Jacobi structures revisited

Jacobi algebroids, that is graded Lie brackets on the Grassmann algebra associated with a vector bundle which satisfy a property similar to that of the Jacobi brackets, are introduced. They turn out to be equivalent to generalized Lie algebroids in the sense of Iglesias and Marrero and can be viewed also as odd Jacobi brackets on the supermanifolds associated with the vector bundles. Jacobi bialgebroids are defined in the same manner. A lifting procedure of elements of this Grassmann algebra to multivector fields on the total space of the vector bundle which preserves the corresponding brackets is developed. This gives the possibility of associating canonically a Lie algebroid with any local Lie algebra in the sense of Kirillov.Comment: 20 page

Focus Group. TRIADS experiences and developments. A panel discussion.

The Tripartite Interactive Assessment Delivery System (TRIADS) is an advanced computer-based assessment system designed to provide the widest possible flexibility in assessment design and delivery. Initially developed at the University of Derby it was evaluated in some forty-five departments at twenty-seven UK universities in twenty-four disciplines as part of the HEFCE-FDTL ‘Assessment of Learning Outcomes’ project (Liverpool, Derby and Open Universities 1996-2001). In the three papers that follow, the outcomes of this evaluation are summarized together with subsequent developments and examples of applications of TRIADS at Cardiff Dental School and Birkbeck College, University of London

Classical field theory on Lie algebroids: Variational aspects

The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be morphisms of Lie algebroids. In addition to the standard case, our formalism includes as particular examples the case of systems with symmetry (covariant Euler-Poincare and Lagrange Poincare cases), Sigma models or Chern-Simons theories.Comment: Talk deliverd at the 9th International Conference on Differential Geometry and its Applications, Prague, September 2004. References adde

Cyclotron Resonance in the Layered Perovskite Superconductor Sr2RuO4

We have measured the cyclotron masses in Sr2RuO4 through the observation of periodic-orbit-resonances - a magnetic resonance technique closely related to cyclotron resonance. We obtain values for the alpha, beta and gamma Fermi surfaces of (4.33+/-0.05)me, (5.81+/-0.03)me and (9.71+/-0.11)me respectively. The appreciable differences between these results and those obtained from de Haas- van Alphen measurements are attributable to strong electron-electron interactions in this system. Our findings appear to be consistent with predictions for a strongly interacting Fermi liquid; indeed, semi-quantitative agreement is obtained for the electron pockets beta and gamma.Comment: 4 pages + 3 figure

Decoherence suppression via environment preparation

To protect a quantum system from decoherence due to interaction with its environment, we investigate the existence of initial states of the environment allowing for decoherence-free evolution of the system. For models in which a two-state system interacts with a dynamical environment, we prove that such states exist if and only if the interaction and self-evolution Hamiltonians share an eigenstate. If decoherence by state preparation is not possible, we show that initial states minimizing decoherence result from a delicate compromise between the environment and interaction dynamics.Comment: 4 pages, 2 figure

Nash Codes for Noisy Channels

This paper studies the stability of communication protocols that deal with transmission errors. We consider a coordination game between an informed sender and an uninformed decision maker, the receiver, who communicate over a noisy channel. The sender's strategy, called a code, maps states of nature to signals. The receiver's best response is to decode the received channel output as the state with highest expected receiver payoff. Given this decoding, an equilibrium or "Nash code" results if the sender encodes every state as prescribed. We show two theorems that give sufficient conditions for Nash codes. First, a receiver-optimal code defines a Nash code. A second, more surprising observation holds for communication over a binary channel which is used independently a number of times, a basic model of information transmission: Under a minimal "monotonicity" requirement for breaking ties when decoding, which holds generically, EVERY code is a Nash code.Comment: More general main Theorem 6.5 with better proof. New examples and introductio

Effect of inorganic or organic copper fed without or with added sulfur and molybdenum on the performance, indicators of copper status, and hepatic mRNA in dairy cows

