Generalization of the effective Wiener-Ikehara theorem

International audienceWe consider the classical Wiener–Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known asymptotic evaluation of the transformed function, when the usual conditions of the Wiener-Ikehara theorem hold. However, our version also provides an effective error term, not known thus far in this generality. The crux of the proof is a proper asymptotic variation of the lemmas of Ganelius and Tenenbaum, also constructed for the sake of an effective version of the Wiener–Ikehara theorem

Pure braid subgroups of braided Thompson's groups

We describe pure braided versions of Thompson's group F. These groups, $BF$ and $\hat{BF}$, are subgroups of the braided versions of Thompson's group V, introduced by Brin and Dehornoy. Unlike V, elements of F are order-preserving self-maps of the interval and we use pure braids together with elements of F thus preserving order. We define these groups and give normal forms for elements and describe infinite and finite presentations of these groups.Comment: 26 pages, 6 figures, with updated bibliograph

On one-dimensional models for hydrodynamics

To date it has not been possible to prove whether or not the three-dimensional incompressible Euler equations develop singular behaviour in finite time. Some possible singular scenarios, as for instance shock-waves, are very important from a physical point of view, since they imply the connection among the macroscopic and the microscopic scale. Therefore, the appearence of this type of singularity or a similar one might be interpreted as a possible explanation of the transition to turbulence. In order to clarify the question, some one-dimensional models for ideal incompressible hydrodynamics have been introduced and analyzed, and it was proven that shock-waves appear in finite time within this type of flow. In this work we question the validity of these models and analyze the physical meaning that the occurrence of a singularity in an incompressible flow, if it happens, may have

The 2011 February superoutburst of the dwarf nova SDSS J112003.40+663632.4

We report unfiltered photometry of SDSS J112003.40+663632.4 during the 2011 February outburst which revealed the presence of superhumps with peak-to-peak amplitude of up to 0.22 magnitudes showing this to be an SU UMa type dwarf nova. The outburst amplitude was 5.4 magnitudes above mean quiescence and it lasted at least 12 days. The mean superhump period during the plateau phase was Psh = 0.07057(19) d.Comment: Accepted for publication in the Journal of the British Astronomical Association. 12 pages, 5 figure

Detection of Supergranulation Alignment in Polar Regions of the Sun by Helioseismology

We report on a new phenomenon of `alignment' of supergranulation cells in the polar regions of the Sun. Recent high-resolution datasets obtained by the Solar Optical Telescope onboard the Hinode satellite enabled us to investigate supergranular structures in high-latitude regions of the Sun. We have carried out a local helioseismology time-distance analysis of the data, and detected acoustic travel-time variations due to the supergranular flows. The supergranulation cells in both the north and south polar regions show systematic alignment patterns in the north-south direction. The south-pole datasets obtained in a month-long Hinode campaign indicate that the supergranulation alignment property may be quite common in the polar regions. We also discuss the latitudinal dependence of the supergranulation cell sizes; the data show that the east-west cell size decreases towards higher latitudes.Comment: 7 pages, 5 figures. Accepted for publication in ApJ Letters. Minor modifications in figures and text

Magnetohydrodynamics of the Weakly Ionized Solar Photosphere

We investigate the importance of ambipolar diffusion and Hall currents for high-resolution comprehensive ('realistic') photospheric simulations. To do so we extended the radiative magnetohydrodynamics code \emph{MURaM} to use the generalized Ohm's law under the assumption of local thermodynamic equilibrium. We present test cases comparing analytical solutions with numerical simulations for validation of the code. Furthermore, we carried out a number of numerical experiments to investigate the impact of these neutral-ion effects in the photosphere. We find that, at the spatial resolutions currently used (5-20 km per grid point), the Hall currents and ambipolar diffusion begin to become significant -- with flows of 100 m/s in sunspot light bridges, and changes of a few percent in the thermodynamic structure of quiet-Sun magnetic features. The magnitude of the effects is expected to increase rapidly as smaller-scale variations are resolved by the simulations.Comment: accepted Ap

Negative powers of Laguerre operators

We study negative powers of Laguerre differential operators in $\R$, $d\ge1$. For these operators we prove two-weight $L^p-L^q$ estimates, with ranges of $q$ depending on $p$. The case of the harmonic oscillator (Hermite operator) has recently been treated by Bongioanni and Torrea by using a straightforward approach of kernel estimates. Here these results are applied in certain Laguerre settings. The procedure is fairly direct for Laguerre function expansions of Hermite type, due to some monotonicity properties of the kernels involved. The case of Laguerre function expansions of convolution type is less straightforward. For half-integer type indices $\alpha$ we transfer the desired results from the Hermite setting and then apply an interpolation argument based on a device we call the {\sl convexity principle} to cover the continuous range of $\alpha\in[-1/2,\infty)^d$. Finally, we investigate negative powers of the Dunkl harmonic oscillator in the context of a finite reflection group acting on $\R$ and isomorphic to $\mathbb Z^d_2$. The two weight $L^p-L^q$ estimates we obtain in this setting are essentially consequences of those for Laguerre function expansions of convolution type.Comment: 30 page

Emissions from pre-Hispanic metallurgy in the South American atmosphere

Peer reviewedPublisher PD