Stability of switched linear differential systems

We study the stability of switched systems where the dynamic modes are described by systems of higher-order linear differential equations not necessarily sharing the same state space. Concatenability of trajectories at the switching instants is specified by gluing conditions, i.e. algebraic conditions on the trajectories and their derivatives at the switching instant. We provide sufficient conditions for stability based on LMIs for systems with general gluing conditions. We also analyse the role of positive-realness in providing sufficient polynomial-algebraic conditions for stability of two-modes switched systems with special gluing conditions

Eisenstein Series and String Thresholds

We investigate the relevance of Eisenstein series for representing certain $G(Z)$-invariant string theory amplitudes which receive corrections from BPS states only. $G(Z)$ may stand for any of the mapping class, T-duality and U-duality groups $Sl(d,Z)$, $SO(d,d,Z)$ or $E_{d+1(d+1)}(Z)$ respectively. Using $G(Z)$-invariant mass formulae, we construct invariant modular functions on the symmetric space $K\backslash G(R)$ of non-compact type, with $K$ the maximal compact subgroup of $G(R)$, that generalize the standard non-holomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincar\'e upper half-plane. Comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one- and $g$-loop string amplitudes, we obtain a manifestly T-duality invariant representation of the latter, conjecture their non-perturbative U-duality invariant extension, and analyze the resulting non-perturbative effects. This includes the $R^4$ and $R^4 H^{4g-4}$ couplings in toroidal compactifications of M-theory to any dimension $D\geq 4$ and $D\geq 6$ respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms renumbered, plus minor corrections; v3: relation (1.7) to math Eis series clarified, eq (3.3) and minor typos corrected, final version to appear in Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde

TWO-PION EXCHANGE NUCLEAR POTENTIAL - CHIRAL CANCELLATIONS

We show that chiral symmetry is responsible for large cancellations in the two-pion exchange nucleon-nucleon interaction, which are similar to those occuring in free pion-nucleon scattering.Comment: REVTEX style, 5 pages, 3 PostScrip figures compressed, tarred and uuencode

On the dimensional dependence of duality groups for massive p-forms

We study the soldering formalism in the context of abelian p-form theories. We develop further the fusion process of massless antisymmetric tensors of different ranks into a massive p-form and establish its duality properties. To illustrate the formalism we consider two situations. First the soldering mass generation mechanism is compared with the Higgs and Julia-Toulouse mechanisms for mass generation due to condensation of electric and magnetic topological defects. We show that the soldering mechanism interpolates between them for even dimensional spacetimes, in this way confirming the Higgs/Julia-Toulouse duality proposed by Quevedo and Trugenberger \cite{QT} a few years ago. Next, soldering is applied to the study of duality group classification of the massive forms. We show a dichotomy controlled by the parity of the operator defining the symplectic structure of the theory and find their explicit actions.Comment: Reference [8] has been properly place

Homogeneous abundance analysis of dwarf, subgiant and giant FGK stars with and without giant planets

We have analyzed high-resolution and high signal-to-noise ratio optical spectra of nearby FGK stars with and without detected giant planets in order to homogeneously measure their photospheric parameters, mass, age, and the abundances of volatile (C, N, and O) and refractory (Na, Mg, Si, Ca, Ti, V, Mn, Fe, Ni, Cu, and Ba) elements. Our sample contains 309 stars from the solar neighborhood (up to the distance of 100 pc), out of which 140 are dwarfs, 29 are subgiants, and 140 are giants. The photospheric parameters are derived from the equivalent widths of Fe I and Fe II lines. Masses and ages come from the interpolation in evolutionary tracks and isochrones on the HR diagram. The abundance determination is based on the equivalent widths of selected atomic lines of the refractory elements and on the spectral synthesis of C_2, CN, C I, O I, and Na I features. We apply a set of statistical methods to analyze the abundances derived for the three subsamples. Our results show that: i) giant stars systematically exhibit underabundance in [C/Fe] and overabundance in [N/Fe] and [Na/Fe] in comparison with dwarfs, a result that is normally attributed to evolution-induced mixing processes in the envelope of evolved stars; ii) for solar analogs only, the abundance trends with the condensation temperature of the elements are correlated with age and anticorrelated with the surface gravity, which is in agreement with recent studies; iii) as in the case of [Fe/H], dwarf stars with giant planets are systematically enriched in [X/H] for all the analyzed elements, except for O and Ba (the former due to limitations of statistics), confirming previous findings in the literature that not only iron has an important relation with the planetary formation; and iv) giant planet hosts are also significantly overabundant for the same metallicity when the elements from Mg to Cu are combined together.Comment: 20 pages, 16 figures, 8 table