Simplifying the solution of Ljunggren's equation X2+1=2Y4

In 1942 Ljunggren gave a very complicated proof of the fact that the only positive integer solutions of the equation X2+1=2Y4 are (X, Y)=(1, 1) and (239,13). In the present paper we give a simpler solution of Ljunggren's problem. This is accomplished by reducing the problem to a Thue equation and then solving it by using a deep result of Mignotte and Waldschmidt on linear forms in logarithms and continued fractions

Insensitivity of the elastic proton-nucleus reaction to the neutron radius of 208Pb

The sensitivity--or rather insensitivity--of the elastic proton-nucleus reaction to the neutron radius of 208Pb is investigated using a non-relativistic impulse-approximation approach. The energy region (Tlab=500 MeV and Tlab=800 MeV) is selected so that the impulse approximation may be safely assumed. Therefore, only free nucleon-nucleon scattering data are used as input for the optical potential. Further, the optical potential includes proton and neutron ground-state densities that are generated from accurately-calibrated models. Even so, these models yield a wide range of values (from 0.13 fm to 0.28 fm) for the poorly known neutron skin thickness in 208Pb. An excellent description of the experimental cross section is obtained with all neutron densities. We have invoked analytic insights developed within the eikonal approximation to understand the insensitivity of the differential cross section to the various neutron densities. As the diffractive oscillations of the cross sections are controlled by the matter radius of the nucleus, the large spread in the neutron skin among the various models gets diluted into a mere 1.5% difference in the matter radius. This renders ineffective the elastic reaction as a precision tool for the measurement of neutron radii.Comment: 17 pages with 5 figure

How do entrepreneurial portfolios respond to income taxation?

We investigate how personal income taxes affect the portfolio share of personal wealth that entrepreneurs invest in their own business. In a reformulation of the standard portfolio choice model that allows for underreporting of private business income to tax authorities, we show that a fall in the tax rate may increase investment in risky entrepreneurial business equity at the intensive margin, but decrease entrepreneurial investment at the extensive margin. To test these hypotheses, we use household survey panel data for Germany eliciting the personal wealth composition in detail in 2002, 2007, and 2012. We analyze the effects of personal income taxes on the portfolio shares of six asset classes of private households, including private business equity. In a system of simultaneous demand equations in first differences, we identify the tax effects by an instrumental variables approach exploiting tax reforms during our observation period. To account for selection into entrepreneurship, we use changes in entry regulation into skilled trades. Estimation results are consistent with the predictions of our theoretical model. An important policy insight is that lower taxes drive out businesses that are viable only due to tax avoidance or evasion, but increase investment in private businesses that are also worthwhile in the absence of taxes

A multiwavelength study on the high-energy behaviour of Fermi/LAT pulsars

Using archival as well as freshly acquired data, we assess the X-ray behaviour of the Fermi/LAT gamma-ray pulsars listed in the First Fermi source catalog. After revisiting the relationships between the pulsars' rotational energy losses and their X and gamma-ray luminosities, we focus on the distance-indipendent gamma to X-ray flux ratios. When plotting our Fgamma/Fx values as a function of the pulsars' rotational energy losses, one immediately sees that pulsars with similar energetics have Fgamma/Fx spanning 3 decades. Such spread, most probably stemming from vastly different geometrical configurations of the X and gamma-ray emitting regions, defies any straightforward interpretation of the plot. Indeed, while energetic pulsars do have low Fgamma/Fx values, little can be said for the bulk of the Fermi neutron stars. Dividing our pulsar sample into radio-loud and radio-quiet subsamples, we find that, on average, radio-quiet pulsars do have higher values of Fgamma/Fx, implying an intrinsec faintness of their X-ray emission and/or a different geometrical configuration. Moreover, despite the large spread mentioned above, statistical tests show a lower scatter in the radio-quiet dataset with respect to the radio-loud one, pointing to a somewhat more constrained geometry for the radio-quiet objects with respect to the radio-loud ones.Comment: 39 pages, 5 figures, 3 tables. To be published in Astrophysical Journa

The inpatient burden of abdominal and gynecological adhesiolysis in the US

<p>Abstract</p> <p>Background</p> <p>Adhesions are fibrous bands of scar tissue, often a result of surgery, that form between internal organs and tissues, joining them together abnormally. Postoperative adhesions frequently occur following abdominal surgery, and are associated with a large economic burden. This study examines the inpatient burden of adhesiolysis in the United States (i.e., number and rate of events, cost, length of stay [LOS]).</p> <p>Methods</p> <p>Hospital discharge data for patients with primary and secondary adhesiolysis were analyzed using the 2005 Healthcare Cost and Utilization Project's Nationwide Inpatient Sample. Procedures were aggregated by body system.</p> <p>Results</p> <p>We identified 351,777 adhesiolysis-related hospitalizations: 23.2% for primary and 76.8% for secondary adhesiolysis. The average LOS was 7.8 days for primary adhesiolysis. We found that 967,332 days of care were attributed to adhesiolysis-related procedures, with inpatient expenditures totaling $2.3 billion ($1.4 billion for primary adhesiolysis; $926 million for secondary adhesiolysis). Hospitalizations for adhesiolysis increased steadily by age and were higher for women. Of secondary adhesiolysis procedures, 46.3$220 million in attributable costs.</p> <p>Conclusions</p> <p>Adhesiolysis remain an important surgical problem in the United States. Hospitalization for this condition leads to high direct surgical costs, which should be of interest to providers and payers.</p

NICER observations of MAXI J1820+070 suggest a rapidly-brightening black hole X-ray binary in the hard state

NICER observed the new X-ray transient MAXI J1820+070 (ATel #11399, #11400, #11403, #11404, #11406, #11418, #11420, #11421) on multiple occasions from 2018 March 12 to 14. & nbsp;During this time the source brightened rapidly, from a total NICER mean count rate of 880 count/s on March 12 to 2800 count/s by March 14 17:00 & nbsp;UTC, corresponding to a change in 2-10 keV modelled flux (see below) from 1.9E-9 to 5E-9 erg cm-2 s-1. & nbsp; The broadband X-ray spectrum is absorbed by a low column density (fitting the model given below, we obtain 1.5E21 cm-2), in keeping with the low Galactic column in the direction of the source (ATel #11418; Dickey & Lockman, 1990, ARAA, 28, 215; Kalberla et al. 2005, A &A, 440, 775) and consists of a hard power-law component with weak reflection features (broad iron line and narrow 6.4 keV line core) and an additional soft X-ray component