Post's correspondence problem for hyperbolic and virtually nilpotent groups

Post's Correspondence Problem (the PCP) is a classical decision problem in theoretical computer science that asks whether for pairs of free monoid morphisms $g, h\colon\Sigma^*\to\Delta^*$ there exists any non-trivial $x\in\Sigma^*$ such that $g(x)=h(x)$. Post's Correspondence Problem for a group $\Gamma$ takes pairs of group homomorphisms $g, h\colon F(\Sigma)\to \Gamma$ instead, and similarly asks whether there exists an $x$ such that $g(x)=h(x)$ holds for non-elementary reasons. The restrictions imposed on $x$ in order to get non-elementary solutions lead to several interpretations of the problem; we consider the natural restriction asking that $x \notin \ker(g) \cap \ker(h)$ and prove that the resulting interpretation of the PCP is undecidable for arbitrary hyperbolic $\Gamma$, but decidable when $\Gamma$ is virtually nilpotent. We also study this problem for group constructions such as subgroups, direct products and finite extensions. This problem is equivalent to an interpretation due to Myasnikov, Nikolev and Ushakov when one map is injective.Comment: 17 page

PROPERTIES OF THE 24 DAY MODULATION IN GX 13+1 FROM NEAR-INFRARED AND X-RAY OBSERVATIONS

A 24 day period for the low-mass X-ray binary (LMXB) GX 13+1 was previously proposed on the basis of seven years of RXTE All-Sky Monitor (ASM) observations and it was suggested that this was the orbital period of the system. This would make it one of the longest known orbital periods for a Galactic LMXB powered by Roche lobe overflow. We present here the results of (1) K-band photometry obtained with the SMARTS Consortium CTIO 1.3 m telescope on 68 nights over a 10 month interval; (2) continued monitoring with the RXTE ASM, analyzed using a semi-weighted power spectrum instead of the data filtering technique previously used; and (3) Swift Burst Alert Telescope (BAT) hard X-ray observations. Modulation near 24 days is seen in both the K band and additional statistically independent ASM X-ray observations. However, the modulation in the ASM is not strictly periodic. The periodicity is also not detected in the Swift BAT observations, but modulation at the same relative level as seen with the ASM cannot be ruled out. If the 24 day period is the orbital period of system, this implies that the X-ray modulation is caused by structure that is not fixed in location. A possible mechanism for the X-ray modulation is the dipping behavior recently reported from XMM-Newton observations

X-ray Nova XTE J1550-564: RXTE Spectral Observations

Excellent coverage of the 1998 outburst of the X-ray Nova XTE J1550-564 was provided by the Rossi X-ray Timing Explorer. XTE J1550-564 exhibited an intense (6.8 Crab) flare on 1998 September 19 (UT), making it the brightest new X-ray source observed with RXTE. We present a spectral analysis utilizing 60 Proportional Counter Array spectra from 2.5-20 keV spanning 71 days, and a nearly continuous All Sky Monitor light curve. The spectra were fit to a model including multicolor blackbody disk and power-law components. XTE J1550-564 is observed in the very high, high/soft, and intermediate canonical outburst states of Black Hole X-ray Novae.Comment: 14 pages including 1 table and 4 figures, Accepted to ApJ Letter

Self Organization and a Dynamical Transition in Traffic Flow Models

A simple model that describes traffic flow in two dimensions is studied. A sharp {\it jamming transition } is found that separates between the low density dynamical phase in which all cars move at maximal speed and the high density jammed phase in which they are all stuck. Self organization effects in both phases are studied and discussed.Comment: 6 pages, 4 figure

ROSSI X-RAY TIMING EXPLORER AND BeppoSAX OBSERVATIONS OF THE TRANSIENT X-RAY PULSAR XTE J1859+083

We present observations of the 9.8 s X-ray pulsar XTE J1859+083 made with the All Sky Monitor (ASM) and Proportional Counter Array (PCA) on board the Rossi X-ray Timing Explorer, and the Wide Field Camera (WFC) on board BeppoSAX. The ASM data cover a 12 year time interval and show that an extended outburst occurred between approximately MJD 50,250 and 50,460 (1996 June 16 to 1997 January 12). The ASM data excluding this outburst interval suggest a possible modulation with a period of 60.65 ± 0.08 days. Eighteen sets of PCA observations were obtained over an approximately one month interval in 1999. The flux variability measured with the PCA appears consistent with the possible period found with the ASM. The PCA measurements of the pulse period showed it to decrease nonmonotonically and then to increase significantly. Doppler shifts due to orbital motion rather than accretion torques appear to be better able to explain the pulse period changes. Observations with the WFC during the extended outburst give a position that is consistent with a previously determined PCA error box, but which has a significantly smaller error. The transient nature of XTE J1859+083 and the length of its pulse period are consistent with it being a Be/neutron star binary. The possible 60.65 day orbital period would be of the expected length for a Be star system with a 9.8 s pulse period

