An elementary proof of the uniqueness of invariant product measures for some infinite dimensional processesUne preuve élémentaire de l'unicité des mesures invariantes produits pour certains processus en dimension infinie

Consider an infinite dimensional diffusion process with state space , where T is the circle, and defined by an infinitesimal generator L which acts on local functions f as . Suppose that the coefficients a_i and b_i are smooth, bounded, of finite range, have uniformly bounded second order partial derivatives, that a_i are uniformly bounded from below by some strictly positive constant, and that a_i is a function only of η_i. Suppose that there is a product measure ν which is invariant. Then if ν is the Lebesgue measure or if d=1,2, it is the unique invariant measure. Furthermore, if ν is translation invariant, it is the unique invariant, translation invariant measure. The proofs are elementary. Similar results can be proved in the context of an interacting particle system with state space , with uniformly positive bounded flip rates which are finite range. To cite this article: A.F. Ram??rez, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 139–144     

Friedel-Crafts alkylation of indoles with epoxides catalyzed by nanocrystalline titanium(IV) oxide

Friedel-Crafts alkylation of indoles with epoxides to afford 3-alkyl indole derivatives at room temperature with moderate to good yields and high regioselectivity using nanocrystalline titanium(IV) oxide catalyst is described.     

Calculated elastic constants of dilute alloys based on bcc metals

The elastic constants of dilute alloys based on bcc metals have been calculated using the Green’s function method obtaining explicit expressions for change in elastic constants in terms oft-matrix. The crystal impurity problem is discussed within an impurity model containing central and non-central force constant changes extended up to second neighbours of the impurity. The effect of volume change on elastic constants and a contribution from electron pressure term are considered. Numerical results for changes in three elastic moduli have been presented for a number of dilute alloys based on Mo, Nb, W, Ta and V.     

Dynamic mechanical analysis

Using dynamic mechanical analysis (DMA) we have studied thermal degradation for a system containing a diglycidyl ether of bisphenol A (DGEBA) and 1,3-bisaminomethylcylohexane (1,3-BAC). The changes of dynamic mechanical properties during thermal degradation indicated a shift of the glass transition temperature (T _g) to higher temperatures and a decrease in the peak value of the dynamic loss factor (tan δ) with an increasing of aging time. The value of dynamic storage modulus (E′) at the rubbery state showed an increase with aging time, whiteE′ at the glassy state only underwent a moderate change with increased thermal degradation. From these results it can be argued that thermal degradation during the stage prior to the onset of the severe degradation involves structural changes in the epoxy system, as further crosslinking and loss of dangling chains in the crosslinked network.     

Synthesis and characterization of some novel cyanonitrosyl complexes of chromium(I) with Mannich bases,aromatic aldehyde oximes and syn-phenyl-2-pyridylketoxime

Some new low-spin hexacoordinated cyanonitrosyl complexes of Cr¹ of the type [Cr(NO)(CN)₂(L)₂(H₂)], where L is an aromatic aldehyde oxime or Mannich base, have been prepared by the interaction or K₃[Cr(NO)(CN)₅]· H₂O with L in aqueous AcOH, and characterized by a range of physico-chemical techniques, I.r. data suggest that all the oxime derivatives and Mannich bases act as monodentate ligands by coordinating through the aromatic nitrogen. TMC 2564     

Evaluation of the drag force by integrating the energy dissipation rate in stokes flow for 2D domains using the FEM

The total drag force on the surface of a body, which is the sum of the form drag and the skin friction drag in a 2D domain, is numerically evaluated by integrating the energy dissipation rate in the whole domain for an incompressible Stokes fluid. The finite element method is used to calculate both the energy dissipation rate in the whole domain as well as the drag on the boundary of the body. The evaluation of the drag and the energy dissipation rate are post-processing operations which are carried out after the velocity field and the pressure field for the flow over a particular profile have been obtained. The results obtained for the flow over three different but constant area profiles—a circle, an ellipse and a cross-section of a prolate spheroid—with uniform inlet velocity are presented and it is shown that the total drag force times the velocity is equal to the total energy dissipation rate in the entire finite flow domain. Hence, by calculating the energy dissipation rate in the domain with unit velocity specified at the far-field boundary enclosing the domain, the drag force on the boundary of the body can be obtained.     

ESR and optical study of Mn doped potassium hydrogen sulphate

The ESR spectrum of Mn²⁺ doped potassium hydrogen sulphate at liquid nitrogen temperature (77 K) has been analyzed and site of entered Mn²⁺ in the lattice has been discussed. The values of the zero field parameters that give good fit to the observed ESR spectra have been obtained. The obtained g, A, B, D, E and a values are 2.0002, 66×10⁻⁴ cm⁻¹, 26×10⁻⁴ cm⁻¹, 59×10⁻⁴ cm⁻¹, 32×10⁻⁴ cm⁻¹ and −8×10⁻⁴ cm⁻¹, respectively. The percentage of covalency of the metal-ligand bond has also been estimated. From the optical absorption study at room temperature, the distortion has been suggested. The observed bands are assigned as transitions from the ⁶A_1g(S) ground state to various excited quartet levels of Mn²⁺ ion in a cubic crystalline field. The electron repulsion and crystal field parameters B, C, Dq and α providing good fit to the observed optical spectra have been evaluated and the values obtained for the parameters are B=627 cm⁻¹, C=2580 cm⁻¹ , Dq=790 cm⁻¹ and α=76 cm⁻¹.     

Asymmetric synthesis of 6-(2′,3′,4′,5′,6′-pentafluorophenyl)-δ-lactones via “allyl”boranes: application for the synthesis of fluorinated analog of key pharmacophore of statin drugs

Asymmetric “allyl”boration of pentafluorobenzaldehyde with various α-pinene based “allyl”boranes provides homoallylic alcohols in high de and ee; the alcohols have been converted into δ-lactones via acryloylation, ring-closing metathesis and hydrogenation. Pentafluorophenyl analog of key pharmacophore of statin drugs has been synthesized using diastereoselective epoxidation and regioselective reduction as key steps.     

Classification of graded Hecke algebras for complex reflection groups

The graded Hecke algebra for a finite Weyl group is intimately related to the geometry of the Springer correspondence. A construction of Drinfeld produces an analogue of a graded Hecke algebra for any finite subgroup of GL(V). This paper classifies all the algebras obtained by applying Drinfeld's construction to complex reflection groups. By giving explicit (though nontrivial) isomorphisms, we show that the graded Hecke algebras for finite real reflection groups constructed by Lusztig are all isomorphic to algebras obtained by Drinfeld's construction. The classification shows that there exist algebras obtained from Drinfeld's construction which are not graded Hecke algebras as defined by Lusztig for real as well as complex reflection groups. Received: July 25, 2001