On Binary Computation Structures

Based on a modification of Moss' and Parikh's topological modal language [8], we study a generalization of a weakly expressive fragment of a certain propositional modal logic of time. We define a bimodal logic comprising operators for knowledge and nexttime. These operators are interpreted in binary computation structures. We present an axiomatization of the set T of theorems valid for this class of semantical domains and prove – as the main result of this paper – its completeness. Moreover, the question of decidability of T is treated.     

De Bruijn cycles for covering codes

A de Bruijn covering code is a q‐ary string S so that every q‐ary string is at most R symbol changes from some n‐word appearing consecutively in S. We introduce these codes and prove that they can have size close to the smallest possible covering code. The proof employs tools from field theory, probability, and linear algebra. Included is a table of the best known bounds on the lengths of small binary de Bruijn covering codes, up to R = 11 and n = 13, followed by several open questions in this area. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Asymptotic Regimes of Magnetic Bianchi Cosmologies

We consider the asymptotic dynamics of the Einstein-Maxwell field equations for the class of non-tilted Bianchi cosmologies with a barotropic perfect fluid and a pure homogeneous source-free magnetic field, with emphasis on models of Bianchi type VII₀, which have not been previously studied. Using the orthonormal frame formalism and Hubble-normalized variables, we show that, as is the case for the previously studied class A magnetic Bianchi models, the magnetic Bianchi VII₀ cosmologies also exhibit an oscillatory approach to the initial singularity. However, in contrast to the other magnetic Bianchi models, we rigorously establish that typical magnetic Bianchi VII₀ cosmologies exhibit the phenomena of asymptotic self-similarity breaking and Weyl curvature dominance in the late-time regime.     

Weak matching rules for quasicrystals

Weak matching rules for a quasicrystalline tiling are local rules that ensure that fluctuations in perp-space are uniformly bounded. It is shown here that weak matching rules exist forN-fold symmetric tilings, whereN is any integer not divisible by four. The result suggests that, contrary to previous indications, quasicrystalline ground states are not confined to those symmetries for which the incommensurate ratios of wavevectors are quadratic irrationals. An explicit method of constructing weak matching rules forN-fold symmetric tilings in two dimensions is presented. It is shown that the generalization of the construction yields weak matching rules in the case of icosahedral symmetry as well.     

Synthesis of dityrosine cross-linked peptide dimers using the Miyaura-Suzuki reaction

[reaction: see text] Since peroxidase-catalyzed dityrosine formation is inefficient for peptides, we have developed alternative conditions for intermolecular dityrosine formation using the Miyaura-Suzuki reaction. A one-pot reaction is effective for cross-linking short peptides, but longer peptides inhibit the Suzuki step, mandating a traditional two-step procedure using potassium acetate for the Miyaura reaction and potassium carbonate for the Suzuki coupling. These palladium-based methods are complementary to the well-established peroxidase-catalyzed oxidative phenolic coupling of full-length proteins.     

The CeO(2)(+) Cation: Gas-Phase Reactivity and Electronic Structure

"Bare" CeO(2)(+) ions can be prepared in the gas phase by consecutive oxidation of Ce(+) with O(2) and NO(2). The ability to activate saturated and unsaturated hydrocarbons is investigated by use of Fourier-transform ion cyclotron resonance mass spectrometry. In the reactions of CeO(2)(+) with linear and branched alkanes C-H bond activation is observed almost exclusively. In contrast, both oxygen-atom transfer and C-H bond activation processes occur when thermalized CeO(2)(+) cations react with simple alkenes and aromatic compounds. C-C bond activation is not observed at all. Insight into the structural and electronic properties of neutral CeO(2) and cationic CeO(2)(+) is provided by means of quasirelativistic density-functional and ab initio pseudopotential calculations. They reveal a (2)Sigma(u)(+) ground state for CeO(2)(+) which is best described as a linear cerium dioxide with a resonating pi bond. Finally, we discuss the influence of oxo ligands on the chemistry of the cationic CeO(n)()(+) (n = 0-2) species toward hydrocarbons.     

OPTICAL AND THERMAL CHARACTERIZATION OF NATURAL (Sepia officinalis) MELANIN

Abstract The optical properties and the thermal diffusivity of natural cuttlefish ( Sepia officinalis ) melanin have been measured. The optical absorption and scattering properties of melanin particles were determined at 580 nm and 633 nm, using photometric and photothermal techniques. For the photometric studies, the absorption and the transport scattering coefficients were determined from the measurements of diffuse reflectance and transmittance. The scattering anisotropy was obtained from an additional measurement of the total attenuation coefficient and independently obtained by goniometry. For photothermal studies, pulsed photothermal radiometry was used to deduce the absorption and transport scattering coefficients via a model based on optical diffusion theory. Pulsed photothermal radiometry was also used to provide the thermal diffusivity of solid melanin pressed pellets.