On Anosov energy levels of hamiltonians on twisted cotangent bundles

LetT ^* M denote the cotangent bundle of a manifoldM endowed with a twisted symplectic structure [1]. We consider the Hamiltonian flow generated (with respect to that symplectic structure) by a convex HamiltonianH: T ^* M, and we consider a compact regular energy level ofH, on which this flow admits a continuous invariant Lagrangian subbundleE. When dimM3, it is known [9] that such energy level projects onto the whole manifoldM, and thatE is transversal to the vertical subbundle. Here we study the case dimM=2, proving that the projection property still holds, while the transversality property may fail. However, we prove that in the case whenE is the stable or unstable subbundle of an Anosov flow, both properties hold.     

Convergence de mesures spectrales aléatoires et applications à des principes d'invariance

Nous présentons un cadre unificateur pour un certain nombre de résultats connus de convergence en loi pour des processus admettant une représentation linéaire par rapport à un bruit blanc faible pour lequel il existe un principe dinvariance faible. Nous montrons que ce principe dinvariance est équivalent à la convergence dune suite de mesures aléatoires spectrales. Ceci permet daffaiblir les hypothèses usuelles et donc dobtenir des résultats nouveaux de convergence en loi, notamment pour des processus à longue portée.     

Optimal Paths for Symmetric Actions in the Unitary Group

Given a positive and unitarily invariant Lagrangian ${\mathcal{L}}$ defined in the algebra of matrices, and a fixed time interval ${[0,t_0]\subset\mathbb R}$ , we study the action defined in the Lie group of ${n\times n}$ unitary matrices ${\mathcal{U}(n)}$ by $$\mathcal{S}(\alpha)=\int_0^{t_0} \mathcal{L}(\dot\alpha(t))\,dt, $$ where ${\alpha:[0,t_0]\to\mathcal{U}(n)}$ is a rectifiable curve. We prove that the one-parameter subgroups of ${\mathcal{U}(n)}$ are the optimal paths, provided the spectrum of the exponent is bounded by π. Moreover, if ${\mathcal{L}}$ is strictly convex, we prove that one-parameter subgroups are the unique optimal curves joining given endpoints. Finally, we also study the connection of these results with unitarily invariant metrics in ${\mathcal{U}(n)}$ as well as angular metrics in the Grassmann manifold.     

Unstable Particles, Gauge Invariance and the Δ++ Resonance Parameters

The elastic and radiative ⁺ p scattering are studied in the framework of an effective Lagrangian model for the ⁺⁺ resonance and its interactions. The finite width effects of this spin-3/2 resonance are introduced in the scattering amplitudes through a complex mass scheme to respect electromagnetic gauge invariance. The resonant pole ( ⁺⁺) and background contributions ( ⁰, , , and neutron states) are separated according to the principles of the analytic S-matrix theory. The mass and width parameters of the ⁺⁺ obtained from a fit to experimental data on the total cross section are in agreement with the results of a model-independent analysis based on the analytic S-matrix approach. The magnetic dipole moment determined from the radiative ⁺ p scattering is nuclear magnetons.     

Alternative formulations for the Set Packing Problem and their application to the Winner Determination Problem

An alternative formulation for the set packing problem in a higher dimension is presented. The addition of a new family of binary variables allows us to find new valid inequalities, some of which are shown to be facets of the polytope in the higher dimension. We also consider the Winner Determination Problem, which is equivalent to the set packing problem and whose special structure allows us to easily implement these valid inequalities in a very easy way. The computational experiments illustrate the performance of the valid inequalities and obtain good results.     

Use of hydrogen peroxide to achieve interference-free stripping voltammetric determination of copper at the bismuth-film electrode

In this work, a new approach is presented to allow interference-free determination of Cu (II) by stripping voltammetry using the bismuth-film electrode. The addition of hydrogen peroxide to the electroanalytical cell has promoted complete resolution between re-dissolution peaks of Bi (III) and Cu (II). The absence of interference could be evaluated by the correlation coefficient (r > 0.99) between Cu (II) concentration and its shifted current peak (at +212 mV) while achieving a slightly fluctuation of the bismuth current peak at −180 mV. Studies were performed aiming towards the optimum conditions for trace determination of Cu (II) using hydrogen peroxide. The methodology was applied to a real sample (sugarcane spirits) and the results were compared to those from graphite furnace atomic absorption spectrometry. The analytical parameters of merit and the results of the analysis indicated that the analytical methodology could be readily used for trace determination of Cu (II).     

How important are temperature effects for cluster polarizabilities?

