Representations of Hecke Algebras and Dilations of Semigroup Crossed Products

A family of Hecke C^*-algebras can be realised as crossed productsby semigroups of endomorphisms. It is shown by dilating representationsof the semigroup crossed product that the category of representationsof the Hecke algebra is equivalent to the category of continuousunitary representations of a totally disconnected locally compactgroup.     

On Bernstein Algebras Satisfying Chain Conditions

Our aim in this article is to study Noetherian and Artinian Bernstein algebras. We show that for Bernstein algebras which are either Jordan or nuclear, each of the Noetherian and Artinian conditions implies finite dimensionality. This result fails for general Noetherian or Artinian Bernstein algebras. We also investigate the relationships between the three finiteness conditions: Noetherian, Artinian, and finitely generated. Especially, we prove that Noetherian Bernstein algebras are finitely generated.     

Bounded-degree polyhedronization of point sets

In 1994 Grünbaum showed that, given a point set S in ${\mathbb{R}}^3$, it is always possible to construct a polyhedron whose vertices are exactly S. Such a polyhedron is called a polyhedronization of S. Agarwal et al. extended this work in 2008 by showing that there always exists a polyhedronization that can be decomposed into a union of tetrahedra (tetrahedralizable). In the same work they introduced the notion of a serpentine polyhedronization for which the dual of its tetrahedralization is a chain. In this work we present a randomized algorithm running in $O(n{\log }^{6}n)$ expected time which constructs a serpentine polyhedronization that has vertices with degree at most 7, answering an open question by Agarwal et al.     

Integrability of subdifferentials of directionally Lipschitz functions

Using a quantitative version of the subdifferential characterization of directionally Lipschitz functions, we study the integrability of subdifferentials of such functions over arbitrary Banach space.

     

Improved lower bounds for the online bin stretching problem

We use game theory techniques to automatically compute improved lower bounds on the competitive ratio for the bin stretching problem. Using these techniques, we improve the best lower bound for this problem to 19/14. We explain the technique and show that it can be generalized to compute lower bounds for any online or semi-online packing or scheduling problem.     

An investigation of motion correction algorithms for pediatric spinal cord DTI in healthy subjects and patients with spinal cord injury

Patient and physiological motion can cause artifacts in DTI of the spinal cord which can impact image quality and diffusion indices. The purpose of this investigation was to determine a reliable motion correction method for pediatric spinal cord DTI and show effects of motion correction on DTI parameters in healthy subjects and patients with spinal cord injury. Ten healthy subjects and ten subjects with spinal cord injury were scanned using a 3 T scanner. Images were acquired with an inner field-of-view DTI sequence covering cervical spine levels C1 to C7. Images were corrected for motion using two types of transformation (rigid and affine) and three cost functions. Corrected images and transformations were examined qualitatively and quantitatively using in-house developed code. Fractional anisotropy (FA) and mean diffusivity (MD) indices were calculated and tested for statistical significance pre- and post- motion correction. Images corrected using rigid methods showed improvements in image quality, while affine methods frequently showed residual distortions in corrected images. Blinded evaluation of pre and post correction images showed significant improvement in cord homogeneity and edge conspicuity in corrected images (p < 0.0001). The average FA changes were statistically significant (p < 0.0001) in the spinal cord injury group, while healthy subjects showed less FA change and were not significant. In both healthy subjects and subjects with spinal cord injury, quantitative and qualitative analysis showed the rigid scaled-least-squares registration technique to be the most reliable and effective in improving image quality.     

Ultrasonic characterization of heavy metal TeO2–WO3–PbO glasses below room temperature

The longitudinal ultrasonic attenuation measurements have been made using pulse echo method at fundamental frequencies of 2, 4, 6 and 8 MHz in 20WO₃–(80−x) TeO₂–xPbO ternary tellurite glasses (x=10, 12.5, 15, 17.5 and 20 mol%) in the temperature range 160–280 K. The results showed the presence of a broad peak which shifts to higher temperature with increasing frequency. The ultrasonic attenuation peaks suggest that the experimental behavior is controlled by thermally activated structural relaxations. The internal friction, acoustic activation energy, deformation potential, relaxation strength, number of loss centers and density of state have been calculated both as a function of temperature and PbO content. The acoustic activation energy was found to decrease from 0.156 to 0.135 eV with the increase of PbO content. The results showed that both the number of loss centers and their activation energy decrease with the atomic ring size. An increase in the density of state is observed with addition of PbO content at the same frequency in the whole range of temperature which is associated with structural units formed when PbO is added.     

Water-Assisted Concerted Proton-Electron Transfer at Co(II)-Aquo Sites in Polyoxotungstates With Photogenerated RuIII(bpy)33+ Oxidant

The cobalt substituted polyoxotungstate [Co₆(H₂O)₂(α-B-PW₉O₃₄)₂(PW₆O₂₆)]¹⁷⁻ ( Co6 ) displays fast electron transfer (ET) kinetics to photogenerated Ru^III(bpy)₃³⁺, 4 to 5 orders of magnitude faster than the corresponding ET observed for cobalt oxide nanoparticles. Mechanistic evidence has been acquired indicating that: (i) the one-electron oxidation of Co6 involves Co(II) aquo or Co(II) hydroxo groups (abbreviated as Co6(II) −OH ₂ and Co6(II) −OH, respectively, whose speciation in aqueous solution is associated to a pK_a of 7.6), and generates a Co(III)−OH moiety ( Co6(III) −OH), as proven by transient absorption spectroscopy; (ii) at pH>pK_a, the Co6(II) −OH→Ru^III(bpy)₃³⁺ ET occurs via bimolecular kinetics, with a rate constant k close to the diffusion limit and dependent on the ionic strength of the medium, consistent with reaction between charged species; (iii) at pH <pK_a, the process involves Co6(II) − OH₂ → Co6(III)−OH transformation and proceeds via a multiple-site, concerted proton electron transfer (CPET) where water assists the transfer of the proton, as proven by the absence of effect of buffer base concentrations on the rate of the ET and by a H/D kinetic isotope in a range of 1.2–1.4. The reactivity of water is ascribed to its organization on the surface of the polyanionic scaffold through hydrogen bond networking involving the Co(II)−OH₂ group.