Instabilities in Zakharov Equations for Laser Propagation in a Plasma

F.Linares, G.Ponce, J-C.Saut have proved that a non-fully dispersive Zakharov system arising in the study of Laser-plasma interaction, is locally well posed in the whole space, for fields vanishing at infinity. Here we show that in the periodic case, seen as a model for fields non-vanishing at infinity, the system develops strong instabilities of Hadamard's type, implying that the Cauchy problem is strongly ill-posed

The ROSAT Deep Cluster Survey: the X-ray Luminosity Function out to z=0.8

We present the X-ray Luminosity Function (XLF) of the ROSAT Deep Cluster Survey (RDCS) sample over the redshift range 0.05-0.8. Our results are derived from a complete flux-limited subsample of 70 galaxy clusters, representing the brightest half of the total sample, which have been spectroscopically identified down to the flux limit of 4*10^{-14} erg/cm^2/s (0.5-2.0 keV) and have been selected via a serendipitous search in ROSAT-PSPC pointed observations. The redshift baseline is large enough that evolutionary effects can be studied within the sample. The local XLF (z < 0.25) is found to be in excellent agreement with previous determinations using the ROSAT All-Sky Survey data. The XLF at higher redshifts, when combined with the deepest number counts constructed to date (f>2*10^{-14} arg/cm^2/s), reveal no significant evolution at least out to z=0.8, over a luminosity range 2*10^{42}-3*10^{44} erg/s in the [0.5-2 keV] band. These findings extend the study of cluster evolution to the highest redshifts and the faintest fluxes probed so far in X-ray surveys. They complement and do not necessarily conflict with those of the Einstein Extended Medium Sensitivity Survey, leaving the possibility of negative evolution of the brightest end of the XLF at high redshifts.Comment: 12 pages, 4 figures, LaTeX (aasms4.sty). To appear in ApJ Letter

Optimal Quantum Circuits for General Two-Qubit Gates

In order to demonstrate non-trivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortest possible sequence of one-qubit and two-qubit gates. We contribute to this effort by providing a method to construct an optimal quantum circuit for a general two-qubit gate that requires at most 3 CNOT gates and 15 elementary one-qubit gates. Moreover, if the desired two-qubit gate corresponds to a purely real unitary transformation, we provide a construction that requires at most 2 CNOTs and 12 one-qubit gates. We then prove that these constructions are optimal with respect to the family of CNOT, y-rotation, z-rotation, and phase gates.Comment: 6 pages, 8 figures, new title, final journal versio

Modification of chiral dimethyl tartrate through transesterification : immobilisation on POSS and enantioselectivity reversion in Sharpless asymmetric epoxidation

Modification of dimethyl tartrate has been investigated through transesterification with aminoalcohols to provide reactive functionalities for the covalent bonding of chiral tartrate to polyhedral oligomeric silsesquioxanes. The transesterification of dimethyl tartrate has been widely studied by means of using different catalytic systems and reaction conditions. Through the proper selection of both, the catalytic system and the reaction conditions, it is possible to achieve the mono- or the bis-substituted tartrate derivative as sole products. All the intermediate chiral tartrate-derived ligands were successfully used in the homogeneous enantioselective epoxidation of allylic alcohols providing moderate enantiomeric excess over the products. Attached amine groups have been used to support the modified tartrate ligands onto a haloaryl-functionalized silsesquioxane moiety. This final chiral tartrate ligand displays enantioselectivity reversion in the asymmetric epoxidation of allylic alcohols with regards to the starting dimethyl tartrate ligand, having both molecules them the same chiral sign. However, the POSS-containing ligand can be easily recovered in almost quantitative yield and reused in asymmetric epoxidation reactions. In addition, recovered silsesquioxane-pendant ligand, though displaying decreasing catalytic activity in recycling epoxidation tests, showed very stable enantioselective behavior

Advanced Mid-Water Tools for 4D Marine Data Fusion and Visualization

Mapping and charting of the seafloor underwent a revolution approximately 20 years ago with the introduction of multibeam sonars -- sonars that provided complete, high-resolution coverage of the seafloor rather than sparse measurements. The initial focus of these sonar systems was the charting of depths in support of safety of navigation and offshore exploration; more recently innovations in processing software have led to approaches to characterize seafloor type and for mapping seafloor habitat in support of fisheries research. In recent years, a new generation of multibeam sonars has been developed that, for the first time, have the ability to map the water column along with the seafloor. This ability will potentially allow multibeam sonars to address a number of critical ocean problems including the direct mapping of fish and marine mammals, the location of mid-water targets and, if water column properties are appropriate, a wide range of physical oceanographic processes. This potential relies on suitable software to make use of all of the new available data. Currently, the users of these sonars have a limited view of the mid-water data in real-time and limited capacity to store it, replay it, or run further analysis. The data also needs to be integrated with other sensor assets such as bathymetry, backscatter, sub-bottom, seafloor characterizations and other assets so that a “complete” picture of the marine environment under analysis can be realized. Software tools developed for this type of data integration should support a wide range of sonars with a unified format for the wide variety of mid-water sonar types. This paper describes the evolution and result of an effort to create a software tool that meets these needs, and details case studies using the new tools in the areas of fisheries research, static target search, wreck surveys and physical oceanographic processes

Closed but provocative questions: curves enclosing unit area

This article describes a task leading to work on curve sketching, simultaneous equations and integration to find the area enclosed between two curves. An initial closed question is used to confront students with a provocative answer, which they then explore in a much more open-ended way

On the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approach

We consider a metric graph $\mathcal{G}$ made of two graphs $\mathcal{G}_1$ and $\mathcal{G}_2$ attached at one point. We derive a formula relating the spectral determinant of the Laplace operator $S_\mathcal{G}(\gamma)=\det(\gamma-\Delta)$ in terms of the spectral determinants of the two subgraphs. The result is generalized to describe the attachment of $n$ graphs. The formulae are also valid for the spectral determinant of the Schr\"odinger operator $\det(\gamma-\Delta+V(x))$.Comment: LaTeX, 8 pages, 7 eps figures, v2: new appendix, v3: discussions and ref adde