State-of-the-art first-principle all-electron density functional theory calculations on small sodium clusters are performed to study the temperature dependency of their polarizabilities. For this purpose Born-Oppenheimer molecular dynamics simulations with more than 100,000 time steps (>200 ps) are recorded employing gradient corrected functionals in combination with a double-zeta valence polarization basis set. For each cluster 18 trajectories between 50 and 900 K are collected. The cluster polarizabilities are then calculated along these trajectories employing a triple-zeta valence polarization basis set augmented with field-induced polarization functions. The analysis of these calculations shows that the temperature dependency of the sodium cluster polarizabilities varies strongly with cluster size. For several clusters characteristic changes in the polarizability per atom as a function of temperature are observed. It is shown that the inclusion of finite temperature effects resolves the long-standing mismatch between calculated and measured sodium cluster polarizabilities.     

Ultra-fast chromatographic micro-assay for quantification of diphenidol in plasma: application in an oral multi-dose switchability trial

Pharmacokinetics of diphenidol (DPN) is limited due to the lack of analytical methodology. Here, a micro-assay for DPN quantification was developed, by coupling ultra-performance liquid chromatography with tandem mass spectrometry. The procedure involved plasma precipitation and injection of supernatant into UPLC with an Acquitytrade mark C18 column. Detection was in positive electrospray, following transitions of m/z 310.3 --> 292.3 and m/z 275.3 --> 230.2 for DPN and chlorphenamine (internal standard), respectively. The method was linear with a range of 4-400 ng/mL, and a 2 min run time. This method was applied in a switchability trial, where both formulations of DPN were bioequivalent.     

Pressure- and temperature-induced association of arborescent polystyrene-graft-poly(ethylene oxide) copolymers at the air-water interface

The influence of surface pressure and subphase temperature on the association of arborescent polystyrene- graft-poly(ethylene oxide) (PS- g-PEO) copolymers at the air-water interface was investigated using the Langmuir balance and atomic force microscopy (AFM) techniques. These dendritic molecules form stable condensed monolayers with surface compressional moduli >250 mN/m. The variation in film thickness observed as a function of surface pressure suggests that at low surface pressures (gaslike phase) the PEO chains remain adsorbed at the air-water interface. At higher surface pressures (condensed phase), the PEO chains partially desorb into the subphase and adopt a more brushlike conformation. Large islandlike clusters with a broad size distribution were observed for samples with PEO contents of up to 15% by weight. In contrast, copolymers with PEO contents of 22-43% displayed enhanced side-by-side association into ribbonlike superstructures upon compression. The same effect was observed even in the absence of compression when the subphase temperature was increased from 12 to 27 degrees C. The temperature-induced association was attributed to increased van der Waals attractive forces between the PS cores relative to the steric repulsive forces between PEO chains in the coronas because the solvent quality for the PEO segments decreased at higher temperatures. The restricted number of superstructures observed for arborescent copolymers as compared with linear- and star-branched PS-PEO block copolymers is attributed to the enhanced structural rigidity of the molecules due to branching.     

N,N′-bis(substituted-phenyl)oxamides and their dinuclear pentacoordinate nickel(II) complexes

The preparation, spectroscopic characterization and magnetic study of N,N′-bis(substituted-phenyl)oxamidate-bridged nickel(II) dinuclear complexes of formula {[Ni(N₃-mc)]₂(μ-CONC₆H₄-X)}(PF₆)₂ (N₃-mc = 2,4,4-trimethyl-1,5,9-triazacyclo-dodec-1-ene (Me₃-N₃-mc) or 2,4,4,9-tetramethyl-1,5,9-triazacyclododec-1-ene (Me₄-N₃-mc), X = 2-Cl, 4-Cl, 2-OCH₃, 4-OCH₃) are reported. These paramagnetic nickel(II) complexes have been characterized by both one- and two-dimensional (COSY) ¹H NMR techniques. The COSY spectrum of 5 has allowed to achieve the assignment of the phenyl protons of the N,N′-diphenyloxamidate. The crystal structures of [Ni(Me₃-N₃-mc)(μ-CONC₆H₄-4-Cl)]₂(PF₆)₂ (6), [Ni(Me₃-N₃-mc)(μ-CONC₆H₄-4-OMe)]₂(PF₆)₂ (8) and [Ni(Me₄-N₃-mc)(μ-CONC₆H₄-2-Cl)]₂(PF₆)₂ (9) have been determined and their magnetic properties have been studied. The value of magnetic coupling between the two nickel(II) ions across the oxamidate bridge [J = − 37.6 (6), −39.9 (8) and −39.7 cm⁻¹ (9)] is sensitive to the distortion of the coordination sphere of the metal ions and the topology of the molecular bridge.