrW₂O₈ and ZrMo₂O₈ produces trigonal ZrM₂O₈ (M = W, Mo) at 740 and 300–400°C, respectively. Cubic ZrW₂O₈ can be prepared using non-hydrolytic sol-gel methods by seeding with small amounts of preprepared cubic material, and the formation of the trigonal polymorph can be suppressed completely. Seeds with a small particle size are necessary for the preparation of cubic ZrW₂O₈. In contrast, seeding of ZrMo₂O₈ gels with either cubic ZrMo₂O₈ or cubic ZrW₂O₈ only lowers the temperature at which the trigonal phase crystallizes.     

The rate of homolysis of adducts of peroxynitrite to the C=O double bond.

Nucleophilic addition of the peroxynitrite anion, ONOO(-), to the two prototypical carbonyl compounds, acetaldehyde and acetone, was investigated in the pH interval 7.4-14. The process is initiated by fast equilibration between the reactants and the corresponding tetrahedral adduct anion, the equilibrium being strongly shifted to the reactant side. The adduct anion also undergoes fast protonation by water and added buffers. Consequently, the rate of the bimolecular reaction between ONOO(-) and the carbonyl is strongly dependent on the pH and on the concentration of the buffer. The pK(a) of the carbonyl-ONOO adduct was estimated to be approximately 11.8 and approximately 12.3 for acetone and acetaldehyde, respectively. It is shown that both the anionic and the neutral adducts suffer fast homolysis along the weak O-O bond to yield free alkoxyl and nitrogen dioxide radicals. The yield of free radicals was determined to be about 15% with both carbonyl compounds at low and high pH, while the remainder collapses to molecular products in the solvent cage. The rate constants for the homolysis of the adducts vary from ca. 3 x 10(5) to ca. 5 x 10(6) s(-1), suggesting that they cannot act as oxidants in biological systems. This small variation around a mean value of about 10(6) s(-1) suggests that the O-O bond in the adduct is rather insensitive to its protonation state and to the nature of its carbonyl precursor. An overall reaction scheme was proposed, and all the corresponding rate constants were evaluated. Finally, thermokinetic considerations were employed to argue that the formation of dioxirane as an intermediate in the reaction of ONOO(-) with acetone is an unlikely process.     

Physically based molecular device model in a transient circuit simulator

Two efficient, physically based models for the real-time simulation of molecular device characteristics of single molecules are developed. These models assume that through-molecule tunnelling creates a steady-state Lorentzian distribution of excess electron density on the molecule and provides for smooth transitions for the electronic degrees of freedom between the tunnelling, molecular-excitation, and charge-hopping transport regimes. They are implemented in the fREEDA™ transient circuit simulator to allow for the full integration of nanoscopic molecular devices in standard packages that simulate entire devices including CMOS circuitry. Methods are presented to estimate the parameters used in the models via either direct experimental measurement or density-functional calculations. The models require 6–8 orders of magnitude less computer time than do full a priori simulations of the properties of molecular components. Consequently, molecular components can be efficiently implemented in circuit simulators. The molecular-component models are tested by comparison with experimental results reported for 1,4-benzenedithiol.     

Validation of a simple, sensitive method for the determination of beta-estradiol in bovine urine using gas-chromatography negative-ion chemical ionization mass spectrometry

A new method is presented for the analysis of 17[small beta]-estradiol in bovine urine. After deconjugation, the sample is cleaned up using an OASIS[trade mark sign] HLB disposable cartridge and extracted into 1-chlorobutane. The hormone is derivatized using pentafluorobenzoyl chloride. The derivatized estradiol is quantitated using gas-chromatography negative-ion chemical ionization mass spectrometry. Calibrations, obtained using spiked blank urine, are linear in the range of 100-1000 pg mL(-1) with CC[small alpha] approximately 170 pg mL(-1) and CC[small beta] of 287 pg mL(-1). Recoveries are in the range of 80 to 130%. The method is rugged, rapid and sensitive when compared to other hormone methods.     

Ring expansion-annulation strategy for the synthesis of substituted azulenes and oligoazulenes. 2. Synthesis of azulenyl halides, sulfonates, and azulenylmetal compounds and their application in transition-metal-mediated coupling reactions

A "ring expansion-annulation strategy" for the synthesis of substituted azulenes is described based on the reaction of beta'-bromo-alpha-diazo ketones with rhodium carboxylates. The key transformation involves an intramolecular Buchner reaction followed by beta-elimination of bromide, tautomerization, and in situ trapping of the resulting 1-hydroxyazulene as a carboxylate or triflate ester. Further synthetic elaboration of the azulenyl halide and sulfonate annulation products can be achieved by employing Heck, Negishi, Stille, and Suzuki coupling reactions. Reaction of the azulenyl triflate 84 with pinacolborane provides access to the azulenylboronate 91, which participates in Suzuki coupling reactions with alkenyl and aryl iodides. The application of these coupling reactions to the synthesis of biazulenes, terazulene 101, and related oligoazulenes is described, as well as the preparation of the azulenyl amino acid derivative 110.     

Study on the retention behaviour of low-molar-mass polystyrenes and polyesters in reversed-phase liquid chromatography by evaluation of thermodynamic parameters

Polymers can be characterized under sorption conditions, to obtain information on molar mass and chemical composition. In order to get a better understanding of their retention behaviour under such conditions, the evaluation of thermodynamic parameters obtained from van't Hoff analyses on low-molar-mass polystyrenes (PS) and polyesters (PE) in various THF–water mixtures on a C₁₈ column is described in this study. Linear van't Hoff behaviour was observed in almost all cases. Negative values for both ΔH and ΔS were found for both PS and PE oligomers, which increase with increasing %THF. For ΔS this is explained from multi-site attachment effects. For PS, the non-linear relations between ΔH and ΔS, and degree of polymerization (p) could be properly described by the Stockmayer–Fixman equation. Although less clear, similar trends were found for PE. For PS, evidence for penetration effects of oligomer chains into the bonded chains was obtained. Martin plots for both PS and PE were shown to be non-linear in all investigated eluent compositions. The extent of non-linearity is suggested to depend on the conformation of a polymer in solution. No distinct enthalpy–entropy-compensation temperature (EECT) independent of p was found for PS, thus confirming the findings of an earlier study in which no exact molar mass independence was found under critical conditions. Further evaluation of EECT for PS oligomers revealed a retention mechanism independent of the binary eluent composition. This indicates that conclusions from this study can also be used for a qualitative understanding of sorption mechanisms in the gradient elution mode. Finally, for PS it was shown that ΔG equals zero under critical conditions, thus confirming theoretical predictions.     

Resonant state expansions of the continuum

It is shown that the set of bound states and single-pa tide esonances consisting of the outgoing solutions of the Schödinge equation can be used as a ep esentation to describe p ocesses taking place in the continuum part of nuclear spectra. This is the first thoough investigation of completeness properties using realistic nuclear wave functions.This work was supported in part by the OTKA Foundation Hungary (contract number 3010) and by the Swedish Natural Science Research Council.