Bose-Mesner Algebras attached to Invertible Jones Pairs

In 1989, Vaughan Jones introduced spin models and showed that they could be used to form link invariants in two different ways--by constructing representations of the braid group, or by constructing partition functions. These spin models were subsequently generalized to so-called 4-weight spin models by Bannai and Bannai; these could be used to construct partition functions, but did not lead to braid group representations in any obvious way. Jaeger showed that spin models were intimately related to certain association schemes. Yamada gave a construction of a symmetric spin model on $4n$ vertices from each 4-weight spin model on $n$ vertices. In this paper we build on recent work with Munemasa to give a different proof to Yamada's result, and we analyse the structure of the association scheme attached to this spin model.Comment: 23 page

Hamming graphs in Nomura Algebras

Let A be an association scheme on q\geq 3 vertices. We show that the Bose-Mesner algebra of the generalized Hamming scheme H(n,A), for n\geq 2, is not the Nomura algebra of a type II matrix. This result gives examples of formally self-dual Bose-Mesner algebras that are not the Nomura algebras of type II matrices.Comment: 15 pages, minor revisio

Four-Weight Spin Models and Jones Pairs

We introduce and discuss Jones pairs. These provide a generalization and a new approach to the four-weight spin models of Bannai and Bannai. We show that each four-weight spin model determines a ``dual'' pair of association schemes

Orthographic knowledge of Chinese in adults of 40 to 65 years

A dissertation submitted in partial fulfilment of the requirements for the Bachelor of Science (Speech and Hearing Sciences), University of Hong Kong, April 30, 1992.Also available in print.Thesis (B.Sc)--University of Hong Kong, 1992published_or_final_versionSpeech and Hearing SciencesBachelorBachelor of Science in Speech and Hearing Science

Investigation of Dairy Wastewater Using Biowish

Various bacterial products from BiOWiSHTM Technologies have been tested in dairy wastewater experiments to determine the bacterial mixes’ ability for enhanced degradation of biochemical oxygen demand (BOD), solids, and nitrate concentrations. The dairy wastewater was augmented with various bacterial composition obtained from BiOWiSHTM. The bacterial mixes experimented were US Aqua, Thai Aqua, BMT, Osprey, Fruit Wash, KLB, LCM1, and MDG. Method development was a crucial process to optimize and test the effects of the BiOWiSHTM Technologies bacterial mixes. After 5 experiments, the BOD tests showed that for some of the tests, the redosage of bacteria helped further drive the BOD concentrations to be lower than the control. With redose, the samples reduced BOD by 10 – 55% to samples that were not redosed. Although the redose adds supplemental BOD initially, the addition showed that in some cases, the bacterial sample BOD is lower than without any redose. For the solids testing, different solids tests showed either conclusive impacts of bioaugmentation or no effect. For the total solids (TS) and total suspended solids (TSS) tests, both showed about a 10% decrease or increase in solids throughout the experiments. The smaller solids components, volatile suspended solids (VSS), did demonstrate that the bacterial mixes reduced organic suspended solids more than the control. The bioaugmented samples reduced the VSS organic material by 5 – 15% compared to the control with BiOWiSHTM. Particle size distribution (PSD) tests provided a breakdown of which particle sizes were increasing and decreasing. Those samples bioaugmented with BiOWiSHTM showed that smaller particles (0.7 µm pore size) were getting assimilated by the bacteria which produced more bacteria (larger pore sizes of 5 µm). After the bacteria ran out of food, the sequentially smaller pore size (2.5 µm) increased while the smaller pore sizes (1.6 µm and 0.7 µm) remained low. The rate limiting step was determined to be 1.6 – 2.5 µm where the control’s zero rate constant was +1.4 mg/L-day whereas the USA and TA was -1.1 mg/L-day and -1.4 mg/L-day respectively. Thus, the BiOWiSHTM samples decreased TSS in smaller pore size filters by about 10 – 20% more than the control. Ion chromatography (IC) measured that nitrate levels were clearly reduced by 30 – 50% adding the BiOWiSHTM bacteria compared to the control. Therefore, the additional bacteria further denitrified the nitrate (NO3-) than if no BiOWiSHTM was added. Denitrification experiments were performed for pure Bacillus spores, KLB, that showed a 90% decrease of NO3- to the control. Keywords: bioaugmentation, BiOWiSHTM, BOD, dairy wastewater, dissolved solids, ion chromatography, nitrate, particle size distribution, redose, suspended solids, total solids, volatile suspended solid