Application of covering techniques to families of curves

Much success in finding rational points on curves has been obtained by using Chabauty's Theorem, which applies when the genus of a curve is greater than the rank of the Mordell-Weil group of the Jacobian. When Chabauty's Theorem does not directly apply to a curve C, a recent modification has been to cover the rational points on C by those on a covering collection of curves D$_i$, obtained by pullbacks along an isogeny to the Jacobian; one then hopes that Chabauty's Theorem applies to each D$_i$. So far, this latter technique has been applied to isolated examples. We apply, for the first time, certain covering techniques to infinite families of curves. We find an infinite family of curves to which Chabauty's Theorem is not applicable, but which can be solved using bielliptic covers, and other infinite families of curves which even resist solution by bielliptic covers. A fringe benefit is an infinite family of Abelian surfaces with non-trivial elements of the Tate-Shafarevich group killed by a bielliptic isogeny

Holographic data storage in a DX-center material

We report on the optical storage of digital data in a semiconductor sample containing DX centers. The diffraction efficiency and the bit-error-rate performance of multiplexed data images are shown to agree well with a simple model of the material. Uniform storage without an exposure schedule is demonstrated. The volume sensitivity is found to be ~10^3 times that of LiNBO3:Fe. The importance of coherent addition of scattered light with diffracted light in holographic data storage is discussed

Did increasing the state pension age in Ireland affect the retirement rate of 65-year-olds? Quarterly Economic Commentary Special Article, Autumn 2017

In January 2014, the qualifying age for the Irish contributory state pension increased from 65 to 66 years. Individuals born after 1 January 1949 could no longer qualify for the pension at age 65, while individuals born before this date could still qualify, provided they had the required social insurance contributions. In this paper, we examine whether this change in the qualifying age had a causal effect on the retirement rate of 65-year-olds in Ireland. To do this, we compare the retirement rates of two groups of 65-year-olds in 2014; one group was born just after the cut-off date, thereby making them ineligible for the state pension at age 65, while the other group was born just before the cut-off date, making them potentially eligible, subject to meeting the insurance contribution requirements. We do not find clear evidence that the change in the retirement age had a causal effect on the retirement rate or the employment and unemployment rates of 65-year-olds in 2014

There’s always the river: social and environmental equity in rapidly urbanising landscapes in India

In the pursuit of sustainable and liveable cities, Indian built environment practitioners and policymakers are understandably focused on aspects of infrastructure, sanitation and health, given the problems of pollution and environmental degradation are significant urban problems. However, there is little demonstration of understanding of the part that landscape could play in tackling such issues. To explore this, the paper examines two urban rivers in India. It calls on interviews with practitioners, residents and users in Madurai and Ahmedabad, focusing on access and use of the river to explore social and environmental equity. The findings suggest that free, public and safe access to the rivers have reduced over time in both cities, for different reasons. Perceived environmental quality of both rivers has also worsened. We suggest that urban river infrastructure should be reconceptualised to explore the feasibility and acceptability of a more holistic approach to understanding Indian riparian urban landscapes

Florence Valley : An Abandoned Stream Valley, Florence Township, Erie County, Ohio

Author Institution: U.S.D.A. Soil Conservation Service, Sandusky, OhioAn abandoned stream valley, here called Florence Valley, was found in eastern Erie County, Ohio. Florence Valley is about one mile long and connects the valleys of Chappel Creek and the Vermilion River. There is evidence that Florence Valley was formed as a result of the capture of a tributary of the Vermilion River by Chappel Creek. Chappel Creek, at the junction of Florence Valley and the valley of Chappel Creek, has a rightangled bend, which displays morphology characteristic of an "elbow-of-capture." The gradient of the eastern two-thirds of Florence Valley slopes toward the Vermilion River. Because the Vermilion River is more deeply entrenched than is Chappel Creek, this stream capture must have taken place at a time when the base level was at a higher elevation, when Chappel Creek had a shorter course and steeper gradient than did the Vermilion River. These conditions are believed to have existed during the time of Lake Maumee III

Dirac Cat States in Relativistic Landau Levels

We show that a relativistic version of Schrodinger cat states, here called Dirac cat states, can be built in relativistic Landau levels when an external magnetic field couples to a relativistic spin 1/2 charged particle. Under suitable initial conditions, the associated Dirac equation produces unitarily Dirac cat states involving the orbital quanta of the particle in a well defined mesoscopic regime. We demonstrate that the proposed Dirac cat states have a purely relativistic origin and cease to exist in the non-relativistic limit. In this manner, we expect to open relativistic quantum mechanics to the rich structures of quantum optics and quantum information.Comment: Revtex4, color figures, submitted for publicatio

Australian SMEs waste to landfill

Landfill waste has a negative impact on the environment and small and medium sized enterprises (SMEs) are believed to be significant contributors. There is little government or scholarly research, however, quantifying the collective volume of waste SMEs send to landfill. Where studies do exist they measure total volumes (landfill and recycling combined) and/or do not distinguish between specific waste streams (e.g. wood) and subcategories (e.g. dust). This paper contributes to knowledge by giving insight into the collective volume of waste of 404 SMEs, reconceptualising SME waste into subcategories and by measuring landfill volumes. It presents findings from these 404 Australian SMEs which found that, in descending order, cardboard, paper, plastic wrap, wood dust and particleboard were the subcategories these SMEs sent to landfill in the greatest volumes. It also argues that this reconceptualisation, and associated data collection protocols, have the potential to enable scholars and policy makers to determine the waste subcategories to which SMEs contribute most, formulate targeted interventions and research or evaluate environmental outcomes. © 2014 © 2014 Environment Institute of Australia and New Zealand Inc

Computer recommendations for an automatic approach and landing system for V/STOL aircraft. Volume 2 - Equations

Automatic approach and landing system for V/STOL aircraf