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

Three Dimensional Distorted Black Holes: Initial Data and Evolution

We present a new class of 3D black hole initial data sets for numerical relativity. These data sets go beyond the axisymmetric, ``gravity wave plus rotating black hole'' single black hole data sets by creating a dynamic, distorted hole with adjustable distortion parameters in 3D. These data sets extend our existing test beds for 3D numerical relativity, representing the late stages of binary black hole collisions resulting from on-axis collision or 3D spiralling coalescence, and should provide insight into the physics of such systems. We describe the construction of these sets, the properties for a number of example cases, and report on progress evolving them.Comment: 3 pages, 2 postscript figures, LaTeX, uses mprocl.sty (available at http://shemesh.fiz.huji.ac.il/MG8/submission.html) To appear in the proceedings of the Marcel Grossmann 8 (Jerusalem, 1997

A powerful and highly variable off-nuclear X-ray source in the composite starburst/Seyfert 2 galaxy NGC 4945

We report on a powerful and variable off-nuclear X-ray source in the nearby spiral galaxy NGC 4945. Two ROSAT PSPC observations show the source to brighten in 0.5--2.0 keV flux by a factor of about 9 on a time-scale of 11 months or less. It is seen by ASCA about one month after the second PSPC pointing, and is seen to have dimmed by a factor of > 7 in a ROSAT HRI pointing about one year after the second PSPC pointing. Its maximum observed 0.8--2.5 keV luminosity is about 8E38 erg/s, making it brighter than any known persistent X-ray binary in the Milky Way. Its total X-ray luminosity is probably larger than 1.2E39 erg/s. The observed variability argues against a superbubble interpretation, and the off-nuclear position argues against a low-luminosity active galactic nucleus. The source is therefore probably either an ultra-powerful X-ray binary or an ultra-powerful supernova remnant. Optical monitoring has not identified any supernovae in NGC 4945 during the time of the X-ray observations, and any supernova would have had to have been either very highly absorbed or intrinsically optically faint.Comment: 5 pages, uuencoded compressed tar file, MNRAS in pres

X-ray absorption in the strong FeII narrow-line Seyfert 1 galaxy Mrk 507

We present results from spectral analysis of ASCA data on the NLS1 Mrk 507. This galaxy was found to have an exceptionally flat ROSAT spectrum among the NLS1s. The ASCA spectrum however shows a clear absorption feature in the energy band below 2 keV, which partly accounts for the flat spectrum observed with the ROSAT PSPC. The absorption is mainly due to cold gas with a column density of (2-3)E21 cm-2. A reanalysis of the PSPC data indicates that the absorber is slightly ionized, covers only part of the central source, or there is extra soft thermal emission from an extended region. There is also evidence that the X-ray absorption is complex; an edge feature marginally detected at 0.84 keV suggests the presence of an additional high ionization absorber which imposes a strong OVIII edge on the spectrum. After correction for the absorption, the photon index of the intrinsic continuum, 1.8, obtained from the ASCA data is quite similar to that of ordinary Seyfert 1 galaxies. Mrk 507 still has one of the flattest continuum slopes among NLS1, but is no longer exceptional. The strong optical FeII emission remains unusual in the light of the correlation between FeII strengths and steepness of soft X-ray slope.Comment: 6 pages, 3 Postscript figures, to be published in MNRA

ROSAT PSPC and Hri Observations of the Composite Starburst/Seyfert 2 Galaxy NGC 1672

The nearby barred spiral galaxy NGC 1672 is thought to have a weak Seyfert nucleus in addition to its strong starburst activity. Observations with the PSPC and HRI instruments on board the ROSAT X-ray satellite show that three X-ray sources with luminosities (1--2)\times 10^{40} erg/s are clearly identified with NGC 1672. The strongest X-ray source lies at the nucleus, and the other two lie near the ends of the prominent bar, locations that are also bright in H-alpha and near-infrared images. The nuclear source is resolved by the HRI on about the scale of the recently identified nuclear ring, and one of the sources at the ends of the bar is also probably resolved. The X-ray spectrum of the nuclear source is quite soft, having a Raymond--Smith plasma temperature of about 0.7 keV and little evidence for intrinsic absorption. The ROSAT band X-ray flux of the nuclear source appears to be dominated not by X-ray binary emission but rather by diffuse gas emission. While the properties of the nuclear source are generally supportive of a superbubble interpretation, its large density and emission measure stretch the limits that can be comfortably accommodated by such models. We do not detect direct emission from the putative Seyfert nucleus, although an alternative model for the nuclear source is thermal emission from gas that is photoionized by a hidden Seyfert nucleus. The spectra of the other two X-ray sources are harder than that of the nuclear source, and superbubble models for them have the same strengths and weaknesses.Comment: 11 pages, uuencoded compressed postscript, MNRAS in pres

Etching of High Purity Zinc

A method of etching high purity zinc to reveal various etch figures on {101¯0} planes is presented in this paper. Etch figures are formed by polishing in a dichromic acid solution after the introduction of mercury to the crystal surface. No measurable aging time is required to form etch figures at newly formed dislocation sites when mercury is on the surface prior to deformation. The mercury concentrates at the sites where etch figures form and may be removed by vacuum distillation and chemical polishing before it appreciably affects the purity of the bulk of the crystal

D-string on near horizon geometries and infinite conformal symmetry

We show that the symmetries of effective D-string actions in constant dilaton backgrounds are directly related to homothetic motions of the background metric. In presence of such motions, there are infinitely many nonlinearly realized rigid symmetries forming a loop (or loop like) algebra. Near horizon (AdS) D3 and D1+D5 backgrounds are discussed in detail and shown to provide 2d interacting field theories with infinite conformal symmetry.Comment: 5 pages, revtex, no figures; symmetry transformations for BI action added, coupling of D-string to RR 2-form in D1-D5 background corrected; final version, to appear in Phys. Rev. Let