Geometrically Formal Homogeneous Metrics of Positive Curvature

A Riemannian manifold is called geometrically formal if the wedge product of harmonic forms is again harmonic, which implies in the compact case that the manifold is topologically formal in the sense of rational homotopy theory. A manifold admitting a Riemannian metric of positive sectional curvature is conjectured to be topologically formal. Nonetheless, we show that among the homogeneous Riemannian metrics of positive sectional curvature a geometrically formal metric is either symmetric, or a metric on a rational homology sphere.     

Two-electron reductive reactivity of trivalent uranium tetraphenylborate complexes of (C5Me5) and (C5Me4H)

The reductive reactivity of the (BPh₄)¹⁻ ligand in pentamethylcyclopentadienyl [(C₅Me₅)₂U][(μ-η²:η¹-Ph)₂BPh₂] (1) was compared with that of the tetramethyl analog, [(C₅Me₄H)₂U][(μ-η⁶:η¹-Ph)(μ-η¹:η¹-Ph)BPh₂] (2) using PhSSPh as a probe to determine if the mode of (BPh₄)¹⁻ bonding affected the reduction. Both complexes act as two-electron reductants to form (C₅Me₄R)₂U(SPh)₂ [R = Me, 3; H, 4], but only in the R = H case could the product be crystallographically characterized. An improved synthesis of 1 from [(C₅Me₅)₂UH]₂ (5) and [Et₃NH][BPh₄] is also reported as well as its reaction with MeCN that provides another route to the unusual, parallel-ring, uranium metallocene [(C₅Me₅)₂U(NCMe)₅][BPh₄]₂ (6).     

Synthesis, structure, and 15N NMR studies of paramagnetic lanthanide complexes obtained by reduction of dinitrogen

The recently discovered LnZ3/M and LnZ2Z'/M methods of reduction (Ln = lanthanide; M = alkali metal; Z, Z' = monoanionic ligands that allow these combinations to generate "LnZ2" reactivity) have been applied to provide the first crystallographically characterized dinitrogen complexes of cerium, [C5Me5)2(THF)Ce]2(mu-eta2.eta2-N2) and [(C5Me4H)2(THF)Ce]2(mu-eta2.eta2-N2), so that the utility of 15N NMR spectroscopy with paramagnetic lanthanides could be determined. [(C5Me5)2(THF)Pr]2(mu-eta2.eta2-N2) and [(C5Me4H)2(THF)Pr]2(mu-eta2.eta2-N2) were also synthesized, crystallographically characterized, and studied by 15N NMR methods. The data were compared to those of [(C5Me5)2Sm]2(mu-eta2.eta2-N2). [(C5Me5)2(THF)Ce]2(mu-eta2.eta2-N2) and [(C5Me5)2(THF)Pr]2(mu-eta2.eta2-N2) are unlike their (C5Me4H)1- analogs in that the solvating THF molecules are cis rather than trans. Structural information on precursors, (C5Me4H)3Ce, (C5Me4H)3Pr, and the oxidation product [(C5Me5)2Ce]2(mu-O) is also presented.     

Insights into the mechanism of reaction of [(C5Me5)2Sm(II)(thf)2] with CO2 and COS by DFT studies

Reaction mechanisms for the oxidative reactions of CO(2) and COS with [(C(5)Me(5))(2)Sm] have been investigated by means of DFT methods. The experimental formation of oxalate and dithiocarbonate complexes is explained. Their formation involve the samarium(III) bimetallic complexes [(C(5)Me(5))(2)Sm-CO(2)-Sm(C(5)Me(5))(2)] and [(C(5)Me(5))(2)Sm-COS-Sm(C(5)Me(5))(2)] as intermediates, respectively, ruling out radical coupling for the formation of the oxalate complex.     

Isolation of (CO)1- and (CO2)1- radical complexes of rare earths via Ln(NR2)3/K reduction and [K2(18-crown-6)2]2+ oligomerization

Deep-blue solutions of Y(2+) formed from Y(NR(2))(3) (R = SiMe(3)) and excess potassium in the presence of 18-crown-6 at -45 °C under vacuum in diethyl ether react with CO at -78 °C to form colorless crystals of the (CO)(1-) radical complex, {[(R(2)N)(3)Y(μ-CO)(2)][K(2)(18-crown-6)(2)]}(n), 1. The polymeric structure contains trigonal bipyramidal [(R(2)N)(3)Y(μ-CO)(2)](2-) units with axial (CO)(1-) ligands linked by [K(2)(18-crown-6)(2)](2+) dications. Byproducts such as the ynediolate, [(R(2)N)(3)Y](2)(μ-OC≡CO){[K(18-crown-6)](2)(18-crown-6)}, 2, in which two (CO)(1-) anions are coupled to form (OC≡CO)(2-), and the insertion/rearrangement product, {(R(2)N)(2)Y[OC(═CH(2))Si(Me(2))NSiMe(3)]}[K(18-crown-6)], 3, are common in these reactions that give variable results depending on the specific reaction conditions. The CO reduction in the presence of THF forms a solvated variant of 2, the ynediolate [(R(2)N)(3)Y](2)(μ-OC≡CO)[K(18-crown-6)(THF)(2)](2), 2a. CO(2) reacts analogously with Y(2+) to form the (CO(2))(1-) radical complex, {[(R(2)N)(3)Y(μ-CO(2))(2)][K(2)(18-crown-6)(2)]}(n), 4, that has a structure similar to that of 1. Analogous (CO)(1-) and (OC≡CO)(2-) complexes of lutetium were isolated using Lu(NR(2))(3)/K/18-crown-6: {[(R(2)N)(3)Lu(μ-CO)(2)][K(2)(18-crown-6)(2)]}(n), 5, [(R(2)N)(3)Lu](2)(μ-OC≡CO){[K(18-crown-6)](2)(18-crown-6)}, 6, and [(R(2)N)(3)Lu](2)(μ-OC≡CO)[K(18-crown-6)(Et(2)O)(2)](2), 6a.     

H,C, N and S stable isotopes and mineral profiles to objectively guarantee the authenticity of grated hard cheeses

In compliance with the European law (EC No. 510/2006), geographical indications and designations of origin for agricultural products and foodstuffs must be protected against mislabelling. This is particularly important for PDO hard cheeses, as Parmigiano Reggiano, that can cost up to the double of the no-PDO competitors.     

Polar manifolds and actions

A group action is called polar if there exists an immersed submanifold (a section) which intersects all orbits orthogonally. We show how to construct a manifold admitting a polar group action by prescribing its isotropy groups along a fundamental domain in the section. This generalizes a classical construction for cohomogeneity-one manifolds.We give many examples showing the richness of this class of group actions and relate the topology of the section to the topology of the manifold.     

A variational approach for compact homogeneous Einstein manifolds

((no abstract given))