On L-spaces and left-orderable fundamental groups

Examples suggest that there is a correspondence between L-spaces and three-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditions for several large classes of manifolds. In particular, we prove that they are equivalent for any closed, connected, orientable, geometric three-manifold that is non-hyperbolic, a family which includes all closed, connected, orientable Seifert fibred spaces. We also show that they are equivalent for the twofold branched covers of non-split alternating links. To do this we prove that the fundamental group of the twofold branched cover of an alternating link is left-orderable if and only if it is a trivial link with two or more components. We also show that this places strong restrictions on the representations of the fundamental group of an alternating knot complement with values in $\text{ Homeo}_+(S^1)$ .     

Investigating statistical approximations with computer graphics

This paper describes the use of interactive computer graphics software to explore the notion of the approximation of one statistical distribution by another. In particular, the authors illustrate how such programs can be used to investigate the normal approximation to the binomial distribution, the Poisson approximation to the binomial distribution, the convergence of t‐distributions to the normal distribution, and the limiting behaviour of the chi‐squared distribution. The discussions include possible methods using such programs, either in a classroom setting on a demonstration basis or on an individual student basis for independent study in a computer laboratory setting.     

Nonaqueous synthesis of TiO2 nanocrystals using TiF4 to engineer morphology, oxygen vacancy concentration, and photocatalytic activity

Control over faceting in nanocrystals (NCs) is pivotal for many applications, but most notably when investigating catalytic reactions which occur on the surfaces of nanostructures. Anatase titanium dioxide (TiO(2)) is one of the most studied photocatalysts, but the shape dependence of its activity has not yet been satisfactorily investigated and many questions still remain unanswered. We report the nonaqueous surfactant-assisted synthesis of highly uniform anatase TiO(2) NCs with tailorable morphology in the 10-100 nm size regime, prepared through a seeded growth technique. Introduction of titanium(IV) fluoride (TiF(4)) preferentially exposes the {001} facet of anatase through in situ release of hydrofluoric acid (HF), allowing for the formation of uniform anatase NCs based on the truncated tetragonal bipyramidal geometry. A method is described to engineer the percentage of {001} and {101} facets through the choice of cosurfactant and titanium precursor. X-ray diffraction studies are performed in conjunction with simulation to determine an average NC dimension which correlates with results obtained using electron microscopy. In addition to altering the particle shape, the introduction of TiF(4) into the synthesis results in TiO(2) NCs that are blue in color and display a broad visible/NIR absorbance which peaks in the infrared (λ(max) ≈ 3400 nm). The blue color results from oxygen vacancies formed in the presence of fluorine, as indicated by electron paramagnetic resonance (EPR) and X-ray photoelectron spectroscopy (XPS) studies. The surfactants on the surface of the NCs are removed through a simple ligand exchange procedure, allowing the shape dependence of photocatalytic hydrogen evolution to be studied using monodisperse TiO(2) NCs. Preliminary experiments on the photoreforming of methanol, employed as a model sacrificial agent, on platinized samples resulted in high volumes of evolved hydrogen (up to 2.1 mmol h(-1) g(-1)) under simulated solar illumination. Remarkably, the data suggest that, under our experimental conditions, the {101} facets of anatase are more active than the {001}.     

Giant magnetoelastic effect at the opening of a spin-gap in Ba3BiIr2O9

As compared to 3d (first-row) transition metals, the 4d and 5d transition metals have much more diffuse valence orbitals. Quantum cooperative phenomena that arise due to changes in the way these orbitals overlap and interact, such as magnetoelasticity, are correspondingly rare in 4d and 5d compounds. Here, we show that the 6H-perovskite Ba(3)BiIr(2)O(9), which contains 5d Ir(4+) (S = 1/2) dimerized into isolated face-sharing Ir(2)O(9) bioctahedra, exhibits a giant magnetoelastic effect, the largest of any known 5d compound, associated with the opening of a spin-gap at T* = 74 K. The resulting first-order transition is characterized by a remarkable 4% increase in Ir-Ir distance and 1% negative thermal volume expansion. The transition is driven by a dramatic change in the interactions among Ir 5d orbitals, and represents a crossover between two very different, competing, ground states: one that optimizes direct Ir-Ir bonding (at high temperature), and one that optimizes Ir-O-Ir magnetic superexchange (at low temperature).     

Minimal covers of the prisms and antiprisms

This paper contains a classification of the regular minimal abstract polytopes that act as covers for the convex polyhedral prisms and antiprisms. It includes a detailed discussion of their topological structure, and completes the enumeration of such covers for convex uniform polyhedra. Additionally, this paper addresses related structural questions in the theory of string C-groups.     

