Solutions to Donaldson's hyperkaehler reduction on a curve

We study an infinite-dimensional hyperk\ue4hler reduction introduced by Donaldson and associated with the constant scalar curvature equation on a Riemann surface. It is known that the corresponding moment map equations admit special solutions constructed from holomorphic quadratic differentials. Here we obtain a more general existence result and so a larger hyperk\ue4hler moduli space

Jets from Sub-Parsec to Kiloparsec Scales: A Physical Connection

The Chandra discovery of bright X-ray emission from kpc-scale jets allows insight into the physical parameters of the jet flow at large scale. At the opposite extreme, extensive studies of the inner relativistic jets in Blazars with multiwavelength observations, yield comparable information on sub-parsec scales. In the framework of simple radiation models for the emission regions we compare the physical parameters of jets on these two very different scales in the only two well studied Blazars for which large-scale emission has been resolved by Chandra. Notably, we find that the relativistic Doppler factors and powers derived independently at the two scales are consistent, suggesting that the jet does not suffer severe deceleration or dissipation. Moreover the internal equipartition pressures in the inner jet and in the external X-ray bright knots scale inversely with the jet cross section as expected in the simple picture of a freely expanding jet in equipartition.Comment: 4 figures, accepted by Ap

HST Observations of the Optical Jets of PKS 0521-365, 3C371, and PKS 2201+044

HST observations have led to the discovery of the optical counterpart of the radio jet of PKS 2201+044, and to a detailed analysis of the optical jets of PKS 0521-365 and 3C371. At HST spatial resolution these jets are well resolved, displaying knotty morphologies. When compared with radio maps of appropriate resolution, a clear one-to-one correspondence between optical and radio structures is found, showing that all detected optical structures are indeed related to the radio synchrotron emission. Photometry of the brightest knots shows that the radio-to-optical spectral index and the derived intensity of the equipartition magnetic field are approximately constant along the jet. Thus, present observations suggest that the electron energy distribution does not change significantly all along the jet.Comment: Accepted for publications on the Astrphysical Journal. Contains 14 pages and 5 figure

Evidence for anisotropic motion of the clouds in broad-line regions of BL Lacertae objects

The masses of central massive black holes in BL Lac objects are estimated from their host galaxy absolute magnitude at R-band by using the empirical relation between absolute magnitude of host galaxy and black hole mass. Only a small fraction of BL Lac objects exhibit weak broad-line emission, and we derive the sizes of the broad-line regions (BLRs) in these BL Lac objects from the widths of their broad emission lines on the assumption of the clouds being virilized in BLRs. It is found that the sizes of the BLRs in these sources are usually 2-3 orders of magnitude larger than that expected by the empirical correlation between BLR size and optical luminosity defined by a sample of Seyfert galaxies and quasars. We discuss a variety of possibilities and suggest it may probably be attributed to anisotropic motion of the BLR clouds in these BL Lac objects. If the BLR geometry of these sources is disk-like, the viewing angles between the axis and the line of sight are in the range of 2-12 degrees, which is consistent with the unification schemes.Comment: 5 pages, accepted for publication in Ap

Ultrasound Guidance in Paravertebral Injections of Oxygen-Ozone: Treatment of Low Back Pain

Background: Paravertebral injection of ozone is an established clinical practice for the treatment of Low Back Pain (LBP). The role of Ultrasound Guidance (USG) in mini invasive procedures has become important in many clinical practice thanks to the greater precision this technique can add. As matter of fact, a large volume of ozone in a single administration may have some adverse or side effects. In this study we wanted to verify if the use of USG in Oxygen/ Ozone (O2/O3) infiltrations could allow the administration of a smaller volume of gas mixture, increasing the safety and the comfort of the procedure itself, obtaining however similar or better results in pain decrease. Methods: We compared two groups of 25 patients affected by LBP, undergoing 10 infiltrations of O2/O3, by using USG (group U) or only anatomical landmarks (group AL). Pain intensity, by calculating Visual Analogical Scale (VAS) difference before and after the treatment, and the discomfort were evaluated in both groups. Results: The mean of the VAS before the treatment was 6.44 in group U and 6.48 in group AL. The mean of the VAS after the treatment was 2.22 in group U and 3.04 in group AL. The mean of discomfort rate was 2.84 in group U and 5.44 in group AL. The number of patients with unbearable discomfort was 0 in group U and 7 in group AL. Conclusions: As many other treatment, also paravertebral injections of O2/O3 benefits of the advantages of the US device which makes this treatment safer and more accurate