Exponentiality of First Passage Times of Continuous Time Markov Chains

Let \((X,\mathbb{P}_{x})\) be a continuous time Markov chain with finite or countable state space S and let T be its first passage time in a subset D of S. It is well known that if μ is a quasi-stationary distribution relative to T, then this time is exponentially distributed under  \(\mathbb {P}_{\mu}\) . However, quasi-stationarity is not a necessary condition. In this paper, we determine more general conditions on an initial distribution μ for T to be exponentially distributed under  \(\mathbb{P}_{\mu}\) . We show in addition how quasi-stationary distributions can be expressed in terms of any initial law which makes the distribution of T exponential. We also study two examples in branching processes where exponentiality does imply quasi-stationarity.     

Hydrophilic non-ionic polymer networks. Synthesis and application to size exclusion chromatography in aqueous media

Polystyrene networks with elastic chains of known length and containing pendant poly(ethylene oxide) chains selectively attached to the crosslinks were obtained by anionic block-copolymerization. Such networks can exhibit a residual swelling-degree in water that allows easy access to the network-pores. One network with known characteristics was used as a column filling in S.E.C. with water as eluent. Even under high driving pressures, the mechanical strength of this material appears to be satisfactory. In the present example, the domain of selectivity extends from approx. 100–5000.     

Uniqueness to elliptic and parabolic Hamilton–Jacobi–Bellman equations with non-smooth boundary

In the framework of viscosity solutions, we give an extension of the strong comparison result for Hamilton–Jacobi–Bellman (HJB) equations with Dirichlet boundary conditions to the case of some non-smooth domains. In particular, it may be applied to parabolic problems on cylindrical domains. To cite this article: S. Chaumont, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Uranyl coordination in ionic liquids: the competition between ionic liquid anions, uranyl counterions, and Cl- anions investigated by extended X-ray absorption fine structure and UV-visible spectroscopies and molecular dynamics simulations

The first coordination sphere of the uranyl cation in room-temperature ionic liquids (ILs) results from the competition between its initially bound counterions, the IL anions, and other anions (e.g., present as impurities or added to the solution). We present a joined spectroscopic (UV-visible and extended X-ray absorption fine structure)-simulation study of the coordination of uranyl initially introduced either as UO2X2 salts (X-=nitrate NO3-, triflate TfO-, perchlorate ClO4-) or as UO2(SO4) in a series of imidazolium-based ILs (C4mimA, A-=PF6-, Tf2N-, BF4- and C4mim=1-methyl-3-butyl-imidazolium) as well as in the Me3NBuTf2N IL. The solubility and dissociation of the uranyl salts are found to depend on the nature of X- and A-. The addition of Cl- anions promotes the solubilization of the nitrate and triflate salts in the C4mimPF6 and the C4mimBF4 ILs via the formation of chloro complexes, also formed with other salts. The first coordination sphere of uranyl is further investigated by molecular dynamics (MD) simulations on associated versus dissociated forms of UO2X2 salts in C4mimA ILs as a function of A- and X- anions. Furthermore, the comparison of UO2Cl(4)2-, 2 X- complexes with dissociated X- anions, to the UO2X2, 4 Cl- complexes with dissociated chlorides, shows that the former is more stable. The case of fluoro complexes is also considered, as a possible result of fluorinated IL anion's degradation, showing that UO2F42- should be most stable in solution. In all cases, uranyl is found to be solvated as formally anionic UO2XnAmClp2-n-m-p complexes, embedded in a cage of stabilizing IL imidazolium or ammonium cations.     

Reversible Soft Mechanochemical Control of Biaryl Conformations through Crosslinking in a 3D Macromolecular Network

Tuning the dihedral angle (DA) of axially chiral compounds can impact biological activity, catalyst efficiency, molecular motor performance, or chiroptical properties. Herein, we report gradual, controlled, and reversible changes in molecular conformation of a covalently linked binaphthyl moiety within a 3D polymeric network by application of a macroscopic stretching force. We managed direct observation of DA changes by measuring the circular dichroism signal of an optically pure BINOL-crosslinked elastomer network. Stretching the elastomer resulted in a widening of the DA between naphthyl rings when the BINOL was doubly grafted to the elastomer network; no effect was observed when a single naphthyl ring of the BINOL was grafted to the elastomer network. We have determined that ca. 170 % extension of the elastomers led to the transfer of a mechanical force to the BINOL moiety of 2.5 kcal mol⁻¹ Å⁻¹ (ca. 175 pN) in magnitude and results in the opening of the DA of BINOL up to 130°.     

Supported Catalytically Active Supramolecular Hydrogels for Continuous Flow Chemistry

Inspired by biology, one current goal in supramolecular chemistry is to control the emergence of new functionalities arising from the self‐assembly of molecules. In particular, some peptides can self‐assemble and generate exceptionally catalytically active fibrous networks able to underpin hydrogels. Unfortunately, the mechanical fragility of these materials is incompatible with process developments, relaying this exciting field to academic curiosity. Here, we show that this drawback can be circumvented by enzyme‐assisted self‐assembly of peptides initiated at the walls of a supporting porous material. We applied this strategy to grow an esterase‐like catalytically active supramolecular hydrogel (CASH) in an open‐cell polymer foam, filling the whole interior space. Our supported CASH material is highly efficient towards inactivated esters and enables the kinetic resolution of racemates. This hybrid material is robust enough to be used in continuous flow reactors, and is reusable and stable over months.     

Chiral discrimination of dansyl-amino-acid enantiomers on teicoplanin phase: sucrose-perchlorate anion dependence

The chiral recognition mechanism for a series of d,l-dansyl-amino-acids (test solutes) on a teicoplanin stationary phase was investigated in reversed phase liquid chromatography (RPLC). The effect of both a surface tension modifier (sucrose) and a chaotropic agent (perchlorate anion) on the enantiomeric separation was studied by varying their concentration, c, in the mobile phase. The thermodynamic data supported the fact that the sucrose molecule acted only on the hydrophobic part of the interaction teicoplanin/dansyl-amino-acid and not on the specific chiral part. It was demonstrated that the enhancement of the separation factor observed as the perchlorate salt concentration increased in the mobile phase was enthalpically controlled owing to stereoselective bonding interactions. Such behavior was used to optimize the chromatographic conditions for separation of dansyl-amino-acids on teicoplanin.     

High-performance liquid chromatographic determination of bromazepam in human plasma

An assay using high-performance liquid chromatography has been developed for the determination of bromazepam in plasma. After a single-step extraction from basified samples with dichloromethane, using decarboxyloflazepate as an internal standard, samples were analysed using a reversed-phase Nova Pak 5-microns column with a mobile phase of methanol - phosphate buffer (60 + 40) adjusted to pH 7.6. The drugs were detected at 239 nm and the limit of detection was found to be 3 micrograms l-1 for bromazepam. The method is simple, rapid and sensitive and permits bromazepam levels in clinical and pharmacokinetic studies to be monitored.