Unique infinite expansions in noninteger bases

Contrary to the classical situation, in noninteger bases almost all numbers have a continuum of distinct expansions. However, the set of numbers having a unique expansions also has a rich topological and combinatorial structure. We clarify the connection of this set with the sets of numbers having a unique infinite or doubly infinite expansion.     

Asymptotics for Christoffel Functions with Varying Weights

We prove sharp asymptotics for Christoffel functions λ_n(w²ⁿ, · ) with respect to varying weights w²ⁿ. The result has an interpretation in the theory of statistical-mechanical models of quantum systems, and it is sufficiently strong to yield asymptotics for Christoffel functions for weights defined on several intervals.     

Kinetics of the photoaquation of Hexacyanoferrate(II) ion

Kinetics of the photoaquation of hexacyanoferrate(II) ion in aqueous solution were studied potentiometrically and spectrophotometrically. Supposing the simplest mechanism (see Fig. 3. in text), the photoaquation in alkaline medium can be well described. The value of the constants at pH = ll.0 are: ø = 0.8-1.0, k₆ = (3.0 ± 0.5) × 10^?8 s^?1 and k_?6 = 1.5 ± 0.2 mol^?1 dm₃ s^?1. To describe the photoaquation in neutral medium t was extended (k′ = 3.33 x 10² mol^?1 dm³s^?1). The quantum yield in acidic medium can be calculated by combination of ø values of different protonated complexes. The reversibility of photoaquation in alkaline medium is also explained by the scheme.     

Denisov's theorem on recurrence coefficients

Recently Denisov (aka Dennisov) (Proc. Amer. Math. Soc.) has proved the following remarkable extension of Rakhmanov's theorem (Math. USSR-Sb. 46 (1983) 105; Russian Original, Mat. Sb. 118 (1982) 104) (see also (Mate et al., Constr. Approx., 1 (1985) 63; Nevai, J. Approx. Theory 65 (1991) 322)) which was conjectured in (Nevai, in: Approximation Theory IV, Vol. II, Academic Press, New York, 1989, pp. 449–489, Conjecture 2.7, p. 453).     

Some problems of A. Kroó on multiple Chebyshev polynomials

Three problems of A. Kroó on multiple Chebyshev polynomials are solved using the Borsuk–Ulam antipodal theorem.     

Minimizing analyte electrolysis in electrospray ionization mass spectrometry using a redox buffer coated emitter electrode

An emitter electrode with an electroactive poly(pyrrole) (PPy) polymer film coating was constructed for use in electrospray ionization mass spectrometry (ESI‐MS). The PPy film acted as a surface‐attached redox buffer limiting the interfacial potential of the emitter electrode. While extensive oxidation of selected analytes (reserpine and amodiaquine) was observed in positive ion mode ESI using a bare metal (gold) emitter electrode, the oxidation was suppressed for these same analytes when using the PPy‐coated electrode. A semi‐quantitative relationship between the rate of oxidation observed and the interfacial potential of the emitter electrode was shown. The redox buffer capacity, and therefore the lifetime of the redox buffering effect, correlated with the oxidation potential of the analyte and with the magnitude of the film charge capacity. Online reduction of the PPy polymer layer using negative ion mode ESI between analyte injections was shown to successfully restore the redox buffering capacity of the polymer film to its initial state. Published in 2010 by John Wiley & Sons, Ltd.     

One-dimensional metallic conducting pathway of cyclohexyl-substituted spiro-biphenalenyl neutral radical molecular crystal

The unprecedented metallic character of the cyclohexyl-substituted spiro-biphenalenyl neutral radical molecular crystal (5) suggested by its Pauli paramagnetism [Science 2005, 309, 281] is contradicted by the thermally activated conduction measured along the needle axis of crystal 5 and by an optical gap of Eg = 0.34 eV. Herein we provide the first high quality ab initio electronic structure calculations using density functional theory to reconcile these properties. The calculations point toward 5 being a quasi one-dimensional (1-D) material, with a 1-D conducting pathway along the [101] pi-chain direction. Along any directions other than the pi-chain, conduction is impeded by the small interchain overlap. 5 has a quarter-filled band structure with a density of states of N(Ef) = 7.5 states eV-1 at the Fermi level, leading to a metallic character along the pi-chain.