Valence Delocalization in Prussian Blue Fe[FeII(CN)6]3 · XD2O,by Polarized Neutron Diffraction

Polarized neutron diffraction has been used to investigate the spin delocalization from the high-spin Fe(III) sites to the low-spin Fe(II) in deuteriated Prussian Blue, Fe₄[Fe(CN)₆]₃ · xD₂O. Measurements of the 111, 200, and 400 reflections were made on a powdered sample at 3 K and 4.8 T using a neutron wavelength of 1.074 Å. The expectation value of S at the Fe(II) site is - 0.008 ± 0.028 corresponding to an upper limit of about 5% of an electron for the spin delocalization.     

Bildung siliciumorganischer Verbindungen. 80. Die Si-Metallierung von 1,3,5-Trisilacyclohexanen mit Übergangsmetallkomplexen

Formation of Organosilicon Compounds. 80. Si-Metalation of 1,3,5-Trisilacyclohexanes by Means of Trisition Metal Complexes Several Si-transition metal-substituted 1,3,5-trisilacyclohexanes are reported. l-Bromo-1,3,5-trisilacyclohexane reacts with the metal carbonyl anions W(CO)₅cp^?, Mo(CO)₃cp-, Cr(CO)₃cp^?, Mn(CO)₃^?, Fe(CO)₂cp^?, or Co(CO)_4minus;, resp., yielding monosubstituted derivatives as 6, e. g.(cp = π-cyclopentadienyl). 1,3-Dibromo-1,3,5-trisilacyclohexane forms disubstituted compounds aa 7, e. g., with 2 moles of the metal carbonyl anions Fe(CO)₂cp^?, Mn(CO)₅^? or Co(CO)₄^?. Starting from (H₂c? SiHBr)₃ compound 13 is accessible by reaction with KCo(CO)₄. In the soluted compounds the metal carbonyl groups occupy the equatorial positions in the chair form of the six membered ring. The reaction of 13 with Co₂(CO)₈ yields 17 , whereas 6 preferrably forms 18 . Starting from (H₂C? SiH₂)3 the reaction with Co₂(CO)₂ preferrably yields 19. The reported compounds are crystalline, air – and moisture – sensitive. The reported formulae are assured by analysis, IR, and NMR investigations.     

A criterion for Hill operators to be spectral operators of scalar type

We derive necessary and sufficient conditions for a Hill operator (i.e., a one-dimensional periodic Schrö dinger operator) H = ?d ² /dx ² + V to be a spectral operator of scalar type. The conditions show the remarkable fact that the property of a Hill operator being a spectral operator is independent of smoothness (or even analyticity) properties of the potential V. In the course of our analysis, we also establish a functional model for periodic Schrödinger operators that are spectral operators of scalar type and develop the corresponding eigenfunction expansion.The problem of deciding which Hill operators are spectral operators of scalar type appears to have been open for about 40 years.     

Linear Representations of the Automorphism Group of a Free Group

Let F _n be the free group on n ≥ 2 elements and Aut(F _n ) its group of automorphisms. In this paper we present a rich collection of linear representations of Aut(F _n ) arising through the action of finite-index subgroups of it on relation modules of finite quotient groups of F _n . We show (under certain conditions) that the images of our representations are arithmetic groups. Received: November 2006, Accepted: March 2007     

Enclosure of the Zero Set of Multivariate Exponential Interval Polynomials

The zero set of one general multivariate exponential polynomial with interval coefficients is enclosed by unions and intersections of closed half-spaces. Tighter enclosures are derived in the bivariate case. Common zeros of polynomial systems can be located by an appropriate intersection of these enclosure sets in an appropriate space. The resulting domains are directly brought into polynomial equation solvers.     

