Synthesis and properties of poly(1-phenyl-1-octyne)s containing stereogenic and chromophoric pendant groups

Poly(1-phenyl-1-octyne)s containing different stereogenic and chromophoric pendants {-[(C6H13)C=C(C6H4-p-CO2-R)]n-R=[(1S)-endo]-(-)-borneyl (P3), (1R,2S,5R)-(-)-menthyl (P4),―C6H4-p-(1R,2S,5R)-(-)-menthyl (P5), 2-napthyl (P6), 4-biphenylyl (P7)} have been designed and synthesized. The polymers are prepared in moderate yields by WCl6-Ph4Sn and possess high molecular weights (Mw up to 64000). The structures and properties of the polymers are characterized and evaluated by NMR, TGA, UV, CD, PL, and EL analyses...     

Theoretical analysis of the influence of the adosorption process on the voltammetric curves in the case of a second order adsorption step followed by a first order charge transfer reaction: Part II. Comparison between linear potential sweep voltammetry and steady state cyclic voltammetry

The voltammetric curves for a 2-step sequential reaction involving a 2nd order adsorption process (such as the catalytic mechanism met in the anodic oxidation of hydrogen) are investigated theoretically by computer calculations. Steady state cyclic voltammetry (s.s.c.v.) is particularly treated by repeating forward and backward sweeps as many times as necessary to reach the steady state. For both l.p.s.v. and s.s.c.v., the usual characteristic features are considered, i.e. E_M, θ_M, i_M as a function of sweep rate υ, especially in the range of υ, where the computed data fit the results derived from analytical solution (quasi-reversible charge transfer, and irreversible charge transfer). In s.s.c.v., indications are given to obtain the kinetic parameters (k₁, k₂, α) from experimental plots.     

A possibilistic-valued multi-criteria decision-making support for marketing activities in e-commerce: Feedback Based Diagnosis System

In this paper we propose a multi-criteria decision making support system, called a “Feedback Based Diagnosis System” (FBDS), to aid the marketing team of an e-commerce (EC) organisation in its activities. The FBDS database is composed of customers’ satisfaction measures. These measures are related to the different services an EC offers to its customers. Thus, they constitute a multi-criteria (MC) evaluation of EC performances. In the general framework of recommender systems, these available MC evaluations are considered as useful information for other customers to help them to objectively, rationally and exhaustively assess and compare the numerous ECs among the ones likely to meet their needs. Our FBDS is not concerned with improving or automating such a recommendation process for customers. Indeed, it is merely EC management team oriented. In fact, the MC feedback database is used to diagnose the EC health and improve its strategy. In the proposed FBDS, a possibilistic framework is combined with the multi criteria representation to capture the variability and the divergence of customers’ evaluations w.r.t. each criterion. Then, an aggregation based on a weighted arithmetic mean (WAM) is proposed to obtain a synthetic appraisal of ECs. The WAM aggregation models the strategy agreed on by the EC management team. Computing the synthesis score of an EC consists in propagating the uncertainty related to its partial scores through the WAM. The possibilistic representation guarantees that no information is lost in the collective evaluation process by the consumers’ community. However, diagnosis indicators are finally proposed to the marketing team to make the interpretation of some possibilistic results more comprehensive when necessary.     

Non-differentiable embedding of Lagrangian systems and partial differential equations

We develop the non-differentiable embedding theory of differential operators and Lagrangian systems using a new operator on non-differentiable functions. We then construct the corresponding calculus of variations and we derive the associated non-differentiable Euler-Lagrange equation, and apply this formalism to the study of PDEs. First, we extend the characteristics method to the non-differentiable case. We prove that non-differentiable characteristics for the Navier-Stokes equation correspond to extremals of an explicit non-differentiable Lagrangian system. Second, we prove that the solutions of the Schrödinger equation are non-differentiable extremals of the Newton?s Lagrangian.     

Quantum derivatives and the Schrödinger equation

We define a scale derivative for non-differentiable functions. It is constructed via quantum derivatives which take into account non-differentiability and the existence of a minimal resolution for mean representation. This justify heuristic computations made by Nottale in scale-relativity. In particular, the Schrödinger equation is derived via the scale-relativity principle and Newton’s fundamental equation of dynamics.     

Hyperbolicity, transversality and analytic first integrals

Let A be a (normally) hyperbolic compact invariant manifold of an analytic diffeomorphism f of an analytic manifold M. We assume that the stable and unstable manifold of A intersect transversally (in an admissible way), the dynamics on A is ergodic and the modulus of the eigenvalues associated to the stable and unstable manifold, respectively, satisfy a non-resonance condition. In the case where A is a point or a torus, we prove that the discrete dynamical system associated to f does not admit an analytic first integral. The proof is based on a triviality lemma, which is of combinatorial nature, and a geometrical lemma. The same techniques, allow us to prove analytic non-integrability of Hamiltonian systems having Arnold diffusion. In particular, using results of Xia, we prove analytic non-integrability of the elliptic restricted three-body problem, as well as the planar three-body problem.     

Steric Effects on Reaction Rates. Part VIII. The Significance of Front Strain Release in Solvolysis of Bridgehead Derivatives

The steric requirements of leaving groups for 14 bridgehead derivatives have been examined using MM2 calculations. The strain varies almost monotonously throughout the series upon variation of the leaving group from H to C1, OH, CH₃, CH₃CH₂O, (CH₃)₃CO, (CH₃)₃C and no significant trends for differential F-strain effects are detected expect for the perhydrophenalene derivative 13 . The experimental rates of solvolysis of bridgehead derivatives correlate well with the calculated steric energy differences between substrate R-X and the corresponding carbenium ion R⊕. However, the strain calculations using the more recent force-fields ( MM2 ) disagree, in part, with those reported in the literature: chloride and p-toluenesulfonate leaving groups correlate with identical slopes, and the perhydrotriquinacene derivative 10 shows no anomalous behavior. The calculations suggest that F-strain and C,C-hyperconjugation should not play any dominant role in bridgehead solvolysis.