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     

Joint production of ϕ mesons andπ ±,π 0,p,\bar p,K s 0 andK ± in hadronic interactions

The joint production of ? mesons andπ ^±,π ⁰,p, \(\bar p\) ,K _s ⁰ andK ^± is investigated using a sample of 600,000 inclusive ? meson events obtained in hadron Be interactions with incidentπ ^±,p, \(\bar p\) andK ^± beams. Evidence is presented for the joint production of ? mesons and strange particles produced with non-strange incident beams. With incidentK ^± beam the number of additional strange particles is suppressed. The results are found to be in agreement with the qualitative predictions of a parton fusion model. The comparison with the Lund model for lowp _T processes is fair.     

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).