Sub-stochastic matrix analysis for bounds computation—Theoretical results

Performance evaluation of complex systems is a critical issue and bounds computation provides confidence about service quality, reliability, etc. of such systems. The stochastic ordering theory has generated a lot of works on bounds computation. Maximal lower and minimal upper bounds of a Markov chain by a st-monotone one exist and can be efficiently computed. In the present work, we extend simultaneously this last result in two directions. On the one hand, we handle the case of a maximal monotone lower bound of a family of Markov chains where the coefficients are given by numerical intervals. On the other hand, these chains are sub-chains associated to sub-stochastic matrices. We prove the existence of this maximal bound and we provide polynomial time algorithms to compute it both for discrete and continuous Markov chains. Moreover, it appears that the bounding sub-chain of a family of strictly sub-stochastic ones is not necessarily strictly sub-stochastic. We establish a characterization of the families of sub-chains for which these bounds are strictly sub-stochastic. Finally, we show how to apply these results to a classical model of repairable system. A forthcoming paper will present detailed numerical results and comparison with other methods.     

A refinement of the Bernštein-Kušnirenko estimate

A theorem of Kušnirenko and Bernštein (also known as the BKK theorem) shows that the number of isolated solutions in a torus to a system of polynomial equations is bounded above by the mixed volume of the Newton polytopes of the given polynomials, and this upper bound is generically exact. We improve on this result by introducing refined combinatorial invariants of polynomials and a generalization of the mixed volume of convex bodies: the mixed integral of concave functions. The proof is based on new techniques and results from relative toric geometry.     

Mixed finite element methods for unilateral problems: convergence analysis and numerical studies

In this paper, we propose and study different mixed variational methods in order to approximate with finite elements the unilateral problems arising in contact mechanics. The discretized unilateral conditions at the candidate contact interface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers in the saddle-point formulation. A priori error estimates are established and several numerical studies corresponding to the different choices of the discretized unilateral conditions are achieved.

     

Determination de la structure de perfluoroalcenes a chaines longues par R.M.N. du 19F 2éme Partie : Perfluoroalcenes 2–3 et 4

The fluoride ion induced isomerisation of 1-perfluoroalkenes R_FCFCF₂ (R_F=C₄F₉, (I) -C₅F₁₁ (II), -C₆F₁₃ (III), -C₇F₁₅(IV) has been studied in the polar solvents DMF and VMSO. The reaction gives a mixture which changes to the thermodynamically stable isomer. ¹⁹F n.m.r. spectroscopy allows characterisation of products and shows that all alkenes formed are $\text{cis}$-derivatives. The products formed are explained on the basis of a cyclic intermediate involving participation of the metal cation.     

Reactions SRN1 en serie heterocyclique: II. Reactivite du methyl-1 chloromethyl-2 nitro-5 imidazole.

1-Methyl-2-chloromethyl-5-nitroimidazole reacts with tertiary nitronate anions in excess to afford in high yields the previously unknown 1-methyl-5-nitro-imidazoles bearing a trisubstituted ethylenic double bond in the 2 position. These compounds are ascribed to a C-alkylation reaction according to the S_RN1 mechanism followed by base-promoted nitrous acid elimination.     

Real-time NMR studies of electrochemical double-layer capacitors

(11)B NMR spectroscopy has been used to investigate the sorption of BF(4)(-) anions on a highly porous, high surface area carbon, and different binding sites have been identified. By implementing in situ NMR approaches, the migration of ions between the electrodes of the supercapacitors and changes in the nature of ion binding to the surface have been observed in real time.     

