The AF structure of non commutative toroidal Z/4Z orbifolds

For any irrational theta and rational number p/q such that q|qtheta-p|<1, a projection e of trace q|qtheta-p| is constructed in the the irrational rotation algebra A_theta that is invariant under the Fourier transform. (The latter is the order four automorphism U mapped to V, V mapped to U^{-1}, where U, V are the canonical unitaries generating A_theta.) Further, the projection e is approximately central, the cut down algebra eA_theta e contains a Fourier invariant q x q matrix algebra whose unit is e, and the cut downs eUe, eVe are approximately inside the matrix algebra. (In particular, there are Fourier invariant projections of trace k|qtheta-p| for k=1,...,q.) It is also shown that for all theta the crossed product A_theta rtimes Z_4 satisfies the Universal Coefficient Theorem. (Z_4 := Z/4Z.) As a consequence, using the Classification Theorem of G. Elliott and G. Gong for AH-algebras, a theorem of M. Rieffel, and by recent results of H. Lin, we show that A_theta rtimes Z_4 is an AF-algebra for all irrational theta in a dense G_delta.Comment: 35 page

Bicategories of spans as cartesian bicategories

Bicategories of spans are characterized as cartesian bicategories in which every comonad has an Eilenberg-Moore ob ject and every left adjoint arrow is comonadic

Solidification in soft-core fluids: disordered solids from fast solidification fronts

Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different mechanisms, depending on the depth of the quench. For shallow quenches, the front propagation is via a nonlinear mechanism. For deep quenches, front propagation is governed by a linear mechanism and in this regime we are able to determine the front speed via a marginal stability analysis. We find that the density modulations generated behind the advancing front have a characteristic scale that differs from the wavelength of the density modulation in thermodynamic equilibrium, i.e., the spacing between the crystal planes in an equilibrium crystal. This leads to the subsequent development of disorder in the solids that are formed. For the one-component fluid, the particles are able to rearrange to form a well-ordered crystal, with few defects. However, solidification fronts in a binary mixture exhibiting crystalline phases with square and hexagonal ordering generate solids that are unable to rearrange after the passage of the solidification front and a significant amount of disorder remains in the system.Comment: 18 pages, 14 fig

Submillimeter Spectrum of Formic Acid

We have measured new submillimeter-wave data around 600 GHz and around 1.1 THz for the 13C isotopologue of formic acid and for the two deuterium isotopomers; in each case for both the trans and cis rotamer. For cis-DCOOH and cis-HCOOD in particular only data up to 50 GHz was previously available. For all species the quality and quantity of molecular parameters has been increased providing new measured frequencies and more precise and reliable frequencies in the range of existing and near-future submillimeter and far-infrared astronomical spectroscopy instruments such as Herschel, SOFIA and ALMA

Cartesian Bicategories II

The notion of cartesian bicategory, introduced by Carboni and Walters for locally ordered bicategories, is extended to general bicategories. It is shown that a cartesian bicategory is a symmetric monoidal bicategory

Neutron spin-echo study of the critical dynamics of spin-5/2 antiferromagnets in two and three dimensions

We report a neutron spin-echo study of the critical dynamics in the $S=5/2$ antiferromagnets MnF$_2$ and Rb$_2$MnF$_4$ with three-dimensional (3D) and two-dimensional (2D) spin systems, respectively, in zero external field. Both compounds are Heisenberg antiferromagnets with a small uniaxial anisotropy resulting from dipolar spin-spin interactions, which leads to a crossover in the critical dynamics close to the N\'eel temperature, $T_N$. By taking advantage of the $\mu\text{eV}$ energy resolution of the spin-echo spectrometer, we have determined the dynamical critical exponents $z$ for both longitudinal and transverse fluctuations. In MnF$_2$, both the characteristic temperature for crossover from 3D Heisenberg to 3D Ising behavior and the exponents $z$ in both regimes are consistent with predictions from the dynamical scaling theory. The amplitude ratio of longitudinal and transverse fluctuations also agrees with predictions. In Rb$_2$MnF$_4$, the critical dynamics crosses over from the expected 2D Heisenberg behavior for $T\gg T_N$ to a scaling regime with exponent $z = 1.387(4)$, which has not been predicted by theory and may indicate the influence of long-range dipolar interactions

Allopurinol use yields potentially beneficial effects on inflammatory indices in those with recent ischemic stroke: a randomized, double-blind, placebo-controlled trial

&lt;p&gt;&lt;b&gt;Background and Purpose&lt;/b&gt;: Elevated serum uric acid level is associated with poor outcome and increased risk of recurrent events after stroke. The xanthine oxidase inhibitor allopurinol lowers uric acid but also attenuates expression of inflammatory adhesion molecules in murine models, reduces oxidative stress in the vasculature, and improves endothelial function. We sought to investigate whether allopurinol alters expression of inflammatory markers after acute ischemic stroke.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Methods&lt;/b&gt;: We performed a randomized, double-blind, placebo-controlled trial to investigate the safety, tolerability, and effect of 6 weeks’ treatment with high- (300 mg once a day) or low- (100 mg once a day) dose allopurinol on levels of uric acid and circulating inflammatory markers after ischemic stroke.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Results&lt;/b&gt;: We enrolled 50 patients with acute ischemic stroke (17, 17, and 16 in the high, low, and placebo groups, respectively). Mean (&#177;SD) age was 70 (&#177;13) years. Groups had similar characteristics at baseline. There were no serious adverse events. Uric acid levels were significantly reduced at both 7 days and 6 weeks in the high-dose group (by 0.14 mmol/L at 6 weeks, P=0.002). Intercellular adhesion molecule-1 concentration (ng/mL) rose by 51.2 in the placebo group, rose slightly (by 10.6) in the low-dose allopurinol group, but fell in the high-dose group (by 2.6; difference between groups P=0.012, Kruskal-Wallis test).&lt;/p&gt; &lt;p&gt;&lt;b&gt;Conclusion&lt;/b&gt;: Allopurinol treatment is well tolerated and attenuates the rise in intercellular adhesion molecule-1 levels seen after stroke. Uric acid levels were lowered with high doses. These findings support further evaluation of allopurinol as a preventive measure after stroke.&lt;/p&gt