Unsolvability Cores in Classification Problems

Classification problems have been introduced by M. Ziegler as a generalization of promise problems. In this paper we are concerned with solvability and unsolvability questions with respect to a given set or language family, especially with cores of unsolvability. We generalize the results about unsolvability cores in promise problems to classification problems. Our main results are a characterization of unsolvability cores via cohesiveness and existence theorems for such cores in unsolvable classification problems. In contrast to promise problems we have to strengthen the conditions to assert the existence of such cores. In general unsolvable classification problems with more than two components exist, which possess no cores, even if the set family under consideration satisfies the assumptions which are necessary to prove the existence of cores in unsolvable promise problems. But, if one of the components is fixed we can use the results on unsolvability cores in promise problems, to assert the existence of such cores in general. In this case we speak of conditional classification problems and conditional cores. The existence of conditional cores can be related to complexity cores. Using this connection we can prove for language families, that conditional cores with recursive components exist, provided that this family admits an uniform solution for the word problem

A Wide-Field View of Leo II -- A Structural Analysis Using the SDSS

Using SDSS I data, we have analysed the stellar distribution of the Leo II dwarf spheroidal galaxy (distance of 233 kpc) to search for evidence of tidal deformation. The existing SDSS photometric catalogue contains gaps in regions of high stellar crowding, hence we filled the area at the centre of Leo II using the DAOPHOT algorithm applied to the SDSS images. The combined DAOPHOT-SDSS dataset contains three-filter photometry over a 4x4 square degree region centred on Leo II. By defining a mask in three-filter colour-magnitude space, we removed the majority of foreground field stars. We have measured the following Leo II structural parameters: a core radius of r_c = 2.64 +/- 0.19 arcmin (178 +/- 13 pc), a tidal radius of r_t = 9.33 +/- 0.47 arcmin (632 +/- 32 pc) and a total V-band luminosity of L_V = (7.4 +/- 2.0) times 10^5 L_sun (M_V = -9.9 +/- 0.3). Our comprehensive analysis of the Leo II structure did not reveal any significant signs of tidal distortion. The internal structure of this object contains only mild isophotal twisting. A small overdensity was discovered appoximately 4.5 tidal radii from the Leo II centre, however we conclude it is unlikely to be material tidally stripped from Leo II based on its stellar population, and is most likely a foreground overdensity of stars. Our results indicate that the influence of the Galactic graviational field on the structure of Leo II has been relatively mild. We rederived the mass-to-light ratio of this system using existing kinematic data combined with our improved structural measurements, and favour the scenario in which Leo II is strongly dominated by dark matter with (M/L)_V ~ 100 in solar units.Comment: 41 pages, 15 figures, accepted for publication in the Astronomical Journa

The probability distribution of a trapped Brownian particle in plane shear flows

We investigate the statistical properties of an over-damped Brownian particle that is trapped by a harmonic potential and simultaneously exposed to a linear shear flow or to a plane Poiseuille flow. Its probability distribution is determined via the corresponding Smoluchowski equation, which is solved analytically for a linear shear flow. In the case of a plane Poiseuille flow, analytical approximations for the distribution are obtained by a perturbation analysis and they are substantiated by numerical results. There is a good agreement between the two approaches for a wide range of parameters.Comment: 5 pages, 4 figur

Particles held by springs in a linear shear flow exhibit oscillatory motion

The dynamics of small spheres, which are held by linear springs in a low Reynolds number shear flow at neighboring locations is investigated. The flow elongates the beads and the interplay of the shear gradient with the nonlinear behavior of the hydrodynamic interaction among the spheres causes in a large range of parameters a bifurcation to a surprising oscillatory bead motion. The parameter ranges, wherein this bifurcation is either super- or subcritical, are determined.Comment: 4 pages, 5 figure

Periodic Accretion From A Circumbinary Disk In The Young Binary UZ Tau E

Close pre-main-sequence binary stars are expected to clear central holes in their protoplanetary disks, but the extent to which material can flow from the circumbinary disk across the gap onto the individual circumstellar disks has been unclear. In binaries with eccentric orbits, periodic perturbation of the outer disk is predicted to induce mass flow across the gap, resulting in accretion that varies with the binary period. This accretion may manifest itself observationally as periodic changes in luminosity. Here we present a search for such periodic accretion in the pre-main-sequence spectroscopic binary UZ Tau E. We present BVRI photometry spanning 3 years; we find that the brightness of UZ Tau E is clearly periodic, with a best-fit period of 19.16 +/- 0.04 days. This is consistent with the spectroscopic binary period of 19.13 days, refined here from analysis of new and existing radial velocity data. The brightness of UZ Tau E shows significant random variability, but the overall periodic pattern is a broad peak in enhanced brightness, spanning more than half the binary orbital period. The variability of the H alpha line is not as clearly periodic, but given the sparseness of the data, some periodic component is not ruled out. The photometric variations are in good agreement with predictions from simulations of binaries with orbital parameters similar to those of UZ Tau E, suggesting that periodic accretion does occur from circumbinary disks, replenishing the inner circumstellar disks and possibly extending the timescale over which they might form planets

In situ observations of ClO in the Antarctic: Evidence for chlorine catalyzed destruction of ozone

Results from a series of 12 ER-2 aircraft flights into the Antarctic polar vortex are summarized. These in situ data define the spatial and temporal distribution of ClO as the aircraft flew at an altitude of approx. 18 km from Punta Arenas (54 deg S latitude) to the base of the Palmer Peninsula (72 deg S latitude), executed a rapid descent to approx. 13 km, turned north and climbed bach to approximately 18 km, returning to Punta Arenas. A general pattern in the ClO distribution is reported: mixing ratios of approximately 10 ppt are found at altitude in the vicinity of 55 deg S increasing to 50 ppt at 60 degrees S. In the vicinity of 65 deg S latitude a steep gradient in the ClO mixing ratio is observed. At a fixed potential temperature, the ClO mixing ratio through this sharp transition increases by an order of magnitude within a very few degrees of latitude, thus defining the edge of the chemical containment vessel. From the edge of that containment vessel to the southern extension of the flights, 72 deg S, a dome of slowly increasing ClO best describes the distribution. Conclusion are drawn from the data

Dynamics of a trapped Brownian particle in shear flows

The Brownian motion of a particle in a harmonic potential, which is simultaneously exposed either to a linear shear flow or to a plane Poiseuille flow is investigated. In the shear plane of both flows the probability distribution of the particle becomes anisotropic and the dynamics is changed in a characteristic manner compared to a trapped particle in a quiescent fluid. The particle distribution takes either an elliptical or a parachute shape or a superposition of both depending on the mean particle position in the shear plane. Simultaneously, shear-induced cross-correlations between particle fluctuations along orthogonal directions in the shear plane are found. They are asymmetric in time. In Poiseuille flow thermal particle fluctuations perpendicular to the flow direction in the shear plane induce a shift of the particle's mean position away from the potential minimum. Two complementary methods are suggested to measure shear-induced cross-correlations between particle fluctuations along orthogonal directions.Comment: 14 pages, 7 figure