Finiteness of Ricci flatN=2 supersymmetric σ-models

We study the ultraviolet behavior of two dimensional supersymmetric non-linear -models with target space an arbitrary Kähler manifoldM, so that the models areN=2 supersymmetric. We point out that these models have an additional fermionic axial symmetry if and only if the metric onM is Ricci flat. We show that the preservation of this symmetry in perturbation theory implies that both bare and renormalized metrics onM are Ricci flat. Combining this result with the constraint ofN=2 supersymmetry requiring that all counter-terms to the metric beyond one-loop order be cohomologically trivial, we argue thatN=2 models defined on Ricci flat Kähler manifolds are on-shell ultraviolet finite to all orders of perturbation theory.     

On estimating a density using Hellinger distance and some other strange facts

Résumé On s'intéresse ici aux possibles vitesses d'estimation d'une densité à support compact dans ^m sous des hypothèses de régularité, lorsque la perte est mesurée par le carré de la distance de Hellinger (on regardera aussi le cas connu des normes pour 1q2) et le risque est le risque minimax sur la famille. On donne une méthode générale permettant de traiter les problèmes dans le cadre de la théorie de l'approximation sous des conditions concernant l'entropie métrique et l' -capacité des familles à estimer. Les rapports entre régularité et entropie métrique étant bien connus, nous pourrons aussi traiter les cas classiques et d'autres qui le sont moins. Sous des conditions de bornes inférieures les vitesses sont celles observées pour la norme mais elles diffèrent dans le cas général. On montre aussi que les restrictions sur la compacité du support ou la régularité sont indispensables et que leur absence mène à l'impossibilité d'obtenir une estimation raisonnable en ce sens que n'importe quelle suite d'estimateurs sera arbitrairement mauvaise en un point au moins. Un résultat analogue est vrai sous des conditions de régularité.

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This work was carried out during a visit of the author at the Mathematical Sciences Research Institute at Berkeley     

Synthesis of peptides based onβ-(N1-uracilyl)-α-alanine

The synthesis of peptides which include a DL--(N₁-uracilyl)--alanine (DL-willardiine) residue as an N-terminal or C-terminal group was investigated, dipeptides of DL-willardiine with glycine and L-tyrosine were obtained, and DL-willardiyl-DL-willardiine was synthesized; the latter is the simplest representative of the family of monotonic homopeptides which contain, as a repeating side substituent, a natural nucleic base capable of participation in intermolecular interactions of the complementary type.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 404–408, March, 1971.     

Synthesis of polycyclic structures by the Diels-Alder reaction of inner-outer-ring 1,3-bis(trimethylsilyloxy)dienes

A Diels-Alder reaction of novel inner-outer-ring 1,3-silyloxydienes 5-8 with a variety of dienophiles to afford highly functionalized polycyclic structures is reported. The inner-outer-ring 1,3-silyloxydienes 5-8 containing five- to seven-membered carbocyclic and heterocyclic rings were prepared in a single reaction vessel from 2-acetylcyclocarbonyls in quantitative yields. The Diels-Alder reaction with 1,4-benzoquinone (BQ), dimethyl acetylenedicarboxylate (DMAD), and methyl vinyl ketone (MVK) proceeded smoothly at room temperature, affording functionalized polycyclic naphthols, phenols, and enones with high regioselectivity and good yields (39-75%). Moreover, dienes 5-8 also reacted in a hetero-Diels-Alder reaction with benzaldehyde (BA) and N-benzylideneaniline (NBA) in the presence of catalytic amounts of ZnCl2, affording substituted polycyclic pyranones and pyridinones in good yields (40-93%). Overall, our synthetic strategy provides straightforward access to an interesting set of polycyclic structures useful for natural and nonnatural product synthesis.     

Determination of lithium in human serum by electrothermal atomic absorption spectrometry

An efficient method was developed for the determination of nanogram levels of lithium in biological samples. Serum samples from human subjects from southeastern Spain, treated or not treated with lithium carbonate, were analyzed by electrothermal atomic absorption spectrometry. The samples were previously treated with a matrix modifier consisting of 0.1% Triton X-100 and injected through a graphite tube with L'vov platform. The Li concentrations measured by the procedure described for the 3 certified reference samples used were not significantly different (p > 0.05) than certified levels. Sample recoveries and variability during several days, with coefficients of variation from 4.00 to 14.8%, demonstrated the reliability and accuracy of this technique. Mean Li concentration determined in the serum of individuals with psychiatric disorders treated with Li (n = 117, 5.077 +/- 1.795 microg Li/mL) was significantly higher (p < 0.001) than that in individuals not treated with Li (n = 24, 1.902 +/- 2.054 ng Li/mL).     

Use of diode-array detectors for the simultaneous spectrophotometric determination of calcium and magnesium by flow injection

A method for the simultaneous flow injection spectrophotometric determination of calcium and magnesium with Arsenazo III based on the use of diode-array detector and merging zones is described. The method is applicable to the resolution of mixtures in which the chromogenic reagent has a high absorbance and its spectrum strongly overlaps those of its complexes. In resolving the mixtures, the excess reagent is considered as another component. Quantitation is based on the normal absorbance and first-derivative absorbance spectra. The method is applied to 0.2–1.5 μg ml^?1 Ca and 0.1–1.0 μg ml^?1 Mg. The analysis rate is 50 h^?1.     

Synthesis and properties of esters and amido esters of 1-(2-thienyl)-2,2,2-trichloroethylphosphorous acid

Conclusions The esterification of amido- and ester-amidophosphites with 1-(2-thienyl)-2,2,2-trichloroethanol gave the l-(2-thienyl)-2,2,2-trichloroethyl dialkyl- and 1-(2-thienyl)-2,2,2-trichloroethyl alkylamidophosphites, which easily add sulfur or are oxidized to the corresponding thiophosphates and phosphates.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 182–187, January, 1981.     

Determination of four nitroimidazole residues in poultry meat by liquid chromatography-mass spectrometry

A multi-residue liquid chromatography-mass spectrometry (LC-MS) assay method is described for the determination of four nitroimidazoles in poultry muscle. The extraction procedure is based on liquid-liquid extraction with ethyl acetate followed by an evaporation step. A deuterated internal standard is used. The LC separation was made on a C18 bonded silica column with an aqueous formic acid (0.2%) solution-methanol-acetonitrile (81:13:6) mobile phase. Following electrospray ionization, the protonated molecular ion [M+H]+ is obtained for each compound. Monitoring several ions for each nitroimidazole provides the specificity required for confirmatory assay. Validation of the method was performed to estimate linearity, intra-day and inter-day repeatability, accuracy and detection limit. The present method is capable of identifying nitroimidazole residues in muscle at levels below 5 microg/kg.