Asymptotic behaviour of the domain of analyticity of invariant curves of the standard map

In this paper we consider the standard map, and we study the invariant curve obtained by analytical continuation, with respect to the perturbative parameter E, of the invariant circle of rotation number the golden mean corresponding to the case E=0. We show that, if we consider the parameterization that conjugates the dynamics of this curve to an irrational rotation, the domain of definition of this conjugation has an asymptotic boundary of analyticity when E->0 (in the sense of the singular perturbation theory). This boundary is obtained studying the conjugation problem for the so-called semi-standard map. To prove this result we have used KAM-like methods adapted to the framework of singular perturbation theory, as well as matching techniques to join di erent pieces of the conjugation, obtained in different parts of its domain of analyticity

On the numerical computation of Diophantine rotation numbers of analytic circle maps

In this paper we present a numerical method to compute Diophantine rotation numbers of circle maps with high accuracy. We mainly focus on analytic circle diffeomorphisms, but the method also works in the case of (enough) finite differentiability. The keystone of the method is that, under these conditions, the map is conjugate to a rigid rotation of the circle. Moreover, albeit it is not fully justified by our construction, the method turns to be quite efficient for computing rational rotation numbers. We discuss the method through several numerical examples

Asymptotic size of Herman rings of the complex standard family by quantitative quasiconformal surgery

In this paper we consider the complexification of the Arnold standard family of circle maps given by $\widetilde F_{\alpha,\epsilon}(u)=ue^{i\alpha} e^{({\epsilon}/{2}) (u-{1}/{u})}$, with $\alpha=\alpha(\epsilon)$ chosen so that $\widetilde F_{\alpha(\epsilon),\epsilon}$ restricted to the unit circle has a prefixed rotation number $\theta$ belonging to the set of Brjuno numbers. In this case, it is known that $\widetilde F_{\alpha(\epsilon),\epsilon}$ is analytically linearizable if $\epsilon$ is small enough and so it has a Herman ring $\widetilde U_{\epsilon}$ around the unit circle. Using Yoccoz's estimates, one has that the size$\widetilde R_\epsilon$ of $\widetilde U_{\epsilon}$ (so that $\widetilde U_{\epsilon}$ is conformally equivalent to $\{u\in{\mathbb C}: 1/\widetilde R_\epsilon < |u| < \widetilde R_\epsilon\}$) goes to infinity as $\epsilon\to 0$, but one may ask for its asymptotic behavior. We prove that $\widetilde R_\epsilon=({2}/{\epsilon})(R_0+\mathcal{O}(\epsilon\log\epsilon))$, where R0 is the conformal radius of the Siegel disk of the complex semistandard map $G(z)=ze^{i\omega}e^z$, where $\omega= 2\pi\theta$. In the proof we use a very explicit quasiconformal surgery construction to relate $\widetilde F_{\alpha(\epsilon),\epsilon}$ and G, and hyperbolic geometry to obtain the quantitative result

Generalized analytical results on n-ejection–collision orbits in the RTBP: analysis of bifurcations

In the planar circular restricted three-body problem and for any value of the mass parameter µ¿(0,1) and n=1 , we prove the existence of four families of n-ejection–collision (n-EC) orbits, that is, orbits where the particle ejects from a primary, reaches n maxima in the (Euclidean) distance with respect to it and finally collides with the primary. Such EC orbits have a value of the Jacobi constant of the form C=3µ+Ln2/3(1-µ)2/3 , where L>0 is big enough but independent of µ and n. In order to prove this optimal result, we consider Levi-Civita’s transformation to regularize the collision with one primary and a perturbative approach using an ad hoc small parameter once a suitable scale in the configuration plane and time has previously been applied. This result improves a previous work where the existence of the n-EC orbits was stated when the mass parameter µ>0 was small enough. Moreover, for decreasing values of C, there appear some bifurcations which are first numerically investigated and afterward explicit expressions for the approximation of the bifurcation values of C are discussed. Finally, a detailed analysis of the existence of n-EC orbits when µ¿1 is also described. In a natural way, Hill’s problem shows up. For this problem, we prove an analytical result on the existence of four families of n-EC orbits, and numerically, we describe them as well as the appearing bifurcations.Peer ReviewedPostprint (author's final draft

