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

Foliations associated to harmonic maps and some complex two ball quotients

The purpose of the article is to study a foliation associated to a lattice-equivariant harmonic map of small rank from a complex ball to another. The result is related to rigidity of some complex ball quotients

Productivity in endowments : sectoral evidence for Hong Kong's aggregate growth

The author provides sectoral evidence that sheds new light on the current debate regarding the sources of growth of the East Asian miracle. The author tests both the productivity-driven and endowment-driven hypotheses using Hong Kong's sectoral data. The results show that most of the growth in the services sector is driven by the rapidly accumulating capital endowments, and not by productivity growth. In addition, productivity growth in the manufacturing sector is also unimpressive. The manufacturing sector is more labor intensive and its growth is hindered by the reallocation of resources into the services sector as a result of the growth of capital endowments and imports. Overall, sectoral evidence supports the endowment-driven hypothesis for Hong Kong's aggregate growth.Water and Industry,Banks&Banking Reform,Environmental Economics&Policies,Economic Theory&Research,Industrial Management,Economic Theory&Research,Environmental Economics&Policies,Banks&Banking Reform,Economic Growth,Industrial Management

Book Review: Industrial Policy and Development: The Political Economy of Capabilities Accumulation, by Cimoli, M., Dosi, G. and Stiglitz, J.E., Oxford: Oxford University Press, 2009; pp. xix, 575.

- book review