Weak approximation of averaged diffusion processes

We derive expansion results in order to approximate the law of the average of the marginal of diffusion processes. The average is computed w.r.t. a general parameter that is involved in the diffusion dynamics. Our approximation is based on the use of proxys with normal distribution or log-normal distribution, so that the expansion terms are explicit. We provide non asymptotic error bounds, which justifies the expansion accuracy as the time or the diffusion coefficients are small in a suitable sense.     

Large time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations

In this paper, we study the large time behavior of solutions of a class of parabolic fully nonlinear integro-differential equations in a periodic setting. In order to do so, we first solve the ergodic problem (or cell problem), i.e. we construct solutions of the form $\lambda t + v(x).$ We then prove that solutions of the Cauchy problem look like those specific solutions as time goes to infinity. We face two key difficulties to carry out this classical program: (1) the fact that we handle the case of “mixed operators” for which the required ellipticity comes from a combination of the properties of the local and nonlocal terms and (2) the treatment of the superlinear case (in the gradient variable). Lipschitz estimates previously proved by the authors (2012) and Strong Maximum principles proved by the third author (2012) play a crucial role in the analysis.     

Semicontinuous viscosity solutions for quasiconvex Hamiltonians

The main theorem connecting convex Hamiltonians and semicontinuous viscosity solutions due to Barron and Jensen is extended to quasiconvex Hamiltonians. Some applications are indicated.     

Quantum Experimental Data in Psychology and Economics

We prove a theorem which shows that a collection of experimental data of probabilistic weights related to decisions with respect to situations and their disjunction cannot be modeled within a classical probabilistic weight structure in case the experimental data contain the effect referred to as the ‘disjunction effect’ in psychology. We identify different experimental situations in psychology, more specifically in concept theory and in decision theory, and in economics (namely situations where Savage’s Sure-Thing Principle is violated) where the disjunction effect appears and we point out the common nature of the effect. We analyze how our theorem constitutes a no-go theorem for classical probabilistic weight structures for common experimental data when the disjunction effect is affecting the values of these data. We put forward a simple geometric criterion that reveals the non classicality of the considered probabilistic weights and we illustrate our geometrical criterion by means of experimentally measured membership weights of items with respect to pairs of concepts and their disjunctions. The violation of the classical probabilistic weight structure is very analogous to the violation of the well-known Bell inequalities studied in quantum mechanics. The no-go theorem we prove in the present article with respect to the collection of experimental data we consider has a status analogous to the well known no-go theorems for hidden variable theories in quantum mechanics with respect to experimental data obtained in quantum laboratories. Our analysis puts forward a strong argument in favor of the validity of using the quantum formalism for modeling the considered psychological experimental data as considered in this paper.     

Lanthanide luminescence efficiency in eight- and nine-coordinate complexes: Role of the radiative lifetime

The photophysical parameters for the sensitization of metal-centred luminescence are analyzed in two series of complexes with tridentate and hexadentate ligands having N_xO_y chelating units. In particular, the radiative lifetime τ_rad is experimentally estimated for 29 nine-coordinate Eu^III complexes and 10 eight- and nine-coordinate Yb^III complexes. The known dependence of τ_rad on refractive index is substantiated by comparing data for solid-state samples and solutions. Moreover, a clear dependence of τ_rad with the coordination environment is evidenced and in the case of Eu^III, a comparison between τ_rad and the nephelauxetic effect generated by the ligands is attempted. Altogether, this extensive analysis points to the importance of having a handle on τ_rad when designing ligands for highly luminescent lanthanide-containing molecular edifices. This, in turn, should stimulate initiating theoretical considerations to unravel a reliable relationship between τ_rad and the electronic structure of the ligands.     

Diastereoselective trimolecular condensation between indole,Meldrum’s acid and chiral sugar-derived aldehydes

The trimolecular condensation of indole, Meldrum’s acid and chiral, sugar-derived aldehydes took place in good yield and high diastereoselectivity. The absolute configuration of the α-carbon of the chiral aldehydes ensured a predictable diastereocontrol of the newly created stereogenic centre except for (3aR,5S,6S,6aR)-6-benzyloxy-2,2-dimethyl-tetrahydrofuro[3,2-d][1,3]dioxole-5-carbaldehyde 3i. In this case, the opposite stereochemistry may be explained by a less congested conformer of the Knoevenagel-adduct intermediate.     

Micellar behavior of well‐defined polystyrene‐based block copolymers with triethoxysilyl reactive groups and their hydrolysis–condensation

Block copolymers of acryloxy propyl triethoxysilane and styrene were prepared through nitroxide‐mediated polymerization using alkoxyamine initiators based on N‐tert‐butyl‐1‐diethylphosphono‐2,2‐dimethylpropyl nitroxide. The copolymers were characterized by ¹H NMR, size exclusion chromatography and differential scanning calorimetry. Their micellar behavior in dioxane/methanol solutions was examined through static light scattering and transmission electron microscopy (TEM). TEM indicated the successful formation of spherical micelles which were subsequently frozen by the sol–gel process. Hydrolysis–condensation of the reactive ethoxysilyl side groups was followed by FTIR, ¹H NMR, and ²⁹Si NMR. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 784–793, 2010     

Chiral diphosphines and diphosphinites derived from 2,2-biphosphole: Stereodynamic ligands for asymmetric catalysis

In this account, the recent advances on chiral stereochemically dynamic 2,2’-biphosphole ligands for applications in asymmetric catalysis are reported. In the first part, the synthesis of stereodynamic diphosphines and diphosphinites derived from 2,2’-biphosphole is presented. The second part describes the kinetic dynamic resolution to give diastereo- and enantiopure complexes. Applications in asymmetric allylic substitution, hydroformylation and hydrogenation are presented in the last part.