Use of benchtop exactive high resolution and high mass accuracy orbitrap mass spectrometer for screening in horse doping control

Liquid chromatography-mass spectrometry (LC-MS) has been widely used in doping control laboratories over the last two decades. Currently, simple quadrupole, triple quadrupole and ion trap are the most commonly employed analyzers in toxicological analysis. Nevertheless, the main lack of these technologies is the restricted number of target compounds simultaneously screened without loss of sensitivity. In this article we present an innovative screening approach routinely applied in the French horse doping control laboratory based on high resolution (50000) and high mass accuracy (<5 ppm) in full scan MS mode for more than 235 target analytes screened from an initial volume of 5 mL of urine. The sample preparation was classically founded on solid phase extraction by means of reverse phase C18 cartridges. LC-MS analyses were carried out on a Shimadzu binary HPLC pumps linked to a C18 Sunfire column associated with the high resolution exactive benchtop orbitrap mass spectrometer. This screening was performed alternatively in positive-negative ionization mode during the same run. Thus, the identification of compounds of interest was made using their exact mass in positive-negative ionization mode at their expected retention time. All data obtained were processed by ToxID software (ThermoFisherScientific) which is able to identify a molecule by theoretical mass and retention time. In order to illustrate this innovative technology applied in our laboratory, sample preparation, validation data performed on 20 target compounds from 16 different horse urine samples, chromatograms and spectra will be discussed in this paper.     

Photochemical electron transfer mediated addition of naphthylamine derivatives to electron-deficient alkenes

Using photochemical electron transfer, N,N-dimethylnaphthylamine derivatives are added to α,β-unsaturated carboxylates. The addition takes place exclusively in the α-position of electron-deficient alkenes and mainly in the 4-position of N,N-dimethylnaphthalen-1-amine. A minor regioisomer results from the addition in the 5-position of this naphthylamine. A physicochemical study reveals that the fluorescence quenching of N,N-dimethylnaphthalen-1-amine is diffusion-controlled and that the back electron transfer is highly efficient. Therefore no transformation is observed at lower concentrations. To overcome this limitation and to induce an efficient transformation, minor amounts of water or another proton donor as well as an excess of the naphthylamine derivative are necessary. A mechanism involving a contact radical ion pair is discussed. Isotopic labeling experiments reveal that no hydrogen is directly transferred between the substrates. The hydrogen transfer to the furanone moiety observed in the overall reaction therefore results from an exchange with the reaction medium. An electrophilic oxoallyl radical generated from the furanone reacts with the naphthylamine used in excess. Concerning some mechanistic details, the reaction is compared with radical and electrophilic aromatic substitutions. The transformation was carried out with a variety of electron-deficient alkenes. Sterically hindered furanone derivatives are less reactive under standard conditions. In a first experiment, such a compound was transformed using heterogeneous electron transfer photocatalysis with TiO(2).     

Initiation of Radical Chain Reactions of Thiol Compounds and Alkenes without any Added Initiator: Thiol‐Catalyzed cis/trans Isomerization of Methyl Oleate

A kinetic study of the dodecanethiol‐catalyzed cis/trans isomerization of methyl oleate (cis‐ 2 ) without added initiator was performed by focusing on the initiation of the radical chain reaction. The reaction orders of the rate of isomerization were 2 and 0.5 for 1 and cis‐ 2 , respectively, and an overall kinetic isotope effect k_H/k_D of 2.8 was found. The initiation was shown to be a complex reaction. The electron‐donor/‐acceptor (EDA) complex of dodecanethiol ( 1 ) and cis‐ 2 formed in a pre‐equilibrium reacts with thiol 1 to give a stearyl and a sulfuranyl radical through molecule‐assisted homolysis (MAH) of the sulfur–hydrogen bond. Fragmentation of the latter gives the thiyl radical, which catalyzes the cis/trans isomerization. A computational study of the EDA complex, MAH reaction, and the sulfuranyl radical calculated that the activation energy of the isomerization was in good agreement with the experimental result of E_A=82 kJ M ^?1. Overall, the results may explain that the thermal generation of thiyl radicals without any initiator is responsible for many well‐known thermally initiated addition reactions of thiol compounds to alkenes and their respective polymerizations and for the low shelf‐life stability of cis‐unsaturated thiol compounds and of mixtures of alkenes and thiol compounds.