The median procedure in cluster analysis and social choice theory

Classical approachs for fitting and aggregation problems, specially in cluster analysis, social choice theory and paired comparisons methods, consist in the minimization of a remoteness function between relational data and a relational model. The notion of median, with its algebraic, metric, geometrical and statistical aspects, allow a unified treatment of many of base problems. Properties of median procedures are organized according to four directions: stabilities and axiomatic characterizations; Arrow-like properties; combinatorial properties; effective computational possibilities. Finally, interesting mathematical problems, related to the notion of median are surveyed.     

Synthesis of new allenic prostanoids

New allenic prostanoids 5c, d, 7,9c, and 15b have been prepared by total synthesis. In each case a cuprate-propargylic acetate reaction was used as the key step.     

Untersuchungen zur atomspektroskopischen spurenanalyse in AIIIBV-halbleiter-mikroproben—IV: Vergleich der bestimmung von tellurspuren im GaP und GaAs durch AAS,AFS und AES

Methods are described for the determination of trace tellurium in acid solution in the absence and presence of the inorganic matrices As, P, Ga, GaP and GaAs and for the direct determination in solid GaP and GAs. The following methods were used: AAS with electrothermal atomization, AFS with electrothermal atomization, and AES with d.c. arc excitation. The conditions for each of the methods were optimized and the analytical results were compared. It is shown that AAS with electrothermal atomization gives the best absolute and also relative limit of detection for trace tellurium (90 pg Te, or 4 ppm Te in GaAs or GaP). Therefore this method is recommended for the determination of trace tellurium in very small samples of A^IIIB_V-semiconductors.     

Alcoyl-gluco-alcaloides: nouveaux composes isoles de pauridiantha lyalii brem (rubiacees)

La structure destrans fe´ruloyl-6′ ettrans sinapoyl-6′ lyaloside, isole´s des feuilles dePauridiantha Lyalii, ae´te´de´termine´e par de´gradation chimique et par spectroscopie (Masse, RMN¹H et¹³C). Ces compose´s font partie d'un groupe structural caracte´rise´par un enchai?nement alcaloide-monoterpe`ne-ose-acide (C<sub>6</sub>-C<sub>3</sub>), groupe dont un seul repre´sentant semble avoire´te´isole´jusqu'a`pre´sent. Leur fonction dans le ve´ge´tal est discute´e.     

Subdirect decompositions of finite commutative semigroups

The Ponizovskîi decomposition of a finite commutative semigroup yields all shortest elementary subdirect decompositions of that semigroup.     

Existence et prolongement des solutions holomorphes des équations aux dérivées partielles

Sans résumé     

{2,6‐Bis­[(di­methyl­amino)­methyl]pyridine‐κ3N}(2,2‐methyl­enediphenolato‐κ2O,O′)­dioxouranium(VI) acetone solvate

In the title compound, [UO₂(C₁₃H₁₀O₂)(C₁₁H₁₉N₃)]·C₃H₆O, the U atom is in a pentagonal–bipyramidal environment, with the three N atoms of the 2,6‐bis­[(di­methyl­amino)­methyl]­pyridine ligand and the two O atoms of the dianionic 2,2′‐methyl­ene­diphenolate ligand in the equatorial plane. The geometry is compared with that of previously reported 1:2 uranyl–diphenoxide complexes.