Réactions d'addition-élmination à partir d'hétérocycles germaniés du type . III. Cas des diéthyl-2,2-germa-2-oxazolidines-1,3 (R = et; X = O; Y = NH,NMe)

Addition-elimination reactions from germanium heterocycles . III. 2,2-Diethyl-2-germa-1,-3-oxazolidines (R = Et; X = O; Y = NH, NMe) . The reactions of 2,2-diethyl-2-germa-1,3-oxazolidines with heterocumulenes (PhNCO, PhNCS, CS₂, CO₂, CH₂?C?O) and carbonyl compounds (aldehydes and ketones) are studied. Generally, monoinsertion derivatives are formed by addition of one molecule of the unsaturated compound accross the Ge? N bond. This bond is always the most reactive center of the molecule. In the case of the carbonyl compounds used, diinsertion may occur in a second step by a further addition across a Ge? O bond. Generally, this latter reaction is reversible. By thermal eliminat on of (Et₂GeO)_n or (Et₂GeS)₃ the monoaddition derivatives yield the corresponding oxazolidines and thiooxazolidines. The mechanisms of these reactions are discussed.     

On Anosov energy levels of hamiltonians on twisted cotangent bundles

LetT ^* M denote the cotangent bundle of a manifoldM endowed with a twisted symplectic structure [1]. We consider the Hamiltonian flow generated (with respect to that symplectic structure) by a convex HamiltonianH: T ^* M, and we consider a compact regular energy level ofH, on which this flow admits a continuous invariant Lagrangian subbundleE. When dimM3, it is known [9] that such energy level projects onto the whole manifoldM, and thatE is transversal to the vertical subbundle. Here we study the case dimM=2, proving that the projection property still holds, while the transversality property may fail. However, we prove that in the case whenE is the stable or unstable subbundle of an Anosov flow, both properties hold.     

Self and mutual admittance of slot antennas on a dielectric half-space

In this paper, an efficient implementation of the spectral domain moment technique is presented for computing the self and mutual coupling between slot antennas on a dielectric half-space. It is demonstrated that by the proper selection of the weighting functions in the method of moments, the analytic evaluation or simplification of the transverse moment integrals is enabled. This results into a significant reduction of the required computational labor. The method is then utilized in order to provide design data for the self and mutual admittances between two slot antennas on a dielectric substrate lens in the case of fused quartz ( _r =3.80), crystal quartz ( _r =4.53), silicon ( _r =11.9) and GaAs ( _r =12.8). The presented technique and associated results are useful when designing twin slot quasi-optical receivers, imaging arrays, phased arrays or power-combining arrays of slot elements at millimeter-wave frequencies.     

On the Haar measure of the quantumSU(N) group

We prove that the Haar state associated to the compact matrix quantum groupSU (N) is faithful for ]–1,1[,0, and anyN2.     

Simultaneous determination of copper and lead in ethanol fuel by anodic stripping voltammetry

The presence of trace metals in car fuels plays an important role in the engine maintenance. In addition, these metals contribute for the environmental contamination in big cities and their control is necessary. Square Wave Stripping Voltammetry (SWSV) is a very sensitive technique for elemental trace determination and was applied for ethanol fuel analysis. The first studies were done searching for the best conditions for copper determination in alcoholic medium, utilizing gold electrodes. During these studies, the possibility of the simultaneous determination of copper and lead in the same experiment was observed. Two procedures for the analysis of these metals were adopted: The direct quantification of metals in alcohol–water mixtures and a second way that involves the evaporation of the organic solvent and re-suspension of the ions with water+electrolyte. Good recovery values were obtained for synthetic samples spiked with known amounts of metals. The results obtained for the two methods were in good agreement. The detection limits for copper and lead in 75% ethanol–water ratio solution were calculated as 120 and 235 ng l⁻¹, respectively, for 15-min deposition time.     

An exact homology sequences approach to the controllability of systems

Some results are given on the homology groups of the abstract simplicial complex associated to a multivariable control system, as an extension of the central result of J. Casti (J. Math. Anal. Appl.68 (1979), 347–370) to the multivariable case. The method used is “polyhedral dynamics” as termed by J. Casti, who introduced it. A given control system is mapped into a simplicial complex and then its homological structure is studied. These results, obtained in the multivariable case by the use of the Mayer-Vietoris homology sequence and of the relative homology sequence, present topological invariants for control systems thus creating the possibility of a new topological classification of multivariable systems. An example is given to clarify the approach.     

Design of ordered bimetallic complexes,Part 2:Trans-1,2-cyclohexanediaminetetraacetate bimetallates

Summary Knowledge of the kinetic and thermodynamic behaviour of aqueous solutions containing two divalent cations andtrans-1,2-cyclohexanediaminetetraacetate has been used to design synthetic pathways to ordered bimetallic complexesPart 1: E. Escriva, A. Fuertes and D. Beltran,Transition Met. Chem.,9, 184 (1984).     

Photobleaching of compounds of the 5,10,15,20-Tetrakis(m-hydroxyphenyl)porphyrin Series (m-THPP,m-THPC,and m-THPBC)

[reaction: see text] 5,10,15,20-Tetrakis(m-hydroxyphenyl)porphyrin (m-THPP) yielded novel quinonoid porphyrins upon irradiation in aqueous methanol. True photobleaching was observed for 5,10,15,20-tetrakis(m-hydroxyphenyl)chlorin (m-THPC) and 5,10,15,20-tetrakis(m-hydroxyphenyl)bacteriochlorin (m-THPBC) under the same conditions; several fragmentation products (imides, methyl p-hydroxybenzoate, dipyrrin derivatives) were recognized.     

Theory of the photodissociation of ozone in the Hartley continuum: potential energy surfaces, conical intersections, and photodissociation dynamics

Ab initio potential energy and transition dipole moment surfaces are presented for the five lowest singlet even symmetry electronic states of ozone. The surfaces are calculated using the complete active space self consistent field method followed by contracted multireference configuration interaction (MRCI) calculations. A slightly reduced augmented correlation consistent valence triple-zeta orbital basis set is used. The ground and excited state energies of the molecule have been computed at 9282 separate nuclear geometries. Cuts through the potential energy surfaces, which pass through the geometry of the minimum of the ground electronic state, show several closely avoided crossings. Close examination, and higher level calculations, very strongly suggests that some of these seemingly avoided crossings are in fact associated with non-symmetry related conical intersections. Diabatic potential energy and transition dipole moment surfaces are created from the computed ab initio adiabatic MRCI energies and transition dipole moments. The transition dipole moment connecting the ground electronic state to the diabatic B state surface is by far the strongest. Vibrational-rotational wavefunctions and energies are computed using the ground electronic state. The energy level separations compare well with experimentally determined values. The ground vibrational state wavefunction is then used, together with the diabatic B<--X transition dipole moment surface, to form an initial wavepacket. The analysis of the time-dependent quantum dynamics of this wavepacket provides the total and partial photodissociation cross sections for the system. Both the total absorption cross section and the predicted product quantum state distributions compare well with experimental observations. A discussion is also given as to how the observed alternation in product diatom rotational state populations might be explained.