Moduli of (1, 7)–Polarized Abelian Surfaces via Syzygies

We prove that the moduli space X(1,7) of (1,7)–polarized abelian surfaces with canonical level–structure is birational to the Fano 3–fold V₂₂ of polar hexagons of the Klein quartic (7). In particular X(1,7) is rational and the birational map to ℙ³ is defined over ℚ. As a byproduct we obtain explicitely the equations of the (1,7)–very–ample–polarized abelian surfaces embedded in ℙ⁶.     

Asymmetric magnetization reversal on exchange biased CoO/Co bilayers

We study magnetic hysteresis loops after field cooling of a CoO/Co bilayer by MOKE and polarized neutron reflectivity. The neutron scattering reveals that the first magnetization reversal after field cooling is dominated by domain wall movement, whereas all subsequent reversals proceed essentially by rotation of the magnetization. In addition, off-specular diffuse scattering indicates that the first magnetization reversal induces an irreversible change of the domain state in the antiferromagnet.     

Mass distributions of two-dimensional extreme-value copulas and related results

Working with Markov kernels (conditional distributions) and right-hand derivatives D ⁺ A of Pickands dependence functions A we study the way two-dimensional extreme-value copulas (EVCs) C _A distribute mass. Underlining the usefulness of working directly with D ⁺ A, we give first an alternative simple proof of the fact that EVCs with piecewise linear A can be expressed as weighted geometric mean of some EVCs whose dependence functions A have at most two edges and present a generalization of this result. After showing that the discrete component of the Markov kernel of C _A concentrates its mass on the graphs of some increasing homeomorphisms f _t , we determine which EVC assigns maximum mass to the union of the graphs of \(f_{t_{1}},\ldots ,f_{t_{N}}\), derive the absolutely continuous component of an arbitrary EVC C _A and deduce that the minimum copula M is the only (purely) singular EVC. Additionally, we prove the existence of EVCs C _A which, despite their simple analytic form, exhibit the following surprisingly singular behavior: the discrete, the absolutely continuous and the singular component of the Lebesgue decomposition of the Markov kernel \(K_{C_{A}}(x,\cdot )\) of C _A have full support [0,1] for every x∈[0,1].     

Five-dimensional incommensurate structure of the melilite electrolyte [CaNd]2[Ga]2[Ga2O7]2

Melilite-type gallium oxides are potential intermediate temperature electrolytes for solid oxide fuel cells. Single crystals of [CaNd](2)[Ga](2)[Ga(2)O(7)](2) grown using an optical floating zone furnace have been investigated using transmission electron microscopy and powder and single-crystal X-ray diffraction. The anion array topologically conforms to a [(3.5.4.5)(2), 3.5.3.5] network that contains distorted pentagonal tunnels. The distortion is necessary to achieve space filling and accommodate structural misfit between the layers. Satisfactory bond lengths and angles are obtained through two-dimensional modulation in the tetragonal based plane, leading to five-dimensional symmetry in the superspace group P(4?)2(1)m(α,α,0)00s((a?)a,0)000, α = 0.2319(2), with modulation vectors q(1) = α(a* + b*) and q(2) = α(-a* + b*). Both displacive and occupational modulations are found. Through this mechanism, melilites are primed to accommodate mobile oxygen interstitials, suggesting a rational approach to crystallochemical tailoring that will enhance ionic diffusion and optimize electrolyte performance.     

Annular tautomerism: experimental observations and quantum mechanics calculations

The use of MP2 level quantum mechanical (QM) calculations on isolated heteroaromatic ring systems for the prediction of the tautomeric propensities of whole molecules in a crystalline environment was examined. A Polarisable Continuum Model was used in the calculations to account for environment effects on the tautomeric relative stabilities. The calculated relative energies of tautomers were compared to relative abundances within the Cambridge Structural Database (CSD) and the Protein Data Bank (PDB). The work was focussed on 84 annular tautomeric forms of 34 common ring systems. Good agreement was found between the calculations and the experimental data even if the quantity of these data was limited in many cases. The QM results were compared to those produced by much faster semiempirical calculations. In a search for other sources of the useful experimental data, the relative numbers of known compounds in which prototropic positions were often substituted by heavy atoms were also analysed. A scheme which groups all annular tautomeric transformations into 10 classes was developed. The scheme was designed to encompass a comprehensive set of known and theoretically possible tautomeric ring systems generated as part of a previous study. General trends across analogous ring systems were detected as a result. The calculations and statistics collected on crystallographic data as well as the general trends observed should be useful for the better modelling of annular tautomerism in the applications such as computer-aided drug design, small molecule crystal structure prediction, the naming of compounds and the interpretation of protein—small molecule crystal structures.     

