Salem numbers and Pisot numbers via interlacing

We present a general construction of Salem numbers via rational functions whose zeros and poles mostly lie on the unit circle and satisfy an interlacing condition. This extends and unifies earlier work. We then consider the "obvious" limit points of the set of Salem numbers produced by our theorems, and show that these are all Pisot numbers, in support of a conjecture of Boyd. We then show that all Pisot numbers arise in this way. Combining this with a theorem of Boyd, we show that all Salem numbers are produced via an interlacing construction.Comment: 21 pages, 5 figures, updated in response to reviewer comment

Dual mutualistic associations in sainfoin (Onobrychis viciifolia Scop.) : a thesis presented in partial fulfilment of the requirements for the degree of Master of Agricultural Science in Agronomy at Massey University

Recent studies established that many legumes, when infected with the appropriate Rhizobium spp. and arbuscular fungi, nodulated better and exhibited greater dinitrogen fixation than plants infected with only the rhizobia. A similar study, therefore, was carried out in a glasshouse using sainfoin (Onobrychis viciifolia Scop.), a legume that is rapidly gaining recognition as a potential forage crop in New Zealand and other parts of the world. Pre-germinated seeds (cv. Fakir) were planted in sterilized soils and incubated with an effective Rhizobium spp. (strain NZP 5301), a mixture of endophytes (Gigaspora magarita Becker & Hall, Glomus fasciculata (Thax. sensu Gerd.) Gerdemann & Trappe and Glomus tenuis (Greenall) Hall), or both eht rhizobia and endophytes. The experiment also included a control, without any inoculation. Endophyte infection, nodulation and dinitrogen fixation, total nitrogen and phosphorus concentrations, and plant growth and development were determined on eleven sequential samplings over about twenty weeks, up to the stage of green inflorescence. Arbuscular mycorrhiza formation did not occur with the first endophyte inoculation, containing Gigaspora magarita Becker & Hall, even after 93 days of growth. This is probably because the inoculum used consisted of a low quantity of viable spores and mycelia. The second inoculation, containing the three endophyte species, produced only a low degree of infection between day 115 and 137, possibly because the extensive root lignification and relatively higher root phosphorus concentration (0.50%) restricted fungal invasion and establishment within the root cortex. Mycorrhiza formation did not increase phosphate uptake, improve nodulation and dinitrogen fixation, or increase plant growth. This is due probably to the already well-developed root systems that were efficiently exploiting the small soil volume within the bags. Rhizobia-inoculated plants produced more nodules, larger nodules and consequently, a greater nodule dry weight than the uninoculated plants. The nodules produced in the inoculated plants were red instead of green as in the uninoculated plants, and exhibited a greater dinitrogen fixation. As a result, these inoculated plants contained a higher concentration of shoot, root and nodule nitrogen, and a greater dry weight accumulation in the shoots and nodules. The shoot and nodule phosphorus concentrations, however, were lower in the rhizobia-inoculated than in the uninoculated plants due to the greater amount of shoot and nodule tissues which caused a dilution effect. These rhizobia effects on nodulation and dinitrogen fixation, nitrogen and phosphorus concentrations, and plant growth and development became more prominent with time. The relatively higher nodule phosphorus concentration when compared with the shoot and root phosphorus concentrations suggests that phosphorus was presumably required in large quantities by the dinitrogen-fixing system

Oral History Interview with Low Kee Yang: Conceptualising SMU

This is an abridged version of the original interview. Please contact the Library at [email protected] for access to the full version of the transcript and/or audio recording.</p

Effect of panel type and ethnicity on apples in Singapore using temporal dominance method : a thesis presented in fulfilment of the requirements for the degree of Master of Food Technology at Massey University, Albany, New Zealand

Recently, there has been an increased in oral processing studies focusing on the detection of changes in sensational attributes of food product in real time. However, the integration of sensational and emotional attributes with liking is a relatively new line of enquiry, yet if pursued may enable a deeper understanding of the sensory and emotional experience of consumers. This study successfully trials a new system combining temporal dominance of sensation (TDS), emotion (TDE) and liking (TDL) to examine the impact of training and ethnicity on the real time sensory evaluation of popular apple varieties currently being sold in Singapore. A short training (60 minutes) with food references was proven to be highly beneficial and had generated a higher dominance rate, faster first dominant attribute detected, lower variation in the dominant attribute selected and frequent complex textural attributes chosen, showing a better understanding of the terms used. The number of attributes used and dominant end time were however not affected by training. Contrary to TDE, a positive emotional or sensational attribute dominant did not relate to a direct relationship with liking. Non-dominant sensational or emotional attributes might have interfered in the liking observed. Training aside from improving the understanding of attributes used was also found to close the gap between hedonic scores and frequency liking counts. Ethnicity effects were subsequently examined using a Semi Trained Panel consisting of 8 Chinese, 7 Indian and 6 Malay with differing results observed. Chinese were more expressive and positive in the attributes chosen in TDS and TDE while Malay was the opposite. Fibrous (Chinese and Indian) and floral (Chinese) were picked up more readily by different ethnicities. Differences in product where Granny Smith evoked disliking in Malay and Indian, was positively rated by Chinese. These variations could mainly be due to differences in cultural practises and diet. The incorporation of TDS and TDL provided better product understanding than the narrow hedonic range obtained. Furthermore, the mapping of TDS, TDE and TDL curves suggested the ability to condense information allowing dynamic relation to be drawn in a single graph. However, due to the qualitative nature of the graphs, the interpretation of result might be subjective