Graph complexes in deformation quantization

Kontsevich's formality theorem and the consequent star-product formula rely on the construction of an $L_\infty$-morphism between the DGLA of polyvector fields and the DGLA of polydifferential operators. This construction uses a version of graphical calculus. In this article we present the details of this graphical calculus with emphasis on its algebraic features. It is a morphism of differential graded Lie algebras between the Kontsevich DGLA of admissible graphs and the Chevalley-Eilenberg DGLA of linear homomorphisms between polyvector fields and polydifferential operators. Kontsevich's proof of the formality morphism is reexamined in this light and an algebraic framework for discussing the tree-level reduction of Kontsevich's star-product is described.Comment: 39 pages; 3 eps figures; uses Xy-pic. Final version. Details added, mainly concerning the tree-level approximation. Typos corrected. An abridged version will appear in Lett. Math. Phy

The infrared and molecular environment surrounding the Wolf-Rayet star WR130

We present a study of the molecular CO gas and mid/far infrared radiation arising from the environment surrounding the Wolf-Rayet (W-R) star 130. We use the multi-wavelength data to analyze the properties of the dense gas and dust, and its possible spatial correlation with that of Young Stellar Objects (YSOs). We use CO J=1-0 data from the FCRAO survey as tracer of the molecular gas, and mid/far infrared data from the recent WISE and Herschel space surveys to study the dust continuum radiation and to identify a population of associated candidate YSOs. The spatial distribution of the molecular gas shows a ring-like structure very similar to that observed in the HI gas, and over the same velocity interval. The relative spatial distribution of the HI and CO components is consistent with a photo-dissociation region. We have identified and characterized four main and distinct molecular clouds that create this structure. Cold dust is coincident with the dense gas shown in the CO measurements. We have found several cYSOs that lie along the regions with the highest gas column density, and suggest that they are spatially correlated with the shell. These are indicative of regions of star formation induced by the strong wind and ionization of the WR star.Comment: 15 pages, 12 figures, 6 Tables. Accepted for publication in MNRA

Trabajando la demostración con profesorado de secundaria en formación

Trabajar la demostración en el aula es interesante no sólo por su importancia desde el punto de vista del quehacer matemático, sino por su contribución a la comprensión de los conceptos matemáticos involucrados (Hanna, 1995). Esta necesidad ha sido recogida de forma desigual en los distintos planes de estudios españoles desde 1934 (Ibañes & Ortega, 2002). La LOMCE establece el aprendizaje de la demostración como obligatorio y transversal a todos los contenidos. Sin embargo, los contenidos relativos a la demostración se presentan en forma de lista sin un orden lógico que ayude al profesor a planificar su enseñanza. Así, surge el interés de llevar a cabo actividades de formación de profesorado de secundaria relacionadas con la demostración, que involucren tanto aspectos relativos a la práctica de la demostración, como a su enseñanza y aprendizaje

Closedness of star products and cohomologies

We first review the introduction of star products in connection with deformations of Poisson brackets and the various cohomologies that are related to them. Then we concentrate on what we have called ``closed star products" and their relations with cyclic cohomology and index theorems. Finally we shall explain how quantum groups, especially in their recent topological form, are in essence examples of star products.Comment: 16 page

