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.     

La méthyl-9-trihydroxy-2,3,7-fluorone-6, réactif microqualitatif de l'antimoine

Résumé La méthyl-9-trihydroxy-2,3,7-fluorone-6 permet de déceler les ions de l'antimoine, en présence de tous autres cations et anions. Les conditions deph (ph = 4) sont à observer rigoureusement.Ce nouveau réactif est avantageusement utilisé dans la méthode d'analyse à la touche ou par empreinte.Les limites de sensibilité sont: en godet 0,2; sur papier gélatine 0,5; sur papier filtre 0,8.

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Summary Methyl-9-trihydroxy-2,3,7-fluorone-6 is a reagent which allows to detect antimony ion in the presence of all the other cations and anions. Aph value of 4 must be strictly maintained.This new reagent can be advantageously applied for spot test and offprint analysis.Limits of identification: On the spot test plate 0,2; On gelatine paper 0,5; On filter paper 0,8.

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Zusammenfassung Das Methyl-9-trioxy-2,3,7-fluoron-6 gestattet den Nachweis des Antimonions in Gegenwart aller anderen Kationen und Anionen. Dieph-Bedingungen (ph = 4) sind streng einzuhalten.Dieses neue Reagens läßt sich mit Vorteil zur Tüpfel- oder Abdruckanalyse verwenden.Erfassungsgrenzen: auf der Tüpfelplatte 0,2; auf Gelatinepapier 0,5; auf Filtrierpapier 0,8.

     

Peroxisome Proliferator-Activated Receptors target family landscape: A chemometrical approach to ligand selectivity based on protein binding site analysis

The Peroxisome Proliferator-Activated Receptors (PPARs) are nuclear receptors which over the last couple of years have been the focus of considerable research efforts aiming to identify compounds with well-defined selectivity profiles for the treatment of metabolic diseases. The ligand binding domains (LBD) of the three known PPAR subtypes exhibit between 60 and 70% sequence identity. To gain insight into the structural determinants of selectivity for the PPAR subtypes, a set of 13 crystal structures of PPAR LBD were classified, using the GRID/CPCA approach. As a result, nearly all of the crystal structures of each different PPAR subtype were found clustered in different regions of the CPCA score plots, and hydrophobic as well as steric interactions were identified as the major determinants of PPAR subtypes selectivity. Furthermore, interpretation of the GRID/CPCA model in structural terms led to the identification of LBD regions which could be targeted to improve the selectivity for a given PPAR subtype. Our findings are consistent with published structure-activity relationships for PPAR ligands as well as with site-directed mutagenesis results.