Nonexistence Certificates for Ovals in a Projective Plane of Order Ten

In 1983, a computer search was performed for ovals in a projective plane of order ten. The search was exhaustive and negative, implying that such ovals do not exist. However, no nonexistence certificates were produced by this search, and to the best of our knowledge the search has never been independently verified. In this paper, we rerun the search for ovals in a projective plane of order ten and produce a collection of nonexistence certificates that, when taken together, imply that such ovals do not exist. Our search program uses the cube-and-conquer paradigm from the field of satisfiability (SAT) checking, coupled with a programmatic SAT solver and the nauty symbolic computation library for removing symmetries from the search.Comment: Appears in the Proceedings of the 31st International Workshop on Combinatorial Algorithms (IWOCA 2020

The problem of mutually unbiased bases in dimension 6

We outline a discretization approach to determine the maximal number of mutually unbiased bases in dimension 6. We describe the basic ideas and introduce the most important definitions to tackle this famous open problem which has been open for the last 10 years. Some preliminary results are also listed

Removal of martensite stabilisation in CANTiM shape memory alloy by post-quench ageing

Step quenching from the solid solution temperature is a common treatment to enhance the shape memory properties in many copper-based shape memory alloys (SMAs). However, the martensite stabilisation problem is more serious in step quenched Cu-Al-Ni-Mn-Ti (CANTiM) SMAs. After step quenching, martensite in CANTiM cannot reverse transform to its parent phase. In contrast, fast quenching rates usually lead to better shape memory properties in CANTiM SMA. When the alloy is directly quenched into KOH, martensite stabilisation is still present. However, martensite stabilisation can be removed by post-quench ageing at 100°C. In rapid quenching from high temperature, a large number of defects such as vacancies are usually produced. The martensite stabilisation due to fast quenching is attributed to the pinning effect of these excessive vacancies. After post-quench ageing, the concentration of vacancies is lowered and thus the pinning effect is reduced. This paper reports the behaviour of vacancies at different cooling rates in different quenching medium, and the effect of post-quench ageing. The evolution of vacancies in the alloy is studied using positron annihilation techniques. In contrast to the martensite stabilisation due to ageing at higher temperatures, the martensite stabilisation due to fast quenching rate can be removed by a carefully chosen low temperature ageing programme.link_to_subscribed_fulltex

Dynamic studies on Cu-based shape memory alloy using positron lifetime spectroscopy

This paper describes a positron lifetime study of properties and dynamic behavior of vacancies in CuZnAlMnZr alloy during aging at room temperature (RT) after Direct- and Step-quenching. It is found that there is only one type of vacancy in CuZnAlMnZr which has no effect on the shape memory properties of CuZnAlMnZr and the vacancy recovery process is quite slow after Direct-quenching and no recovery process after Step-quenching, and the CuZnAlMnZr alloy has better thermal stability than the ordinary CuZnAl alloy. During the long measurement period, a software stabilization technique has been adopted and the reliability of the software has been checked.link_to_subscribed_fulltex

Colorectal cancer screening behaviour and associated factors among Chinese aged 50 and above in Hong Kong - A population-based survey

Purpose: This study reports the uptake rate of colorectal cancer screening among Chinese people aged 50 or above and the identified factors associated with the likelihood of undergoing such screening. Methods: A cross-sectional population-based telephone survey was conducted in Hong Kong during the period 2 to 28 May 2007. The survey covered demographics, perceived health status and susceptibility to cancer, utilisation of complementary medicine, family history of cancer and cancer screening behaviour. Results: The survey was completed by 2004 Hong Kong Chinese residents aged 50 or older (response rate = 66.6%). The uptake rate of a fecal occult blood test and a colonoscopy was 12% and 19% respectively. Factors associated with colorectal cancer screening behaviour included: male participants, ex-smokers, with cancer or other serious disease, a family history of cancer, perceived health status fair or poor, regular visits to a doctor to look after health, and utilisation of complementary medicine. Conclusions: The uptake rate of this study population was low though an increasing trend did appear. Heath education and promotion programmes may focus on these identified factors to facilitate colorectal cancer screening in a Chinese population. © 2011 Elsevier Ltd.link_to_subscribed_fulltex

Colorectal cancer testing and associated factors among older Chinese adults

Letter to the Editorlink_to_subscribed_fulltex