Unexpected local extrema for the Sendov conjecture

Let S(n) be the set of all polynomials of degree n with all roots in the unit disk, and define d(P) to be the maximum of the distances from each of the roots of a polynomial P to that root's nearest critical point. In this notation, Sendov's conjecture asserts that d(P)<=1 for every P in S(n). Define P in S(n) to be locally extremal if d(P)>=d(Q) for all nearby Q in S(n), and note that maximizing d(P) over all locally extremal polynomials P would settle the Sendov conjecture. Prior to now, the only polynomials known to be locally extremal were of the form P(z)=c(z^n+a) with |a|=1. In this paper, we determine sufficient conditions for real polynomials of a different form to be locally extremal, and we use these conditions to find locally extremal polynomials of this form of degrees 8, 9, 12, 13, 14, 15, 19, 20, and 26.Comment: 10 pages, AMS-LaTeX, no figures. The Maple code and results used in this paper are included in the source files. We constructed an unexpected locally extremal polynomial of degree 8 in version 1, then added degrees 12, 14, 20 and 26 in version 2, and degrees 9, 13, 15 and 19 in version

A Nightmare Revisited: The Resotration of the Canadian War Museum’s 8.8 cm Flak Gun

The German 8.8 cm Flugabwehrkanone (flak) gun is one of the most famous weapons of the Second World War. It was greatly feared by Allied soldiers and airmen alike. Just as every tank they encountered was a Tiger, so too was every German gun an “88.” In December 1998, the Canadian War Museum set out to restore the 88 in the museum’s collection and return to public view one of the few such artifacts in Canada. The museum’s gun was in extremely poor condition, and needed major work. Its components had been disassembled before it had come to the museum and had obviously been at the mercy of the elements for many years. In order to return this complicated weapon as close as possible to its original specifications, an enormous amount of technical information had to be amassed. Some of this should be of interest to readers of this journal, both as an account of a gun that wreaked havoc amongst Canadian soldiers in the Second World War, and as an insight into the nature of museum restoration procedures. The Friends of the Canadian War Museum raised $10,000 for the gun’s restoration, and without their funding the project could not have been undertaken. Several companies bid on the project and Musetek Ltd. won the contract. Work commenced during the second week of January 1999 and the gun’s restoration was completed by the first week of April 1999. The following article will be divided into three sections: 1) the history and development of the 8.8 cm; 2) the process of identifying the particular gun owned by the CWM, and 3) the story of the gun’s restoration

Sustainable construction for the future - the role of government in energy efficiency and sustainability in buildings

This paper will summarise the findings from a study that explored the link between dwelling design, or type, and energy efficiencies in sub-tropical climates. An increasing number of government and private sector development companies are initiating projects that aim to deliver enhanced environmental outcomes at both sub-divisional and dwelling levels. The study used AccuRate, a new thermal modelling tool developed by CSIRO that responds to the need to improve ventilation modelling. The study found that dwellings developed in conjunction with the Departments of Housing and Public Works have set the benchmark. It provides a snapshot of the energy efficiency of a range of dwelling types found in recent subdivisions. However, the trend toward increasing urban densities may reduce the likelihood that cooling breezes will be available to cool dwellings. The findings are relevant to regulators, designers and industry in all states interested in reducing the energy used to cool dwellings in summer

Energy efficient multi storey residential developments

Worldwide, the current pattern of urban development is unsustainable and metropolitan planning and development strategies deliver poor environmental outcomes in relation to energy production. As a result, an increasing number of governments and private sector development companies are initiating projects that aim to deliver enhanced environmental outcomes rather than a ‘business as usual’ approach. This paper will summarise the findings from a study that explored the link between building orientation and energy efficiencies in sub-tropical and tropical climates. The study used a new thermal modelling software tool developed by CSIRO that responds more accurately to residential heating and cooling energy performance in those climate zones. This software tool responds to industry criticisms regarding cold climate modelling systems that do not make sufficient allowance for natural ventilation. The study examined a range of low, medium and high-density dwelling types and investigated the impact of orientation, insulation, ventilation and shading devices on energy efficiencies. This paper will examine the findings from the medium and high-density case study developments as these are relevant to residential developments in many South East Asian countries, such as Singapore, Hong Kong and Malaysia. Finally, the paper will explore the potential benefits that medium and high-density residential developments have in the development of ‘solar cities’ and ‘solar suburbs’

How to achieve sustainability : regulatory challenges

The importance of designing sustainable buildings is gaining greater acceptance worldwide. Evidence of this is how regulators are incorporating sustainable design principles into building regulations and requirements. The aim being to increase the number of sustainable buildings and move from a traditional voluntary compliance to one that is mandatory. However, developing regulations that actually achieve these aims can be a difficult exercise. Several countries in South East Asia, such as Singapore and Malaysia, have performance based building regulations that are supplemented by prescriptive measures for achieving the desired performance. Australia too has similar building regulations and has had energy efficiency regulations within the Building Code of Australia for over a decade. This paper explores some of the difficulties and problems that Australian regulators have experienced with the performance-based method and the prescriptive or “deemed-to-comply” method and measures that have been taken to try and overcome these problems. These experiences act as a useful guide to all regulators considering the incorporation of sustainable design measures into their countries building regulations. The paper also speculates on future environmental requirements being incorporated into regulations, including the possibility of non-residential buildings being required to meet minimum energy efficiency requirements, and the possible systems that would need to be in place before such requirements were included. Finally, the paper looks at a possible way forward using direct assessment from electronic designs and introduces several software tools that are currently being developed that move towards achieving this goal. Keywords: Sustainable buildings, Performance-based, Regulations, Energy efficiency, Assessment tools