Jensen's inequality for g-expectation: part 1

Briand et al. (Electron. Comm. Probab. 5 (2000) 101–117) gave a counterexample and proposition to show that given g,g-expectations usually do not satisfy Jensen's inequality for most of convex functions. This yields a natural question, under which conditions on g, do g-expectations satisfy Jensen's inequality for convex functions? In this paper, we shall deal with this question in the case that g is convex and give a necessary and sufficient condition on g under which Jensen's inequality holds for convex functions. To cite this article: Z. Chen et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Hydrogen abstraction and dimerisation reactions of some organo-transition metal free radicals

The 17-electron species [M(CO)_5χL_χ] (M  Mn, Re, χ  0; M  Mn, Re; L  Ph₃P, χ  1, 2; M  Mn, Re; L  (o-MeC₆H₄O)₃P, χ  2; M  Mn; L  (p-ClC₆H₄O)₃P, (PhO)₃P, χ  2; M  Mn; L  P(OMe)₃, χ  3) have been generated by one electron oxidation of the corresponding anions and show typical radical reactivity, undergoing dimerisation or hydride abstraction in reactions controlled by steric effects. Evidence is presented for the source of the hydrogen atom. The 19-electron species [M(CO)₃(η⁷-C₇H₇)]^? (M  Cr, Mo) and [Fe(CO)₃(η⁵-C₆H₇)]^?, generated by reduction of the corresponding cations, undergo dimerisation at the organic ligand. Similar treatment of [Fe(CO)₂-L(η-cp)]⁺ (L  CO, PPh₃, P(OPh)₃, Me₂CO) yields [Fe₂(CO)₄(η-cp)₂] and these reduction reactions are rationalised in terms of the nature of the HOMO in the intermediate radical. Similar reduction of [Rh(diphos)₂]⁺ yield the 17-electron intermediate [Rh(diphos)₂] and this also undergoes hydrogen abstraction.     

Synthesis of octahydroquinolines through the Lewis acid catalyzed reaction of vinyl allenes and imines

The reaction of vinyl allenes with imines under Lewis acid catalysis has been explored. Vinyl allenes in which the allenic portion of the molecule is tri- or tetrasubstituted gave octahydroquinoline derivatives as single isomers together with a minor compound formed by an ene reaction of the imine with the allene. Compounds in which the allene is 1,3-disubstituted do not react under the conditions assayed.     

On-line Surface Area Measurement of Concentrated Slurries using low field spin-lattice relaxation NMR

A method for the rapid on-line determination of surface area and solids content in flowing concentrated slurries using low field NMR spin-lattice relaxation measurements has been developed and demonstrated. The relationship between flow and spin-lattice relaxation time (T₁) of protons in water at 20 MHz was examined using aqueous copper sulfate solutions. The ability to measure surface area and solids concentration in both stagnant (stopped flow) and flowing systems via NMR was demonstrated using several different concentrated aqueous titania and glass slurries (20 to 80 weight percent) for which the dried powder surface area was previously determined via nitrogen adsorption/BET analysis and the solids content determined gravimetrically. Surface areas were also calculated from particle size analysis and found to vary by up to an order of magnitude from the adsorption and NMR results.     

Mesoporous Silica Nanoparticles Decorated with Carbosilane Dendrons as New Non‐viral Oligonucleotide Delivery Carriers

A novel nanosystem based on mesoporous silica nanoparticles covered with carbosilane dendrons grafted on the external surface of the nanoparticles is reported. This system is able to transport single‐stranded oligonucleotide into cells, avoiding an electrostatic repulsion between the cell membrane and the negatively charged nucleic acids thanks to the cationic charge provided by the dendron coating under physiological conditions. Moreover, the presence of the highly ordered pore network inside the silica matrix would make possible to allocate other therapeutic agents within the mesopores with the aim of achieving a double delivery. First, carbosilane dendrons of second and third generation possessing ammonium or tertiary amine groups as peripheral functional groups were prepared. Hence, different strategies were tested in order to obtain their suitable grafting on the outer surface of the nanoparticles. As nucleic acid model, a single‐stranded DNA oligonucleotide tagged with a fluorescent Cy3 moiety was used to evaluate the DNA adsorption capacity. The hybrid material functionalised with the third generation of a neutral dendron showed excellent DNA binding properties. Finally, the cytotoxicity as well as the capability to deliver DNA into cells, was tested in vitro by using a human osteoblast‐like cell line, achieving good levels of internalisation of the vector DNA/carbosilane dendron‐functionalised material without affecting the cellular viability.     

The mechanism of the addition of tetrachloromethane to oct-1-ene catalysed by [Mo2(CO)6(η-Cp)2]

A study of the reaction of CCl₄ with oct-1-ene in the presence of catalytic amounts of [Mo₂(CO)₆(η-Cp)₂] has shown that in the early stages it proceeds by a redox-catalysed mechanism. However, gradual decomposition of the catalyst leads to the intervention of a radical chain pathway.     

The use of SO2Cl2 in organometallic chemistry. Convenient high yield syntheses of [Fe(η-C5H5)(CO)3] [FeCl4] and [M(CO5Cl] (M = Mn or Re)

Depending on the substrate and the reaction conditions, SO₂Cl₂ is a useful reagent which brings about either chlorination or the formation of cationic species on reaction with transition metal carbonyl complexes.     

Criticality conditions for some random environment population processes

Some random environment population processes are considered. Using a coupling argument, a criticality condition is obtained. The criticality parameter governs whether the process dies out or fluctuates about a positive finite constant, which is explicitly computed.     

Complete (1)H and (13)C assignments of the four major saponins from Dioscorea villosa (wild yam)

Complete (1)H and (13)C spectral assignments for the four major steroidal saponins isolated by methanolic extraction of the roots of Dioscorea villosa, collected in North Carolina, United States (in summer and autumn), are presented in this paper. The structures were determined by a combination of (1)H, (13)C and 2D NMR techniques and were found to be ((3beta,25R)-26-(beta-D-glucopyranosyloxy)-22-methoxyfurost-5-en-3-yl-O-beta-D-glucopyranosyl-(1 --> 3)-O-beta-D-glucopyranosyl-(1 --> 4)-O-[alpha-L-rhamnopyranosyl-(1 --> 2)]-beta-D-glucopyranoside (1) (or methyl parvifloside), ((3beta,25R)-26-(beta-D-glucopyranosyloxy)-22 methoxyfurost-5-en-3-yl-O-alpha-L-rhamnopyranosyl-(1 --> 2)-O-[beta-D-gluco- pyranosyl-(1 --> 4)]-beta-D-glucopyranoside (2) (or methyl protodeltonin), (3beta,25R)-spirost-5-en-3-yl-O-beta-D-glucopy ranosyl-(1 --> 3)-O-beta-D-glucopyranosyl-(1 --> 4)-O-[alpha-L-rhamnopyranosyl-(1 --> 2)]-beta-D-glucopyranoside (3) (or Zingiberensis saponin I) and (3beta,25R)-spirost-5-en-3-yl-O-alpha-L-rhamnopyranosyl-(1 --> 2)-O-[beta-Ds-glucopyranosyl -(1 --> 4)]-beta-D-glucopyranoside (4) (or deltonin).     

Parametric estimation for simple branching diffusion processes, II

Consider a simple branching diffusion process, which is a branching process in which the individuals move and live and die in space. The offspring distribution has finite moments of all orders. A parametric estimation theory is presented, using time slice data. This involves the use of third order cumulant spectra to identify and estimate the parameters.