An Interdisciplinary Approach to a Dental Information Technology Course

Purpose: To develop an interdisciplinary course to teach dental students about evidence-based dentistry, development of search strategies, critical appraisal of literature, and dental informatics. [See PDF for complete abstract

An Extended and More Sensitive Search for Periodicities in RXTE/ASM X-ray Light Curves

We present the results of a systematic search in approximately 14 years of Rossi X-ray Timing Explorer All-Sky Monitor data for evidence of periodicities not reported by Wen et al. (2006). Two variations of the commonly used Fourier analysis search method have been employed to achieve significant improvements in sensitivity. The use of these methods and the accumulation of additional data have resulted in the detection of the signatures of the orbital periods of eight low-mass X-ray binary systems and of ten high-mass X-ray binaries not listed in the tables of Wen et al.Comment: 20 pages, 22 figures, in emulateapj format; submitted to ApJ

Complete RXTE Spectral Observations of the Black Hole X-ray Nova XTE J1550-564

We report on the X-ray spectral behavior of the exceptionally bright X-ray nova XTE J1550-564 during its 1998-99 outburst. Our study is based on 209 pointed observations using the PCA and HEXTE instruments onboard the Rossi X-ray Timing Explorer spanning 250 days and covering the entire double-peaked eruption that occurred from 1998 September until 1999 May. The spectra are fit to a model including multicolor blackbody disk and power-law components. The source is observed in the very high and high/soft outburst states of black hole X-ray novae. During the very high state, when the power-law component dominated the spectrum, the inner disk radius is observed to vary by more than an order of magnitude; the radius decreased by a factor of 16 in one day during a 6.8 Crab flare. If the larger of these observed radii is taken to be the last stable orbit, then the smaller observed radius would imply that the inner edge of the disk is inside the event horizon! However, we conclude that the apparent variations of the inner disk radius observed during periods of increased power-law emission are probably caused by the failure of the multicolor disk/power-law model; the actual physical radius of the inner disk may remain fairly constant. This interpretation is supported by the fact that the observed inner disk radius remains approximately constant over 120 days in the high state, when the power-law component is weak, even though the disk flux and total flux vary by an order of magnitude. The mass of the black hole inferred by equating the approximately constant inner disk radius observed in the high/soft state with the last stable orbit for a Schwarzschild black hole is M_BH = 7.4 M_sun (D/6 kpc) (cos i)^{-1/2}.Comment: Submitted to ApJ, 20 pages including 6 figures + 4 large table

DISCOVERY OF TWO NEW THERMALLY BLOATED LOW-MASS WHITE DWARFS AMONG THE KEPLER BINARIES

We report the discovery of two new low-mass, thermally bloated, hot white dwarfs among the Kepler sample of eclipsing binaries. These are KIC 9164561 and KIC 10727668 with orbital periods of 1.2670 and 2.3058 days, respectively. The current primary in both systems is an A star of about 2 M[subscript ʘ]. This brings the number of similar binaries among the Kepler sample to six, and the two new systems have the shortest orbital periods among them. The white dwarf (WD) in KIC 9164561 has the largest thermal bloating, compared to its cold degenerate radius, of about a factor of 14. We utilize radial velocity measurements of the A star in KIC 9164561 to determine the WD mass rather accurately: 0.197 ± 0.005 M[subscript ʘ]. The mass of the WD in KIC 10727668 is based on the Doppler boosting signal in the Kepler photometry and is less accurately determined to be 0.266 ± 0.035 M[subscript ʘ]. Based on the inferred radii and effective temperatures of these two white dwarfs, we are able to make an independent theoretical estimate of their masses to within ~0.01 M[subscript ʘ] based on evolutionary models of their cooling history after they lose their hydrogen-rich envelopes. We also present evidence that there is a third body in the KIC 9164561 system with an orbital period of 8–14 yr.Spain. Ministerio de Economia y Competitividad (Grant ESP2013-48391-C4-2 R)National Aeronautics and Space Administration (Kepler Participating Scientist Program