On the X-ray number of almost smooth convex bodies and of convex bodies of constant width

The X-ray numbers of some classes of convex bodies are investigated. In particular, we give a proof of the X-ray Conjecture as well as of the Illumination Conjecture for almost smooth convex bodies of any dimension and for convex bodies of constant width of dimensions 3, 4, 5 and 6

CCD photometry and new models of 5 minor planets

We present new R filtered CCD observations of 5 faint and moderately faint asteroids carried out between October, 1998 and January, 1999. The achieved accuracy is between 0.01-0.03 mag, depending mainly on the target brightness. The obtained sinodic periods and amplitudes: 683 Lanzia - 4.6+/-0.2 h, 0.13 mag; 725 Amanda - >3.0 h, >=0.40 mag; 852 Wladilena - 4.62+/-0.01 h, 0.32 mag (December, 1998) and 0.27 mag (January, 1999); 1627 Ivar - 4.80+/-0.01, 0.77 mag (December, 1998) and 0.92 mag (January, 1999). The Near Earth Object 1998 PG unambiguously showed doubly-periodic lightcurve, suggesting the possibility of a relatively fast precession (P_1=1.3 h, P_2=5.3 h). Collecting all data from the literature, we determined new models for 3 minor planets. The resulting spin vectors and triaxial ellipsoids have been calculated by an amplitude-method. Sidereal periods and senses of rotation were calculated for two asteroids (683 and 1627) by a modified epoch-method. The results are: 683 - lambda_p=15/195+/-25 deg, beta_p=52+/-15 deg, a/b=1.15+/-0.05, b/c=1.05+/-0.05, P_sid=0.1964156+/-0.0000001 d, retrograde; 852 - lambda_p=30/210+/-20 deg, beta_p=30+/-10 deg, a/b=2.3+/-0.3, b/c=1.2+/-0.2; 1627 - lambda_p=145/325+/-8 deg, beta_p=34+/-6 deg, a/b=2.0+/-0.1, b/c=1.09+/-0.05, P_sid=0.1999154+/-0.0000003 d, retrograde. The obtained shape of 1627 is in good agreement with radar images by Ostro et al. (1990).Comment: 8 pages, accepted for publication in Astronomy and Astrophysics Suppl. Serie

Generalized Kac's Lemma for Recurrence Time in Iterated Open Quantum Systems

We consider recurrence to the initial state after repeated actions of a quantum channel. After each iteration a projective measurement is applied to check recurrence. The corresponding return time is known to be an integer for the special case of unital channels, including unitary channels. We prove that for a more general class of quantum channels the expected return time can be given as the inverse of the weight of the initial state in the steady state. This statement is a generalization of the Kac lemma for classical Markov chains

Pushing the limits: K2 observations of the trans-Neptunian objects 2002 GV31 and (278361) 2007 JJ43

We present the first photometric observations of trans-Neptunian objects (TNOs) taken with the Kepler space telescope, obtained in the course of the K2 ecliptic survey. Two faint objects have been monitored in specifically designed pixel masks that were centered on the stationary points of the objects, when their daily motion was the slowest. In the design of the experiment, only the apparent path of these objects were retrieved from the detectors, i.e. the costs in terms of Kepler pixels were minimized. Because of the faintness of the targets we employ specific reduction techniques and co-added images. We measure rotational periods and amplitudes in the unfiltered Kepler band as follows: for (278361) 2007 JJ43 and 2002 GV31 we get P_rot=12.097 h and P_rot=29.2 h while 0.10 and 0.35 mag for the total amplitudes, respectively. Future space missions, like TESS and PLATO are not well suited to this kind of observations. Therefore, we encourage to include the brightest TNOs around their stationary points in each observing campaign to exploit this unique capability of the K2 Mission -- and therefore to provide unbiased rotational, shape and albedo characteristics of many objects.Comment: Accepted for publication in ApJ Letters, 5.2 pages in emulateapj style, misspelled 2007 JJ43 designation correcte

Evidence for fresh frost layer on the bare nucleus of comet Hale--Bopp at 32 AU distance

