Ordering the braid groups

We give an explicit geometric argument that Artin's braid group $B_n$ is right-orderable. The construction is elementary, natural, and leads to a new, effectively computable, canonical form for braids which we call left-consistent canonical form. The left-consistent form of a braid which is positive (respectively negative) in our order has consistently positive (respectively negative) exponent in the smallest braid generator which occurs. It follows that our ordering is identical to that of Dehornoy, constructed by very different means, and we recover Dehornoy's main theorem that any braid can be put into such a form using either positive or negative exponent in the smallest generator but not both. Our definition of order is strongly connected with Mosher's normal form and this leads to an algorithm to decide whether a given braid is positive, trivial, or negative which is quadratic in the length of the braid word.Comment: 24 pages, 10 figure

Viking navigation

A comprehensive description of the navigation of the Viking spacecraft throughout their flight from Earth launch to Mars landing is given. The flight path design, actual inflight control, and postflight reconstruction are discussed in detail. The preflight analyses upon which the operational strategies and performance predictions were based are discussed. The inflight results are then discussed and compared with the preflight predictions and, finally, the results of any postflight analyses are presented

Fermiology and electronic homogeneity of the superconducting overdoped cuprate Tl-2201 revealed by quantum oscillations

We report an angular quantum oscillation study of Tl_2Ba_2CuO_{6+delta} for two different doping levels (Tc = 10K and 26 K) and determine the Fermi surface size and topology in considerable detail. Our results show that Fermi liquid behavior is not confined to the edge of the superconducting dome and is robust up to at least T_c^{max}/3.5. Superconductivity is found to survive up to a larger doping p_c = 0.31 than in La_{2-x}Sr_xCuO_4. Our data imply that electronic inhomogeneity does not play a significant role in the loss of superconductivity and superfluid density in overdoped cuprates, and point towards a purely magnetic or electronic pairing mechanismComment: 4 page

Spectroscopic Evidence for Multiple Order Parameter Components in the Heavy Fermion Superconductor CeCoIn_5

Point-contact spectroscopy was performed on single crystals of the heavy-fermion superconductor CeCoIn_5 between 150 mK and 2.5 K. A pulsed measurement technique ensured minimal Joule heating over a wide voltage range. The spectra show Andreev-reflection characteristics with multiple structures which depend on junction impedance. Spectral analysis using the generalized Blonder-Tinkham-Klapwijk formalism for d-wave pairing revealed two coexisting order parameter components, with amplitudes Delta_1 = 0.95 +/- 0.15 meV and Delta_2 = 2.4 +/- 0.3 meV, which evolve differently with temperature. Our observations indicate a highly unconventional pairing mechanism, possibly involving multiple bands.Comment: 4 pages, 3 figure

Implementation of the Backlund transformations for the Ablowitz-Ladik hierarchy

The derivation of the Backlund transformations (BTs) is a standard problem of the theory of the integrable systems. Here, I discuss the equations describing the BTs for the Ablowitz-Ladik hierarchy (ALH), which have been already obtained by several authors. The main aim of this work is to solve these equations. This can be done in the framework of the so-called functional representation of the ALH, when an infinite number of the evolutionary equations are replaced, using the Miwa's shifts, with a few equations linking tau-functions with different arguments. It is shown that starting from these equations it is possible to obtain explicit solutions of the BT equations. In other words, the main result of this work is a presentation of the discrete BTs as a superposition of an infinite number of evolutionary flows of the hierarchy. These results are used to derive the superposition formulae for the BTs as well as pure soliton solutions.Comment: 20 page

Evolution of the Fermi surface of BaFe_2(As_{1-x}P_x)_2 on entering the superconducting dome

