On the Strong Homotopy Lie-Rinehart Algebra of a Foliation

It is well known that a foliation F of a smooth manifold M gives rise to a rich cohomological theory, its characteristic (i.e., leafwise) cohomology. Characteristic cohomologies of F may be interpreted, to some extent, as functions on the space P of integral manifolds (of any dimension) of the characteristic distribution C of F. Similarly, characteristic cohomologies with local coefficients in the normal bundle TM/C of F may be interpreted as vector fields on P. In particular, they possess a (graded) Lie bracket and act on characteristic cohomology H. In this paper, I discuss how both the Lie bracket and the action on H come from a strong homotopy structure at the level of cochains. Finally, I show that such a strong homotopy structure is canonical up to isomorphisms.Comment: 41 pages, v2: almost completely rewritten, title changed; v3: presentation partly changed after numerous suggestions by Jim Stasheff, mathematical content unchanged; v4: minor revisions, references added. v5: (hopefully) final versio

There are no multiply-perfect Fibonacci numbers

Here, we show that no Fibonacci number (larger than 1) divides the sum of its divisors

Kerr black hole lensing for generic observers in the strong deflection limit

We generalize our previous work on gravitational lensing by a Kerr black hole in the strong deflection limit, removing the restriction to observers on the equatorial plane. Starting from the Schwarzschild solution and adding corrections up to the second order in the black hole spin, we perform a complete analytical study of the lens equation for relativistic images created by photons passing very close to a Kerr black hole. We find out that, to the lowest order, all observables (including shape and shift of the black hole shadow, caustic drift and size, images position and magnification) depend on the projection of the spin on a plane orthogonal to the line of sight. In order to break the degeneracy between the black hole spin and its inclination relative to the observer, it is necessary to push the expansion to higher orders. In terms of future VLBI observations, this implies that very accurate measures are needed to determine these two parameters separately.Comment: 17 pages, 4 figures, one section added, to appear on Physical Review

Nori 1-motives

Let EHM be Nori's category of effective homological mixed motives. In this paper, we consider the thick abelian subcategory EHM_1 generated by the i-th relative homology of pairs of varieties for i = 0,1. We show that EHM_1 is naturally equivalent to the abelian category M_1 of Deligne 1-motives with torsion; this is our main theorem. Along the way, we obtain several interesting results. Firstly, we realize M_1 as the universal abelian category obtained, using Nori's formalism, from the Betti representation of an explicit diagram of curves. Secondly, we obtain a conceptual proof of a theorem of Vologodsky on realizations of 1-motives. Thirdly, we verify a conjecture of Deligne on extensions of 1-motives in the category of mixed realizations for those extensions that are effective in Nori's sense

Clues on the evolution of the Carina dwarf spheroidal galaxy from the color distribution of its red giant stars

The thin red giant branch (RGB) of the Carina dwarf spheroidal galaxy appears at first sight quite puzzling and seemingly in contrast with the presence of several distinct bursts of star formation. In this Letter, we provide a measurement of the color spread of red giant stars in Carina based on new BVI wide-field observations, and model the width of the RGB by means of synthetic color-magnitude diagrams. The measured color spread, Sigma{V-I}=0.021 +/- 0.005, is quite naturally accounted for by the star-formation history of the galaxy. The thin RGB appears to be essentially related to the limited age range of its dominant stellar populations, with no need for a metallicity dispersion at a given age. This result is relatively robust with respect to changes in the assumed age-metallicity relation, as long as the mean metallicity over the galaxy lifetime matches the observed value ([Fe/H] = -1.91 +/- 0.12 after correction for the age effects). This analysis of photometric data also sets some constraints on the chemical evolution of Carina by indicating that the chemical abundance of the interstellar medium in Carina remained low throughout each episode of star formation even though these episodes occurred over many Gyr.Comment: 4 pages, 3 figures, accepted for publication in the Astrophysical Journal Letter

Dimensional crossover and incipient quantum size effects in superconducting niobium nanofilms

Superconducting and normal state properties of sputtered Niobium nanofilms have been systematically investigated, as a function of film thickness in a d=9-90 nm range, on different substrates. The width of the superconducting-to-normal transition for all films remained in few tens of mK, thus remarkably narrow, confirming their high quality. We found that the superconducting critical current density exhibits a pronounced maximum, three times larger than its bulk value, for film thickness around 25 nm, marking the 3D-to-2D crossover. The extracted magnetic penetration depth shows a sizeable enhancement for the thinnest films, aside the usual demagnetization effects. Additional amplification effects of the superconducting properties have been obtained in the case of sapphire substrates or squeezing the lateral size of the nanofilms. For thickness close to 20 nm we also measured a doubled perpendicular critical magnetic field compared to its saturation value for d>33 nm, indicating shortening of the correlation length and the formation of small Cooper pairs in the condensate. Our data analysis evidences an exciting interplay between quantum-size and proximity effects together with strong-coupling effects and importance of disorder in the thinnest films, locating the ones with optimally enhanced critical properties close to the BCS-BEC crossover regime

