Positive curvature and the elliptic genus

We prove several results about the vanishing of the elliptic genus on positively curved Spin manifolds with logarithmic symmetry rank. The proofs are based on the rigidity of the elliptic genus and Kennard's improvement of the Connectedness Lemma for transversely intersecting, totally geodesic submanifolds.Comment: 15 pages. Paper was rewritten. To appear in New York Journal of Mathematic

New Results from an old Friend: The Crab Nebula and its Pulsar

We summarize here the results, most of which are preliminary, of a number of recent observations of the Crab nebula system with the Chandra X-Ray Observatory. We discuss four different topics: (1) The motion on long (> 1yr) time scales of the southern jet. (2) The discovery that pulsar is not at the center of the projected ring on the sky and that the ring may well lie on the axis of symmetry but appears to be displaced at a latitude of about 5 degrees. (Note that this deprojection is by no means unique.) (3) The results and puzzling implications of the Chandra phase-resolved spectroscopy of the pulsar when compared to observations of pulse-phase variations of similar and dissimilar measures in other regions of the spectrum. (4) The search for the X-ray location of the site of the recently-discovered gamma-ray flaring. We also comment briefly on our plan to use the Chandra data we obtained for the previous project to study the nature of the low-energy flux variations recently detected at hard X-ray energies.Comment: 6 pages, 5 figures, submitted to the proceedings of the conference: "The Extreme and Variable High Energy Sky", 19-23 September 2011, Chia Laguna (Cagliari) - Ital

The Complicated Evolution of the ACIS Contamination Layer over the Mission Life of the Chandra X-ray Observatory

The Chandra X-ray Observatory was launched almost 19 years ago and has been delivering spectacular science over the course of its mission. The Advanced CCD Imager Spectrometer is the prime instrument on the satellite, conducting over 90% of the observations. The CCDs operate at a temperature of -120 C and the optical blocking filter in front of the CCDs is at a temperature of approximately -60C. The surface of the OBF has accumulated a layer of contamination over the course of the mission. We have been characterizing the thickness, chemical composition, and spatial distribution of the contamination layer as a function of time over the mission. All three have exhibited significant changes with time. There has been a dramatic decrease in the accumulation rate of the contaminant starting in 2017. The lower accumulation rate may be due to a decrease in the deposition rate or an increase in the vaporization rate or a combination of the two. We show that the current calibration file which models the additional absorption of the contamination layer is significantly overestimating that additional absorption by using the standard model spectrum for the supernova remnant 1E 0102.2-7219 developed by the International Astronomical Consortium for High Energy Calibration. In addition, spectral data from the cluster of galaxies known as Abell 1795 and the Blazar Markarian 421 are used to generate a model of the absorption produced by the contamination layer. The Chandra X-ray Center calibration team is preparing a revised calibration file that more accurately represents the complex time dependence of the accumulation rate, the spatial dependence, and the chemical composition of the contaminant. Given the rapid changes in the contamination layer over the past year, future calibration observations at a higher cadence will be necessary to more accurately monitor such changes.Comment: 15 pages, 10 figures, SPIE Astronomical Instruments and Telescopes 2018, Conference Series, 1069

Inclusive CP Asymmetries in Semileptonic Decays of B Mesons

We estimate the sensitivity of single lepton CP violation measurements with respect to that of traditional di-lepton measurements. We find that the sensitivity of the single lepton method is better than that of the di-lepton method. The achievable sensitivity with the currently available data is already in the range relevant to standard model predictions. We also give general expressions for inclusive decay time distributions on $\Upsilon 4S$ where the other $B$ is not measured, which will be used to obtain time dependent asymmetries. The expression is of general use whenever one deals with inclusive time-dependent as well as time-integrated measurements in $\Upsilon(4S)\to B^0\bar B^0$ where the final state of the other $B$ is not reconstructed or when only the time difference is measured.Comment: 7 pages, 1 figure. Two references added, and a few typos correcte

Adaptive Perturbation Theory: Quantum Mechanics and Field Theory

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, $H$, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly. In this talk I will introduce the method in the context of the pure anharmonic oscillator and then apply it to the case of tunneling between symmetric minima. After that, I will show how this method can be applied to field theory. In that discussion I will show how one can non-perturbatively extract the structure of mass, wavefunction and coupling constantComment: 10 pages, 4 figures, uses psfig.sty. Conference talk Light Cone 2005 -- Cairns This paper is being replaced to add references to previously published work that I became aware of after posting the pape

DOES AFFIRMATIVE ACTION AFFECT PRODUCTIVITY IN THE INDIAN RAILWAYS?

