Parametric attosecond pulse amplification far from the ionization threshold from high order harmonic generation in He+^+

Parametric amplification of attosecond coherent pulses around 100 eV at the single-atom level is demonstrated for the first time by using the 3D time-dependent Schr{\"o}dinger equation in high-harmonic generation processes from excited states of He$^+$. We present the attosecond dynamics of the amplification process far from the ionization threshold and resolve the physics behind it. The amplification of a particular central photon energy requires the seed XUV pulses to be perfectly synchronized in time with the driving laser field for stimulated recombination to the He$^+$ ground state and is only produced in a few specific laser cycles in agreement with the experimental measurements. Our simulations show that the amplified photon energy region can be controlled by varying the peak intensity of the laser field. Our results pave the way to the realization of compact attosecond pulse intense XUV lasers with broad applications

Sur les exposants de Lyapounov des applications meromorphes

Let f be a dominating meromorphic self-map of a compact Kahler manifold. We give an inequality for the Lyapounov exponents of some ergodic measures of f using the metric entropy and the dynamical degrees of f. We deduce the hyperbolicity of some measures.Comment: 27 pages, paper in french, final version: to appear in Inventiones Mat

Farkas-Type Results for Vector-Valued Functions with Applications

The main purpose of this paper consists of providing characterizations of the inclusion of the solution set of a given conic system posed in a real locally convex topological space into a variety of subsets of the same space defined by means of vector-valued functions. These Farkas-type results are used to derive characterizations of the weak solutions of vector optimization problems (including multiobjective and scalar ones), vector variational inequalities, and vector equilibrium problems.This research was partially supported by MINECO of Spain and FEDER of EU, Grant MTM2014-59179-C2-1-P, by the project DP160100854 from the Australian Research Council, and by the project B2015-28-04: “A new approach to some classes of optimization problems” from the Vietnam National University - HCM city, Vietnam

A Multi-Size Study of Gold Nanoparticle Degradation and Reformation in Ceramic Glazes

Most traditional ceramic glazes employ high amounts of transition metal colorants that are toxic to the environment and can cause health issues in humans through surface leaching. Gold nanoparticles (Au-NPs) have been found to be environmentally friendly and non-toxic alternative metal colorant in ceramic glazes. The plasmon band observed with Au-NPs can result in vibrant solutions by manipulating NP size, shape, and concentration; however, the effects of traditional firing in both reductive and oxidative kilns on Au-NPs are poorly understood. Aside from ancient art processes whose mechanisms have not been fully explored, the use of Au-NPs as suspended ceramic glaze colorants remains somewhat unexplored. Au-NPs have been previously reported to diminish in size during sintering and possess significant differences in concentration with respect to reduction and oxidation firing atmospheres. As a means of studying possible degradation/renucleation processes within the glaze during firing, a systematic study introducing different diameter Au-NPs into the glaze materials was conducted with transmission electron microscopy and reflectance spectroscopy used to probe possible mechanisms which showed changes to Au-NP diameter and color intensity, making this work applicable to industry and art current practices

Detection of chloronium and measurement of the 35Cl/37Cl isotopic ratio at z=0.89 toward PKS1830-211

We report the first extragalactic detection of chloronium (H2Cl+), in the z=0.89 absorber in front of the lensed blazar PKS1830-211. The ion is detected through its 1_11-0_00 line along two independent lines of sight toward the North-East and South-West images of the blazar. The relative abundance of H2Cl+ is significantly higher (by a factor ~7) in the NE line of sight, which has a lower H2/H fraction, indicating that H2Cl+ preferably traces the diffuse gas component. From the ratio of the H2^35Cl+ and H2^37Cl+ absorptions toward the SW image, we measure a 35Cl/37Cl isotopic ratio of 3.1 (-0.2; +0.3) at z=0.89, similar to that observed in the Galaxy and the solar system.Comment: Accepted for publication in A&A Lette

On The Global Renormalization and Regularization of Several Complex Variable Zeta Functions by Computer

This review concerns the resolution of a special case of Knizhnik-Zamolodchikov equations ($KZ_3$) using our recent results on combinatorial aspects of zeta functions on several variables and software on noncommutative symbolic computations. In particular, we describe the actual solution of $(KZ_3)$ leading to the unique noncommutative series, $\Phi_{KZ}$, so-called Drinfel'd associator (or Drinfel'd series). Non-trivial expressions for series with rational coefficients, satisfying the same properties with $\Phi_{KZ}$, are also explicitly provided due to the algebraic structure and the singularity analysis of the polylogarithms and harmonic sums

On the solutions of universal differential equation by noncommutative Picard-Vessiot theory

Basing on Picard-Vessiot theory of noncommutative differential equations and algebraic combinatorics on noncommutative formal series with holomorphic coefficients, various recursive constructions of sequences of grouplike series converging to solutions of universal differential equation are proposed. Basing on monoidal factorizations, these constructions intensively use diagonal series and various pairs of bases in duality, in concatenation-shuffle bialgebra and in a Loday's generalized bialgebra. As applications, the unique solution, satisfying asymptotic conditions, of Knizhnik-Zamolodchikov equations is provided by d\'evissage

Families of eulerian functions involved in regularization of divergent polyzetas

Extending the Eulerian functions, we study their relationship with zeta function of several variables. In particular, starting with Weierstrass factorization theorem (and Newton-Girard identity) for the complex Gamma function, we are interested in the ratios of $\zeta(2k)/\pi^{2k}$ and their multiindexed generalization, we will obtain an analogue situation and draw some consequences about a structure of the algebra of polyzetas values, by means of some combinatorics of noncommutative rational series. The same combinatorial frameworks also allow to study the independence of a family of eulerian functions.Comment: preprin

A spectral line survey in the 2 mm and 1.3 mm windows toward the carbon rich envelope of IRC +10216

We present the results of our spectral line surveys in the 2 mm and 1.3 mm windows toward the carbon rich envelope of IRC +10216. Totally 377 lines are detected, among which 360 lines are assigned to 57 known molecules (including 29 rare isotopomers and 2 cyclic isomers). Only 17 weak lines remain unidentified. Rotational lines of isotopomers 13CCH and HN13C are detected for the first time in IRC +10216. The detection of the formaldehyde lines in this star is also confirmed. Possible abundance difference among the three 13C substituted isotopic isomers of HC3N is reported. Isotopic ratios of C and O are confirmed to be non-solar while those of S and Si to be nearly solar. Column densities have been estimated for 15 molecular species. Modified spectroscopic parameters have been calculated for NaCN, Na13CN, KCN and SiC2. Transition frequencies from the present observations were used to improve the spectroscopic parameters of Si13CC, 29SiC2 and 30SiC2.Comment: 17 pages of text, 18 pages of 14 tables, 35 pages of 4 figures, a typo corrected in Abstrac

On Proper Polynomial Maps of C2.\mathbb{C}^2.

Two proper polynomial maps $f_1, f_2 \colon \mathbb{C}^2 \longrightarrow \mathbb{C}^2$ are said to be \emph{equivalent} if there exist $\Phi_1, \Phi_2 \in \textrm{Aut}(\mathbb{C}^2)$ such that $f_2=\Phi_2 \circ f_1 \circ \Phi_1$. We investigate proper polynomial maps of arbitrary topological degree $d \geq 2$ up to equivalence. Under the further assumption that the maps are Galois coverings we also provide the complete description of equivalence classes. This widely extends previous results obtained by Lamy in the case $d=2$.Comment: 15 pages. Final version, to appear in Journal of Geometric Analysi