The effect of inorganic (INORG) or organic (ORG) Cu, fed without (−) or with (+) additional S and Mo on Cu status and performance was examined using 56 early lactation dairy cows in a 2 × 2 factorial study design. Supplementary Cu was added as either CuSO4 or BioplexCu (Alltech Inc., Nicholasville, KY) to provide an additional 10 mg of Cu/kg of dry matter (DM), with S added at 1.5 g/kg of DM and Mo at 6.8 mg/kg of DM to reduce Cu bioavailability. The basal ration was composed of corn and grass silages (2:1 respectively, DM basis) and straight feeds. Cows commenced the study at wk 7 of lactation and remained on treatment for 16 wk. An interaction existed between Cu source and added S and Mo on DM intake, with cows offered INORG− Cu having an increased intake compared with those offered INORG+ or ORG− Cu. Milk yield averaged 35.4 kg/d, and was 5% higher with milk fat content 6% lower in cows fed INORG compared with ORG Cu, but milk fat yield, energy-corrected milk yield, and milk protein content did not differ between treatments. A trend existed for cows to have a higher body weight gain when offered ORG compared with INORG Cu. Cows fed diets containing INORG Cu had a higher milk concentration of C17:0 and C18:3n-3 compared with those fed diets containing ORG Cu. Cows fed added S and Mo had a lower milk concentration of C17:0 and C18:0 compared with those that were not supplemented. No effect was observed of dietary treatment on plasma Cu concentration, which averaged 13.1 µmol/L, except during wk 12 when cows receiving added S and Mo had a lower concentration. No effect was observed of Cu source on mean plasma Mo concentrations, but during wk 16 cows offered INORG Cu had a higher concentration than those offered ORG Cu. Hepatic Cu levels decreased by approximately 0.9 mg/kg of DM per day when fed additional S and Mo, but no effect of Cu source was observed. A trend existed for hepatic ATPase, Cu++ transporting, beta polypeptide (ATP7B) to be upregulated in cows when fed S and Mo along with ORG but not INORG Cu. In conclusion, the inclusion of an ORG compared with an INORG source of Cu reduced milk yield but increased milk fat concentration and body weight gain, with no effect on energy-corrected milk yield. Little effect was observed of dietary Cu supply on plasma mineral concentration, liver mRNA abundance, or milk fatty acid profile, whereas the addition of S and Mo reduced hepatic Cu concentrations

Local structures of polar wurtzites Zn_{1-x}Mg_{x}O studied by Raman and {67}Zn/{25}Mg NMR spectroscopies and by total neutron scattering

Local compositions and structures of Zn_{1-x}Mg_{x}O alloys have been investigated by Raman and solid-state {67}Zn/{25}Mg nuclear magnetic resonance (NMR) spectroscopies, and by neutron pair-distribution-function (PDF) analyses. The E2(low) and E2(high) Raman modes of Zn_{1-x}Mg_{x}O display Gaussian- and Lorentzian-type profiles, respectively. At higher Mg substitutions, both modes become broader, while their peak positions shift in opposite directions. The evolution of Raman spectra from Zn_{1-x}Mg_{x}O solid solutions are discussed in terms of lattice deformation associated with the distinct coordination preferences of Zn and Mg. Solid-state magic-angle-spinning (MAS) NMR studies suggest that the local electronic environments of {67}Zn in ZnO are only weakly modified by the 15% substitution of Mg for Zn. {25}Mg MAS spectra of Zn_{0.85}Mg_{0.15}O show an unusual upfield shift, demonstrating the prominent shielding ability of Zn in the nearby oxidic coordination sphere. Neutron PDF analyses of Zn_{0.875}Mg_{0.125}O using a 2x2x1 supercell corresponding to Zn_{7}MgO_{8} suggest that the mean local geometry of MgO_{4} fragments concurs with previous density functional theory (DFT)-based structural relaxations of hexagonal wurtzite MgO. MgO_{4} tetrahedra are markedly compressed along their c-axes and are smaller in volume than ZnO_{4} units by ~6%. Mg atoms in Zn_{1-x}Mg_{x}O have a shorter bond to the $c$-axial oxygen atom than to the three lateral oxygen atoms, which is distinct from the coordination of Zn. The precise structure, both local and average, of Zn_{0.875}Mg_{0.125}O obtained from time-of-flight total neutron scattering supports the view that Mg-substitution in ZnO results in increased total spontaneous polarization.Comment: 12 pages, 14 figures, 2 table

Vortex lattice structures of Sr2_2RuO4_4

The vortex lattice structures of Sr$_2$RuO$_4$ for the odd parity representations of the superconducting state are examined for the magnetic field along the crystallographic directions. Particular emphasis is placed upon the two dimensional representation which is believed to be relevant to this material. It is shown that when the zero-field state breaks time reversal symmetry, there must exist two superconducting transitions when there is a finite field along a high symmetry direction in the basal plane. Also it is shown that a square vortex lattice is expected when the field is along the $c$-axis. The orientation of the square lattice with respect to the underlying ionic lattice yields information as to which Ru 4d orbitals are relevant to the superconducting state.Comment: 5 pages, 2 figure