Spatially resolved physical and chemical properties of the planetary nebula NGC 3242

Optical integral-field spectroscopy was used to investigate the planetary nebula NGC 3242. We analysed the main morphological components of this source, including its knots, but not the halo. In addition to revealing the properties ofthe physical and chemical nature of this nebula, we also provided reliable spatially resolved constraints that can be used for future photoionisation modelling of the nebula. The latter is ultimately necessary to obtain a fully self-consistent 3D picture of the physical and chemical properties of the object. The observations were obtained with the VIMOS instrument attached to VLT-UT3. Maps and values for specific morphological zones for the detected emission-lines were obtained and analysed with routines developed by the authors to derive physical and chemical conditions of the ionised gas in a 2D fashion. We obtained spatially resolved maps and mean values of the electron densities, temperatures, and chemical abundances, for specific morphological structures in NGC 3242. These results show the pixel-to-pixel variations of the the small- and large-scale structures of the source. These diagnostic maps provide information free from the biases introduced by traditional single long-slit observations. In general, our results are consistent with a uniform abundance distribution for the object, whether we look at abundance maps or integrated fluxes from specified morphological structures. The results indicate that special care should be taken with the calibration of the data and that only data with extremely good signal-to-noise ratio and spectral coverage should be used to ensure the detection of possible spatial variations.Comment: 11 pages, 8 figures accepted for publication in Astronomy & Astrophysic

Negative modes and the thermodynamics of Reissner-Nordstr\"om black holes

We analyse the problem of negative modes of the Euclidean section of the Reissner-Nordstr\"om black hole in four dimensions. We find analytically that a negative mode disappears when the specific heat at constant charge becomes positive. The sector of perturbations analysed here is included in the canonical partition function of the magnetically charged black hole. The result obeys the usual rule that the partition function is only well-defined when there is local thermodynamical equilibrium. We point out the difficulty in quantising Einstein-Maxwell theory, where the so-called conformal factor problem is considerably more intricate. Our method, inspired by hep-th/0608001, allows us to decouple the divergent gauge volume and treat the metric perturbations sector in a gauge-invariant way.Comment: 24 pages, 1 figure; v2 minor changes to fit published versio

The Quantum Algebraic Structure of the Twisted XXZ Chain

We consider the Quantum Inverse Scattering Method with a new R-matrix depending on two parameters $q$ and $t$. We find that the underlying algebraic structure is the two-parameter deformed algebra $SU_{q,t}(2)$ enlarged by introducing an element belonging to the centre. The corresponding Hamiltonian describes the spin-1/2 XXZ model with twisted periodic boundary conditions.Comment: LateX file, 9 pages, Minor changes (including authors` names in the hep-th heading

Estimation of Risk-Neutral Density Surfaces

Option price data is often used to infer risk-neutral densities for future prices of an underlying asset. Given the prices of a set of options on the same underlying asset with different strikes and maturities, we propose a nonparametric approach for estimating risk-neutral densities associated with several maturities. Our method uses bicubic splines in order to achieve the desired smoothness for the estimation and an optimization model to choose the spline functions that best fit the price data. Semidefinite programming is employed to guarantee the nonnegativity of the densities. We illustrate the process using synthetic option price data generated using log-normal and absolute diffusion processes as well as actual price data for options on the S&P500 index. We also used the risk-neutral densities that we computed to price exotic options and observed that this approach generates prices that closely approximate the market prices of these options.

Synthesis and properties of Co-doped titanate nanotubes and their optical sensitization with methylene blue

Here we report on a novel chemical route to synthesize homogenous cobalt doped titanate nanotubes (CoTNT), using an amorphous Co-doped precursor. The influence of the synthesis temperature, autoclave dwell time and metal doping on the structural and microstructural as well as on the optical properties of the synthesized titanate nanotubes is studied and discussed. The optical band gaps of the CoTNT samples are red shifted in comparison with the values determined for the undoped samples, such red shifts bringing the absorption edge of the CoTNT samples into the visible region. CoTNT materials also demonstrate particular high adsorption ability for methylene blue, the amount of the adsorbed dye being higher than the one predictable for a monolayer formation. This suggests the possibility of intercalation of the dye molecule between the TiO6 layers of the TNT structure. It is also shown that the methylene blue sensitized Co-doped nanostructures are highly stable under UV radiation and present a strong and broad absorption in the visible region.Comment: 31 pages, 3 tables, 7 figure

Some boundary effects in quantum field theory

We have constructed a quantum field theory in a finite box, with periodic boundary conditions, using the hypothesis that particles living in a finite box are created and/or annihilated by the creation and/or annihilation operators, respectively, of a quantum harmonic oscillator on a circle. An expression for the effective coupling constant is obtained showing explicitly its dependence on the dimension of the box.Comment: 12 pages, Late