Photoactivatable organometallic pyridyl ruthenium(II) arene complexes

The synthesis and characterization of a family of piano-stool RuII arene complexes of the type [(η6-arene)Ru(N,N′)(L)][PF6]2, where arene is p-cymene (p-cym), hexamethylbenzene (hmb), or indane (ind), N,N′ is 2,2′-bipyrimidine (bpm), 1,10-phenanthroline (phen), 1,10-phenanthroline-5,6-dione (phendio), or 4,7-diphenyl-1,10-phenanthroline (bathophen), and L is pyridine (Py), 4-methylpyridine (4-MePy), 4-methoxypyridine (4-MeOPy), 4,4′-bipyridine (4,4′-bpy), 4-phenylpyridine (4-PhPy), 4-benzylpyridine (4-BzPy), 1,2,4-triazole (trz), 3-acetylpyridine (3-AcPy), nicotinamide (NA), or methyl nicotinate (MN), are reported, including the X-ray crystal structures of [(η6-p-cym)Ru(bpm)(4-MePy)]2+ (2), [(η6-p-cym)Ru(bpm)(4-BzPy)]2+ (6), [(η6-p-cym)Ru(bpm)(trz)]2+ (7), [(η6-p-cym)Ru(phen)(Py)]2+ (10), and [(η6-ind)Ru(bpy)(Py)]2+ (13). These complexes can selectively photodissociate the monodentate ligand (L) when excited with UVA or white light, allowing strict control of the formation of the reactive aqua species [(η6-arene)Ru(N,N′)(OH2)]2+ that otherwise would not form in the dark. The photoproducts were characterized by UV–vis absorption and 1H NMR spectroscopy. DFT and TD-DFT calculations were employed to characterize the excited states and to obtain information on the photochemistry of the complexes. All the RuII pyridine complexes follow a relatively similar photochemical L-ligand dissociation mechanism, likely to occur from a series of 3MC triplet states with dissociative character. The photochemical process proved to be much more efficient when UVA-range irradiation was used. More strikingly, light activation was used to phototrigger binding of these potential anticancer agents with discriminating preference toward 9-ethylguanine (9-EtG) over 9-ethyladenine (9-EtA). Calf thymus (CT)-DNA binding studies showed that the irradiated complexes bind to CT-DNA, whereas the nonirradiated forms bind negligibly. Studies of CT-DNA interactions in cell-free media suggest combined weak monofunctional coordinative and intercalative binding modes. The RuII arene complexes [(η6-p-cym)Ru(bpm)(Py)]2+ (1), [(η6-p-cym)Ru(bpm)(4-MeOPy)]2+ (3), [(η6-p-cym)Ru(4,4′-bpy)]2+ (4), [(η6-hmb)Ru(bpm)(Py)]2+ (8), [(η6-ind)Ru(bpm)(Py)]2+ (9), [(η6-p-cym)Ru(phen)(Py)]2+ (10), [(η6-p-cym)Ru(bathophen)(Py)]2+ (12), [(η6-p-cym)Ru(bpm)(NA)]2+ (15), and [(η6-p-cym)Ru(bpm)(MN)]2+ (16) were cytotoxic toward A2780 human ovarian cancer cell line in the absence of photoirradiation (IC50 values in the range of 9.0–60 μM)

The Magnetic Sensitivity of the Ba II D1 and D2 Lines of the Fraunhofer Spectrum

The physical interpretation of the spectral line polarization produced by the joint action of the Hanle and Zeeman effects offers a unique opportunity to obtain empirical information about hidden aspects of solar and stellar magnetism. To this end, it is important to achieve a complete understanding of the sensitivity of the emergent spectral line polarization to the presence of a magnetic field. Here we present a detailed theoretical investigation on the role of resonance scattering and magnetic fields on the polarization signals of the Ba II D1 and D2 lines of the Fraunhofer spectrum, respectively at 4934 \AA\ and 4554 \AA. We adopt a three-level model of Ba II, and we take into account the hyperfine structure that is shown by the $^{135}$Ba and $^{137}$Ba isotopes. Despite of their relatively small abundance (18%), the contribution coming from these two isotopes is indeed fundamental for the interpretation of the polarization signals observed in these lines. We consider an optically thin slab model, through which we can investigate in a rigorous way the essential physical mechanisms involved (resonance polarization, Zeeman, Paschen-Back and Hanle effects), avoiding complications due to radiative transfer effects. We assume the slab to be illuminated from below by the photospheric solar continuum radiation field, and we investigate the radiation scattered at 90 degrees, both in the absence and in the presence of magnetic fields, deterministic and microturbulent. We show in particular the existence of a differential magnetic sensitivity of the three-peak Q/I profile that is observed in the D2 line in quiet regions close to the solar limb, which is of great interest for magnetic field diagnostics.Comment: 40 pages, 1 table and 19 figures. Accepted for publication in The Astrophysical Journal (ApJ

Perfectly Translating Lattices on a Cylinder

We perform molecular dynamics simulations on an interacting electron gas confined to a cylindrical surface and subject to a radial magnetic field and the field of the positive background. In order to study the system at lowest energy states that still carry a current, initial configurations are obtained by a special quenching procedure. We observe the formation of a steady state in which the entire electron-lattice cycles with a common uniform velocity. Certain runs show an intermediate instability leading to lattice rearrangements. A Hall resistance can be defined and depends linearly on the magnetic field with an anomalous coefficient reflecting the manybody contributions peculiar to two dimensions.Comment: 13 pages, 5 figure