CMB in a box: causal structure and the Fourier-Bessel expansion

This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light-cone of the observer. This happens order by order in a series expansion in powers of the visibility $\gamma=e^{-\mu}$, where $\mu$ is the optical depth to Thompson scattering. We show that the CMB anisotropies are regulated by spacetime window functions which have support only inside the past light-cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. In that expansion, for each multipole $l$ there is a discrete tower of momenta $k_{i,l}$ (not a continuum) which can affect physical observables, with the smallest momenta being $k_{1,l} ~ l$. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation - no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies. (Abridged)Comment: 23 pages, 7 figure

The effects of tax incentives for small firms on employment levels

This paper will examine the effects of tax incentives for small businesseson employment level evaluating a program with this purpose implemented in Brazil in the 1990s. We first develop a theoretical framework which guides both the de nition of the parameters of interest and their identi cation. Selection problems both into the treatment group and into the data sampleare tackled by combining fi xed effects methods and regression discontinuity design on alternative sub-samples of a longitudinal database of manufacturing fi rms. The results show that on the one hand the size composition of thetreated fi rms may be changed due to the survival of some smaller fi rms that would have exited had it not been eligible to the program. On the other hand, the treated fi rms who do not depend on the program to survive do employ more workers.

Memristors using solution-based IGZO nanoparticles

Solution-based indium-gallium-zinc oldde (IGZO) nanoparticles deposited by spin coating have been investigated as a resistive switching layer in metal-insulator-metal structures for nonvolatile memory applications. Optimized devices show a bipolar resistive switching behavior, low programming voltages of +/- 1 V, on/off ratios higher than 10, high endurance, and a retention time of up to 104 s. The better performing devices were achieved with annealing temperatures of 200 degrees C and using asymmetric electrode materials of titanium and silver. The physics behind the improved switching properties of the devices is discussed in terms of the oxygen deficiency of IGZO. Temperature analysis of the conductance states revealed a nonmetallic filamentary conduction. The presented devices are potential candidates for the integration of memory functionality into low-cost System-on-Panel technology.National Funds through FCT - Portuguese Foundation for Science and Technology [UID/CTM/50025/2013, SFRH/BDP/99136/2013]; FEDER [POCI-01-0145-FEDER-007688]info:eu-repo/semantics/publishedVersio