Here we report that the activity of comet Hale--Bopp ceased between late 2007 and March, 2009, at about 28 AU distance from the Sun. At that time the comet resided at a distance from the Sun that exceeded the freeze-out distance of regular comets by an order of magnitude. A Herschel Space Observatory PACS scan was taken in mid-2010, in the already inactive state of the nucleus. The albedo has been found to be surprisingly large (8.1$\pm$0.9%{}), which exceeds the value known for any other comets. With re-reduction of archive HST images from 1995 and 1996, we confirm that the pre-perihelion albedo resembled that of an ordinary comet, and was smaller by a factor of two than the post-activity albedo. Our further observations with the Very Large Telescope (VLT) also confirmed that the albedo increased significantly by the end of the activity. We explain these observations by proposing gravitational redeposition of icy grains towards the end of the activity. This is plausible for such a massive body in a cold environment, where gas velocity is lowered to the range of the escape velocity. These observations also show that giant comets are not just the upscaled versions of the comets we know but can be affected by processes that are yet to be fully identified.Comment: 7 pages, 6 figures, accepted for publication in Ap

Quantized recurrence time in iterated open quantum dynamics

The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of systems that includes classical Markov chains and unitary discrete time quantum walks on networks. Starting from a pure state, the time evolution is induced by repeated applications of a general quantum channel, in each timestep followed by a measurement to detect whether the system has returned to the original state. We prove that if the superoperator is unital in the relevant Hilbert space (the part of the Hilbert space explored by the system), then the expectation value of the return time is an integer, equal to the dimension of this relevant Hilbert space. We illustrate our results on partially coherent quantum walks on finite graphs. Our work connects the previously known quantization of the expected return time for bistochastic Markov chains and for unitary quantum walks, and shows that these are special cases of a more general statement. The expected return time is thus a quantitative measure of the size of the part of the Hilbert space available to the system when the dynamics is started from a certain state

THREE-DIMENSIONAL STABLY ADMISSIBLE PREY-PREDATOR MODELS

This paper deals with the most interesting three dimensional Volterra systems, which have first a sign stable interaction matrix. This matrix is stably admissible too. Then we consider a balanced interaction matrix, which is not sign stable, because it has a cycle, but it is stably admissible, and lost we consider an interesting not stably admissible case

Main-Belt Asteroids in the K2 Engineering Field of View

Unlike NASA's original Kepler Discovery Mission, the renewed K2 Mission will stare at the plane of the Ecliptic, observing each field for approximately 75 days. This will bring new opportunities and challenges, in particular the presence of a large number of main-belt asteroids that will contaminate the photometry. The large pixel size makes K2 data susceptible to the effect of apparent minor planet encounters. Here we investigate the effects of asteroid encounters on photometric precision using a sub-sample of the K2 Engineering data taken in February, 2014. We show examples of asteroid contamination to facilitate their recognition and distinguish these events from other error sources. We conclude that main-belt asteroids will have considerable effects on K2 photometry of a large number of photometric targets during the Mission, that will have to be taken into account. These results will be readily applicable for future space photometric missions applying large-format CCDs, such as TESS and PLATO.Comment: accepted for publication in AJ, 6 page

The 106Cd(α, α)106Cd elastic scattering in a wide energy range for γ process studies

Date of Acceptance: 15/04/2015Alpha elastic scattering angular distributions of the 106Cd(α, α)106Cd reaction were measured at three energies around the Coulomb barrier to provide a sensitive test for the α + nucleus optical potential parameter sets. Furthermore, the new high precision angular distributions, together with the data available from the literature were used to study the energy dependence of the locally optimized α + nucleus optical potential in a wide energy region ranging from ELab=27.0MeV down to 16.1 MeV.The potentials under study are a basic prerequisite for the prediction of α-induced reaction cross sections and thus, for the calculation of stellar reaction rates used for the astrophysical γ process. Therefore, statistical model predictions using as input the optical potentials discussed in the present work are compared to the available 106Cd + alpha cross section data.Peer reviewe