Emission from Large-scale Jets in Quasars

We consider the emission processes in the large-scale jets of powerful quasars based on the results obtained with the VLA, Spitzer, Hubble, and Chandra. We show that two well-known jets, 3C 273 and PKS 1136-135, have two distinct spectral components on large-scales: (1) the low-energy (LE) synchrotron spectrum extending from radio to infrared, and (2) the high-energy (HE) component arising from optical and extending to X-rays. The X-ray emission in quasar jets is often attributed to inverse-Compton scattering of cosmic microwave background (CMB) photons by radio-emitting electrons in a highly relativistic jet. However, recent data prefer synchrotron radiation by a second distinct population as the origin of the HE component. We anticipate that optical polarimetry with Hubble will establish the synchrotron nature of the HE component. Gamma-ray observations with GLAST (renamed as the Fermi Gamma-ray Space Telescope), as well as future TeV observations, are expected to place important constraints on the jet models.Comment: 4 pages, 4 figures, to appear in a special issue of the International Journal of Modern Physics D, proceedings of "High Energy Phenomena in Relativistic Outflows", held in Dublin Sept 200

The expected area of the Wiener sausage swept by a disc

The expected areas of the Wiener sausages swept by a disc attached to the two-dimensional Brownian Bridge joining the origin to a point x over a time interval [0,t] are computed. It is proved that the leading term of the expectation is given by Ramanujan's function if (x,t) remains in a parabolic region. The corresponding result for unconditioned process is also obtained.Comment: To appear in Stochastic Processes and their Applications 123 (2013) 191-21

Value Assignments to Observables Depending on a History of Context Change

The functional composition principle is generalized by taking into account of history of context change. Analysis of Peres' example shows hysteresis of value assignments. It is shown that value assignments which depend on the history of context change are possible in the case that the Hilbert space of state vectors is finite dimensional.Comment: 22 pages. Errors in the previous proof of Proposition 5 were corrected. This is the full version of "On Hysteresis of Value Assignments to Observables during Changes of Context" in Foundations of Probability and Physics - 4, eds. A. Yu. Khrennikov et al., AIP Conf. Proc. 889, 2007, pp. 422-42