KAM-tori near an analytic elliptic fixed point

We study the accumulation of an elliptic fixed point of a real analytic Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with Diophantine frequency vector \o_0 is always accumulated by invariant complex analytic KAM-tori. Indeed, the following alternative holds: If the Birkhoff normal form of the Hamiltonian at the invariant point satisfies a R\"ussmann transversality condition, the fixed point is accumulated by real analytic KAM-tori which cover positive Lebesgue measure in the phase space (in this part it suffices to assume that \o_0 has rationally independent coordinates). If the Birkhoff normal form is degenerate, there exists an analytic subvariety of complex dimension at least $d+1$ passing through 0 that is foliated by complex analytic KAM-tori with frequency $\omega_0$. This is an extension of previous results obtained in \cite{EFK} to the case of an elliptic fixed point

Almost reducibility for finitely differentiable SL(2,R)-valued quasi-periodic cocycles

Quasi-periodic cocycles with a diophantine frequency and with values in SL(2,R) are shown to be almost reducible as long as they are close enough to a constant, in the topology of k times differentiable functions, with k great enough. Almost reducibility is obtained by analytic approximation after a loss of differentiability which only depends on the frequency and on the constant part. As in the analytic case, if their fibered rotation number is diophantine or rational with respect to the frequency, such cocycles are in fact reducible. This extends Eliasson's theorem on Schr\"odinger cocycles to the differentiable case

Analyse par spectrométrie de masse d’hormones stéroïdiennes dans les eaux usées et abattement par oxydation chimique

Thèse réalisée en cotutelle avec Michèle Prévost (Ph.D), Professeure titulaire au département des génies civil, géologique et des mines de l'École Polytechnique de Montréal.Les preuves quant aux effets des hormones stéroïdiennes sur l’écosystème aquatique et terrestre sont clairement démontrées dans la littérature et ce à des concentrations très faibles. Les sources responsables du déversement de ces composés dans l'environnement aquatique sont multiples et découlent majoritairement de leur consommation autant humaine qu’animale. Diverses maladies chez l’humain sont soupçonnées d’être le résultat de l’exposition aux hormones stéroïdiennes et autres perturbateurs endocriniens. Le risque associé à des années d’exposition, avec les éventuels effets cumulatifs ou synergiques de ces substances, ne doit pas être ignoré et une approche préventive plutôt que réactive doit être adoptée. Dans cette optique, de nouvelles méthodes analytiques ont été développées pour permettre la détection et la quantification des hormones stéroïdiennes dans les eaux de surface et les eaux usées. La première méthode proposée se base sur la diode laser à désorption thermique munie d’une source à ionisation à pression atmosphérique, LDTD-APCI, couplée à la spectrométrie de masse en tandem (MS/MS). L’avantage de la LDTD-APCI est le temps d’analyse très court, soit 15 secondes par échantillon, comparativement à plusieurs minutes par les méthodes séparatives conventionnelles par chromatographie gazeuse ou liquide. Les paramètres impliqués dans l’optimisation de la source LDTD-APCI sont discutés afin de mieux comprendre leur impact sur l’efficacité de l’ionisation et le développement de la méthode. La pré-concentration d’échantillons d’eau de surface a été effectuée par une extraction sur phase solide (SPE) manuelle afin de valider la méthode d’analyse et de montrer son applicabilité pour des échantillons réels. La LDTD-APCI-MS/MS permet d’atteindre des limites de détection entre 13 et 43 ng L-1. La seconde approche proposée est le développement d’une méthode par SPE automatisée couplée à la chromatographie liquide (LC) avec la spectrométrie de masse en tandem (MS/MS). Les volumes d’injections peuvent se faire entre 1 et 10 mL, en fonction de la concentration attendue des hormones stéroïdiennes et du type de matrice. L’analyse des hormones stéroïdiennes dans les eaux usées a été effectuée pour deux usines avec différents modes de traitement. L’impact de l’étape de pré-traitement de l’échantillon, c’est-à-dire l’étape de filtration et la préservation de l’échantillon ont également été étudié. La SPE-LC-APCI-MS/MS a permis d’obtenir des résultats reproductibles avec un important gain de temps (15 min par échantillon), comparativement à la SPE manuelle suivi d’une analyse par LC-MS/MS. Les limites de détections obtenues dans les eaux usées étaient entre 8 et 60 ng L-1. Dans l’objectif de trouver des solutions pour éliminer les hormones stéroïdiennes dans les usines de traitements d’eau potable, leur oxydation par le chlore et le potassium de permanganate a été considérée. L’impact du pH, de la nature de l’eau (eau ultrapure versus eau usée) et de la température sur les constantes de vitesse d’oxydation du deuxième ordre a été évalué et discuté. Les rendements d’oxydation des oestrogènes par le chlore était entre 53% et 97% avec des temps de demi-vies entre 0.6 et 53 min alors que pour les progestagènes avec le potassium permanganate l’abattement variait de 78 à 97% avec des demi-vies de 10 à 60 min.The effect of steroid hormones on the aquatic and terrestrial environment is well documented and can occur at very low concentrations. The primary sources responsible for their introduction in the environment are numerous, but they originate mainly from human and animal releases. Several human health issues are thought to be the result of exposure to steroid hormones as well as other endocrine disruptive compounds. The risks associated with years of exposure, in conjunction with the cumulative or synergic effect of these substances, must not be ignored. Therefore, a pro-active, rather than reactive, approach should be considered. With this in mind, new analytical methods were developed for the detection and quantification of steroid hormones in surface and waste waters. The first was based on a novel sample introduction method, the laser diode thermal desorption with an atmospheric chemical ionization source, the LDTD-APCI, coupled with tandem mass spectrometry (MS/MS). The main advantages of the LDTD-APCI is the short analysis time, i.e. 15 seconds per sample, because no chromatographic separation is used prior to ionization. The optimization of several parameters (laser power, laser pattern, transfer gas flow rate as well as deposition volume and solvent) involved in the LDTD-APCI source are discussed in order to better understand their impact on the efficiency of ionization and method development. The sample pre-concentration of analytes in surface water was performed by manual solid phase extraction (SPE) to demonstrate method applicability to real environmental samples. The LDTD-APCI-MS/MS method detection limits range from 13 to 43 ng L-1 for the selected steroid hormones. The second approach consisted of an on-line SPE method followed by liquid chromatography coupled tandem mass spectrometry LC-MS/MS with injection volumes ranging from 1 to 10 mL, depending upon the expected steroid hormone concentrations and matrix type. The method was applied to wastewater samples from two treatment plants with different processes. The role of sample pre-treatment, i.e. the filtration step and conservation conditions, on the analyses was evaluated. The on-line SPE-LC-MS/MS gave reproducible values while reducing sample preparation time (15 min per sample), compared to manual SPE followed by an LC-MS/MS analysis. The limits of detection of the method for the selected steroid hormones ranged from 8 to 60 ng L-1. In order to better eliminate the selected steroid hormones in drinking water treatment plants, their oxidation by chlorine and potassium permanganate was determined. The effect of pH, temperature and type of water matrix (ultrapure versus wastewater) on the second order rate constants was assessed and discussed. The oxidation yields by chlorine for estrogens were between 53 and 97% with half-lives from 0.6 min to 53 min, whereas for progestogens with potassium permanganate the corresponding yields ranged from 78 to 94% with half-lives ranging from 10 min and 60 min

