Probing Helical Magnetic Fields in AGN by Rotation Measure Gradients Studies

One of the tools that can provide evidence about the existence of helical magnetic fields in AGN is the observation of rotation measure gradients across the jet. Such observations have been previously made successfully, proving that such gradients are far from being rare, but common and typically persistent over several years, although some of them may show a reversal in the direction along the jet. Further studies of rotation measure gradients can help us in our understanding of the magnetic field properties and structure in the base of the jets. We studied Very Long Baseline Array (VLBA) polarimetric observations of 8 sources consistent of some quasars and BL Lacs at 12, 15, 22, 24 and 43 GHz and we find that all but two sources show indications of rotation measure gradients, either parallel or perpendicular to the jet. We interpret gradients perpendicular to the jet as indications of the change of the line of sight of the magnetic field due to its helicity, and gradients parallel to the jet as the decrease of magnetic field strength and/or electron density as we move along the jet. When comparing our results with the literature, we find tentative evidence of a rotation measure gradient flip, which can be explained as a change of the pitch angle or jet bending.Comment: 4 pages, 2 figures. Contribution for the Proceedings of HEPRO3 (Barcelona, 27 June - 1 July 2011). To be published on the International Journal of Modern Physics Conference Series, edited by J.M. Paredes, M. Rib\'o, F.A. Aharonian and G.E. Romer

Volume-preserving normal forms of Hopf-zero singularity

A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a non-zero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any non-degenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified R\"{o}ssler and generalized Kuramoto--Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple

Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones

We apply the averaging theory of first order for discontinuous differential systems to study the bifurcation of limit cycles from the periodic orbits of the uniform isochronous center of the differential systems ẋ = -y+x, y = x + xy, and ẋ = -y + xy, y = x + xy, when they are perturbed inside the class of all discontinuous quadratic and cubic polynomials differential systems with four zones separately by the axes of coordinates, respectively. Using averaging theory of first order the maximum number of limit cycles that we can obtain is twice the maximum number of limit cycles obtained in a previous work for discontinuous quadratic differential systems perturbing the same uniform isochronous quadratic center at origin perturbed with two zones separately by a straight line, and 5 more limit cycles than those achieved in a prior result for discontinuous cubic differential systems with the same uniform isochronous cubic center at the origin perturbed with two zones separately by a straight line. Comparing our results with those obtained perturbing the mentioned centers by the continuous quadratic and cubic differential systems we obtain 8 and 9 more limit cycles respectively

Evaluation in a Cytokine Storm Model in Vivo of the Safety and Efficacy of Intravenous Administration of PRS CK STORM (Standardized Conditioned Medium Obtained by Coculture of Monocytes and Mesenchymal Stromal Cells)

Our research group has been developing a series of biological drugs produced by cocul-ture techniques with M2-polarized macrophages with different primary tissue cells and/or mesen-chymal stromal cells (MSC), generally from fat, to produce anti-inflammatory and anti-fibrotic ef-fects, avoiding the overexpression of pro-inflammatory cytokines by the innate immune system at a given time. One of these products is the drug PRS CK STORM, a medium conditioned by allogenic M2-polarized macrophages, from coculture, with those macrophages M2 with MSC from fat, whose composition, in vitro safety, and efficacy we studied. In the present work, we publish the results obtained in terms of safety (pharmacodynamics and pharmacokinetics) and efficacy of the intravenous application of this biological drug in a murine model of cytokine storm associated with severe infectious processes, including those associated with COVID-19. The results demonstrate the safety and high efficacy of PRS CK STORM as an intravenous drug to prevent and treat the cytokine storm associated with infectious processes, including COVID-19