Weak density of smooth maps for the Dirichlet energy between manifolds

We prove that given a simply connected compact manifold M and a closed manifold N, any map in the Sobolev space W ^1,2(M,N) can be approximated weakly by smooth maps between M and N. Submitted: September 2002, Final version: November 2002.     

Discriminant of a generic projection of a minimal normal surface singularity

Let (S,0) be a rational complex surface singularity with reduced fundamental cycle, also known as a minimal singularity. Using a fundamental result of M. Spivakovsky, we explain how to describe the equisingularity type of the discriminant curve for a generic projection of (S,0) onto $\text{(}\text{C}{}^2\text{,0)}$ from the resolution of (S,0). To cite this article: R. Bondil, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Efficient indirect electrochemical in-situ regeneration of nadh:electrochemically driven enzymatic reduction of pyruvate catalyzed by d-ldh

Using [Cp(Me)₅Rh(bipy)C1]C1 (1) as redox catalyst for the continous NADH regeneration it was possible to perform an electrochemically driven enzymatic reduction of pyruvate to D-lactate catalyzed by D-LDH at a rate of 5 turnovers per hour. This is by a factor of 20 faster than the best results obtained until now. Current yields of 50 to 70 % may be obtained.     

The stereospecific epoxidation of olefins catalysed by ruthenium

Epoxidation of olefins by sodium periodate is effected by the catalysis of RuCl₃, (H₂O)_n associated with bipyridyl. The reaction is stereospecific for both cis and trans alkenes.     

Structural characterization and magnetic properties of sandwich-type tungstoarsenate complexes. Study of a mixed-valent VIV2/VV heteropolyanion

Complexes K11Na1[As2W18(Mn(H2O))3O66]x27H2O (1) and Na12[As2W18(Co(H2O))3O66]x34H2O (2) have been characterized. 1 crystallizes in the orthorhombic space group Pnma, with a = 30.6484(4) A, b = 14.9946(2) A, and c = 19.17080(10) A (Z = 4), while 2 crystallizes in the monoclinic space group C2/c, with a = 14.124(2) A, b = 23.294(3) A, c = 32.247(3) A, and beta = 98.935(10) degrees (Z = 4). Structures of the anions of 1 and 2 are similar, the divalent metals adopting a square pyramidal environment. K11[As2W18(VO)3O66]x23H2O (3) crystallizes in the orthorhombic space group Pnma, with a = 30.6240(5) A, b = 14.9861(2) A, and c = 19.2651(3) A (Z = 4). The structure has revealed a disorder on two of the three metals linking the [alpha-AsW9O33]9- parts. For these two vanadium atoms, the V=O bonds are directed alternatively toward the inside or the outside of the [alpha-AsW9O33]9- cavity. The remaining vanadium shows a V=O bond always directed toward the outside of the cavity. Titration of VIV by CeIV revealed that 3 is the mixed-valent VIV2VV species. Magnetic measurements are in agreement with this formulation. The high-temperature molar magnetic susceptibility of a powdered sample of 3 clearly confirms the presence of two d1 centers. The two VIV are antiferromagnetically coupled, with J = -2.9 cm-1 and g = 1.93. Crystallographic data do not permit the location of the two VIV to be distinguished from the location of the VV. As expected, the Mn(II) are very weakly antiferromagnetically coupled in compound 1. The complex Na8[Ni(H2O)6]2[As2W18(Ni(H2O))3O66]x20H2O (4) has been synthesized. The anion crystallized with two octahedral [Ni(H2O)6]2+ as counterions. Magnetic data have been fitted assuming that the only exchange-coupled centers are the nickels of the polyanion. 4 exhibits an antiferromagnetic coupling with J = -1.7 cm-1, g = 2.27, and theta = -1.5 K.     

Colorful Friedel-Crafts chemistry of meso-tetraarylporphyrins. An unexpected route to porphyrinic spiro dimers

Under Friedel-Crafts conditions, meso-tetraarylporphyrins give porphyrin spiro dimers in good yield. This reaction involves acylation, acid-catalyzed cyclization, and dimerization. A stable dimer possessing three additional six-membered rings could be isolated and its structure determined. By modifying the substrate and reagents, intermediates could be isolated and characterized. The reactivity of the substrates, the side-reactions, and the concentration requirements to form the dimers, all explain why this reaction remained apparently unexplored in the widely used meso-tetraarylporphyrin series. [reaction: see text]     

Heptakis-6-(5-methylene-thioureido-5′-methyl-2,2′-bipyridyl)-β-cyclodextrin: synthesis and metal complexation study

A new heptapode heptakis-6-(5-methylene-thioureido-5′-methyl-2,2′-bipyridyl)-β-cyclodextrin was prepared and its complexation properties towards metal cations were investigated. Substituting the urea functions by the corresponding thioureas promoted the inversion of the metal coordination selectivity. Preliminary results showed the heptapode unable to complex lanthanides but authorise selective complexation of ‘soft’ and ‘borderline’ metal cations.     

Ultrasensitive single-cell proteomics workflow identifies >1000 protein groups per mammalian cell

We report on the combination of nanodroplet sample preparation, ultra-low-flow nanoLC, high-field asymmetric ion mobility spectrometry (FAIMS), and the latest-generation Orbitrap Eclipse Tribrid mass spectrometer for greatly improved single-cell proteome profiling. FAIMS effectively filtered out singly charged ions for more effective MS analysis of multiply charged peptides, resulting in an average of 1056 protein groups identified from single HeLa cells without MS1-level feature matching. This is 2.3 times more identifications than without FAIMS and a far greater level of proteome coverage for single mammalian cells than has been previously reported for a label-free study. Differential analysis of single microdissected motor neurons and interneurons from human spinal tissue indicated a similar level of proteome coverage, and the two subpopulations of cells were readily differentiated based on single-cell label-free quantification.

The combination of nanodroplet sample preparation, ultra-low-flow nanoLC, high-field asymmetric ion mobility spectrometry (FAIMS) and latest-generation mass spectrometry instrumentation provides dramatically improved single-cell proteome profiling.