Minimum Restraint Functions for unbounded dynamics: general and control-polynomial systems

We consider an exit-time minimum problem with a running cost, $l\geq 0$ and unbounded controls. The occurrence of points where $l=0$ can be regarded as a transversality loss. Furthermore, since controls range over unbounded sets, the family of admissible trajectories may lack important compactness properties. In the first part of the paper we show that the existence of a $p_0$-minimum restraint function provides not only global asymptotic controllability (despite non-transversality) but also a state-dependent upper bound for the value function (provided $p_0>0$). This extends to unbounded dynamics a former result which heavily relied on the compactness of the control set. In the second part of the paper we apply the general result to the case when the system is polynomial in the control variable. Some elementary, algebraic, properties of the convex hull of vector-valued polynomials' ranges allow some simplifications of the main result, in terms of either near-affine-control systems or reduction to weak subsystems for the original dynamics.Comment: arXiv admin note: text overlap with arXiv:1503.0344

The value function of an asymptotic exit-time optimal control problem

We consider a class of exit--time control problems for nonlinear systems with a nonnegative vanishing Lagrangian. In general, the associated PDE may have multiple solutions, and known regularity and stability properties do not hold. In this paper we obtain such properties and a uniqueness result under some explicit sufficient conditions. We briefly investigate also the infinite horizon problem

Spectral variability in Swift and Chandra observations of the Ultraluminous source NGC 55 ULX1

NGC 55 ULX1 is a bright Ultraluminous X-ray source located 1.78 Mpc away. We analysed a sample of 20 Swift observations, taken between 2013 April and August, and two Chandra observations taken in 2001 September and 2004 June. We found only marginal hints of a limited number of dips in the light curve, previously reported to occur in this source, although the uncertainties due to the low counting statistics of the data are large. The Chandra and Swift spectra showed clearly spectral variability which resembles those observed in other ULXs. We can account for this spectral variability in terms of changes in both the normalization and intrinsic column density of a two-components model consisting of a blackbody (for the soft component) and a multicolour accretion disc (for the hard component). We discuss the possibility that strong outflows ejected by the disc are in part responsible for such spectral changes.Comment: 9 pages, 6 figure; accepted to be published on MNRA

Diurnal experiment data report, 19-20 March 1974

Temperature and wind data are presented from 70 small meteorological sounding rockets launched from eight selected launch sites in the Western Hemisphere. Table 1 gives a complete listing of the launch sites involved and the altitude of temperature and wind observations successfully completed

Non-Gaussian features of primordial magnetic fields in power-law inflation

We show that a conformal-invariance violating coupling of the inflaton to electromagnetism produces a cross correlation between curvature fluctuations and a spectrum of primordial magnetic fields. According to this model, in the case of power-law inflation, a primordial magnetic field is generated with a nearly flat power spectrum and rms amplitude ranging from nG to pG. We study the cross correlation, a three-point function of the curvature perturbation and two powers of the magnetic field, in real and momentum space. The cross-correlation coefficient, a dimensionless ratio of the three-point function with the curvature perturbation and magnetic field power spectra, can be several orders of magnitude larger than expected as based on the amplitude of scalar metric perturbations from inflation. In momentum space, the cross-correlation peaks for flattened triangle configurations, and is three orders of magnitude larger than the squeezed triangle configuration. These results suggest likely methods for distinguishing the observational signatures of the model.Comment: 15 pages, 2 figure