Network Mutual Information and Synchronization under Time Transformations

We investigate the effect of general time transformations on the phase synchronization (PS) phenomenon and the mutual information rate (MIR) between pairs of nodes in dynamical networks. We demonstrate two important results concerning the invariance of both PS and the MIR. Under time transformations PS can neither be introduced nor destroyed and the MIR cannot be raised from zero. On the other hand, for proper time transformations the timing between the cycles of the coupled oscillators can be largely improved. Finally, we discuss the relevance of our findings for communication in dynamical networks.Comment: 15 p

Stroke Survivors Control the Temporal Structure of Variability During Reaching in Dynamic Environments

Learning to control forces is known to reduce the amount of movement variability (e.g., standard deviation; SD) while also altering the temporal structure of movement variability (e.g., approximate entropy; ApEn). Such variability control has not been explored in stroke survivors during reaching movements in dynamic environments. Whether augmented feedback affects such variability control, is also unknown. Chronic stroke survivors, assigned randomly to a control/experimental group, learned reaching movements in a dynamically changing environment while receiving either true feedback of their movement (control) or augmented visual feedback (experimental). Hand movement variability was analyzed using SD and ApEn. A significant change in variability was determined for both SD and ApEn. Post hoc tests revealed that the significant decrease in SD was not retained after a week. However, the significant increase in ApEn, determined on both days of training, showed significant retention effects. In dynamically changing environments, chronic stroke survivors reduced the amount of movement variability and made their movement patterns less repeatable and possibly more flexible. These changes were not affected by augmented visual feedback. Moreover, the learning patterns characteristically involved the control of the nonlinear dynamics rather than the amount of hand movement variability. The absence of transfer effects demonstrated that variability control of hand movement after a stroke is specific to the task and the environment