Using the de Haas-van Alphen effect we have measured the evolution of the Fermi surface of BaFe_2(As_{1-x}P_x)_2 as function of isoelectric substitution (As/P) for 0.41<x<1 (T_c up to 25 K). We find that the volume of electron and hole Fermi surfaces shrink linearly with decreasing x. This shrinking is accompanied by a strong increase in the quasiparticle effective mass as x is tuned toward the maximum T_c. It is likely that these trends originate from the many-body interaction which give rise to superconductivity, rather than the underlying one-electron bandstructure.Comment: 4 page

Linking covariant and canonical LQG: new solutions to the Euclidean Scalar Constraint

It is often emphasized that spin-foam models could realize a projection on the physical Hilbert space of canonical Loop Quantum Gravity (LQG). As a first test we analyze the one-vertex expansion of a simple Euclidean spin-foam. We find that for fixed Barbero-Immirzi parameter \gamma=1 the one vertex-amplitude in the KKL prescription annihilates the Euclidean Hamiltonian constraint of LQG. Since for \gamma=1 the Lorentzian part of the Hamiltonian constraint does not contribute this gives rise to new solutions of the Euclidean theory. Furthermore, we find that the new states only depend on the diagonal matrix elements of the volume. This seems to be a generic property when applying the spin-foam projector.Comment: 33 pages, several figure

Imaginative Representations of Two- and Three-Dimensional Matrices in Children with Nonverbal Learning Disabilities

Children with non-verbal learning disabilities (NLD) are characterized by high verbal and poor non-verbal intelligence, poor cognitive abilities, school difficulties, and—sometimes—depressive symptoms. NLD children lack visuospatial working memory, but it is not clear whether they encounter difficulties in mental imagery tasks. In the present study, NLD adolescents without depressive symptoms, depressed adolescents without NLD symptoms, and a control group were administered a mental imagery task requiring them to imagine to move along the cells of a 2-D (5 × 5) or 3-D (3 × 3 × 3) matrix. Results showed that NLD adolescents had difficulty at performing the imagery task when a 3-D pattern was involved. It is suggested that 3-D mental imagery tasks tap visuospatial processes which are weak in NLD individuals. In addition, their poor cognitive performance cannot be attributed to a depressive state, as the depressed group had a performance similar to that of controls

Social presence in the 21st Century: an adjustment to the Community of Inquiry framework

The Community of Inquiry framework, originally proposed by Garrison, Anderson and Archer (2000) identifies teaching, social and cognitive presences as central to a successful online educational experience. This article presents the findings of a study conducted in Uruguay between 2007 and 2010. The research aimed to establish the role of cognitive, social and teaching presences in the professional development of 40 English language teachers on Continuous Professional Development (CPD) programmes delivered in blended learning settings. The findings suggest that teaching presence and cognitive presence have themselves 'become social'. The research points to social presence as a major lever for engagement, sense-making and peer support. Based on the patterns identified in the study, this article puts forward an adjustment to the Community of Inquiry framework, which shows social presence as more prominent within the teaching and cognitive constructs than the original version of the framework suggests

A Closed Contour of Integration in Regge Calculus

The analytic structure of the Regge action on a cone in $d$ dimensions over a boundary of arbitrary topology is determined in simplicial minisuperspace. The minisuperspace is defined by the assignment of a single internal edge length to all 1-simplices emanating from the cone vertex, and a single boundary edge length to all 1-simplices lying on the boundary. The Regge action is analyzed in the space of complex edge lengths, and it is shown that there are three finite branch points in this complex plane. A closed contour of integration encircling the branch points is shown to yield a convergent real wave function. This closed contour can be deformed to a steepest descent contour for all sizes of the bounding universe. In general, the contour yields an oscillating wave function for universes of size greater than a critical value which depends on the topology of the bounding universe. For values less than the critical value the wave function exhibits exponential behaviour. It is shown that the critical value is positive for spherical topology in arbitrary dimensions. In three dimensions we compute the critical value for a boundary universe of arbitrary genus, while in four and five dimensions we study examples of product manifolds and connected sums.Comment: 16 pages, Latex, To appear in Gen. Rel. Gra