Restriction of Odd Degree Characters of Sn\mathfrak{S}_n

Let $n$ and $k$ be natural numbers such that $2^k < n$. We study the restriction to $\mathfrak{S}_{n-2^k}$ of odd-degree irreducible characters of the symmetric group $\mathfrak{S}_n$. This analysis completes the study begun in [Ayyer A., Prasad A., Spallone S., Sem. Lothar. Combin. 75 (2015), Art. B75g, 13 pages] and recently developed in [Isaacs I.M., Navarro G., Olsson J.B., Tiep P.H., J. Algebra 478 (2017), 271-282]

Self-Consistent Thermal Accretion Disk Corona Models for Compact Objects: I. Properties of the Corona and the Spectrum of Escaping Radiation

We present the properties of accretion disk corona (ADC) models, where the radiation field, the temperature, and the total opacity of the corona are determined self-consistently. We use a non-linear Monte Carlo code to perform the calculations. As an example, we discuss models where the corona is situated above and below a cold accretion disk with a plane-parallel (slab) geometry, similar to the model of Haardt and Maraschi. By Comptonizing the soft radiation emitted by the accretion disk, the corona is responsible for producing the high-energy component of the escaping radiation. Our models include the reprocessing of radiation in the accretion disk. Here, the photons either are Compton reflected or photo-absorbed, giving rise to fluorescent line emission and thermal emission. The self-consistent coronal temperature is determined by balancing heating (due to viscous energy dissipation) with Compton cooling, determined using the fully relativistic, angle-dependent cross-sections. The total opacity is found by balancing pair productions with annihilations. We find that, for a disk temperature kT_bb \lta 200 eV, these coronae are unable to have a self-consistent temperature higher than \sim 120 keV if the total optical depth is \gta 0.2, regardless of the compactness parameter of the corona and the seed opacity. This limitation corresponds to the angle-averaged spectrum of escaping radiation having a photon index \gta 1.8 within the 5 keV - 30 keV band. Finally, all models that have reprocessing features also predict a large thermal excess at lower energies. These constraints make explaining the X-ray spectra of persistent black hole candidates with ADC models very problematic.Comment: 15 pages, Latex, 9 .eps figures, uses emulateapj.sty (included). To be published in ApJ, October 1, 1997, Vol. 48

Sign conjugacy classes in symmetric groups

A special type of conjugacy classes in symmetric groups is studied and used to answer a question about odd-degree irreducible charactersComment: 9 page

RXTE Observation of Cygnus X-1: Spectral Analysis

We present the results of the analysis of the broad-band spectrum of Cygnus X-1 from 3.0 to 200 keV, using data from a 10 ksec observation by the Rossi X-ray Timing Explorer. The spectrum can be well described phenomenologically by an exponentially cut-off power law with a photon index Gamma = 1.45 +/- 0.02 (a value considerably harder than typically found), e-folding energy E_fold = 162 +/- 9 keV, plus a deviation from a power law that formally can be modeled as a thermal blackbody with temperature kT_bb = 1.2 +/1 0.2 keV. Although the 3 - 30 keV portion of the spectrum can be fit with a reflected power law with Gamma = 1.81 +/- 0.01 and covering fraction f = 0.35 +/- 0.02, the quality of the fit is significantly reduced when the HEXTE data in the 30 - 100 keV range is included, as there is no observed hardening in the power law within this energy range. As a physical description of this system, we apply the accretion disc corona models of Dove, Wilms & Begelman (1997) --- where the temperature of the corona is determined self-consistently. A spherical corona with a total optical depth tau = 1.6 +/- 0.1 and an average temperature kT_c = 87 +/- 5 keV, surrounded by an exterior cold disc, does provide a good description of the data (reduced chi-squared = 1.55). These models deviate from the data by up to 7% in the 5 - 10 keV range, and we discuss possible reasons for these discrepancies. However, considering how successfully the spherical corona reproduces the 10 - 200 keV data, such ``photon-starved'' coronal geometries seem very promising for explaining the accretion processes of Cygnus X-1.Comment: Revised version (added content). 8 pages, 6 figures, 1 table.tex file, latex, uses mn.sty. Accepted for publication in MNRA

