1H and 13C NMR of platinum porphyrins—III. Platinum deuteroporphyrin IX dimethyl ester

¹H and ¹³C NMR spectra of the title compound are reported and peaks assigned by comparison with the free-base porphyrin. Long-range spin—spin coupling is observed between platinum and the macrocyclic protons and carbon atoms. Meso-protons are assigned from line-broadening observed for three of the peaks, possibly caused by residual coupling of these protons to the pyrrole β-protons. Allylic coupling of the pyrrole β-protons to adjacent methyl groups is also noted, and supports the tautomeric model of an 18-atom delocalisation pathway around the macrocycle. The ¹H NMR spectrum of the title compound is more concentration-dependent than that of the free-base porphyrin and probably reflects additional macrocyclic interactions via the platinum atoms.     

Limiting distributions of homogeneous functions of sample spacings for distributions approaching the uniform distribution

Summary X ₁,...,X _n are independent random variables, identically distributed over the unit interval, with common probability density function 1 + r(x)/n for all sufficiently large n, where is a positive constant, and |r(x)| <D. V ₁, ..., V _n+1 are the sample spacings generated by X ₁,..., X _n . It is shown that in many cases, the asymptotic joint distribution of homogeneous functions of V ₁,..., V _n+1 can be found directly from the asymptotic joint distribution of homogeneous functions of independent exponential random variables.Research supported by NSF Grant GP 3783.     

Conforming finite element computations applied to a spatially periodic,harmonic Navier-Stokes problem

In this paper computations in the two dimensional case of a harmonic Navier-Stokes problem with periodic boundary conditions are presented. This study of an incompressible viscous fluid leads to a non-symmetric linear problem (very low Reynolds number). Moreover unknown functions have complex values (monochromatic dynamic behaviour). Numerical treatment of the incompressibility condition is a generalization of the classical treatment of Stokes problem. A mixed formulation, where discrete pressure plays the role of Lagrange multipliers is used (Uzawa algorithm). Two conforming finite element methods are tested on different meshes. The second one uses a classical refinement in the shape function: the so-called bulb function. All computational tests show that the use of a bulb function on each element gives better results than refinement in the mesh without introducing too many degrees of freedom. Finally numerical results are compared to experimental data.     

Rotating ring-disk electrode studies of the reaction of stable radical cations with styrene and isobutyl vinyl ether

An electroanalytical technique has been utilized in a new method for the study of reactive intermediates in polymerization reactions. A ring-disk electrode system generated persistent carbocation radicals whose stability decreased in the order: 1,3,6,8-tetraphenylpyrene (TPP), rubrene (Ru), 9,10-diphenylanthracene (DPA), and 9,10-dimethylanthracene (DMA). Radical cations from these parent compounds flowed to a collecting ring which was controlled potentiostatically to reduce unreacted cations. When styrene or isobytyl vinyl ether was added to the solution, the concentration of carbocation radicals reaching the electrode was reduced. Current collection efficiencies N were determined as a function of rotation speed ω for each monomer concentration. Plots of N^?1 as ω^?1 in the absence of monomer show no dependence on ω (indicative of stable intermediates), but a linear dependence is found with each concentration of monomer. This indicates a first-order dependence on radical cation concentration. The rate constants show a trend in cation reactivities which is in agreement with that obtained by other methods. This technique, however, extends the range of investigation to a much shorter time scale.     

A moment inequality of the Marcinkiewicz–Zygmund type for some weakly dependent random fields

The goal of this note is to give a new moment inequality for sums of some weakly dependent random fields. Our result extends moment bounds given by Wu (2007) or Liu and Lin (2009) for causal autoregressive processes and follows by using recursive applications of the Burkhölder inequality for martingales.     

Well-posedness of a degenernate parabolic equation issuing from two-dimensional perfect fluid dynamics

A degenerate parabolic equation of convection-diffusion type has been proposed by Robert and Sommeria in [12] to describe the relaxation towards statistical equilibrium states in 2D incompressible perfect fluid dynamics. The paper is concerned with the Cauchy problem for this equation. The local existence of a variational soluation is obtained in using the decrease of the (negative) mixing entropy and Schauder theorem. A smoothing effect is used when proving the uniqueness of the variational solutions by youdovitch's method. Finally, global existence of solutions and their asymptotic convergence towards Gibbs states are shown for a large class of initial data.     

Structure and properties of potassium niobato-borophosphate glasses

Bulk glasses of the series (1 ? x)[0.5K₂O–0.1B₂O₃–0.4P₂O₅]–xNb₂O₅ with x = 0–45.7 mol% Nb₂O₅ were prepared by slow cooling in air and investigated by Raman, ³¹P, and ¹¹B MAS NMR spectroscopy. The incorporation of Nb₂O₅ into the parent borophosphate glass results in a substantial increase in the glass transition temperature and chemical durability of glasses. Raman spectra showed that Nb atoms form distorted NbO₆ octahedra, which are isolated at low Nb₂O₅ content, whereas at higher Nb₂O₅ content they form clusters. ¹¹B NMR spectra of the glasses revealed the interaction between Nb₂O₅ and BO₄ tetrahedral units, which results in a partial transformation of tetrahedral BO₄ units to trigonal BO₃ units and the formation of mixed B(OP)_4?n(ONb)_n units.     

Analysis and reconstruction of a pulsed jet in crossflow by multi-plane snapshot POD

In this work, snapshot proper orthogonal decomposition (POD) is used to study a pulsed jet in crossflow where the velocity fields are extracted from stereoscopic particle image velocimetry (SPIV) results. The studied pulsed jet is characterized by a frequency f = 1 Hz, a Reynolds number Re _j  = 500 (based on the mean jet velocity ${\overline{U}_{j}}$  = 1.67 cm/s and a mean velocity ratio of R = 1). Pulsed jet and continuous jet are compared via mean velocity field trajectory and Q criterion. POD results of instantaneous, phase-averaged and fluctuating velocity fields are presented and compared in this paper. Snapshot POD applied on one plane allows us to distinguish an organization of the first spatial eigenmodes. A distinction between “natural modes” and “pulsed modes” is achieved with the results obtained by the pulsed and unforced jet. Secondly, the correlation tensor is established with four parallel planes (multi-plane snapshot POD) for the evaluation of volume spatial modes. These resulting modes are interpolated and the volume velocity field is reconstructed with a minimal number of modes for all the times of the pulsation period. These reconstructions are compared to orthogonal measurements to the transverse jet in order to validate the obtained three-dimensional velocity fields. Finally, this POD approach for the 3D flow field reconstruction from experimental data issued from planes parallel to the flow seems capable to extract relevant information from a complex three-dimensional flow and can be an alternative to tomo-PIV for large volume of measurement.