Oxygen rearrangement of molecular ions of 3-phenylpropionates

The oxygen rearrangement in molecular ions of 3-phenylpropionates has been investigated with the aid of mass analyzed ion kinetic energy spectra. Elimination of an allyl radical followed by expulsion of ketene from the molecular ion of allyl 3-phenylpropionate is shown to result in formation of protonated benzaldehyde. The oxygen rearrangement has been found to be inoperative in ionized methyl 3-methyl-3-phenylbutyrate. [M ? CH₃ ? CH₂CO]⁺ ions in the spectrum of the latter compound are formed by elimination of the 3-methyl substituent and subsequent methoxy migration.     

Synthesis and properties of a novel family of fluorous triphenylphosphine derivatives

A novel approach to the preparation of perfluorotail-functionalized triarylphosphines using a p-silyl substituent as the branching point has been developed. This approach enabled the attachment of between three and nine perfluorotails per phosphorus atom, resulting in the production of highly fluorous tris[p-(1H,1H,2H, 2H-perfluoroalkylsilyl)aryl]phosphines, P[C(6)H(4)-p-SiMe(3)(-)(n)()(CH(2)CH(2)C(x)()F(2)(x)()(+1))(n)()](3) (n = 1, 2, 3; x = 6, 8), containing between 50 and 67 wt % fluorine. (31)P NMR studies indicate that the phosphorus atoms, and consequently the sigma-donor and pi-acceptor properties of these phosphines, are not influenced by the electron-withdrawing perfluoroalkyltails. The fluorous triarylphosphines are readily soluble in fluorous solvents and display fluorous phase preference in several fluorous biphasic systems. The phase partitioning of these fluorous ligands, as well as their donor properties, is discussed in relation to their potential for fluorous biphasic catalyst separation.     

Magnetic structure of Fe−Si−Al films implanted with Al and N ions

Changes in the magnetic structure of Fe–Si–Al films due to Al and N ion implantation were studied by⁵⁷Fe Conversion Electron Mössbauer Spectrometry (CEMS). The peaks of the magnetic sextets due to the crystalline films became broader by implantation with 5×10¹⁶ Al/cm², suggesting the formation of amorphous phases. In the CEM spectrum of one sample with large grains implanted with 1×10¹⁷ Al/cm² a crystalline -Fe phase appeared. N implantation with the same dose did not amorphize the sample but the components with high magnetic hyperfine fields were enhanced.     

Electrostatic lattice coefficients and binding energy of orthorhombic La2-x Sr x CuO4

Three valency models for orthorhombic La_2-x Sr _x CuO₄ were investigated for increasing Sr concentrationsx (0x0.21): 1. Cu²⁺Cu³⁺, 2. apex O^2–O^– and 3. in-plane O^2–O^–. All calculations were done by using structural parameters valid for the temperature range from 10 to 22 K. We thereby calculated the electrostatic interaction energy which, next to ionization potentials and electron affinities, comprises a major of the binding energyE _B of crystals. Second-order effects were accounted for by calculating the strength of ionic dipole moments induced by crystal electric fields at relevant lattice sites. Their largest strengths are comparable to the dipole moment of the water molecule. Three out of five dipoles in La_2-x Sr _x CuO₄ vanish during the transition from the orthorhombic to the tetragonal phase. The binding energy differences between the different models suggest that the system is in a state of model 1. However, the differences are very small, being in the order of 0.3 to 0.76 eV atx=0.13.     

The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family

We here consider testing the hypothesis ofhomogeneity against the alternative of a two-component mixture of densities. The paper focuses on the asymptotic null distribution of 2 log _n , where _n is the likelihood ratio statistic. The main result, obtained by simulation, is that its limiting distribution appears pivotal (in the sense of constant percentiles over the unknown parameter), but model specific (differs if the model is changed from Poisson to normal, say), and is not at all well approximated by the conventional ₍₂₎ ² -distribution obtained by counting parameters. In Section 3, the binomial with sample size parameter 2 is considered. Via a simple geometric characterization the case for which the likelihood ratio is 1 can easily be identified and the corresponding probability is found. Closed form expressions for the likelihood ratio _n are possible and the asymptotic distribution of 2 log _n is shown to be the mixture giving equal weights to the one point distribution with all its mass equal to zero and the ²-distribution with 1 degree of freedom. A similar result is reached in Section 4 for the Poisson with a small parameter value (0.1), although the geometric characterization is different. In Section 5 we consider the Poisson case in full generality. There is still a positive asymptotic probability that the likelihood ratio is 1. The upper precentiles of the null distribution of 2 log _n are found by simulation for various populations and shown to be nearly independent of the population parameter, and approximately equal to the (1–2)100 percentiles of ₍₁₎ ² . In Sections 6 and 7, we close with a study of two continuous densities, theexponential and thenormal with known variance. In these models the asymptotic distribution of 2 log _n is pivotal. Selected (1–) 100 percentiles are presented and shown to differ between the two models.     

On the integrated density of states for crystals with randomly distributed impurities

In the present paper, we discuss spectral properties of a periodic Schrödinger operator which is perturbed by randomly distributed impurities; such operators occur as simple models for crystals (or semi-conductors) with impurities. While the spectrum itself is independent of the concentrationp of impurities, for 0<p<1, we focus our attention on the limiting behavior of the integrated density of states _p of the random Schrödinger operator, inside a spectral gap of the periodic operator, asp0. Denoting byU ₀ the set of eigenvalues (in the gap) of the reference problem having precisely one impurity (located at the origin, say), we show that the integrated density of states concentrates around the points ofU ₀, in the sense that _p (U ) is of orderp, for any fixed -neighborhoodU ofU ₀, while _p (K)C·p ², for any compact subsetK of the gap which does not intersectU .Research partially supported by Deutsche Forschungsgemeinschaft