Bisection is not optimal on the average

Summary We seek the zero of a continuous increasing functionf: [0, 1] [–1, 1] such thatf(0)=–1 andf(1)=1. It is known that the bisection method makes optimal use ofn function evaluations within a worst case analysis. In this paper we study the average error with respect to the natural measure of Graf et al. (1986). We prove that the bisection method is not optimal on the average. Actually, the average error of the bisection method is about (1/2) ⁿ , while the average error of the optimal method is less than ⁿ with some <1/2.     

Photoelectron spectra of important drug molecules: zidovudine and artemisinine

The electronic structures of the anti-HIV drug zidovudine (AZT) and antimalarial drug artemisinine have been investigated by UV photoelectron spectroscopy (UPS), MO calculations, and comparison with the spectra of related molecules. The analysis of their electronic structure is correlated with known biological activities.     

Highly selective synthesis of 2-substituted-5-hydroxy-6-oxo-1,6-dihydropyrimidine-4-carboxylic acid derivatives using a novel protected dihydroxyfumarate

A high yielding (50-96%) route to 2-substituted-5-hydroxy-6-oxo-1,6-dihydropyrimidine-4-carboxylic acid derivatives has been developed using a rationally designed dihydroxyfumarate derivative. The fully unprotected pyrimidinone heterocycle was prepared in quantitative yield upon treatment with HCl.     

Dating of hydrated obsidian surfaces by SIMS-SS

A new approach to dating ancient obsidian artifacts based on the modeling of water diffusion profiles is evaluated using multiple archaeological test cases of known age. Hydrogen profiles from hydrated obsidian surfaces have been collected by secondary ion mass spectrometry (SIMS). The H₂O concentration versus depth profiles are modeled and diffusion ages have been produced. SIMS based dates for fourteen obsidian specimens of well-known age, ranging from 300-7000 years old, have been compared with radiocarbon ages. The convergence between the two dating methods is excellent and validates the new dating approach. This revised version was published online in July 2006 with corrections to the Cover Date.     

Rapid determination of uranium at the nanogram level in geological and biological materials

A rapid method for the determination of uranium at nanogram levels in geological and biological materials is described. The method is based on the separation of 23.5 min²³⁹U, produced on neutron activation, by solvent extraction with TBP from nitric acid medium in the presence of HF, which prevents interference from Th; a number of other possibly interfering elements were shown to be negligibly extracted. The method is selective and sensitive enough for the determination of nanogram levels of uranium in soils, ores and biological samples. Results for some standard reference materials were in good agreement with certified values. Presented at the International Conference on Analytical Chemistry, Interan '76, Prague, August 1976.     

Identification of impurities in acarbose by using an integrated liquid chromatography-nuclear magnetic resonance and liquid chromatography-mass spectrometry approach

The usefulness of applying an integrated LC-NMR and LC-MS approach to acarbose bulk drug impurity profiling is demonstrated. LC-MS and LC-NMR methodologies were employed for the online separation and structural elucidation of a final drug product. Combining data provided by the stop-flow LC-NMR and LC-MS experiments made it possible to identify the main components present in the acarbose sample. Spectral analysis revealed that A and B were known impurities while C was an unknown compound. LC-MS and LC-NMR analyses revealed that C was a pentasaccharide differing from the acarbose in number and nature of sugar subunits in the molecule. It was subsequently isolated and its structure was confirmed by the offline 1- and 2-D NMR experiments, and atom assignment was made.     

Stochastic properties of quadrature formulas

Summary The average error of suitable quadrature formulas and the stochastic error of Monte Carlo methods are both much smaller than the worst case error in many cases. This depends, however, on the classF of functions which is considered and there are counterexamples as well.Nonlinear methods, adaptive methods, or even methods with varying cardinality are not significantly better (with respect to certain stochastic error bounds) than the simplest linear methods .     

Spectres infrarouges et raman des organomagnesiens EtMgX·2Et2O (X = Br,I) cristallises et dissous dans l'ether ethylique

The infrared and Raman spectra of the low-temperature polycrystalline organomagnesium compounds, C₂H₅MgI·2(C₂H₅)₂O and C₂H₅MgBr·2(C₂H₅)₂O and of some deuterated derivatives, C₂H₅MgBr·2(C₂D₅)₂O, CD₃CH₂MgBr·2(C₂H₅)₂O, CH₃CD₂MgBr·2(C₂H₅)₂O and C₂D₅MgBr·2(C₂H₅)₂O have been investigated in the 4000-100 cm^?1 region. An assignment is given for most intramolecular fundamentals of the gauche—gauche isomer of coordinated ether molecules and the effect of coordination on ether frequencies is discussed. The fifteen fundamentals of the “isolated” ethyl group are identified and their frequencies are correlated with those of some hydrocarbons and similar organometallic compounds. The magnesium—ligand stretching vibrations, ν(MgC), ν_asym(MgO₂), ν_sym(MgO₂), ν(MgBr), and ν(MgI) are observed at 485, 317, 301, 248 and 224 cm^?1, respectively; the MgC, MgO and MgBr bond force constants are estimated and correlated with some other structural parameters. The structure of the mixed organomagnesium compound C₂H₅MgBr·2(C₂H₅)₂O in pure liquid state and in ether solution is discussed on the basis of the corresponding Raman spectra. Ethylmagnesium bromide is found to be monomeric in diethyl ether even at high concentrations.     

Methyl group exchange in methyllithiumlithium bromide solutions in diethyl ether

The 220 MHz ¹H NMR spectrum of an ether solution of CH₃Li and LiBr in 10–1 ratio has been examined as a function of temperature. At low temperature distinct resonances, assignable to Li₄(CH₃)₄ and Li₄(CH₃)₃Br, are seen. Methyl group exchange between the two tetramers is observed in the NMR spectra in the temperature interval ?32 to 0°. The exchange is shown to be much slower than the dissociation of Li₄(CH₃)₄ tetramer, measured in other work. It is proposed that the rate-determining step is dissociation of Li₄(CH₃)₃Br to form Li₂(CH₃)₂ and Li₂(CH₃)Br. The rate constant for dissociation, k₂, obeys the equation ln k₂ = 36.0?83303/T.