An extremal problem related to probability

Summary We consider a walk from a stateA ₁ to a stateA _n+1 in which the probability of remaining atA _i isp _i , and the probability of progressing fromA _i toA _i+1 is 1 –p _i . The probabilityW _nk of reachingA _n+1 fromA ₁ in exactlyn + k steps can then be expressed as a polynomial of degreen + k in then variablesp ₁,,p _n . We determine the maximum value ofW _nk and the (unique) choice (p ₁,,p _n ) for which this extremum occurs.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday     

The measure of non-normal sets

Summary It is well-known that almost every number in [0, 1] is normal in base 2, in the sense of Lebesgue measure. Kahane and Salem asked whether the same is true with respect to any Borel measure whose Fourier-Stieltjes coefficients vanish at infinity — in other words, whether the set of non-normal numbers is a set of uniqueness in the wide sense. We show that this is not the case. In fact, we give best-possible conditions on the rate of decay of in order that -almost every number be normal. The techniques include, on the one hand, probability measures with respect to which the binary digits in [0, 1] are independent only by blocks, rather than individually, and on the other hand, the strong law of large numbers for weakly correlated random variables.This work was partially supported by an NSF Graduate Fellowship, NSF Grant MCS-82-01602, and an AMS Research Fellowship.     

Calorimeters for biotechnology

The isothermal and temperature scanning calorimeters manufactured by Calorimetry Sciences Corporation are briefly described. Applications of calorimetry to determine thermodynamics and kinetics of reactions of interest in biotechnology are described with illustrative examples.     

Identification of a highly effective asymmetric phase-transfer catalyst derived from α-methylnaphthylamine

A library of quaternary ammonium salts has been generated via reaction of simple chiral amines with a series of conformationally dynamic biphenyl units. Screening of this library against the alkylation of a glycine imine has led to the identification of a highly effective asymmetric phase-transfer catalyst derived from α-methylnaphthylamine.     

Interfacial electrical properties of DNA-modified diamond thin films: intrinsic response and hybridization-induced field effects

We have investigated the frequency-dependent interfacial electrical properties of nanocrystalline diamond films that were covalently linked to DNA oligonucleotides and how these properties are changed upon exposure to complementary and noncomplementary DNA oligonucleotides. Frequency-dependent electrical measurements at the open-circuit potential show significant changes in impedance at frequencies of >10(4) Hz when DNA-modified diamond films are exposed to complementary DNA, with only minimal changes when exposed to noncomplementary DNA molecules. Measurements as a function of potential show that at 10(5) Hz, the impedance is dominated by the space-charge region of the diamond film. DNA molecules hybridizing at the interface induce a field effect in the diamond space-charge layer, altering the impedance of the diamond film. By identifying a range of impedances where the impedance is dominated by the diamond space-charge layer, we show that it possible to directly observe DNA hybridization, in real time and without additional labels, via simple measurement of the interfacial impedance.     

Chronocoulometric study of the electrochemistry of Prussian blue

During the electrochemical oxidation of Prussian blue (PB) to Prussian yellow (PY), an electrocatalytic oxygen production proceeds at the electrode when aqueous electrolyte solutions are used. The formed oxygen is scavenged by the PY, probably by absorption, and it is consumed during the electrochemical reduction of PY to PB by a heterogeneous chemical reaction of PB with oxygen to PY and hydrogen peroxide. Because of this catalytic regeneration of PY, it is impossible to determine the amount of low-spin iron by chronocoulometry using a potential program in which PB is first oxidized to PY and then the charge is measured to reduce PY to PB. The latter charge is biased by the electrocatalytic PY regeneration.     

New aspects of the electroadsorption of ethyl xanthate on copper electrodes

The interaction of the ethyl xanthate (EX) anion with a copper electrode in a borate buffer solution, pH 9.2, has been investigated by cyclic voltammetry (CV), electrochemical quartz crystal microbalance (EQCM), electrochemical impedance spectroscopy (EIS), and measurements of contact angle (CA) under controlled potential. The results obtained allow establishing that, in the potential range from -0.80 and -0.60 V, two parallel reactions were characterized. These reactions were the ethyl xanthate electroadsorption and the hydrogen evolution reaction (HER). This last reaction has not been described by previous authors. Besides, the EIS measurements show that the mechanism of the HER on copper electrodes is not affected by the presence of a ethyl xanthate species. The EQCM study shows that in the electrodesorption process the departure of each ethyl xanthate species from the copper electrode is accompanied with the simultaneous entry of four to five water molecules. This fact is in accordance with the number of copper atoms involved in the adsorption of one ethyl xanthate species.