Isometric Representations of Totally Ordered Semigroups

Let S be a subsemigroup of an abelian torsion-free group G. If S is a positive cone of G, then all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic. Proved by Murphy, this statement generalized the well-known theorems of Coburn and Douglas. In this note we prove the reverse. If all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic, then S is a positive cone of G. Also we consider G = Z\times Z and prove that if S induces total order on G, then there exist at least two unitarily not equivalent irreducible isometrical representation of S. And if the order is lexicographical-product order, then all such representations are unitarily equivalent.Comment: February 21, 2012. Kazan, Russi

Nitric oxide metabolites in patients with asthma: induced sputum versus blood

AbstractNitric oxide (NO) plays an important role in physiological regulation of the airways. The monitoring of airway inflammation has being observed in bronchial asthma directly, by sputum examination, and indirectly, by measurements in peripheral blood. To investigate the diagnostic value of these two methods, we compared NO metabolites in induced sputum and serum obtained in patients with asthma and control subjects. Hypertonic saline induced sputum and serum were obtained in 13 patients with asthma and 10 control subjects. NO metabolite level was assayed by using modified Griess reaction. Eosinophil cationic protein (ECP) was measured by fluoroimmunoassay, and detected interleukin (IL)-5 by a sandwich ELISA. The accuracy of the tests was measured by plotting the data in receiver operating characteristic (ROC) curves and comparing the area under the curve for NO metabolites. Asthmatic patients, compared with control subjects, had significantly higher NO metabolites in induced sputum (1252·5±203·3 moll−1 vs. 557·2±101±.5 mol l−1, P < 0·01) but not in serum. IL-5 in induced sputum was detected more frequently in patients with asthma than in control subjects [1113 (84·6%) vs. 110 (10%), P < 0·01]. Asthmatic patients, compared with control subjects, had significantly higher ECP concentration in induced sputum (1270·0 ± 197·9 g 1 vs. 154·6 ± 47·4 g l−1, P < 0·01). There were significant positive correlations between NO metabolites in induced sputum and eosinophils, ECP in induced sputum (r=0·58 P<0·05; r=0·64, P<0·01) in patients with asthma but not in serum. The area under the ROC curve showed that NO metabolites in induced sputum (0·78) are more accurate marker than NO metabolites in serum (0·53) (P<0·05). These findings suggest that NO metabolites in induced sputum is a more valuable indicator to monitor asthmatic airway inflammation than those in serum

One-Dimensional Dispersive Magnon Excitation in the Frustrated Spin-2 Chain System Ca3Co2O6

Using inelastic neutron scattering, we have observed a quasi-one-dimensional dispersive magnetic excitation in the frustrated triangular-lattice spin-2 chain oxide Ca3Co2O6. At the lowest temperature (T = 1.5 K), this magnon is characterized by a large zone-center spin gap of ~27 meV, which we attribute to the large single-ion anisotropy, and disperses along the chain direction with a bandwidth of ~3.5 meV. In the directions orthogonal to the chains, no measurable dispersion was found. With increasing temperature, the magnon dispersion shifts towards lower energies, yet persists up to at least 150 K, indicating that the ferromagnetic intrachain correlations survive up to 6 times higher temperatures than the long-range interchain antiferromagnetic order. The magnon dispersion can be well described within the predictions of linear spin-wave theory for a system of weakly coupled ferromagnetic chains with large single-ion anisotropy, enabling the direct quantitative determination of the magnetic exchange and anisotropy parameters.Comment: 7 pages, 6 figures including one animatio

Pressure effects on the heavy-fermion antiferromagnet CeAuSb2

The f-electron compound CeAuSb2, which crystallizes in the ZrCuSi2-type tetragonal structure, orders antiferromagnetically between 5 and 6.8 K, where the antiferromagnetic transition temperature T_N depends on the occupancy of the Au site. Here we report the electrical resistivity and heat capacity of a high-quality crystal CeAuSb2 with T_N of 6.8 K, the highest for this compound. The magnetic transition temperature is initially suppressed with pressure, but is intercepted by a new magnetic state above 2.1 GPa. The new phase shows a dome shape with pressure and coexists with another phase at pressures higher than 4.7 GPa. The electrical resistivity shows a T^2 Fermi liquids behavior in the complex magnetic state, and the residual resistivity and the T^2 resistivity coefficient increases with pressure, suggesting the possibility of a magnetic quantum critical point at a higher pressure.Comment: 5 pages, 5 firure

Heavy-quark meson spectrum tests of the Oktay-Kronfeld action

The Oktay-Kronfeld (OK) action extends the Fermilab improvement program for massive Wilson fermions to higher order in suitable power-counting schemes. It includes dimension-six and -seven operators necessary for matching to QCD through order ${\mathrm{O}}(\Lambda^3/m_Q^3)$ in HQET power counting, for applications to heavy-light systems, and ${\mathrm{O}}(v^6)$ in NRQCD power counting, for applications to quarkonia. In the Symanzik power counting of lattice gauge theory near the continuum limit, the OK action includes all ${\mathrm{O}}(a^2)$ and some ${\mathrm{O}}(a^3)$ terms. To assess whether the theoretical improvement is realized in practice, we study combinations of heavy-strange and quarkonia masses and mass splittings, designed to isolate heavy-quark discretization effects. We find that, with one exception, the results obtained with the tree-level-matched OK action are significantly closer to the continuum limit than the results obtained with the Fermilab action. The exception is the hyperfine splitting of the bottom-strange system, for which our statistical errors are too large to draw a firm conclusion. These studies are carried out with data generated with the tadpole-improved Fermilab and OK actions on 500 gauge configurations from one of MILC's $a\approx0.12$~fm, $N_f=2+1$-flavor, asqtad-staggered ensembles.Comment: 12 pages, 5 figure