HII Shells Surrounding Wolf-Rayet stars in M31

We present the results of an ongoing investigation to provide a detailed view of the processes by which massive stars shape the surrounding interstellar medium (ISM), from pc to kpc scales. In this paper we have focused on studying the environments of Wolf-Rayet (WR) stars in M31 to find evidence for WR wind-ISM interactions, through imaging ionized hydrogen nebulae surrounding these stars. We have conducted a systematic survey for HII shells surrounding 48 of the 49 known WR stars in M31. There are 17 WR stars surrounded by single shells, or shell fragments, 7 stars surrounded by concentric limb brightened shells, 20 stars where there is no clear physical association of the star with nearby H-alpha emission, and 4 stars which lack nearby H-alpha emission. For the 17+7 shells above, there are 12 which contain one or two massive stars (including a WR star) and that are <=40 pc in radius. These 12 shells may be classical WR ejecta or wind-blown shells. Further, there may be excess H-alpha point source emission associated with one of the 12 WR stars surrounded by putative ejecta or wind-blown shells. There is also evidence for excess point source emission associated with 11 other WR stars. The excess emission may arise from unresolved circumstellar shells, or within the extended outer envelopes of the stars themselves. In a few cases we find clear morphological evidence for WR shells interacting with each other. In several H-alpha images we see WR winds disrupting, or punching through, the walls of limb-brightened HII shells.Comment: 20 pages, 4 figures (in several parts: some .jpg and others .ps), accepted to AJ (appearing Oct, 1999

Ultrarobust calibration of an optical lattice depth based on a phase shift

We report on a new method to calibrate the depth of an optical lattice. It consists in triggering the intrasite dipole mode of the cloud by a sudden phase shift. The corresponding oscillatory motion is directly related to the intraband frequencies on a large range of lattice depths. Remarkably, for a moderate displacement, a single frequency dominates this oscillation for the zeroth and first order interference pattern observed after a sufficiently long time-of-flight. The method is robust against atom-atom interactions and the exact value of the extra external confinement of the initial trapping potential.Comment: 7 pages, 6 figure

Metal-Metal Cooperation in the Oxidation of a Flapping Platinum Butterfly by Haloforms: Experimental and Theoretical Evidence

The model 1-DFT for the butterfly complex [{Pt(C¿C*)(µ-pz)}2] (1; HC¿C* = 1-(4-(ethoxycarbonyl)phenyl)-3-methyl-1H-imidazol-2-ylidene) shows two minima in the potential energy surface of the ground state in acetone solution: the butterfly-wing-spreading molecules 1-s, (dPt-Pt ˜ 3.20 Å) and the wing-folding molecules 1-f (dPt-Pt = 3.00 Å). Both minima are very close in energy (¿G° = 1.7 kcal/mol) and are connected through a transition state, which lies only 1.9 kcal/mol above 1-s and 0.2 kcal/mol above 1-f. These very low barriers support a fast interconversion process, resembling a butterfly flapping, and the presence of both conformers in acetone solution. However, the 1-f ratio is so low that it is undetectable in the excitation and emission spectra of 1 in 2-MeTHF of diluted solutions (10-5 M) at 77 K, while it is seen in more concentrated solutions (10-3 M). In acetone solution, 1 undergoes a [2c, 2e] oxidation by CHX3 (X = Cl, Br) in the sunlight to render the Pt2(III, III) compounds [{Pt(C¿C*)(µ-pz)X)}2] (X = Cl (2-Cl), Br (2-Br)). In concentrated solutions, 1 can react with CHCl3 under blue light to give 2-Cl and with CHBr3 in the dark, the latter rendering the compound [BrPt(C¿C*)(µ-pz)2Pt(C¿C*)CHBr2] (3-Br) or mixtures of 2-Br and 3-Br if the reaction is performed under an argon atmosphere or in the air, respectively. Mechanistic studies showed that in concentrated solutions the oxidation processes follow a radical mechanism being the MMLCT-based species 1-f, those which trigger the reaction of 1 with CHBr3 and CHCl3. In the ground state (S0f), it promotes the thermal oxidation of 1 by CHBr3 and in the first singlet excited state (S1f) the blue-light-driven photooxidation of 1 by CHCl3. Complexes, 2-Cl, 2-Br, and 3-Br were selectively obtained and fully characterized, showing Pt-Pt distances (ca. 2.6 Å) shorter than that of the starting complex, 1. They are, together with the analogous [{Pt(C¿C*)(µ-pz)I)}2] and [IPt(C¿C*)(µ-pz)2Pt(C¿C*)CHI2], the only dinuclear metal-metal-bonded PtIII(µ-pz)2PtIII compounds reported to date

Biomaterials for Cardiac Tissue Engineering

Semiotics / semiolog