On analytic properties of Meixner-Sobolev orthogonal polynomials of higher order difference operators

In this contribution we consider sequences of monic polynomials orthogonal with respect to Sobolev-type inner product $$\left\langle f,g\right\rangle= \langle {\bf u}^{\tt M},fg\rangle+\lambda \mathscr T^j f (\alpha)\mathscr T^{j}g(\alpha),$$ where ${\bf u}^{\tt M}$ is the Meixner linear operator, $\lambda\in\mathbb{R}_{+}$, $j\in\mathbb{N}$, $\alpha \leq 0$, and $\mathscr T$ is the forward difference operator $\Delta$, or the backward difference operator $\nabla$. We derive an explicit representation for these polynomials. The ladder operators associated with these polynomials are obtained, and the linear difference equation of second order is also given. In addition, for these polynomials we derive a $(2j+3)$-term recurrence relation. Finally, we find the Mehler-Heine type formula for the $\alpha\le 0$ case

The double torus as a 2D cosmos: groups, geometry and closed geodesics

The double torus provides a relativistic model for a closed 2D cosmos with topology of genus 2 and constant negative curvature. Its unfolding into an octagon extends to an octagonal tessellation of its universal covering, the hyperbolic space H^2. The tessellation is analysed with tools from hyperbolic crystallography. Actions on H^2 of groups/subgroups are identified for SU(1, 1), for a hyperbolic Coxeter group acting also on SU(1, 1), and for the homotopy group \Phi_2 whose extension is normal in the Coxeter group. Closed geodesics arise from links on H^2 between octagon centres. The direction and length of the shortest closed geodesics is computed.Comment: Latex, 27 pages, 5 figures (late submission to arxiv.org

Detector developments for the hypernuclear programme at PANDA

The technical design of the PANDA experiment at the future FAIR facility next to GSI is progressing. At the proposed anti-proton storage ring the spectroscopy of double Lambda hypernuclei is one of the four main topics which will be addressed by the Collaboration. The hypernuclear experiments require (i) a dedicated internal target, (ii) an active secondary target of alternating silicon and absorber material layers, (iii) high purity germanium (HPGe) detectors, and (iv) a good particle identification system for low momentum kaons. All systems need to operate in the presence of a high magnetic field and a large hadronic background. The status of the detector developments for this programme is summarized.Comment: Contributed to 2008 IEEE Nuclear Science Symposium, 19-25 October 2008, Dresden, German

Specsim: The MIRI Medium Resolution Spectrometer Simulator

MIRI, the Mid-InfraRed Instrument, is one of four instruments being built for the James Webb Space Telescope, and is developed jointly between an EuropeanConsortium and the US. In this paper we present a software data simulator for one of MIRI's four instruments: the Integral Field Unit (IFU) Medium Resolution Spectrometer (MIRI-MRS), the first mid-infrared IFU spectrograph, and one of the first IFUs to be used in a space mission. To give the MIRI community a preview of the properties of the MIRI-MRS data products before the telescope is operational, the Specsim tool has been developed to model, in software, the operation of the spectrometer. Specsim generates synthetic data frames approximating those which will be taken by the instrument in orbit. The program models astronomical sources and generates detector frames using the predicted and measured optical properties of the telescope and MIRI. These frames can then be used to illustrate and inform a range of operational activities, including data calibration strategies and the development and testing of the data reduction software for the MIRI-MRS. Specsim will serve as a means of communication between the many consortium members by providing a way to easily illustrate the performance of the spectrometer under different circumstances, tolerances of components and design scenarios.Comment: 8 pages, 5 figures; A high resolution version is available at http://www.roe.ac.uk/~npfl/Publications/lgw+06.ps.gz (Changed URL of high-res version

A Secure Steganographic Algorithm Based on Frequency Domain for the Transmission of Hidden Information

This contribution proposes a novel steganographic method based on the compression standard according to the Joint Photographic Expert Group and an Entropy Thresholding technique. The steganographic algorithm uses one public key and one private key to generate a binary sequence of pseudorandom numbers that indicate where the elements of the binary sequence of a secret message will be inserted. The insertion takes eventually place at the first seven AC coefficients in the transformed DCT domain. Before the insertion of the message the image undergoes several transformations. After the insertion the inverse transformations are applied in reverse order to the original transformations. The insertion itself takes only place if an entropy threshold of the corresponding block is satisfied and if the pseudorandom number indicates to do so. The experimental work on the validation of the algorithm consists of the calculation of the peak signal-to-noise ratio (PSNR), the difference and correlation distortion metrics, the histogram analysis, and the relative entropy, comparing the same characteristics for the cover and stego image. The proposed algorithm improves the level of imperceptibility analyzed through the PSNR values. A steganalysis experiment shows that the proposed algorithm is highly resistant against the Chi-square attack

Surface embedding, topology and dualization for spin networks

Spin networks are graphs derived from 3nj symbols of angular momentum. The surface embedding, the topology and dualization of these networks are considered. Embeddings into compact surfaces include the orientable sphere S^2 and the torus T, and the not orientable projective space P^2 and Klein's bottle K. Two families of 3nj graphs admit embeddings of minimal genus into S^2 and P^2. Their dual 2-skeletons are shown to be triangulations of these surfaces.Comment: LaTeX 17 pages, 6 eps figures (late submission to arxiv.org