Quadratic perturbations of quadratic codimension-four centers

We study the stratum in the set of all quadratic differential systems $\dot{x}=P_2(x,y), \dot{y}=Q_2(x,y)$ with a center, known as the codimension-four case $Q_4$. It has a center and a node and a rational first integral. The limit cycles under small quadratic perturbations in the system are determined by the zeros of the first Poincar\'e-Pontryagin-Melnikov integral $I$. We show that the orbits of the unperturbed system are elliptic curves, and $I$ is a complete elliptic integral. Then using Picard-Fuchs equations and the Petrov's method (based on the argument principle), we set an upper bound of eight for the number of limit cycles produced from the period annulus around the center

Radio Detections During Two State Transitions of the Intermediate Mass Black Hole HLX-1

Relativistic jets are streams of plasma moving at appreciable fractions of the speed of light. They have been observed from stellar mass black holes ($\sim$3$-$20 solar masses, M$_\odot$) as well as supermassive black holes ($\sim$10$^6$$-$10$^9$ M$_\odot$) found in the centres of most galaxies. Jets should also be produced by intermediate mass black holes ($\sim$10$^2$$-$10$^5$ M$_\odot$), although evidence for this third class of black hole has until recently been weak. We report the detection of transient radio emission at the location of the intermediate mass black hole candidate ESO 243-49 HLX-1, which is consistent with a discrete jet ejection event. These observations also allow us to refine the mass estimate of the black hole to be between $\sim$9 $\times$10$^{3}$ M$_\odot$ and $\sim$9 $\times$10$^{4}$ M$_\odot$.Comment: 13 pages, includes supplementary online information. Published in Science in August 201

Systems control theory applied to natural and synthetic musical sounds

Systems control theory is a far developped field which helps to study stability, estimation and control of dynamical systems. The physical behaviour of musical instruments, once described by dynamical systems, can then be controlled and numerically simulated for many purposes. The aim of this paper is twofold: first, to provide the theoretical background on linear system theory, both in continuous and discrete time, mainly in the case of a finite number of degrees of freedom ; second, to give illustrative examples on wind instruments, such as the vocal tract represented as a waveguide, and a sliding flute

Spectral variability modes of GX 339-4 in a hard-to-soft state transition

We report on INTEGRAL observations performed during the 2004 outburst of the bright black hole transient GX 339-4. We analysed IBIS and JEM-X public data starting on 9th August and lasting about one month. During this period GX 339-4 showed spectral state transitions. In order to seek for variability patterns, a principal component analysis (PCA) has been used.Comment: 5 pages, 6 figures, accepted for publication in the proceedings of VI Microquasar workshop: Microquasar and Beyond, 18-22 September 2006 in Como (Italy), eds: T. Belloni et al. (2006

Continuity argument revisited: geometry of root clustering via symmetric products

We study the spaces of polynomials stratified into the sets of polynomial with fixed number of roots inside certain semialgebraic region $\Omega$, on its border, and at the complement to its closure. Presented approach is a generalisation, unification and development of several classical approaches to stability problems in control theory: root clustering ($D$-stability) developed by R.E. Kalman, B.R. Barmish, S. Gutman et al., $D$-decomposition(Yu.I. Neimark, B.T. Polyak, E.N. Gryazina) and universal parameter space method(A. Fam, J. Meditch, J.Ackermann). Our approach is based on the interpretation of correspondence between roots and coefficients of a polynomial as a symmetric product morphism. We describe the topology of strata up to homotopy equivalence and, for many important cases, up to homeomorphism. Adjacencies between strata are also described. Moreover, we provide an explanation for the special position of classical stability problems: Hurwitz stability, Schur stability, hyperbolicity.Comment: 45 pages, 4 figure

Health in urban late medieval North-West Europe: a bioarchaeological study of Caen, Canterbury and Ghent

