Sign changes in the prime number theorem

The Ramanujan Journal - Let V(T) denote the number of sign changes in $$\psi (x) - x$$ for $$x\in [1, T]$$ . We show that $$\liminf _{T\rightarrow \infty } V(T)/\log T\ge \gamma _{1}/\pi +...     

Interspike interval embedding of chaotic signals

According to a theorem of Takens [Lecture Notes in Mathematics (Springer-Verlag, Berlin, 1981), Vol. 898], dynamical state information can be reproduced from a time series of amplitude measurements. In this paper we investigate whether the same information can be reproduced from interspike interval (ISI) measurements. Assuming an integrate-and-fire model coupling the dynamical system to the spike train, there is a one-to-one correspondence between the system states and interspike interval vectors of sufficiently large dimension. The correspondence implies in particular that a data series of interspike intervals, formed in this manner, can be forecast from past history. This capability is demonstrated using a nonlinear prediction algorithm, and is found to be robust to noise. A set of interspike intervals measured from a simple neuronal circuit is studied for deterministic structure using a prediction error statistic. (c) 1995 American Institute of Physics.     

Star-shaped azo-based dipolar chromophores: design, synthesis, matrix compatibility, and electro-optic activity

Three new azo-benzene-based push-pull chromophores with dendritic architecture were synthesized as active materials for electro-optic applications. These chromophores were synthesized in six or seven synthetic steps with an overall yield of around 80% per step and high purity. UV-vis spectroscopy showed significant influence of the transient dipole moment on the observed r(33) values. The chromophores were stable to photochemical oxidation in ambient light and air. The electrical poling conditions were optimized for each chromophore as the T(g) of the composite material varied significantly. The highest EO coefficient achieved was 22-25 pm/V at 1550 nm wavelength. STEM analysis of the blends enabled the correlation of the activity of these large chromophores with the blend morphology. An amorphous polycarbonate host effectively disperses the chromophores in 2-20 nm aggregates in the active materials. However, macrophase separation into 200-500 nm aggregates was observed in a methacrylate host matrix.     

Efficient unimolecular deprotonation of aniline radical cations

[reaction: see text] Deprotonation of the radical cations of aromatic amines, such as anilines, generally occurs much more slowly than other fragmentation reactions. Here we report a stereoelectronic effect involving twisting of the anilino group out of the plane of the benzene ring that results in a significantly increased rate of reactivity toward deprotonation. Quantitative studies of the rate constants for deprotonation as a function of aniline radical cation pKa (Br?nsted plots) demonstrate that the effect is not simply due to a change in the reaction thermodynamics. By combining this stereoelectronic effect with covalent attachment of carboxylate as a base, aniline radical cations that undergo unimolecular deprotonation with rate constants as high as 10(8) s(-1), even in unfavorable protic media, are described.     

Synthesis of benzopyran derivatives,XV Preparation of arylsulfonyloxy-2,2-dimethyl-2H-chromenes

Summary Arylsulfonyloxy-2,2-dimethyl-2H-chromenes (26–35) have been synthesized by reduction of arylsulfonyloxy-2,2-dimethyl-4-chromanones (6–15) followed by dehydration.

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Synthese von Benzopyranderviaten. 15. Mitt.: Darstellung von Arylsulfonyloxy-2,2-dimethyl-2H-chromenen

Zusammenfassung Reduktion von Arylsulfonyloxy-2,2-dimethyl-4-chromanonen (6–15) und anschließende Dehydratisierung liefert Arylsulfonyloxy-2,2-dimethyl-2H-chromene (26–35).

     

Kinetic and thermodynamic characterization of the cobalt and manganese oxyhydroxide cores formed in horse spleen ferritin

Horse spleen ferritin (HoSF) containing 800-1500 cobalt or 250-1200 manganese atoms as Co(O)OH and Mn(O)OH mineral cores within the HoSF interior (Co-HoSF and Mn-HoSF) was synthesized, and the chemical reactivity, kinetics of reduction, and the reduction potentials were measured. Microcoulometric and chemical reduction of HoSF containing the M(O)OH mineral core (M = Co or Mn) was rapid and quantitative with a reduction stoichiometry of 1.05 +/- 0.10 e/M forming a stable M(OH)(2) mineral core. At pH 9.0, ascorbic acid (AH(2)), a two-electron reductant, effectively reduced the mineral cores; however, the reaction was incomplete and rapidly reached equilibrium. The addition of excess AH(2) shifted the reaction to completion with a M(3+)/AH(2) stoichiometry of 1.9-2.1, consistent with a single electron per metal atom reduction. The rate of reaction between M(O)OH and excess AH(2) was measured by monitoring the decrease in mineral core absorbance with time. The reaction was first order in each reactant with second-order rate constants of 0.53 and 4.74 M(-1) min(-1), respectively, for Co- and Mn-HoSF at pH 9.0. From the variation of absorbance with increasing AH(2) concentration, equilibrium constants at pH 9.0 of 5.0 +/- 1.9 for Co-HoSF and 2.9 +/- 0.9 for Mn-HoSF were calculated for 2M(O)OH + AH(2) = 2M(OH)(2) + D, where AH(2) and D are ascorbic acid and dehydroascorbic acid, respectively. Consistent with these equilibrium constants, the standard potential for the reduction of Co(III)-HoSF is 42 mV more positive than that of the ascorbic acid reaction, while the standard potential of Mn(III)-HoSF is 27 mV positive relative to AH(2). Fe(2+) in solution with Co- and Mn-HoSF under anaerobic conditions was oxidized to form Fe(O)OH within the HoSF interior, resulting in partial displacement of the Co or Mn by iron.     

A multi-residue cation-exchange clean up procedure for basic drugs in produce of animal origin

There is considerable interest in maximising the amount of information obtained from animal product analyses, when screening for the presence of veterinary drug residues. One of the barriers to effective multi-residue analysis to date has been a lack of effective clean up procedures to isolate a wide range of residues from the potential interferents, which may be present in both simple and complex (including processed) foods. A cation-exchange clean up has, therefore, been developed for use with acetonitrile extracts of foods, when analysing for several basic drug groups (sulfonamides, benzimidazoles, levamisole, nitroimidazoles, tranquillisers and fluroquinolones). The clean up procedure has also been shown to be effective using a modified extraction solvent for malachite green and leucomalachite green in fish.Several of the key parameters that influence analyte recovery have been investigated and in an optimised procedure, tissue/biofluid samples containing sulfonamides, benzimidazoles, levamisole, nitroimidazoles, tranquillisers and fluoroquinolones are first extracted with acetonitrile. The extract is then dried with sodium sulfate and acidified with glacial acetic acid before loading onto a Bond Elut, strong cation-exchange (SCX) solid phase extraction (SPE) cartridge. Extracts from fish containing malachite green and leucomalachite green can be cleaned up using the same SCX SPE procedure following extraction with citrate buffer/acetonitrile. Typical recoveries of drugs from low level fortified tissues using the optimised procedure lie in the range 53-104% with the exception of carazolol from pig kidney (31%), malachite green from trout (42-51%) and ciprofloxacin from chicken muscle (44%) and from egg (21%).