Landslide generated impulse waves. 2. Hydrodynamic impact craters

Landslide generated impulse waves were investigated in a two-dimensional physical laboratory model based on the generalized Froude similarity. Digital particle image velocimetry (PIV) was applied to the landslide impact and wave generation. Areas of interest up to 0.8 m by 0.8 m were investigated. PIV provided instantaneous velocity vector fields in a large area of interest and gave insight into the kinematics of the wave generation process. Differential estimates such as vorticity, divergence, and elongational and shear strain were extracted from the velocity vector fields. At high impact velocities flow separation occurred on the slide shoulder resulting in a hydrodynamic impact crater, whereas at low impact velocities no flow detachment was observed. The hydrodynamic impact craters may be distinguished into outward and backward collapsing impact craters. The maximum crater volume, which corresponds to the water displacement volume, exceeded the landslide volume by up to an order of magnitude. The water displacement caused by the landslide generated the first wave crest and the collapse of the air cavity followed by a run-up along the slide ramp issued the second wave crest. The extracted water displacement curves may replace the complex wave generation process in numerical models. The water displacement and displacement rate were described by multiple regressions of the following three dimensionless quantities: the slide Froude number, the relative slide volume, and the relative slide thickness. The slide Froude number was identified as the dominant parameter.List of symbols a wave amplitude (L) - b slide width (L) - c wave celerity (LT^–1) - d _g granulate grain diameter (L) - d _p seeding particle diameter (L) - F slide Froude number - g gravitational acceleration (LT^–2) - h stillwater depth (L) - H wave height (L) - l _s slide length (L) - L wave length (L) - M magnification - m _s slide mass (M) - n _por slide porosity - Q _d water displacement rate (L³) - Q _D maximum water displacement rate (L³) - Q _s maximum slide displacement rate - s slide thickness (L) - S relative slide thickness - t time after impact (T) - t _D time of maximum water displacement volume (L³) - t _qD time of maximum water displacement rate (L³) - t _si slide impact duration (T) - t _sd duration of subaqueous slide motion (T) - T wave period (T) - v velocity (LT^–1) - v _p particle velocity (LT^–1) - v _px streamwise horizontal component of particle velocity (LT^–1) - v _pz vertical component of particle velocity (LT^–1) - v _s slide centroid velocity at impact (LT^–1) - V dimensionless slide volume - V _d water displacement volume (L³) - V _D maximum water displacement volume (L³) - V _s slide volume (L³) - x streamwise coordinate (L) - z vertical coordinate (L) - slide impact angle (°) - bed friction angle (°) - x mean particle image x-displacement in interrogation window (L) - _x random displacement x error (L) - _tot total random velocity v error (LT^–1) - _xx streamwise horizontal elongational strain component (1/T) - _xz shear strain component (1/T) - _zx shear strain component (1/T) - _zz vertical elongational strain component (1/T) - water surface displacement (L) - density (ML^–3) - _g granulate density (ML^–3) - _p particle density (ML^–3) - _s mean slide density (ML^–3) - _w water density (ML^–3) - granulate internal friction angle (°) - _y vorticity vector component (out-of-plane) (1/T)     

Topological insulators in magnetic fields: quantum Hall effect and edge channels with a nonquantized θ term

We investigate how a magnetic field induces one-dimensional edge channels when the two-dimensional surface states of three-dimensional topological insulators become gapped. The Hall effect, measured by contacting those channels, remains quantized even in situations where the θ term in the bulk and the associated surface Hall conductivities, σ(xy)(S), are not quantized due to the breaking of time-reversal symmetry. The quantization arises as the θ term changes by ±2πn along a loop around n edge channels. Model calculations show how an interplay of orbital and Zeeman effects leads to quantum Hall transitions, where channels get redistributed along the edges of the crystal. The network of edges opens new possibilities to investigate the coupling of edge channels.     

Whole-body T2* mapping at 1.5 T

This study investigated the feasibility of an MRI protocol providing whole-body T2* maps at 1.5 T. Seven healthy volunteers (mean age=30.1+/-3.7, three women and four men) and two patients (both male, 53 and 46 years old) affected by transfusion-dependent anemias participated in the study. Coronally oriented images of five subsequent body levels were acquired using a fat-suppressed multiecho 2D gradient-echo sequence (12 echo times ranging from 4.8 to 76.3 ms were selected) and afterwards composed. Parametrical T2* maps of the whole body were reconstructed on a pixel-by-pixel basis. For both, healthy volunteers and patients, representative T2* values were computed from extended regions of interest (ROIs). Good-quality whole-body T2* maps were computed in all volunteers and patients. In healthy volunteers, T2* values were assessed in the cerebral white (58.5+/-4.2 ms) and gray (81.4+/-5.5 ms) matter, liver (34.3+/-7.0 ms), spleen (63.5+/-3.3 ms), kidneys (65.4+/-10.3 ms) and skeletal muscles (~30 ms). The liver presented faster relaxation rates in males as compared to females. One patient (serum ferritin concentration=927 microg/dl) showed shortened T2* values in liver (3.6+/-5.5 ms), spleen (3.1+/-4.8 ms), kidneys (11.1+/-7.1 ms) and muscles (25.1+/-3.4 ms). The second patient (serum ferritin concentration=346 microg/dl) presented reduced T2* values in liver (3.9+/-7.3 ms), spleen (20.1+/-9.8 ms) and kidneys (24.6+/-7.7 ms). The presented technique may find clinical application in the assessment of the iron burden in the entire body, and in monitoring of chelation therapies in patients treated with frequent blood transfusions.