Measurement of Drift Velocity in the CMS Barrel Muon Chambers at the CMS Magnet Test Cosmic Challenge

This note reports the results of the analysis performed on the data collected by the CMS Barrel Muon system during the Magnet Test-Cosmic Challenge, aimed to study the Drift Tube chambers behavior at the nominal value of the CMS magnetic field. In particular, the analysis is devoted to the study of the drift velocity in the various equipped regions of the apparatus. It is shown that the drift velocity is significantly affected by the presence of a residual magnetic field in the chamber volume only in the innermost stations, MB1, of Wheel+2; where the maximal variation inside the chamber is of 4 percent, which does not prevent a good functionality of the DT trigger even in this most critical region

Chromium (VI) ion adsorption features of chitosan film and its chitosan/zeolite conjugate 13X film

This research evaluated the importance of the adsorption properties of chitosan a chitosan/zeolite conjugate film for the removal of Cr(VI) ions from solutions in the 5–260 mg/L concentration range, when the pH was adjusted to 4.0 and 6.0. The uptake capacities of the films formed by chitosan and by the chitosan/zeolite conjugate were calculated by mass balance. The equilibrium isotherms were fitted to the Langmuir, Freundlich and Redlich-Peterson models. The chitosan film seems to be a good sorbent for Cr(VI) at pH 4, but its physical instability suggests the need for a more resilient support. Due to this fact zeolite was added to the chitosan matrix in solution and a chitosan/zeolite (CS/Zeo) film was thus formed. The solubility of the film and the characterization of the different matrices by FTIR, TGA and X-Ray showed that a cross-linked structure was formed between the chitosan and zeolite and the solubility of the film increased. In this study, the low manufacturing cost of the CS/Zeo matrix, the good uptake of Cr(VI) at acidic pH (17.28 mg/g) and the non desorption of Cr(VI) from the film in water suggests this combination should be tested in industrial environment.The authors are grateful for the Coordination of Improvement of Higher Education Personnel (CAPES - Brazil) for PhD fellowship and the financial support received from Financier of Studies and Projects (FINEP - Brazil), National Council for Scientific and Technological Development (CNPq - Brazil), Catholic University of Pernambuco (UNICAP - Brazil), University of Minho (UMINHO - Portugal). They also acknowledge Antonio Soares Vicente (UMINHO - Portugal) who kindly supplied the chitosan

Influence of PPh3 moiety in the anticancer activity of new organometallic ruthenium complexes

The effect of the PPh3 group in the antitumor activity of some new organometallic Ruthenium (II) complexes has been investigated. Several complexes of the type [Ru(II)(Cl)(PPh3)(Lig-N)], [Ru(II)(Cl)2(Lig-N)] (where Lig-N=pyridine derivate) and [Ru(II)(Cl)(PPh3)2], have been synthesized and characterized, and an important increment of the antitumor activity and cytotoxicity of the complexes due to the presence of PPh3 moiety has been demonstrated, affording IC50 values of 5.2 μM in HL-60 tumour cell lines. Atomic Force Microscopy, Circular Dichroism and Electrophoresis experiments have proved that these complexes can bind DNA resulting in a distortion of both secondary and tertiary structures. Ethidium bromide displacement Fluorescence Spectroscopy studies and Viscosity measurements support that the presence of PPh3 group induces intercalation interactions with DNA. Indeed, crystallographic analysis, suggest that intra-molecular π-π interactions could be involved in the intercalation within DNA base pairs. Furthermore, HPLC-MS studies have confirmed a strong interaction between Ruthenium complexes and proteins (Ubiquitin and Potato Carboxypeptidase Inhibitor -PCI-) including slower kinetic due to the presence of PPh3 moiety, which could have an important role in detoxification mechanism and others. Finally, Ion Mobility Mass Spectrometry (IMMS) experiments have proved that there is no change in the structural conformation of the proteins owing to their bonding to Ruthenium complexes. This seems particularly important in the case of PCI, that may be a suitable candidate for vehiculizing these complexes in a selective manner into tumour cells. In agreement with these results, further investigations should be carried out to clarify either there is a favoured binding to DNA or to specific proteins, thus to elucidate their main biological target

