Acyl derivatives of N,N′-diaminodibenzo-18-crown-6 ether,their complexing and catalytic properties

Conclusions Complex compounds of bisacyl derivatives of diaminodibenzo-18-crown-6 ether are active catalysts of the two stages of the synthesis of poly(ethylene terephthalate).Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2544–2547, November. 1987.     

A non‐linear and non‐local boundary condition for a diffusion equation in petroleum engineering

This article deals with a boundary value problem for Laplace equation with a non‐linear and non‐local boundary condition. This problem comes from petroleum engineering and is used to obtain an estimation of well productivity. The non‐linear and non‐local boundary condition is written on the well boundary. On the outer reservoir boundaries, we have both Dirichlet and Neumann conditions. In this paper, we prove the existence and uniqueness of a solution to this problem. The existence is proved by Schauder theorem and the uniqueness is obtained under more restricted conditions, when the involved operator is a contraction. Copyright © 2005 John Wiley & Sons, Ltd.     

Conservation de la charge dans les codes PIC

This Note introduces a new integral form of the charge and current deposition scheme given in 1992 by Villasenor and Buneman, which permits the conservation of charge in PIC codes. This integral form extends directly to higher order spline shape factors, whose use produces less numerical noise. We thus get a discrete charge conserving method for high order shape factors. This method extends easily to nonuniform Cartesian grids for first order shape factors. To cite this article: R. Barthelmé, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Direct numerical simulation of settling of a large solid particle during bioconvection

Settling of a large solid particle in bioconvection flow caused by gyrotactic microorganisms is investigated. The particle is released from the top of the bioconvection chamber; its settling pattern depends on whether it is released in the centre of the bioconvection plume or at its periphery. The Chimera method is utilized; a subgrid is generated around a moving particle. The method suggested by Liu and Wang (Comput. Fluid 2004; 33 :223–255) is further developed to account for the presence of a moving boundary in the streamfunction‐vorticity formulation using the finite‐difference method. A number of cases for different release positions of the particle are computed. It is demonstrated that bioconvection can either accelerate or decelerate settling of the particle depending on the initial position of the particle relative to the plume centre. It is also shown that the particle impacts bioconvection plume by changing its shape and location in the chamber. Copyright © 2005 John Wiley & Sons, Ltd.     

Structural relaxation time for various liquids

The structural relaxation time for series of various liquids (alkanes, aliphatic alcohols, and diols) are calculated from published data on the shear viscosity and the heat of evaporation per unit volume. Liquids having a 3D H-bond network (diols) are characterized by relaxation times one to two orders of magnitudes longer than those typical of liquids without such a network (alkanes and aliphatic alcohols).     

Spectrofluorimetric Method for the Determination of Aluminum with Alizarin Red PS

 A simple and direct spectrofluorimetric method has been developed for the determination of aluminum using alizarin red PS (1,2,4-trihydroxy 9,10-anthraquinone-3-sulfonic acid). The method is based on the strong fluorescence (480/564 nm) of Al³⁺ and alizarin red. Experimental parameters such as pH, concentration of the ligand, ionic strength of the solution, reaction time and temperature were optimized in order to maximize the analytical signal. Interferences of several ions (anions and cations) were studied and evaluated. The linear range of the method extends from 3 to 100 μg L⁻¹. Limit of detection (3s_b) was 0.9 μg L⁻¹. The method was tested with a silicate certified reference material. Interferences were eliminated by a liquid extraction with cupferron. Author for correspondence. E-mail: aucelior@rdc.puc-rio.br Received September 10, 2002; accepted January 15, 2003 Published online May 5, 2003     

Geometry of an Accelerated Rotating Disk

We analyze the geometry of a rotating disk with a tangential acceleration in the framework of the theory of Special Relativity, using the kinematic linear differential system that verifies the relative position vector of time-like curves in a Fermi reference. A numerical integration of these equations for a generic initial value problem is made up and the results are compared with those obtained in other works.     

A new type of conformal dynamics

We consider the Lagrangian particle model introduced in [Ann. Phys. 260 (1997) 224] for zero mass but nonvanishing second central charge of the planar Galilei group. Extended by a magnetic vortex or a Coulomb potential the model exhibits conformal symmetry. In the former case we observe an additional SO(2,1) hidden symmetry. By either a canonical transformation with constraints or by freezing scale and special conformal transformations at t=0 we reduce the six-dimensional phase-space to the physically required four dimensions. Then we discuss bound states (bounded solutions) in quantum dynamics (classical mechanics). We show that the Schrödinger equation for the pure vortex case may be transformed into the Morse potential problem thus providing us with an explanation of the hidden SO(2,1) symmetry.     

Rotational spectra of isotopic species of SO2F2: experimental and ab initio structures

The rotational spectra of ³⁴SO₂F₂ and S¹⁸O¹⁶OF₂ have been measured in their ground vibrational state between 9 and 110 GHz. Accurate rotational constants have been derived. Various experimental structures including the average structure have been determined. The ab initio structure has been calculated at the CCSD(T) level of theory. The different structures are compared and the best equilibrium structure is the ab initio structure: r_e(SO)=1.401 (3) Å, r_e(SF)=1.532 (3) Å, ∠_e(OSO)=124.91(20)°, ∠_e(FSF)=95.53 (20)°.