Nash equilibrium point for one kind of stochastic nonzero-sum game problem and BSDEs

In this Note, we deal with one kind of stochastic nonzero-sum differential game problem for N players. Using the theory of backward stochastic differential equations and Malliavin calculus, we give the explicit form of a Nash equilibrium point. To cite this article: J.-P. Lepeltier et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Multiscale dynamics of 1H and 19F in confined ionogels for lithium batteries

We present the first results of the nuclear magnetic relaxation dispersion (NMRD) of the confined proton-bearing cation (BMI) and fluorine-bearing anion (TFSI) pair of ionic liquids (Li⁺-ionogels) confined within a silica-like mesoporous matrices designed for lithium batteries. These results are in favour of a very-correlated dynamical motion of the anion–cation pair within the solid and disordered silica matrix.     

Polymorphism in PbBiOXO4 compounds (X=V, P, As): Part II—PbBiOPO4 and PbBiOAsO4 structures and characterization of related solid solutions

Reinvestigation of PbBiOXO₄ (X=V, P, As) thermal behaviour revealed a phase transition for V- and P-compounds, but no transition for the As-compound. As shown by single-crystal X-ray diffraction and high-resolution neutron powder diffraction, α-PbBiOVO₄ transforms to β-PbBiOVO₄ at 550 °C. The two PbBiOPO₄ varieties are isomorph to the vanadate forms, while PbBiOAsO₄ adopts the β-type structure whatever the temperature. PbBiP_1−xOAs_xO₄ and PbBiV_1−xOM_xO₄ (M=As, P, Cr, Mn) solid solutions display both triclinic and monoclinic domains, and the α→β transition temperature is a function of the substitution rate. The ionic conductivity of these compounds was investigated by impedance spectroscopy. The analysis of free space in the β-PbBiOVO₄ structure allows to propose a one-dimensional oxygen diffusion pathway along [010] when the temperature increases.     

Improved convergence order for augmented penalty algorithms

We refine the speed of convergence analysis for the quadratic augmented penalty algorithm. We improve the convergence order from 4/3 to 3/2 for the first order multiplier iteration. For the second order iteration, we generalize the analysis, and consider a primal–dual variant which asymptotically reduces to a Newton step for the optimality conditions.     

Toward new camptothecins. Part 6: Synthesis of crucial ketones and their use in Friedländer reaction

In the context of the preparation of camptothecin and luotonin A analogs, the synthesis of some key keto-precursors and their use in Friedländer condensation are described. This paper also focuses on the stability of these keto intermediates and emphasizes the major differences between indolizinones and pyrroloquinazolinones series. Noteworthy is also the report of some original structures isolated as by-products of some experiments.     

The magic effect of endocyclic but non-sterically hindering biisoquinoline chelates: From fast-moving molecular shuttles to [3]rotaxanes

The use of 8,8′-diaryl-substituted 3,3′-biisoquinolines allows the construction of new multi-component assemblies that are inaccessible with the 2,9-diaryl-substituted 1,10-phenanthroline ligands previously developed by the Sauvage group. This is due to the sterically non-hindering nature of the new chelates, which makes three-component entanglements around octahedral metal centres such as iron(II), cobalt(II) and ruthenium(II) readily possible. Among the newly synthesized molecular assemblies are [3]rotaxanes and [3]pseudorotaxanes in which two molecular strings pass through a single macrocycle, as well as molecular shuttles that exhibit greatly improved shuttling kinetics when compared to previously investigated molecular machines that are based on copper(I)/copper(II) redox chemistry.     

A unique single carboxylate-bridged spin-frustrated chiral Mn(II) metallatriangle

The reaction between Hmbpymca ligand (prepared in situ from the hydrolysis of 5-methyl-4-cyano-bispyrimidine with NaOH and further neutralization with 2 M HCl) and Mn(ClO(4))(2)·4H(2)O in 1:1 molar ratio afforded the triangulo-trimanganese(II) complex [Mn(3)(bpymca)(3)(H(2)O)(6)]Cl(3)·6H(2)O 1. The chloride anions in this complex come from the HCl used in the neutralization process. The molecular structure of 1 consists of cationic molecular triangles [Mn(3)(μ-mbpymca)(3)(H(2)O)(6)](3+) with C(3) symmetry, chloride anions and crystallization water molecules, all of them involved in an extensive network of hydrogen bonds, leading to a chiral network. Within the [Mn(3)(μ-mbpymca)(3)(H(2)O)(6)](3+) cations, seven-coordinated Mn(II) ions are bridged by both oxygen atoms of the carboxylate groups and exhibit a MnO(5)N(2) compressed pentagonal bipyramidal coordination environment. The temperature dependence of the magnetic susceptibility shows the presence of weak antiferromagnetic interactions between Mn(II) ions mediated by the carboxylate group of the mbpymca ligand and the existence of a 3D antiferromagnetic ordering below 4 K, which has its origin in the AF inter-trimer exchange interactions mediated by the strong hydrogen bonds present in the crystal of 1. The experimental magnetic susceptibility data above 7 K could be satisfactorily fitted to the theoretical analytical expression derived from the spin Hamiltonian H = -J(S(1)S(2) + S(1)S(3) + S(2)S(3)) with J = -0.782(3) cm(-1) and g = 2.092(3). The model predicts a degenerate ground state with an S = 1/2, which is typical of triangular trimetallic spin frustrated systems containing metal with non-integer spins. DFT calculations were performed on the molecular structure as found in the solid state to support the experimental J value and the Mn-O(carb)-Mn as the primarily exchange pathway.