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

A review of knowledge: inter-row hoeing & its associated agronomy in organic cereal & pulse crops

The aim of this project was to establish the “state of the art” for inter-row hoeing and its associated agronomic practices in organic cereal and pulse crops. To achieve this a detailed review of literature was undertaken. • To facilitate inter-row cultivation in cereal and pulse crops, some adjustment of row spacing may be required. For cereals, drilling crops in 25 cm rows can reduce yield compared with normal drilling practice, primarily due to greater intra-specific competition amongst the crop (i.e. competition between crop plants). • The yield penalty resulting from widely spaced crop rows can be minimised using a number of approaches, depending on the drill: 1. Reducing the seed rate in widely spaced crop rows can help to minimise excessive intra-specific competition. 2. Band sowing the crop in wide rows can also help to minimise intra-specific competition as the seed is distributed over a greater area. 3. Using a twin-row arrangement can completely overcome the yield penalty. • The recommended row spacing for peas (up to 20 cm) and beans (up to 35 cm) does not require any further adjustment for inter-row hoeing. • Recent developments in automated guidance of inter-row hoeing equipment mean that weeding operations can now be conducted a much higher speeds (10 km h-1). This has highlighted the limitations of some of the cultivators currently used (e.g. ‘A’ blades), as excessive soil throw can occur at this high speed. Rolling cultivators may prove to be the most suitable at high forward speeds. For manually guided hoes working at slower speeds (5 km h-1), ‘A’ and ‘L’ blades offer an effective low cost solution. • In terms of the timing of inter-row hoeing, it is suggested that weeding operations should be conducted at an early stage in the growing season, as the weeds that emerge with or shortly after the crop are the ones that pose the most significant threat for crop yield. Weeding on two occasions can provide better levels of weed control than weeding once, but weeding more frequently offered little additional benefit. Reductions of weed biomass of up to 99 % have been reported as a result of inter-row hoeing, although this has not always resulted in a positive crop yield response. This is probably due to crop damage resulting from inaccurate hoeing, a problem that can be overcome with automated guidance. • There is some evidence to suggest that mechanical weeding operations can mineralise soil bound nitrogen. • The impact of inter-row hoeing on ground nesting birds is uncertain. Early indications suggest that skylarks prefer to nest directly adjacent to or in the crop row rather than between rows. The information contained within this review should enable farmers to make best use of inter-row hoeing in their arable crops. There are a number of areas that require further research and development: • The interaction of seed rate and row spacing needs to be confirmed in organic systems. • Relatively little is known about the mechanisms of weed kill and the detailed interaction between the cultivator blade, the weed and the soil. This is particularly important with the new automated guidance equipment that allows weeding at high forward speeds. • The timing and frequency of inter-row hoeing has received very little attention. The optimum weed control timings are based on small-plot crop:weed competition studies and need to be verified under field scale management with inter-row hoeing equipment. • Finally, the impact of inter-row hoeing and widely spaced crop rows on ground-nesting birds has not been looked at directly, but is of importance. Please see the main report for a more detailed summary before the full text

Measuring mathematical resilience : an application of the construct of resilience to the study of mathematics

To meet the challenge of accelerating demands for quantitative literacy in the work force, improvements are needed in mathematics education. Student skill must be increased at all ability levels while also reducing the achievement gap across gender, racial and ethnic groups to increase their participation in advanced mathematics coursework and representation in mathematics related careers (National Mathematics Advisory Panel, 2008). Research has shown that affective traits such as motivation and attitude are linked to increased likelihood of taking advanced mathematics courses (Ma, 2006) and are significant predictors of improved cognitive activity and achievement (Buff, Reusser, Rakoczy,& Pauli, 2011; Ethington & Wolfe, 1986). In addition, males generally score more favorably than females on affective variables related to mathematics achievement and persistence (McGraw, Lubienski, & Strutchens, 2006; Sherman & Fennema, 1977; Wilkins and Ma, 2003). Although psychological resilience has been researched extensively (Luthar, Cicchetti, & Becker, 2000; Luthar, 2007) the study of mathematical resilience, defined as a positive adaptive stance to mathematics which allows students to continue learning despite adversity, represents a new approach (Johnston-Wilder & Lee, 2010; Rivera & Waxman, 2011). Math anxiety looks at maladaptive response to learning mathematics and is well-studied (Hembree, 1990; Richardson & Suinn, 1977; Tobias, 1978). In contrast, resilience incorporates factors associated with optimal functioning. Although mathematical resilience has been identified as important for success (Johnston-Wilder & Lee, 2010; Rivera & Waxman, 2011), little consensus exists around its definition and no measures of resilience have been rigorously developed and/or validated. Rivera & Waxman (2011) identified the use of teacher nomination of resilient students as a limitation of their study, further motivating development of an instrument. This presentation will report on efforts to develop and validate an instrument measuring mathematical resilience. Ultimately, the measure will aid in developing and testing models that gauge the role of mathematical resilience in student achievement and persistence in advanced coursework. These models can be used to develop interventions to improve mathematical resilience, achievement, and quantitative literacy (Johnston-Wilder & Lee, 2010)

Spin chains and channels with memory

In most studies of the channel capacity of quantum channels, it is assumed that the errors in each use of the channel are independent. However, recent work has begun to investigate the effects of memory or correlations in the error. This work has led to speculation that interesting non-analytic behaviour may occur in the capacity. Motivated by these observations, we connect the study of channel capacities under correlated error to the study of critical behaviour in many-body physics. This connection enables us the techniques of many-body physics to either completely solve or understand qualitatively a number of interesting models of correlated error. The models can display analogous behaviour to associated many-body systems, including `phase transitions'.Comment: V2: changes in presentation, some additional comments on generalisation. V3: In accordance with published version, most (but not all) details of proofs now included. A separate paper will shortly be submitted separately with all details and more result

Tributes to Professor Robert Berkley Harper

In 1977, I began teaching at The University of Pittsburgh Law School and in short order one of my closest friends during my tenure there was Professor Robert “Bob” Harper. I wondered when I was hired whether I was selected because I looked strikingly similar to Bob, and perhaps the faculty thought my favoring Professor Harper would make my assimilation into the law school faculty that much easier. Students constantly called me Professor Harper and, indeed, many on the faculty called me Bob for several years; I never bothered to correct them. I thought if they paid that little attention to detail in law school, I would just let them go through life missing some of the finer points their education, and life for that matter, has to offer

Analysis of complete positivity conditions for quantum qutrit channels

We present an analysis of complete positivity (CP) constraints on qutrit quantum channels that have a form of affine transformations of generalized Bloch vector. For diagonal (damping) channels we derive conditions analogous to the ones that in qubit case produce tetrahedron structure in the channel parameter space.Comment: 12 pages, 8 figures (.eps), minor changes in the text and formula

The accretion-diffusion scenario for metals in cool white dwarfs

We calculated diffusion timescales for Ca, Mg, Fe in hydrogen atmosphere white dwarfs with temperatures between 5000 and 25000 K. With these timescales we determined accretion rates for a sample of 38 DAZ white dwarfs from the recent studies of Zuckerman et al. (2003) and Koester et al. (2005). Assuming that the accretion rates can be calculated with the Bondi-Hoyle formula for hydrodynamic accretion, we obtained estimates for the interstellar matter density around the accreting objects. These densities are in good agreement with new data about the warm, partially ionized phase of the ISM in the solar neighborhood.Comment: To be published in A&

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