George Inzelt: a tribute on the occasion of his 75th birthday

Journal of Solid State Electrochemistry -     

On Markoff's Inequality

For compact subsets of the real line the Markoff factors increase at least as fast as n ² . In this paper it is shown that there are sets of measure zero with Markoff factors of order n ² . We shall also show that this cannot happen for compact sets of logarithmic capacity zero. In connection with Markoff's inequality for polynomials of two variables we show a set E

On the topological structure of univoque sets

Erd?s, Horváth and Joó discovered some years ago that for some real numbers 1<q<2 there exists only one sequence ci of zeroes and ones such that ∑ciq−i=1. Subsequently, the set U of these numbers was characterized algebraically in [P. Erd?s, I. Joó, V. Komornik, Characterization of the unique expansions 1=∑q−ni and related problems, Bull. Soc. Math. France 118 (1990) 377-390] and [V. Komornik, P. Loreti, Subexpansions, superexpansions and uniqueness properties in non-integer bases, Period. Math. Hungar. 44 (2) (2002) 195-216]. We establish an analogous characterization of the closure of U. This allows us to clarify the topological structure of these sets: is a countable dense set of , so the latter set is perfect. Moreover, since U is known to have zero Lebesgue measure, is a Cantor set.     

Rapid analysis of isomeric exogenous metabolites by differential mobility spectrometry-mass spectrometry

The direct separation of isomeric glucuronide metabolites from propranolol dosed tissue extracts by differential mobility spectrometry-mass spectrometry (DMS-MS) with the use of the polar gas-phase chemical modifier acetonitrile was demonstrated. The DMS gas-phase separation was able to resolve the isomeric metabolites with separation times on the order of milliseconds instead of minutes which is typically required when using pre-ionization chromatographic separation methods. Direct separation of isomeric metabolites from the complex tissue extract was confirmed by implementing a high-performance liquid chromatography (HPLC) separation prior to the DMS-MS analysis to pre-separate the species of interest. The ability to separate isomeric exogenous metabolites directly from a complex tissue extract is expected to facilitate the drug development process by increasing analytical throughput without the requirement for pre-ionization cleanup or separation strategies.     

Utilizing the inherent electrolysis in a chip-based nanoelectrospray emitter system to facilitate selective ionization and mass spectrometric analysis of metallo alkylporphyrins

A commercially available chip-based infusion nanoelectrospray ionization system was used to ionize metallo alkylporphyrins for mass spectrometric detection and structure elucidation by mass spectrometry. Different ionic forms of model compounds (nickel (II), vanadyl (II), copper (II), and cobalt (II) octaethylporphyrin) were created by using two different types of conductive pipette tips supplied with the device. These pipette tips provide the conductive contact to solution at which the electrolysis process inherent to electrospray takes places in the device. The original unmodified, bare carbon-impregnated plastic pipette tips were exploited to intentionally electrochemically oxidize (ionize) the porphyrins to form molecular radical cations for detection. Use of modified pipette tips, with a surface coating devised to inhibit analyte mass transport to the surface or slow the kinetics of the analyte electrochemical reactions, was shown to limit the ionic species observed in the mass spectra of these porphyrins largely, but not exclusively, to the protonated molecule. Under the conditions of these experiments, the effective upper potential limit for oxidation with the uncoated pipette tip was 1.1 V or less, and the coated pipette tips effectively prevented the oxidation of analytes with redox potentials greater than about 0.25 V. Product ion spectra of either molecular ionic species could be used to determine the alkyl chain length on the porphyrin macrocycle. The utility of this electrochemical ionization approach for the analysis of naturally occurring samples was demonstrated using nickel geoporphyrin fractions isolated from Gilsonite bitumen. Acquiring neutral loss spectra as a means to improve the specificity of detection in these complex natural samples was also illustrated.     

Tracking unstable steady states and periodic orbits of oscillatory and chaotic electrochemical systems using delayed feedback control

Experimental results are presented on successful application of delayed-feedback control algorithms for tracking unstable steady states and periodic orbits of electrochemical dissolution systems. Time-delay autosynchronization and delay optimization with a descent gradient method were applied for stationary states and periodic orbits, respectively. These tracking algorithms are utilized in constructing experimental bifurcation diagrams of the studied electrochemical systems in which Hopf, saddle-node, saddle-loop, and period-doubling bifurcations take place.