A Phosphinine-Derived 1-Phospha-7-Bora-Norbornadiene: Frustrated Lewis Pair Type Activation of Triple Bonds

Salt metathesis of 1-methyl-2,4,6-triphenylphosphacyclohexadienyl lithium and chlorobis(pentafluorophenyl)borane affords a 1-phospha-7-bora-norbornadiene derivative 2 . The C≡N triple bonds of nitriles insert into the P−B bond of 2 with concomitant C−B bond cleavage, whereas the C≡C bonds of phenylacetylenes react with 2 to form λ⁴-phosphabarrelenes. Even though 2 must formally be regarded as a classical Lewis adduct, the C≡N and C≡C activation processes observed (and the mild conditions under which they occur) are reminiscent of the reactivity of frustrated Lewis pairs. Indeed, NMR and computational studies give insight into the mechanism of the reactions and reveal the labile nature of the phosphorus–boron bond in 2 , which is also suggested by detailed NMR spectroscopic studies on this compound. Nitrile insertion is thus preceded by ring opening of the bicycle of 2 through P−B bond splitting with a low energy barrier. By contrast, the reaction with alkynes involves formation of a reactive zwitterionic methylphosphininium borate intermediate, which readily undergoes alkyne 1,4-addition.     

Tandem Use of Optical Sensing and Machine Learning for the Determination of Absolute Configuration,Enantiomeric and Diastereomeric Ratios,and Concentration of Chiral Samples

We have developed an optical method for accurate concentration, er, and dr analysis of amino alcohols based on a simple mix‐and‐measure workflow that is fully adaptable to multiwell plate technology and microscale analysis. The conversion of the four aminoindanol stereoisomers with salicylaldehyde to the corresponding Schiff base allows analysis of the dr based on a change in the UV maximum at 420 nm that is very different for the homo‐ and heterochiral diastereomers and of the concentration of the sample using a hypsochromic shift of another absorption band around 340 nm that is independent of the analyte stereochemistry. Subsequent in situ formation of Cu^II assemblies in the absence and presence of base enables quantification of the er values for each diastereomeric pair by CD analysis. Applying a linear programming method and a parameter sweep algorithm, we determined the concentration and relative amounts of each of the four stereoisomers in 20 samples of vastly different stereoisomeric compositions with an averaged absolute percent error of 1.7 %.     

An asymptotic Reissner–Mindlin plate model

A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner–Mindlin plate model.     

Time resolved spectroscopy with femtosecond soft-x-ray pulses

The most challenging application of time resolved spectroscopy is to directly observe the structural and electronic dynamics. Here we present the combination of x-ray absorption spectroscopy with laser driven x-ray sources, offering atomic spatial and temporal resolution. Our new approaches for optimization of laser driven x-ray sources resulted in the demonstration of spatially coherent sub-20 fs x-ray pulses in a range up to several keV. We excited polycrystalline silicon with an ultrashort laser pulse and characterized the collective motion of atoms with time resolved x-ray absorption spectroscopy at a temporal resolution of less than 20 fs. Finally, we have shown the feasibility of probing the dynamics of the electronic structure of silicon and carbon with near edge x-ray absorption spectroscopy.     

Multibeam volume acoustic backscatter imagery and reverberation measurements in the northeastern Gulf of Mexico

Multibeam volume acoustic backscatter imagery and reverberation measurements are derived from data collected in 200-m-deep waters in the northeastern Gulf of Mexico, with the Toroidal Volume Search Sonar (TVSS), a 68-kHz cylindrical sonar operated by the U.S. Navy's Coastal System Station. The TVSS's 360-degree vertical imaging plane allows simultaneous identification of multiple volume scattering sources and their discrimination from backscatter at the sea surface or the seafloor. This imaging capability is used to construct a three-dimensional representation of a pelagic fish school near the bottom. Scattering layers imaged in the mixed layer and upper thermocline are attributed to assemblages of epipelagic zooplankton. The fine scale patchiness of these scatterers is assessed with the two-dimensional variance spectra of vertical volume scattering strength images in the upper and middle water column. Mean volume reverberation levels exhibit a vertical directionality which is attributed to the volume scattering layers. Boundary echo sidelobe interference and reverberation is shown to be the major limitation in obtaining bioacoustic data with the TVSS. Because net tow and trawl samples were not collected with the acoustic data, the analysis presented is based upon comparison to previous biologic surveys in the northeastern Gulf of Mexico and reference to the bioacoustic literature.     

On a Question of Haskell P. Rosenthal Concerning a Characterization of c0 and lp

The following property of a normalized basis in a Banach spaceis considered: any normalized block sequence of the basis hasa subsequence equivalent to the basis. Under uniformity or othernatural assumptions, a basis with this property is equivalentto the unit vector basis of c₀ or l_p. An analogous problem concerningspreading models is also addressed. 2000 Mathematics SubjectClassification 46B20 (primary), 46B15 (secondary).     

Ground states and flux configurations of the two-dimensional Falicov-Kimball model

The Falicov-Kimball model is a lattice model of itinerant spinless fermions (electrons) interacting by an on-site potential with classical particles (ions). We continue the investigations of the crystalline ground states that appear for various filling of electrons and ions for large coupling. We investigate the model for square as well as triangular lattices. New ground states are found and the effects of a magnetic flux on the structure of the phase diagram are studied. The flux phase problem where one has to find the optimal flux configurations and the nuclei configurations is also solved in some cases. Finally we consider a model where the fermions are replaced by hard-core bosons. This model also has crystalline ground states. Therefore their existence does not require the Pauli principle, but only the on-site hard-core constraint for the itinerant particles.