Synthesis, Characterization and Study of Antibacterial Activity of a New Schiff Base Ligand and Its Complexes with Co(II), Ni(II), Cu(II), Cd(II) and Hg(II) Metal Ions

Some coordination complexes of Co(??), Ni(??), Cu(??), Cd(??) and Hg(??) are reacted in ethanol with Schiff base ligand derived from of 2,4,6- trihydroxybenzophenone and 3-aminophenol using microwave irradiation and then reacted with metal salts in ethanol as a solvent in 1:2 ratio (metal: ligand). The ligand [H4L] is characterized by FTIR, UV-Vis, C.H.N, 1H-NMR,13C-NMR, and mass spectra. The metal complexes are characterized by atomic absorption, infrared spectra, electronic spectra, molar conductance, (C.H.N for Ni(??) complex) and magnetic moment measurements. These measurements indicate that the ligand coordinates with metal (??) ion in a tridentate manner through the nitrogen and oxygen atoms of the ligand, octahedral structures are suggested for these complexes. Antibacterial activity of the ligand [H4L] and its complexes are studied against (gram positive) and (gram negative) bacteria [Escherichia coli, Pseudomonas aeruginosa, Staphylococcus aureus and Bacillus]. The proposed structure of the complexes using the program, Chem office (2006) and the general formula has been given for the prepared ligand complexes K2[M(H2L)2]

The Influence of Visual Perception of Self-Motion on Locomotor Adaptation to Unilateral Limb Loading

Self-perception of motion through visual stimulation may be important for adapting to locomotor conditions. Unilateral limb loading is a locomotor condition that can improve stability and reduce abnormal limb movement. In the present study, the authors investigated the effect of self-perception of motion through virtual reality (VR) on adaptation to unilateral limb loading. Healthy young adults, assigned to either a VR or a non-VR group, walked on a treadmill in the following 3 locomotor task periods—no load, loaded, and load removed. Subjects in the VR group viewed a virtual corridor during treadmill walking. Exposure to VR reduced cadence and muscle activity. During the loaded period, the swing time of the unloaded limb showed a larger increase in the VR group. When the load was removed, the swing time of the previously loaded limb and the stance time of the previously unloaded limb showed larger decrease and the swing time of the previously unloaded limb showed a smaller increase in the VR group. Lack of visual cues may cause the adoption of cautious strategies (higher muscle activity, shorter and more frequent steps, changes in the swing and stance times) when faced with situations that require adaptations. VR technology, providing such perceptual cues, has an important role in enhancing locomotor adaptation

Borel-Cantelli sequences

A sequence $\{x_{n}\}_1^\infty$ in $[0,1)$ is called Borel-Cantelli (BC) if for all non-increasing sequences of positive real numbers $\{a_n\}$ with $\underset{i=1}{\overset{\infty}{\sum}}a_i=\infty$ the set $$\underset{k=1}{\overset{\infty}{\cap}} \underset{n=k}{\overset{\infty}{\cup}} B(x_n, a_n))=\{x\in[0,1)\mid |x_n-x|<a_n \text{for} \infty \text{many}n\geq1\}$$ has full Lebesgue measure. (To put it informally, BC sequences are sequences for which a natural converse to the Borel-Cantelli Theorem holds). The notion of BC sequences is motivated by the Monotone Shrinking Target Property for dynamical systems, but our approach is from a geometric rather than dynamical perspective. A sufficient condition, a necessary condition and a necessary and sufficient condition for a sequence to be BC are established. A number of examples of BC and not BC sequences are presented. The property of a sequence to be BC is a delicate diophantine property. For example, the orbits of a pseudo-Anosoff IET (interval exchange transformation) are BC while the orbits of a "generic" IET are not. The notion of BC sequences is extended to more general spaces.Comment: 20 pages. Some proofs clarifie

Soft βc-Generalized Closed Sets

Previously, we introduced and studied the concept of soft open sets in soft topological spaces. This paper is a continuation study of this concept. We introduce and investigate the notion of soft generalized closed sets. We discuss some soft properties of this type of soft sets. Also, we introduce the concepts of soft &nbsp;space and soft &nbsp;space. In addition, we introduce the notion of soft Kernel of a soft set and use it to get a characterization of soft sets to be soft generalized closed sets