Over half of the global population currently lives in an urban environment and this is still increasing rapidly in developing countries. This thesis aims to provide a comparative picture of health in the rapidly developing urban centres in late medieval NW Europe - here defined as northern France, England and Belgium - through bioarchaeological analysis. This study focused on macroscopic methods and “stress indicators” (cribra orbitalia, dental enamel hypoplasia, adult stature and periosteal reaction on the tibiae) as a proxy for health and sanitation in these populations and respiratory disease (periosteal rib lesions and maxillary sinusitis) as a proxy for air quality. A 100 adult skeletons were analysed from the Darnétal cemetery of Caen (12th – 18th century AD), northern France, which had a reputation for poor sanitation. A further 100 adult skeletons were analysed from the cemetery of St. Gregory’s priory in Canterbury (12th – 16th century AD), whose economy is based around entertaining pilgrims and travellers. Lastly, The St. Pieter parish in Ghent (12th – 18th century AD) occupies a unique position on the edge of the town and 83 adult skeletons were analysed from this site. The skeletal evidence did not reflect the differences in sanitary conditions expected originally. Similar results were recorded for average adult stature estimates as well as the prevalence of cribra orbitalia, and dental enamel hypoplasia across the sites. It has been suggested that urban centres throughout the region may have been challenged to provide a healthy living environment. High prevalence rates of maxillary sinisusitis (Caen: 71%, Canterbury: 64%, and Ghent: 61%) and high prevalence rates of periosteal reaction on the ribs in Caen (63%) and Canterbury (63%) suggest significant levels of air pollution in these populations. The unusually high levels of rib lesions in Caen and Canterbury set the agenda for further research into their occurence and the development of recording standards. Lastly, the historical differences between the towns, and the location of the St Pieter parish, challenge the simplistic division of settlements into ‘urban’ and ‘rural’ types. It reveals the perspective for a more nuanced interpretation of urbanisation in NW Europe

Gaia Data Release 2. Kinematics of globular clusters and dwarf galaxies around the Milky Way

AIMS: The goal of this paper is to demonstrate the outstanding quality of the second data release of the Gaia mission and its power for constraining many different aspects of the dynamics of the satellites of the Milky Way. We focus here on determining the proper motions of 75 Galactic globular clusters, nine dwarf spheroidal galaxies, one ultra-faint system, and the Large and Small Magellanic Clouds. METHODS: Using data extracted from the Gaia archive, we derived the proper motions and parallaxes for these systems, as well as their uncertainties. We demonstrate that the errors, statistical and systematic, are relatively well understood. We integrated the orbits of these objects in three different Galactic potentials, and characterised their properties. We present the derived proper motions, space velocities, and characteristic orbital parameters in various tables to facilitate their use by the astronomical community. RESULTS: Our limited and straightforward analyses have allowed us for example to (i) determine absolute and very precise proper motions for globular clusters; (ii) detect clear rotation signatures in the proper motions of at least five globular clusters; (iii) show that the satellites of the Milky Way are all on high-inclination orbits, but that they do not share a single plane of motion; (iv) derive a lower limit for the mass of the Milky Way of 9.1{_₂.₆⁺⁶·²} x 10¹¹ M⊙ based on the assumption that the Leo I dwarf spheroidal is bound; (v) derive a rotation curve for the Large Magellanic Cloud based solely on proper motions that is competitive with line-of-sight velocity curves, now using many orders of magnitude more sources; and (vi) unveil the dynamical effect of the bar on the motions of stars in the Large Magellanic Cloud. CONCLUSIONS: All these results highlight the incredible power of the Gaia astrometric mission, and in particular of its second data release

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Spectral variability of GX 339-4 in a hard-to-soft state transition

We report on INTEGRAL observations of the bright black-hole transient GX 339-4 performed during the period August-September 2004. Our data cover three different spectral states, namely Hard/Intermediate State, Soft/Intermediate State and High/Soft State. We investigate the spectral variability of the source across the different spectral states. The hard X-ray spectrum becomes softer during the HIMS-to-SIMS transition, but it hardens when reaching the HSS state. A principal component analysis demonstrates that most of the variability occurs through two independent modes: a pivoting of the spectrum around 6 keV (responsible for 75% of the variance) and an intensity variation of the hard component (responsible for 21%). The pivoting is interpreted as due to changes in the soft cooling photon flux entering the corona, the second mode as fluctuations of the heating rate in the corona. Our spectral analysis of the spectra of GX 339-4 shows a high energy excess with respect to pure thermal Comptonisation models in the HIMS: a non-thermal power-law component seems to be requested by data. In all spectral states joint IBIS, SPI and JEM-X data are well represented by hybrid thermal/non-thermal Comptonisation (EQPAIR). The spectral evolution seems to be predominantly driven by a reduction of the ratio of the electron heating rate to the soft cooling photon flux in the corona, l_h/l_s. The inferred accretion disc soft thermal emission increases by about two orders of magnitude, while the Comptonised luminosity decreases by at most a factor of 3. This confirms that the softening we observed is due to a major increase in the flux of soft cooling photons in the corona associated with a modest reduction of the electron heating rate.Comment: 11 pages, 6 figures, 4 tables; accepted for publication in MNRAS Main Journa