Doping – Dependent irreversible magnetic properties of Ba(Fe1−xCox)2As2 single crystals

We discuss the irreversible magnetic properties of self-flux grown Ba(Fe_1?xCo_x)₂As₂ single crystals for a wide range of concentrations covering the whole phase diagram from the underdoped to the overdoped regime, x = 0.038, 0.047, 0.058, 0.071, 0.074, 0.10, 0.106 and 0.118. Samples were characterized by a magneto-optical method and show excellent spatial uniformity of the superconducting state down to at least the micrometer scale. The in-plane properties are isotropic, as expected for the tetragonal symmetry, and the overall behavior closely follows classical Bean model of the critical state. The field-dependent magnetization exhibits second peak at a temperature and doping – dependent magnetic field, H_p(T, x). The evolution of this fishtail feature with doping is discussed. In particular we find that H_p, measured at the same reduced temperature for different x, is a unique monotonic function of the superconducting transition temperature, T_c(x), across all dopings. Magnetic relaxation is time-logarithmic and unusually fast. Similar to cuprates, there is an apparent crossover from collective elastic to plastic flux creep above H_p. At high fields, the field dependence of the relaxation rate becomes doping independent. We discuss our results in the framework of the weak collective pinning and show that vortex physics in iron-based pnictide crystals is much closer to high-T_c cuprates than to conventional s-wave (including MgB₂) superconductors.     

Slater-Pauling behavior within quaternary intermetallic borides of the Ti3Co5B2 structure-type

First-principles, density-functional studies of several intermetallic borides of the general type M₂M′Ru_5−nRh_nB₂ (n=0-5; M=Sc, Ti, Nb; M′=Fe, Co) show that the variation in saturation magnetic moment with valence-electron count follows a Slater-Pauling curve, with a maximum moment occurring typically at 66 valence electrons. The magnetic moments in these compounds occur primarily from the 3d electrons of the magnetically active M′ sites, with some contribution from the Ru/Rh sites via magnetic polarization. Electronic DOS curves reveal that a rigid-band approach is a reasonable approximation for the estimation of saturation moments and the analysis of orbital interactions in this family of complex borides. COHP analyses of the M′−M′ orbital interactions indicate optimized interactions in the minority spin states for Co-containing phases, but strong bonding interactions remaining in Fe-containing phases.     

Structural, magnetic, and thermal characteristics of the phase transitions in Gd5GaxGe4−x magnetocaloric materials

Temperature-dependent, single crystal and powder X-ray diffraction studies as well as magnetization, and heat capacity measurements were carried out on two phases of the Gd₅Ga_xGe_4−x system: for x=0.7 and 1.0. Gd₅Ga_0.7Ge_3.3 shows three structure types as a function of temperature: (i) from 165 K to room temperature, the orthorhombic Sm₅Ge₄-type structure exists; (ii) below 150 K, it transforms to a orthorhombic Gd₅Si₄-type structure; and (iii) a monoclinic Gd₅Si₂Ge₂-type component is observed for the intermediate temperature range of 150 K≤T≤165 K. This is the first time that all these three structure types have been observed for the same composition. For Gd₅Ga_1.0Ge_3.0, the room temperature phase belongs to the orthorhombic Pu₅Rh₄-type structure with interslab contacts between main group atoms of 2.837(4) Å. Upon heating above 523 K, it transforms to a Gd₅Si₄-type structure with this distance decreasing to 2.521(7) Å before decomposing above 573 K.     

Low temperature radiolysis of fullerene C<Subscript>60</Subscript> and its solutions in isopropylbenzene and <Emphasis Type="Italic">N</Emphasis>-vinylpyrrolidone

Low-temperature (77 K) radiolysis of solid fullerene C₆₀ and its glassy solutions in isopropylbenzene (IPB) and N-vinylpyrrolidone (N-VP) has been investigated with the use of ESR spectroscopy. Radiationchemical yields for the formation of paramagnetic centers (G _PMC, 1/100 eV) have been determined to be ∼0.001 for pure fullerene and 0.3 and 0.7 for its solutions in IPB and N-VP, respectively. The low value of G _PMC for fullerene indicates a high stability of this form of carbon. The increase in G _PMC in solutions as compared to the pure solvents (0.15 for IPB and 0.3 for N-VP) indicates the sensitizing effect of C₆₀.     

Homogeneous Catalysts with a Mechanical (“Machine‐like”) Action

Molecular machines? The factors involved in and the fundamental nature of a “mechanical” action within molecular catalysis is explored in detail. Such mechanical homogeneous catalysts are rare but not unknown (see graphic). The spatial and temporal nature of their catalytic action is considered. Potential implications for mimicry of enzymes are discussed.