Optimising the controlled release of dexamethasone from a new generation of PLGA-based microspheres intended for intravitreal administration

Successful therapy for chronic diseases affecting the posterior segment of the eye requires sustained drug concentrations at the site of action for extended periods of time. To achieve this, it is necessary to use high systemic doses or frequent intraocular injections, both associated with serious adverse effects. In order to avoid these complications and improve patient`s quality of life, an experimental study has been conducted on the preparation of a new generation of biodegradable poly D-L(lactide-co-glycolide (50:50) (PLGA) polymer microspheres (MSs) loaded with Dxm, vitamin E and/or human serum albumin (HSA). Particles were prepared according to a S/O/W encapsulation method and the 20-40μm fraction was selected. This narrow size distribution is suitable for minimally invasive intravitreal injection by small calibre needles. Characterisation of the MSs showed high Dxm loading and encapsulation efficiency (> 90%) without a strong interaction with the polymer matrix, as revealed by DSC analysis. MSs drug release studies indicated a small burst effect (lower than 5%) during the first five hours and subsequently, drug release was sustained for at least 30 days, led by diffusion and erosion mechanisms. Dxm release rate was modulated when solid state HSA was incorporated into MSs formulation. SDS-PAGE analysis showed that the protein maintained its integrity during the encapsulation process, as well as for the release study. MSs presented good tolerance and lack of cytotoxicity in macrophages and HeLa cultured cells. After 12 months of storage under standard refrigerated conditions (41ºC), MSs retained appropriate physical and chemical properties and analogous drug release kinetics. Therefore, we conclude that these microspheres are promising pharmaceutical systems for intraocular administration, allowing controlled release of the drug

Radioresistance of mesenchymal glioblastoma initiating cells correlates with patient outcome and is associated with activation of inflammatory program

Glioblastoma (GBM) still remains an incurable disease being radiotherapy (RT) the mainstay treatment. Glioblastoma intra-tumoral heterogeneity and GlioblastomaInitiating Cells (GICs) challenge the design of effective therapies. We investigated GICs and non-GICs response to RT in a paired in-vitro model and addressed molecular programs activated in GICs after RT. Established GICs heterogeneously expressed several GICs markers and displayed a mesenchymal signature. Upon fractionated RT, GICs reported higher radioresistance compared to non-GICs and showed lower α- and β-values, according to the Linear Quadratic Model interpretation of the survival curves. Moreover, a significant correlation was observed between GICs radiosensitivity and patient disease-free survival. Transcriptome analysis of GICs after acquisition of a radioresistant phenotype reported significant activation of Proneural-to-Mesenchymal transition (PMT) and pro-inflammatory pathways, being STAT3 and IL6 the major players. Our findings support a leading role of mesenchymal GICs in defining patient response to RT and provide the grounds for targeted therapies based on the blockade of inflammatory pathways to overcome GBM radioresistance

Indoor Air Quality: A Review of Cleaning Technologies

Aims: Indoor air quality (IAQ) has attracted increased attention with the emergence of COVID-19. Ventilation is perhaps the area in which the most changes have been proposed in response to the emergency caused by this virus. However, other strategies are possible, such as source control and the extraction of pollutants. The latter incorporates clean technologies, an emergent area with respect to IAQ. Method: Various air treatment technologies can be used to control contaminants, which are reviewed and discussed in this work, including physicochemical technologies (e.g., filtration, adsorption, UV-photocatalytic oxidation, ultraviolet disinfection and ionization) and biological technologies (e.g., plant purification methods and microalgae-based methods). Results and interpretation: This work reviews currently available solutions and technologies for “cleaning” indoor air, with a focus on their advantages and disadvantages. One of the most common problems in this area is the emission of pollutants that are sometimes more dangerous to human health than those that the technologies were developed to remove. Another aspect to consider is the limitation of each technology in relation to the type of pollutants that need to be removed. Each of the investigated technologies works well for a family of pollutants with similar characteristics, but it is not applicable to all pollutant types. Thus, the optimal solution may involve the use of a combination of technologies to extend the scope of application, in addition to the development of new materials, for example, through the use of nanotechnology