Fractional Differentiation in Passive Vibration Control

From a single-degree-of-freedom model used to illustrate the concept ofvibration isolation, a method to transform the design for suspensioninto a design for robust controller is presented. Fractionaldifferentiation is used to model viscoelastic behaviour of suspension.The use of fractional differentiation not only permits optimisation ofjust four suspension parameters, showing the `compactness' of thefractional derivative operator, but also leads to robustness ofsuspension performance to uncertainty of the sprung mass. As an example,an engine suspension is studied.     

Master Equation and Fokker–Planck Equation: Comparison of Entropy and of Rate Constants

A usual approximation of the master equation is provided by the Fokker–Planck equation. For chemical systems with one species, we prove generally that the prediction of the rate constant of the metastable state given by the Master equation and the Fokker–Planck approximation differ exponentially with respect to the size of the system. We show that this is related to the fact that the entropy of the metastable state is not described correctly by the Fokker–Planck equation. We prove that the rate given by the Fokker–Planck equation overestimates that rate given by the Master equation.     

Synthese et reactivite d''organometalliques perfluores. VII [1] reactivite comparee de derives perfluoroalkyles satures et insatures de l''etain et du mercure vis-a-vis d''electrophiles.

The reactivity of some derivatives of perfluorooctenyl-tin, perfluorooctenyl-mercury and perfluorooctyl-mercury towards protic acids, especially hydrogen chloride, is studied.

The easy cleavage of the tin - sp² carbon bond is painted out, and used to study possibilities of transferring the perfluorooctenyl radical on mercury, upon reaction with mercuric salts.

The mercury-perfluoroalkyl radical bond is shown to be, on the contrary, very resistant to an electrophilic attack.

These results are compared to those concerning the hydrocarbon analogs, and an interpretation, relied to the electronic density on the carbon atom bound to the metallic atom, is given.     

Reactivite des perfluorohalogenoalcanes en presence de couples metalliques—II: Formation de perfluoroolefines a partir des perfluoroiodoalcanes dans les solvants aprotiques dissociants, (DMSO,DMF, HMPT)

The action of zinc-copper couples on perfluoroiodoalkanes C₄F₉I, C₆F₁₃I and C₈F₁₇I was studied in DMSO, DMF, or HMPT; a mixture of isomeric perfluoroolefins was obtained. A general mechanism for the action of these metallic couples, involving a perfluorinated organometallic intermediate, is proposed.     

Note on the stochastic theory of a self-catalytic chemical reaction. I

By using the spectral theory of the master equation, it is shown generally that a self-catalytic chemical system may evolve according to two widely different time scales in this case. The shorter one describes the evolution towards a quasi-stationary state which is the stochastic equivalent of the macroscopic stationary state. The larger time characterizes the final evolution towards total absorption; it is coarsely evaluated for an arbitrary system and more precisely for a non step-by-step reaction. Detailed application to step-by-step reactions is given in a second article.     

On the application of the Onsager-Machlup function to non-linear fluctuations of a thermodynamic variable

The application of the Onsager-Machlup principle to non-linear fluctuations of a thermodynamic variable is discussed. The Onsager law of proportionality of fluxes and forces is obtained by an integral method. Approximate calculation of the transition probabilities and of the most probable evolution are made by taking the diffusion coefficient as a smallness parameter. The results are compared with results obtained by other methods, particularly by Kubo, Matsuo and Kitahara. The asymptotic case of infinite time intervals is discussed summarily.     

Multilevel description of the Rh isotopes in the interacting boson-fermion model

We present a multilevel calculation within the framework of the interacting boson-fermion model (IBFM-1) of the odd-mass ^101–109Rh isotopes. We calculate both positive- and negative-parity states of the same hamiltonian, starting from the $\text{1g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$, $\text{2p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{2p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, $\text{lf}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ and $\text{2d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ single-particle orbitals. We discuss energy spectra, electromagnetic E2 transition rates and one-nucleon transfer properties. We also discuss the influence of the $\text{1f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ orbital on the one-nucleon transfer properties. The results of the calculation for the negative-parity states are compared with the results of the $\text{U(}\text{6}\text{12}$) supersymmetry scheme of the interacting boson model.     

Self-assembled microspheres from f-block elements and nucleoamphiphiles

Hollow microspheres featuring a hybrid lipid-cation multilamellar shell are prepared by hydration of a nucleoside based amphiphile with an aqueous solution containing either actinide or lanthanide salts. The physico-chemical data collected clearly indicate that the formation of these microspheres is a consequence of the following concomitant stabilizing factors: (i) hydrophobic interactions, (ii) nucleobase dimer formation and (iii) phosphate/f-block element salt binding.