Restriction of odd degree characters of Sn

Let n and k be natural numbers such that 2k < n. We study the restriction to Sn−2k of odd-degree irreducible characters of the symmetric group Sn. This analysis completes the study begun in [Ayyer A., Prasad A., Spallone S., Sém. Lothar. Combin. 75 (2015), Art. B75g, 13 pages] and recently developed in [Isaacs I.M., Navarro G., Olsson J.B., Tiep P.H., J. Algebra 478 (2017), 271-282]

Multiple Andreev reflections in diffusive SNS structures

We report new measurements on sup-gap energy structure originating from multiple Andreev reflections in mesoscopic SNS junctions. The junctions were fabricated in a planar geometry with high transparency superconducting contacts of Al deposited on highly diffusive and surface d-doped n++-GaAs. For samples with a normal GaAs region of active length 0.3um the Josephson effect with a maximal supercurrent Ic=3mA at T=237mK was observed. The sub-gap structure was observed as a series of local minima in the differential resistance at dc bias voltages V=2D/ne with n=1,2,4 i.e. only the even sub-gap positions. While at V=2D/e (n=1) only one dip is observed, the n=2, and the n=4 sub-gap structures each consists of two separate dips in the differential resistance. The mutual spacing of these two dips is independent of temperature, and the mutual spacing of the n=4 dips is half of the spacing of the n=2 dips. The voltage bias positions of the sub-gap differential resistance minima coincide with the maxima in the oscillation amplitude when a magnetic field is applied in an interferometer configuration, where one of the superconducting electrodes has been replaced by a flux sensitive open loop.Comment: 20 pages, 7 figure

Tracking the Orbital and Super-orbital Periods of SMC X-1

The High Mass X-ray Binary (HMXB) SMC X-1 demonstrates an orbital variation of 3.89 days and a super-orbital variation with an average length of 55 days. As we show here, however, the length of the super-orbital cycle varies by almost a factor of two, even across adjacent cycles. To study both the orbital and super-orbital variation we utilize lightcurves from the Rossi X-ray Timing Explorer All Sky Monitor (RXTE-ASM). We employ the orbital ephemeris from Wojdowski et al. (1998) to obtain the average orbital profile, and we show that this profile exhibits complex modulation during non-eclipse phases. Additionally, a very interesting ``bounceback'' in X-ray count rate is seen during mid-orbital eclipse phases, with a softening of the emission during these periods. This bounceback has not been previously identified in pointed observations. We then define a super-orbital ephemeris (the phase of the super-orbital cycle as a function of date) based on the ASM lightcurve and analyze the trend and distribution of super-orbital cycle lengths. SMC X-1 exhibits a bimodal distribution of these lengths, similar to what has been observed in other systems (e.g., Her X-1), but with more dramatic changes in cycle length. There is some hint, but not conclusive evidence, for a dependence of the super-orbital cycle length upon the underlying orbital period, as has been observed previously for Her X-1 and Cyg X-2. Using our super-orbital ephemeris we are also able to create an average super-orbital profile over the 71 observed cycles, for which we witness overall hardening of the spectrum during low count rate times. We combine the orbital and super-orbital ephemerides to study the correlation between the orbital and super-orbital variations in the system.Comment: 10 pages, using emulateapj style. To be published in the Astrophysical Journa

Generalized hook lengths in symbols and partitions

In this paper, we present, for any integer d, a description of the set of hooks in a d-symbol. We then introduce generalized hook length functions for a d-symbol, and prove a general result about them, involving the core and quotient of the symbol. We list some applications, for example to the well-known hook lengths in integer partitions. This leads in particular to a generalization of a relative hook formula for the degree of characters of the symmetric group discovered by G. Malle and G. Navarro in [3]