A Tamao–Fleming oxidation route to dipeptides bearing N,O-acetal functionality

Tamao–Fleming oxidation of the N-dimethylphenylsilylmethyl group linked to the nitrogen of a peptide bond enables access to dipeptide N,O-acetal functionality. The N-silylmethyl functionality serves as a latent form of the N,O-acetal which is revealed after peptide bond construction.     

On the dimension of the algebra generated by a boolean matrix

We investigate the subspace of the space of all n × n Boolean (0,1)-matrices, spanned by the powers of an arbitrary matrix. We estimate the maximum dimension of such spaces as a function of n and show that their bases consists of consecutive integer powers of the matrix, starting at I. We also determine the maximum dimension of the space spanned by the powers of as symmetric matrix and characterise the matrices achieving that maximum.     

Homogenization of high frequency nonlinear acoustics equations

High frequency nonlinear acoustics equations proposed in [1] are considered. The acoustic characteristics of the medium rapidly oscillate. This model describes the propagation of pulses of sound shocks generated by supersonic planes, blast waves in atmosphere and ocean, continuous radiation of sound sources. An asymptotic solutions of high frequency nonlinear acoustics equations is constructed (when the characteristic size of inhomogeneity is small with respect to the height of the layer where the problem is posed     

Independent random cascades on Galton-Watson trees

Consider an independent random cascade acting on the positive Borel measures defined on the boundary of a Galton-Watson tree. Assuming an offspring distribution with finite moments of all orders, J. Peyrière computed the fine scale structure of an independent random cascade on Galton-Watson trees. In this paper we use developments in the cascade theory to relax and clarify the moment assumptions on the offspring distribution. Moreover a larger class of initial measures is covered and, as a result, it is shown that it is the Hölder exponent of the initial measure which is the critical parameter in the Peyrière theory.

     

Pareto efficiency,simple game stability,and social structure in finitely repeated games

Simple game (sensu Brown and Vincent, 1987) evolutionary theory, when coupled with social structure measured as non‐random encounter of strategy “clones”, often permits equilibrium refinement leading to Pareto superior outcomes (e.g., Axelrod, 1981; Myerson et al., 1991), a foundational goal of economic game theory (Myerson, 1991: 370–375). This conclusion, derived from analyses of one‐shot and infinitely repeated games, fails for finitely repeated games. While mutant cluster invasion enhances Pareto efficiency of equilibria in the former, it can depress Pareto efficiency in the latter. Cooperative equilibria of finitely repeated games (under economic analysis) can be susceptible to cluster‐invasion by even more Pareto efficient strategies which are not themselves evolutionarily stable. Evolutionary (simple) game theory's ability to eliminate Pareto inferior Nash equilibrium strategies induces vulnerabilities foreign to economic analysis. Simple game analysis of finitely repeated games suggests that social structure, modeled as perennial invasion by mutant‐clusters, can induce cyclic invasion, saturation, and loss of cooperation.     

Poly(terthiophene)s from copolymer precursors via solid‐state oxidative conversion

Herein, we report the synthesis of conducting poly (terthiophene)s using a side chain precursor polymer approach. Random copolymers were prepared by ring opening metathesis polymerization of two norbornylene monomers, one containing a pendant terthiophene group and the other containing a pendant acetate group. Solid‐state oxidative conversion of the terthiophene units was used to produce conductive polymers. Oxidative solid‐state conversion was successful for copolymers containing as little as 1 mol % of terthiophene comonomer. The electrical and optical properties of CPs were studied as a function of the amount of electroactive moiety, terthiophene (3T), present in the copolymer. The CPs were found to have conductivity varying between 10^?1 and 10^?4 S/cm depending on the precursor copolymer compositions. The CPs obtained from all precursors had no significant difference in their energy gaps and showed blue to orange color transitions when switching from the oxidized to the neutral states, respectively. The absorbance intensity at 426 nm for poly(3T) from the precursors fits the Beer–Lambert law corresponding to the range of initial 3T content in the precursor copolymer composition (from 1 to 100 mol %). © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 756–763, 2010