Expected Reflection Distance in G(r, 1, n) after a Fixed Number of Reflections

Extending to r > 1 a formula of the authors, we compute the expected reflection distance of a product of t random reflections in the complex reflection group G(r, 1, n). The result relies on an explicit decomposition of the reflection distance function into irreducible G(r, 1, n)-characters and on the eigenvalues of certain adjacency matrices.Received December 8, 2003     

Crystallization of Arthrobacter sp. strain 1C N-(1-D-carboxyethyl)-L-norvaline dehydrogenase and its complex with NAD+

The novel NAD+-linked opine dehydrogenase from a soil isolate Arthrobacter sp. strain 1C belongs to an enzyme superfamily whose members exhibit quite diverse substrate specificites. Crystals of this opine dehydrogenase, obtained in the presence or absence of co-factor and substrates, have been shown to diffract to beyond 1.8 ? resolution. X-ray precession photographs have established that the crystals belong to space group P21212, with cell parameters a = 104.9, b = 80.0, c = 45.5 ? and a single subunit in the asymmetric unit. The elucidation of the three-dimensional structure of this enzyme will provide a structural framework for this novel class of dehydrogenases to enable a comparison to be made with other enzyme families and also as the basis for mutagenesis experiments directed towards the production of natural and synthetic opine-type compounds containing two chiral centres.     

Compromising Science by Ignorant Instrument Calibration—Need to Revisit Half a Century of Published XPS Data

X‐ray photoelectron spectroscopy (XPS) is an indispensable technique in modern materials science for the determination of chemical bonding as evidenced by more than 10 000 XPS papers published annually. A literature survey reveals that in the vast majority of cases an incorrect referencing of the binding energy scale is used, neglecting warnings that have been formulated from the early days of the technique. Consequences for the data reliability are disastrous and decades of XPS work require revisiting. The purpose of this Viewpoint is to highlight the existing problems, review the criticism and suggest ways forward.     

Fixed points of involutive automorphisms of the Bruhat order

Applying a classical theorem of Smith, we show that the poset property of being Gorenstein^* over Z₂ is inherited by the subposet of fixed points under an involutive poset automorphism. As an application, we prove that every interval in the Bruhat order on (twisted) involutions in an arbitrary Coxeter group has this property, and we find the rank function. This implies results conjectured by F. Incitti. We also show that the Bruhat order on the fixed points of an involutive automorphism induced by a Coxeter graph automorphism is isomorphic to the Bruhat order on the fixed subgroup viewed as a Coxeter group in its own right.     

Time-resolved spectroscopy of freestanding GaN layers grown by halide vapour phase epitaxy

Freestanding GaN layers of various thicknesses grown by HVPE have been studied by time-resolved spectroscopy combined with structural and electrical measurements. We have observed an increase of the PL lifetime with increasing layer thickness; however, a saturation of the recombination times has been detected for the GaN layers thicker than 400 μm. We explain the observed thickness-dependent behavior of the decay times by competition of two nonradiative mechanisms; namely, for layers with thickness less than 400 μm the main nonradiative channel is related to the structural defects, while in thicker layers the recombination decay time is limited by impurities and/or vacancies.     

Pattern avoidance and Boolean elements in the Bruhat order on involutions

We show that the principal order ideal of an element w in the Bruhat order on involutions in a symmetric group is a Boolean lattice if and only if w avoids the patterns 4321, 45312 and 456123. Similar criteria for signed permutations are also stated. Involutions with this property are enumerated with respect to natural statistics. In this context, a bijective correspondence with certain Motzkin paths is demonstrated. This article is largely based on results from the second author’s M.Sc. thesis [15].     

Electronic structure and chemical bonding of amorphous chromium carbide thin films

The microstructure, electronic structure and chemical bonding of chromium carbide thin films with different carbon contents have been investigated with high-resolution transmission electron microscopy, electron energy loss spectroscopy and soft x-ray absorption-emission spectroscopies. Most of the films can be described as amorphous nanocomposites with non-crystalline CrC(x) in an amorphous carbon matrix. At high carbon contents, graphene-like structures are formed in the amorphous carbon matrix. At 47 at.% carbon content, randomly oriented nanocrystallites are formed creating a complex microstructure of three components. The soft x-ray absorption-emission study shows additional peak structures exhibiting non-octahedral coordination and bonding.     

Growth and characterization of epitaxial Ti3GeC2 thin films on 4H-SiC(0001)

Epitaxial Ti₃GeC₂ thin films were deposited on 4° off-cut 4H-SiC(0001) using magnetron sputtering from high purity Ti, C, and Ge targets. Scanning electron microscopy and helium ion microscopy show that the Ti₃GeC₂ films grow by lateral step-flow with {112?0} faceting on the SiC surface. Using elastic recoil detection analysis, atomic force microscopy, and X-Ray diffraction the films were found to be substoichiometric in Ge with the presence of small Ge particles at the surface of the film.     

Phase stability of Crn+ 1GaCn MAX phases from first principles and Cr2GaC thin‐film synthesis using magnetron sputtering from elemental targets

Ab‐initio calculations have been used to investigate the phase stability and magnetic state of Cr_{n+ 1}GaC_n MAX phase. Cr₂GaC (n = 1) was predicted to be stable, with a ground state corresponding to an antiferromagnetic spin configuration. Thin‐film synthesis by magnetron sputtering from elemental targets, including liquid Ga, shows the formation of Cr₂GaC, previously only attained from bulk synthesis methods. The films were deposited at 650 °C on MgO(111) substrates. X‐ray diffraction and high‐resolution transmission electron microscopy show epitaxial growth of (000?) MAX phase. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Combinatorial invariance of Kazhdan–Lusztig–Vogan polynomials for fixed point free involutions

When \(\mathrm {Sp}(2n,\mathbb {C})\) acts on the flag variety of \(\mathrm {SL}(2n,\mathbb {C})\), the orbits are in bijection with fixed point free involutions in the symmetric group \(S_{2n}\). In this case, the associated Kazhdan–Lusztig–Vogan polynomials \(P_{v,u}\) can be indexed by pairs of fixed point free involutions \(v\ge u\), where \(\ge \) denotes the Bruhat order on \(S_{2n}\). We prove that these polynomials are combinatorial invariants in the sense that if \(f:[u,w_0]\rightarrow [u',w_0]\) is a poset isomorphism of upper intervals in the Bruhat order on fixed point free involutions, then \(P_{v,u} = P_{f(v),u'}\) for all \(v\ge u\).