Detecting quantum states with a positive Wigner function beyond mixtures of Gaussian states

We propose a criterion giving a sufficient condition for quantum states of a harmonic oscillator not to be expressible as a convex mixture of Gaussian states. This nontrivial property is inherent to, e.g., a single-photon state and the criterion thus allows one to reveal a signature of the state even in quantum states with a positive Wigner function. The criterion relies on directly measurable photon number probabilities and enables detection of this manifestation of a single-photon state in quantum states produced by solid-state single-photon sources in a weak coupling regime.     

Solvatochromism as an efficient tool to study N,N‐dimethylamino‐ and cyano‐substituted π‐conjugated molecules with an intramolecular charge‐transfer absorption

A representative data set has been gained by the measurement of the electronic absorption spectra of 12 systematically selected push–pull systems with an intramolecular charge‐transfer (CT) absorption and the general structure D–π–A (D = donor, A = acceptor) featuring electron‐withdrawing CN groups, electron‐donating N(CH₃)₂ groups, and various π‐conjugated backbones in 32 solvents with different polarities. The longest‐wavelength absorption maxima λ_max and the corresponding wavenumbers $\tilde {v}_{{\rm max}} $ were evaluated from the UV/Vis spectra measured in 32 well‐selected solvents. The D–π–A push–pull systems were further characterized by quantum‐chemical quantities and simple structural parameters. Structure–solvatochromism relationships were evaluated by multidimensional statistic methods. Whereas solvent polarizability and solvent cavity size proved to be the most important factors affecting the position of λ_max, the solvent polarity was less important. The most important characteristics of organic CT compounds are the energy of the LUMO, the permanent dipole moment, the COSMO (COnductor‐like Screening MOdel) area, the COSMO volume, the number, and ratio of N,N‐dimethylamino and cyano groups, and eventually the number of triple bonds (π‐linkers). A relation between the first‐order polarizability α, the longest‐wavelength absorption maxima λ_max, and the structural features has also been found. The higher‐order polarizabilities β and γ are not related to the observed solvatochromism. Copyright © 2010 John Wiley & Sons, Ltd.     

Support Theorems for the Radon Transform and Cramér-Wold Theorems

This article presents extensions of the Cramér-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions imposed are sharp. The extensions build on a number of results and methods concerned with injectivity properties of the Radon transform. Using a few tools from distribution theory and Fourier analysis we show that the presented injectivity results for the Radon transform lead to Cramér-Wold type results for measures. One purpose of this article is to contribute to making known to probabilists interesting results for the Radon transform that have been developed essentially during the 1980s and 1990s.     

Palladium(II) complexes of Y,C,Y‐chelated phosphines: synthesis,structure, and catalytic activity in Suzuki–Miyaura reaction

The phosphines L¹PPh₂ (1) and L²PPh₂ (2) containing different Y,C,Y‐chelating ligands, L¹ = 2,6‐(^tBuOCH₂)₂C₆H₃^? and L² = 2,6‐(Me₂NCH₂)₂C₆H₃^?, were treated with PdCl₂ and di‐µ‐chloro‐bis[2‐[(N,N‐dimethylamino)methyl]phenyl‐C,N]‐dipalladium(II) and yielded complexes trans‐{[2,6‐(^tBuOCH₂)₂C₆H₃]PPh₂}₂PdCl₂ (3), {[2,6‐(Me₂NCH₂)₂C₆H₃]PPh₂} PdCl₂ (4), {[2,6‐(^tBuOCH₂)₂C₆H₃]PPh₂}Pd(Cl)[2‐(Me₂NCH₂)C₆H₄] (5) and {[2,6‐(Me₂NCH₂)₂C₆H₃]PPh₂}Pd(Cl)[2‐(Me₂NCH₂)C₆H₄] (6) as the result of different ability of starting phosphines 1 and 2 to complex PdCl₂. Compounds 3–6 were characterized by ¹H, ¹³C, ³¹P NMR spectroscopy and ESI‐MS. The molecular structures of 3,4 and 6 were also determined by X‐ray diffraction analysis. The catalytic activity of complexes 3–6 was evaluated in the Suzuki‐Miyaura cross‐coupling reaction. Copyright © 2010 John Wiley & Sons, Ltd.     

Air-coupled ultrasonic assessment of wood veneer

Air-coupled ultrasound (ACU) provides a tool to evaluate wood samples of small or moderate thickness (<30 mm) thereby avoiding direct contact or liquid coupling. Results of through-transmission ACU measurements on wood veneer samples and related products are reported with respect to a wide variety of quality aspects. Fluctuations in the averaged received signal levels appear to be correlated to the presence of natural or machine-induced thickness and density variations, flaws and grain damage, errors produced by the manufacturing process, insufficient bonding on a substrate, etc. In addition it is seen that the variability of the signal levels enables to distinguish between quarter and crown areas.     

Extracting metabolite ions out of a matrix background by combined mass defect,neutral loss and isotope filtration

Mass defect, neutral loss and isotope filtration techniques were applied to electrospray ionization mass spectrometry (ESI‐MS) data obtained for in vivo and in vitro samples of drug metabolism studies. A combination of these post‐acquisition processing techniques was shown to be more powerful than the use of one of these tools alone for the detection in complex matrices of metabolites of candidate drugs with a characteristic isotope pattern (e.g. containing bromine, chlorine, or a high proportion of radiolabeled drug (¹²C/¹⁴C)) or characteristic neutral losses. In combination with ‘all‐in‐one’ data acquisition this methodology is able to perform software‐driven constant neutral loss scanning for an unlimited number of mass differences at any time after analysis. Highly selective MS chromatograms were obtained with excellent correlation with their corresponding radiochromatograms. Copyright © 2009 John Wiley & Sons, Ltd.     

FT-FIR-spectrum and the ground state constants of D2CO

The ground state spectrum of the formaldehyde D₂¹³CO molecule in the range from 25 to 360 cm⁻¹ has been recorded by a Fourier transform infrared spectrometer. The quantum number limits of the assigned transitions are J = 6-54 and K_a = 0-16. The data was fitted into Watson’s A- and S-reduced Hamiltonians in I^r-representation up to eighth order. The determinable constants calculated from both reductions are compared. The standard deviation of the far infrared data is 3.0 MHz. The spectroscopic constants are also calculated to high accuracy at the CCSD(T)/cc-pVQZ level of ab initio theory and agree well with the experimental ones.