Our objective in this paper is to shed some empirical light on a claim often made by critics of affirmative action policies: that increasing the representation of members of marginalized communities in jobs – and especially in relatively skilled positions – comes at a cost of reduced efficiency. We undertake a systematic empirical analysis of productivity in the Indian Railways in order to determine whether increasing proportions of Scheduled Castes and Scheduled Tribes in railway employment – largely a consequence of India's affirmative action policies – have actually reduced productive efficiency in the railway system. We find no evidence that higher percentages of Scheduled Castes and Scheduled Tribes in the railway labour force have reduced productivity. Indeed, some of our results suggest that the opposite is true, providing tentative support for the claim that greater labour force diversity boosts productivity.affirmative action; labour force; productivity; Indian railways

X-ray Polarimetry: a new window on the high energy sky

Polarimetry is widely considered a powerful observational technique in X-ray astronomy, useful to enhance our understanding of the emission mechanisms, geometry and magnetic field arrangement of many compact objects. However, the lack of suitable sensitive instrumentation in the X-ray energy band has been the limiting factor for its development in the last three decades. Up to now, polarization measurements have been made exclusively with Bragg diffraction at 45 degrees or Compton scattering at 90 degrees and the only unambiguous detection of X-ray polarization has been obtained for one of the brightest object in the X-ray sky, the Crab Nebula. Only recently, with the development of a new class of high sensitivity imaging detectors, the possibility to exploit the photoemission process to measure the photon polarization has become a reality. We will report on the performance of an imaging X-ray polarimeter based on photoelectric effect. The device derives the polarization information from the track of the photoelectrons imaged by a finely subdivided Gas Pixel Detector. It has a great sensitivity even with telescopes of modest area and can perform simultaneously good imaging, moderate spectroscopy and high rate timing. Being truly 2D it is non-dispersive and does not require any rotation. This device is included in the scientific payload of many proposals of satellite mission which have the potential to unveil polarimetry also in X-rays in a few years.Comment: Accepted for publication by NIMA. Proceeding of the 1st International Conference on "Frontiers in Diagnostic Technologies", November 25-27 2009, Frascati (Italy). 11 pages, 4 figures, 1 table

Beyond Chandra - the X-ray Surveyor

Over the past 16 years, NASA's Chandra X-ray Observatory has provided an unparalleled means for exploring the universe with its half-arcsecond angular resolution. Chandra studies have deepened our understanding of galaxy clusters, active galactic nuclei, galaxies, supernova remnants, planets, and solar system objects addressing almost all areas of current interest in astronomy and astrophysics. As we look beyond Chandra, it is clear that comparable or even better angular resolution with greatly increased photon throughput is essential to address even more demanding science questions, such as the formation and subsequent growth of black hole seeds at very high redshift; the emergence of the first galaxy groups; and details of feedback over a large range of scales from galaxies to galaxy clusters. Recently, NASA Marshall Space Flight Center, together with the Smithsonian Astrophysical Observatory, has initiated a concept study for such a mission named the X-ray Surveyor. This study starts with a baseline payload consisting of a high resolution X-ray telescope and an instrument set which may include an X-ray calorimeter, a wide-field imager and a dispersive grating spectrometer and readout. The telescope would consist of highly nested thin shells, for which a number of technical approaches are currently under development, including adjustable X-ray optics, differential deposition, and modern polishing techniques applied to a variety of substrates. In many areas, the mission requirements would be no more stringent than those of Chandra, and the study takes advantage of similar studies for other large area missions carried out over the past two decades. Initial assessments indicate that such an X-ray mission is scientifically compelling, technically feasible, and worthy of a high rioritization by the next American National Academy of Sciences Decadal Survey for Astronomy and Astrophysics.Comment: 6 pages, 6 figures, paper 9510-01 presented at SPIE Europe, Prague, April 201