Determination of the individual specific heat capacities of solids from multi-component powder mixtures and polymorphic mixtures

This study describes a method to determine the specific heat capacities of individual solids from multi-component solid mixtures. To achieve this end, powder X-ray diffraction measurements are used to provide information on the number and identity of constituents as well as their compositions while calorimetry measurements give the specific heat capacities of the bulk solid mixtures. The method is applied to investigate three different solid mixture systems, namely (i) ternary organic mixtures containing α-glycine, α-lactose monohydrate, and paracetamol; (ii) ternary inorganic mixtures containing calcium fluoride, titanium nitride, and tungsten carbide; and (iii) polymorphic mixtures of α- and γ-glycine. All systems are investigated at 298.15 K and at atmospheric pressure. The results show that the specific heat capacities of individual solids determined from multi-component solid mixtures are in good agreement with those directly determined from pure solid compounds.     

Oxygen‐Initiated Stereoselective Thermal Isomerisation of a Cyclobutane Derivative in the Solid State

Solid‐state [2+2] photochemical cycloaddition reactions have been extensively studied after the classical work of Schmidt in the 1960s. Of these, trans‐1,2‐bis(4′‐pyridyl)ethylene (bpe) is one of the well‐studied alkenes to synthesize tetrakis(4‐pyridyl)cyclobutane (tpcb). However, almost all the solid‐state [2+2] cycloaddition reactions of bpe yielded, almost exclusively, one of the four possible isomers, namely, the rctt‐tpcb (r=regio c=cis and t=trans). Here we describe a stereoselective synthesis of the tetrahedrally disposed rtct‐tpcb by the solid‐state thermal isomerization of the rctt‐isomer in atmospheric air. We propose that this isomerization occurs through a topochemical unimolecular mechanism by a radical chain pathway, initiated by molecular oxygen. This is supported by the nature of products formed in air and nitrogen, detection of a radical in ESR spectral studies, ESI‐MS crossover experiments, VT PXRD studies along with QM, MD and docking calculations. The formation of a unique isomer by thermal isomerization may be a general phenomenon to quantitatively synthesize other useful stereoisomers from the existing isomers of cyclobutane derivatives.     

Investigation of the chiral structure of the Y/Dy multilayer system by the method of the small-angle scattering of polarized neutrons

The magnetic spiral structure of a Y/Dy sample has been investigated for temperatures from 30 to 190 K by the method of the small-angle scattering of polarized neutrons. The sample is a sequence of layers Y_50nm [Dy_4.3nm /Y_2.8nm ]₃₅₀/Y_234nm /Nd_200nm Al₂O₃ (substrate) that is grown as a single crystal with the [001] axis of the hexagonal lattice, which is perpendicular to the layer plane. The experiments demonstrate the appearance of the magnetic peak below T _N = 165.4 K, which is associated with the helicoidal phase, and the helicoid coherence length is larger than the layer thickness of the Y/Dy layer. The use of polarized neutrons allows the separation of the polarization-independent and polarization-independent components of magnetic scattering. The polarization-independent component of the magnetic neutron cross section is proportional to magnetization squared 〈S _Z 〉², whereas the polarization-dependent component is proportional to the average chirality of the system 〈C〉 = 〈[·S ₁ × S ₂]〉. The critical exponents β_C = 1.02(1) and β = 0.39(1) have been determined for the average chirality and magnetization, respectively. The magnetization critical exponent β for Dy/Y coincides with the exponent obtained for Dy bulk samples. The difference β_C ? 2β = 0.24(2) shows that the chirality can be a component of the order parameter that is independent of magnetization. This experiment corroborates the results that were obtained for the critical chirality in Ho and were reported in Phys. Rev. B 64, 100402(R) (2001).     

Geometry and Algebra of Prime Fano 3-folds of Genus 12

The connection between these Fano 3-folds and plane quartic curves is explained.