Hamilton-Waterloo problem with triangle and C9 factors

The Hamilton-Waterloo problem and its spouse-avoiding variant for uniform cycle sizes asks if Kv, where v is odd (or Kv - F, if v is even), can be decomposed into 2-factors in which each factor is made either entirely of m-cycles or entirely of n-cycles. This thesis examines the case in which r of the factors are made up of cycles of length 3 and s of the factors are made up of cycles of length 9, for any r and s. We also discuss a constructive solution to the general (m,n) case which fixes r and s.

Improving the sustainability of an appropriate technology solution; bone char defluoridation filters in Arusha, Tanzania

High concentrations of fluoride naturally occurring in the ground water in the Arusha region of Tanzania cause dental, skeletal and non-skeletal fluorosis in up to 90% of the region’s population [1]. Symptoms of this incurable but completely preventable disease include brittle, discolored teeth, malformed bones and stiff and swollen joints. The consumption of high fluoride water has also been proven to cause headaches and insomnia [2] and adversely affect the development of children’s intelligence [3, 4]. Despite the fact that this array of symptoms may significantly impact a society’s development and the citizens’ ability to perform work and enjoy a reasonable quality of life, little is offered in the Arusha region in the form of solutions for the poor, those hardest hit by the problem. Multiple defluoridation technologies do exist, yet none are successfully reaching the Tanzanian public. This report takes a closer look at the efforts of one local organization, the Defluoridation Technology Project (DTP), to address the region’s fluorosis problem through the production and dissemination of bone char defluoridation filters, an appropriate technology solution that is proven to work. The goal of this research is to improve the sustainability of DTP’s operations and help them reach a wider range of clients so that they may reduce the occurrence of fluorosis more effectively. This was done first through laboratory testing of current products. Results of this testing show a wide range in uptake capacity across batches of bone char emphasizing the need to modify kiln design in order to produce a more consistent and high quality product. The issue of filter dissemination was addressed through the development of a multi-level, customerfunded business model promoting the availability of filters to Tanzanians of all socioeconomic levels. Central to this model is the recommendation to focus on community managed, institutional sized filters in order to make fluoride free water available to lower income clients and to increase Tanzanian involvement at the management level.

Space trajectories optimization using variable-chromosome-length genetic algorithms

The problem of optimal design of a multi-gravity-assist space trajectories, with free number of deep space maneuvers (MGADSM) poses multi-modal cost functions. In the general form of the problem, the number of design variables is solution dependent. To handle global optimization problems where the number of design variables varies from one solution to another, two novel genetic-based techniques are introduced: hidden genes genetic algorithm (HGGA) and dynamic-size multiple population genetic algorithm (DSMPGA). In HGGA, a fixed length for the design variables is assigned for all solutions. Independent variables of each solution are divided into effective and ineffective (hidden) genes. Hidden genes are excluded in cost function evaluations. Full-length solutions undergo standard genetic operations. In DSMPGA, sub-populations of fixed size design spaces are randomly initialized. Standard genetic operations are carried out for a stage of generations. A new population is then created by reproduction from all members based on their relative fitness. The resulting sub-populations have different sizes from their initial sizes. The process repeats, leading to increasing the size of sub-populations of more fit solutions. Both techniques are applied to several MGADSM problems. They have the capability to determine the number of swing-bys, the planets to swing by, launch and arrival dates, and the number of deep space maneuvers as well as their locations, magnitudes, and directions in an optimal sense. The results show that solutions obtained using the developed tools match known solutions for complex case studies. The HGGA is also used to obtain the asteroids sequence and the mission structure in the global trajectory optimization competition (GTOC) problem. As an application of GA optimization to Earth orbits, the problem of visiting a set of ground sites within a constrained time frame is solved. The J2 perturbation and zonal coverage are considered to design repeated Sun-synchronous orbits. Finally, a new set of orbits, the repeated shadow track orbits (RSTO), is introduced. The orbit parameters are optimized such that the shadow of a spacecraft on the Earth visits the same locations periodically every desired number of days.