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On the separation of basic semialgebraic sets by polynomials

In this paper we show that two disjoint basic closed semialgebraic sets, defined over a real closed field R, can be separated by a polynomial, if one of them has dimension 2. Counterexamples are given in all higher dimensions.     

The optimal amount of isotopic spike solution for ultratrace analysis by isotope dilution mass spectrometry

 Inductively coupled plasma mass spectrometry (ICP-MS) and high resolution inductively coupled plasma mass spectrometry (HR-ICP-MS) are powerful methods of determining metallic impurities in the low- and sub-ppt level in process media such as ultra-pure water used in semiconductor and wafer manufacturing. By using mass spectrometers for analysis, an isotope dilution analysis (IDMS) is possible. The reproducibility of an IDMS is unmatched. For concentration levels near the instrument detection limit a novel method is reported to find the optimal amount of isotopic spike solution. This optimal value can be derived by the law of propagation of uncertainty combined with the Poisson statistics of the measured number of counts. Generally, an excess of isotopic spike solution should be used to provide results of lowest possible uncertainty. The results are presented in a diagram for easy practical use. Received: 14 October 1997 · Accepted: 13 February 1998     

Deuterium exchange of 4-pyrimidones and 4-pyrimidthiones

The hydrogen-deuterium exchange of H-2 in 4-pyrimidone, a number of 1- and 3-alkyl-4-pyrimidones and several of their thione analogs in deuterium oxide at moderate temperatures is reported. This reaction is apparently not susceptible to acid or base catalysis. Cations of the 4-pyrimidones were found not to exchange H-2 at all in acid media. Catalytic amounts of bases do not alter the exchange rates whereas more concentrated alkali decompose the pyrimidone. However, 1,4(3,4)-dihydro-1,3-dimethyl-4-oxopyrimidinium iodide (and its 6-methyl analog) exchange H-2 quite rapidly in neutral deuterium oxide, almost instantly when triethylamine is added as a catalyst, and very slowly in dilute solutions of deuterium chloride in deuterium oxide. Mechanisms are proposed to account for these phenomena.     

Wittig-Olefinierung zu neuen donor- und akzeptor-substituierten 3-Vinylindolen: Optimierte Syntheseverfahren

Summary The optimized Wittig reaction of selectively functionalized 3-acylindoles yield new, and for Diels-Alder reactions highly reactive donor- and acceptor substituted 3-vinylindoles, respectively.

     

(1-Adamantanethio)pyridines and tetrahydropyridines from the reaction of 1-adamantanethiol with pyridine I-oxide in acetic anhydride

The reaction of pyridine 1-oxide with 1-adamantanethiol in acetic anhydride produced a mixture of 2- and 3-(1-adamantanethio)pyridines, 1-aeetyl-2-(1-adamantanethio)-3-hydroxy-4-acetoxy-1,2,3,4-telrahydropyridine and the corresponding 3-acetoxyderivative. Pure substances were separated by means of column chromatography on alumina. The tetrahydropyridines were identified by means of their proton magnetic and mass spectra. 4-(1-Adamantanethio)pyridine was synthesized from 4-chloropyridinc and 1-adamantanethiol. The three isomeric (1-adamantanethio)-pyridines were, each, cleaved by concentrated hydrochloric acid to give 1-chloroadamantane and the corresponding pyridinethiol.     

Rate-equilibrium relationships in hydride transfer reactions: the role of intrinsic barriers

A literature survey on the kinetics of hydride abstractions from CH-groups by carbocations reveals a general phenomenon: Variation of the hydride acceptor affects the rates of hydride transfer to a considerably greater extent than an equal change of the thermodynamic driving force caused by variation of the hydride donor. The origin of this relationship was investigated by quantum chemical calculations on various levels of ab initio and DFT theory for the transfer of an allylic hydrogen from 1-mono- and 1,1-disubstituted propenes (XYC=CH-CH(3)) to the 3-position of 1-mono- and 1,1-disubstituted allyl cations (XYC=CH-CH(2)(+)). The discussion is based on the results of the MP2/6-31+G(d,p)//RHF/6-31+G(d,p) calculations. Electron-releasing substituents X and Y in the hydride donors increase the exothermicity of the reaction, while electron-releasing substituents in the hydride acceptors decrease exothermicity. In line with Hammond's postulate, increasing exothermicity shifts the transition states on the reaction coordinate toward reactants, as revealed by the geometry parameters and the charge distribution in the activated complexes. Independent of the location of the transition state on the reaction coordinate, a value of 0.72 is found for Hammond-Leffler's alpha = deltaDeltaG/deltaDelta(r)G degrees when the hydride acceptor is varied, while alpha = 0.28 when the hydride donor is varied. The value of alpha thus cannot be related with the position of the transition state. Investigation of the degenerate reactions XYC=CH-CH(3) + XYC=CH-CH(2)(+) indicates that the migrating hydrogen carries a partial positive charge in the transition state and that the intrinsic barriers increase with increasing electron-releasing abilities of X and Y. Substituent variation in the donor thus influences reaction enthalpy and intrinsic barriers in the opposite sense, while substituent variation in the acceptor affects both terms in the same sense, in accord with the experimental findings. Marcus theory is employed to treat these effects quantitatively.