Cylindric partitions, W_r characters and the Andrews-Gordon-Bressoud identities

We study the Andrews-Gordon-Bressoud (AGB) generalisations of the Rogers-Ramanujan q-series identities in the context of cylindric partitions. We recall the definition of r-cylindric partitions, and provide a simple proof of Borodin's product expression for their generating functions, that can be regarded as a limiting case of an unpublished proof by Krattenthaler. We also recall the relationships between the r-cylindric partition generating functions, the principal characters of affine sl_r algebras, the M^{r, r+d}_r minimal model characters of W_r algebras, and the r-string abaci generating functions, as well as the relationships between them, providing simple proofs for each. We then set r=2, and use 2-cylindric partitions to re-derive the AGB identities as follows. Firstly, we use Borodin's product expression for the generating functions of the 2-cylindric partitions with infinitely-long parts, to obtain the product sides of the AGB identities, times a factor (q; q)_{\infty}^{-1}, which is the generating function of ordinary partitions. Next, we obtain a bijection from the 2-cylindric partitions, via 2-string abaci, into decorated versions of Bressoud's restricted lattice paths. Extending Bressoud's method of transforming between restricted paths that obey different restrictions, we obtain sum expressions with manifestly non-negative coefficients for the generating functions of the 2-cylindric partitions which contains a factor (q; q)_{\infty}^{-1}. Equating the product and sum expressions of the same 2-cylindric partitions, and canceling a factor of (q; q)_{\infty}^{-1} on each side, we obtain the AGB identities.Comment: 38 page

A computer code for calculations in the algebraic collective model of the atomic nucleus

A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1,1) x SO(5) dynamical group. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code enables a wide range of model Hamiltonians to be analysed. This range includes essentially all Hamiltonians that are rational functions of the model's quadrupole moments $q_M$ and are at most quadratic in the corresponding conjugate momenta $\pi_N$ ($-2\le M,N\le 2$). The code makes use of expressions for matrix elements derived elsewhere and newly derived matrix elements of the operators $[\pi\otimes q \otimes\pi]_0$ and $[\pi\otimes\pi]_{LM}$. The code is made efficient by use of an analytical expression for the needed SO(5)-reduced matrix elements, and use of SO(5)$\,\supset\,$SO(3) Clebsch-Gordan coefficients obtained from precomputed data files provided with the code.Comment: REVTEX4. v2: Minor improvements and corrections. v3: Introduction rewritten, references added, Appendix B.4 added illustrating efficiencies obtained using modified basis, Appendix E added summarising computer implementation, and other more minor improvements. 43 pages. Manuscript and program to be published in Computer Physics Communications (2016

The Orbital Light Curve of Aquila X-1

We obtained R- and I-band CCD photometry of the soft X-ray transient/neutron- star binary Aql X-1 in 1998 June while it was at quiescence. We find that its light curve is dominated by ellipsoidal variations, although the ellipsoidal variations are severely distorted and have unequal maxima. After we correct for the contaminating flux from a field star located only 0.46" away, the peak-to-peak amplitude of the modulation is ~0.25 mag in the R band, which requires the orbital inclination to be greater than 36 degrees. The orbital period we measure is consistent with the 18.95 h period measured by Chevalier & Ilovaisky (1998). During its outbursts the light curve of Aql X-1 becomes single humped. The outburst light curve observed by Garcia et al. (1999) agrees in phase with our quiescent light curve. We show that the single humped variation is caused by a ``reflection effect,'' that is, by heating of the side of the secondary star facing towards the neutron star.Comment: 18 manuscript pages, 7 figures; accepted by A

Particles in RSOS paths

We introduce a new representation of the paths of the Forrester-Baxter RSOS models which represents the states of the irreducible modules of the minimal models M(p',p). This representation is obtained by transforming the RSOS paths, for the cases p> 2p'-2, to new paths for which horizontal edges are allowed at certain heights. These new paths are much simpler in that their weight is nothing but the sum of the position of the peaks. This description paves the way for the interpretation of the RSOS paths in terms of fermi-type charged particles out of which the fermionic characters could be obtained constructively. The derivation of the fermionic character for p'=2 and p=kp'+/- 1 is outlined. Finally, the particles of the RSOS paths are put in relation with the kinks and the breathers of the restricted sine-Gordon model.Comment: 15 pages, few typos corrected, version publishe

Space shuttle engineering and operations support. Avionics system engineering

The shuttle avionics integration laboratory (SAIL) requirements for supporting the Spacelab/orbiter avionics verification process are defined. The principal topics are a Spacelab avionics hardware assessment, test operations center/electronic systems test laboratory (TOC/ESL) data processing requirements definition, SAIL (Building 16) payload accommodations study, and projected funding and test scheduling. Because of the complex nature of the Spacelab/orbiter computer systems, the PCM data link, and the high rate digital data system hardware/software relationships, early avionics interface verification is required. The SAIL is a prime candidate test location to accomplish this early avionics verification

Energy and width measurements of low-Z pionic X-ray transitions

High resolution spectrometric measurement of energy and natural line widths of 2p-1s pionic X ray transitions, as well as muonic transition energies in Li, Be, B, and C isotope

An Economic analysis of the potential for precision farming in UK cereal production

The results from alternative spatial nitrogen application studies are analysed in economic terms and compared to the costs of precision farming hardware, software and other services for cereal crops in the UK. At current prices, the benefits of variable rate application of nitrogen exceed the returns from a uniform application by an average of £22 ha−1 The cost of the precision farming systems range from £5 to £18 ha−1 depending upon the system chosen for an area of 250 ha. The benefits outweigh the associated costs for cereal farms in excess of 80 ha for the lowest price system to 200–300 ha for the more sophisticated systems. The scale of benefits obtained depends upon the magnitude of the response to the treatment and the proportion of the field that will respond. To be cost effective, a farmed area of 250 ha of cereals, where 30% of the area will respond to variable treatment, requires an increase in crop yield in the responsive areas of between 0·25 and 1.00 t ha−1 (at £65 t−1) for the basic and most expensive precision farming systems, respectively

Detection Of KOI-13.01 Using The Photometric Orbit

We use the KOI-13 transiting star-planet system as a test case for the recently developed BEER algorithm (Faigler & Mazeh 2011), aimed at identifying non-transiting low-mass companions by detecting the photometric variability induced by the companion along its orbit. Such photometric variability is generated by three mechanisms, including the beaming effect, tidal ellipsoidal distortion, and reflection/heating. We use data from three Kepler quarters, from the first year of the mission, while ignoring measurements within the transit and occultation, and show that the planet's ephemeris is clearly detected. We fit for the amplitude of each of the three effects and use the beaming effect amplitude to estimate the planet's minimum mass, which results in M_p sin i = 9.2 +/- 1.1 M_J (assuming the host star parameters derived by Szabo et al. 2011). Our results show that non-transiting star-planet systems similar to KOI-13.01 can be detected in Kepler data, including a measurement of the orbital ephemeris and the planet's minimum mass. Moreover, we derive a realistic estimate of the amplitudes uncertainties, and use it to show that data obtained during the entire lifetime of the Kepler mission, of 3.5 years, will allow detecting non-transiting close-in low-mass companions orbiting bright stars, down to the few Jupiter mass level. Data from the Kepler Extended Mission, if funded by NASA, will further improve the detection capabilities.Comment: Accepted to AJ on October 4, 2011. Kepler Q5 Long Cadence data will become publicly available on MAST by October 23. Comments welcome (V2: minor changes, to reflect proof corrections