Electrochemical mass spectrometric studies on 1-cyclopropyl-4-phenyl-1,2,3,6-tetrahydropyridine

Mechanistic studies on chemical and biological one-electron oxidations of cyclic tertiary allylamines are being pursued with the aid of an electrochemical-electrospray ionization mass spectrometric based assay. The results of previous studies on the electrochemical oxidation of 1-cyclopropyl-4-phenyl-1,2,3,6-tetrahydropyridine have documented a two-electron oxidative N-decyclopropylation pathway. The present paper describes the characterization of a second pathway involving an overall four-electron oxidation of this cyclopropylamine. The results document more completely the fate of cyclopropylaminyl radical cations that are thought to be intermediates in enzyme-catalyzed oxidations of aminyl substrates and that may lead to chemically reactive metabolites.     

Improved measurement of the hydrogen 1S-2S transition frequency

We have measured the 1S-2S transition frequency in atomic hydrogen via two-photon spectroscopy on a 5.8 K atomic beam. We obtain f(1S-2S) = 2,466,061,413,187,035 (10) Hz for the hyperfine centroid, in agreement with, but 3.3 times better than the previous result [M. Fischer et al., Phys. Rev. Lett. 92, 230802 (2004)]. The improvement to a fractional frequency uncertainty of 4.2 × 10(-15) arises mainly from an improved stability of the spectroscopy laser, and a better determination of the main systematic uncertainties, namely, the second order Doppler and ac and dc Stark shifts. The probe laser frequency was phase coherently linked to the mobile cesium fountain clock FOM via a frequency comb.     

Pointwise gradient estimates of solutions to onedimensional nonlinear parabolic equations

We present here an improved version of the method introduced by the first author to derive pointwise gradient estimates for the solutions of one-dimensional parabolic problems. After considering a general qualinear equation in divergence form we apply the method to the case of a nonlinear diffusion-convection equation. The conclusions are stated first for classical solutions and then for generalized and mild solutions. In the case of unbounded initial datum we obtain several regularizing effects for t > 0. Some unilateral pointwise gradient estimates are also obtained. The case of the Dirichlet problem is also considered. Finally, we collect, in the last section, several comments showing the connections among these estimates and the study of the free boundaries associated to the solutions of the diffusion-convection equation.     

Waveguide electro-optic modulator in fused silica fabricated by femtosecond laser direct writing and thermal poling

An integrated electro-optic waveguide modulator is demonstrated in bulk fused silica. A Mach-Zehnder interferometer waveguide structure is fabricated by direct writing with a femtosecond laser followed by thermal poling. A 20 degrees electro-optic phase shift is achieved at an operating wavelength of 1.55 microm with an applied voltage of 400 V and an interaction length of 25.6 mm, which correspond to an estimated effective electro-optic coefficient of 0.17 pm/V for the TE-polarized mode.     

Optimality of a Threshold Policy in theM/M/ queue with repeated vacations

Consider anM/M/1 queueing system with server vacations where the server is turned off as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding cost ofh per unit of time and per customer in the system and a fixed cost of each time the server is turned on. We show that there exists a threshold policy that minimizes the long-run average cost criterion. The approach we use was first proposed in Blanc et al. (1990) and enables us to determine explicitly the optimal threshold and the optimal long-run average cost in terms of the model parameters.     

Structure and white luminescence of Eu-activated (Ba,Sr)(13-x)Al(22-2x)Si(10+2x)O66 materials

The optical properties of Eu-activated (Ba,Sr)(13-x)Al(22-2x)Si(10+2x)O66 materials have been determined after the structural reinvestigation of the hypothetical Ba 13Al 22Si 10O 66 material on the basis of the Gebert's model. The white fluorescence and phosphorescence of the (Ba,Sr)(13-x)Al(22-2x)Si(10+2x)O66:Eu series result from the existence of two broad emission bands associated with (8)H-4f(6)5d(1)-->(8)S-4f(7) transitions peaking at 534 and 438 nm, the intensities of which may be tuned at room temperature via the control of the europium concentration and the substitution of Sr for Ba. This suggests the possibility to adjust the emission of the material to white LED requisites.     

Equations du type de Monge-Ampère sur les variétés Riemanniennes compactes,III

Let (V_n, g) be a C^∞ compact Riemannian manifold without boundary. Given the following changes of metric: $\text{g′}{}_{\mathrm{?}}{}^{\mathrm{\pm }}\text{= g +}\text{Hess}\text{? ±}\text{l}\text{α}{}^2\text{(▽ ? ? ▽?),}\text{g}\text{?}{}^{\mathrm{\pm }}\text{= ±?g + α}{}^2\text{Hess}\text{?}$, where a is a fixed constant, we study the corresponding Monge-Ampère equations (1)^±$\text{Log}\text{(¦g′}{}_{\mathrm{?}}{}^{\mathrm{\pm }}\text{¦ ¦g¦}{}^{\mathrm{?1}}\text{) = F(P,▽?;?)}$, (2)^±$\text{Log}\text{(¦}\text{g}\text{?}{}_{\mathrm{?}}{}^{\mathrm{\pm }}\text{¦ ¦g¦}{}^{\mathrm{?1}}\text{) = F(P, ▽?; ?)}$. We first solve Eq. (2)^?, under some simple assumptions on F?C^∞. Then, using an appropriate change of functions that enables us to take advantage of the estimates just carried out for Eq. (2)^?, we extend to Eq.(1)^? all the results proved in our previous articles [5, 6] for the usual Monge-Ampère equation. Although equation (2)⁺ is not locally invertible, and does not even admit a solution for all $\text{F = λ? + ?, λ > 0, f ? C}{}^{\mathrm{\infty }}\text{(V}{}_{\mathrm{n}}\text{)}$, a similar change of functions leads to partial results about Eq. (1)⁺, via C² and C³ estimates for Eq. (2)⁺. Eventually we give some comments and errata of our previous article (P. Delanoë, J. Funct. Anal.41 (1981), 341–353).     

Combined ab initio and classical molecular dynamics simulations of alkyl-lithium aggregates in ethereal solutions

Molecular dynamics simulations of organolithium aggregates in solution are reported for the first time. We use a combined quantum/classical force field (the so-called QM/MM approach) and study ethyl-lithium aggregates in dimethyl ether (DME) solvent. The solutes are described at the Density Functional Theory level while solvent molecules are described using molecular mechanics. NVT Molecular Dynamics simulations at 200 K are carried out in the Born–Oppenheimer approximation. After equilibration, the production phase was run for 80 ps (monomer), 40 ps (dimer) and 26 ps (tetramer). The analysis of the results focuses on Li coordination as a function of aggregate size and we show that the total Li coordination number is always 4. No decoordination has been observed along the simulations. Fluctuations of the structures are predicted to be large in some cases and possible implications on reactivity are discussed.     

A joint theoretical and experimental investigation on the 13C and 1H NMR chemical shifts of coumarin derivatives

¹H and ¹³C NMR chemical shifts of coumarin derivatives have been determined using first principles approaches with and without accounting for the effects of the solvent and compared to experiment in order to assess their reliability. Good linear relationships are obtained between theory and experiment, which allows correcting the calculated values for systematic errors. This is particularly the case when using the PCM scheme to model the solvent effects because the δ values larger than 150 ppm are more difficult to reproduce. The final accuracy of the method amounts to about 1 ppm for ¹³C and 0.05 ppm for ¹H.