In this dissertation, we introduce the notion of Drinfeld modular forms with A-expansions, where instead of the usual Fourier expansion in tⁿ (t being the uniformizer at infinity), parametrized by n ∈ N, we look at expansions in tₐ, parametrized by a ∈ A = F(q)[T]. We construct an infinite family of such eigenforms. Drinfeld modular forms with A-expansions have many desirable properties that allow us to explicitly compute the Hecke action. The applications of our results include: (i) various congruences between Drinfeld eigenforms; (ii) interesting relations between the usual Fourier expansions and A-expansions, and resulting recursive relations for special families of forms with A-expansions; (iii) the computation of the eigensystems of Drinfeld modular forms with A-expansions; (iv) many examples of failure of multiplicity one result, as well as a restrictive multiplicity one result for Drinfeld modular forms with A-expansions; (v) the proof of diagonalizability of the Hecke action in 'non-trivial' cases; (vi) examples of eigenforms that can be represented as non-trivial' products of eigenforms; (vii) an extension of a result of Böckle and Pink concerning the Hecke properties of the space of cuspidal modulo double cuspidal forms for Γ₁(T) to the groups GL₂(F(q)[T]) and Γ₀(T).

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Because lattice theory is so vast, the primary purpose of this paper will be to present some of the general properties of lattices, exhibit examples of lattices, and discuss the properties of distributive and modular lattices.

Let E be an elementary abelian p-group of rank r and k an algebraically closed field of characteristic p. We investigate finitely generated kE-modules of stable constant Jordan type [a][b] with 1 ≤ a, b ≤ p − 1 using the functors Fi from finitely generated kE-modules to vector bundles on the projective space Pr−1 constructed by Benson and Pevtsova. In particular, we study relations on the Chern numbers of the trivial bundle M to obtain restrictions on a and b for sufficiently large ranks and primes. We then study kE-modules with the constant image property and define the constant image layers of a module with respect to its maximal submodule having the constant image property. We prove that almost all such subquotients are semisimple. Focusing on the class of W-modules in rank two, we also calculate the vector bundles Fi(M) for all W-modules M. For E of rank two, we derive a duality formula for kE-modules M of constant Jordan type and their generic kernels K(M). We use this to answer a question of Carlson, Friedlander and Suslin regarding whether or not the submodules J−iK(M) also have constant Jordan type for all i ≥ 0. We show that this question has an affirmative answer whenever p = 3 or J2K(M) = 0. We also show that it has a negative answer in general by constructing a kE-module M of constant Jordan type for p ≥ 5 such that J−1K(M) does not have constant Jordan type. Finally, we use ideas from a theorem of Benson to show that if M is a kE-module of constant Jordan type containing no Jordan blocks of length one, then there always exist submodules of J−1K(M)/J2K(M) having a particularly nice structure.

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This thesis describes a research study in the design, implementation, evaluation and commercialisation of pneumatic motion control systems for modular robots. The research programme was conducted as part of a collaborative study, sponsored by the Science and Engineering Research Council, between Loughborough University and Martonair (UK) Limited. Microprocessor based motion control strategies have been used to produce low cost pneumatic servo-drives which can be used for 'point-to-point' positioning of payloads. Software based realtime control strategies have evolved which accomplish servo-controlled positioning while compensating for drive system non-linearities and time delays. The application of novel compensation techniques has resulted in a significant improvement in both the static and dynamic performance of the drive. A theoretical foundation is presented based on a linearised model of a pneumatic actuator, servo-valve, and load system. The thesis describes the design and evolution of microprocessor based hardware and software for motion control of pneumatic drives. A British Standards based test-facility has allowed control strategies to be evaluated with reference to standard performance criteria. It is demonstrated in this research study that the dynamic and static performance characteristics of a pneumatic motion control system can be dramatically improved by applying appropriate software based realtime control strategies. This makes the application of computer controlled pneumatic servos in manufacturing very attractive with cost performance ratios which match or better alternative drive technologies. The research study has led to commercial products (marketed by Martonair Ltd), in which realtime control algorithms implementing these control strategy designs are executed within a microprocessor based motion controller.

The form of an organism is often closely linked to its function, and this relationship may be particularly important in organisms where individual form is highly flexible due to the repeated iteration of minute multicellular modules. In many modular taxa, including the bryozoans discussed in this thesis, each module is able to function as largely independent units; an individual module can feed independently, has a separate gut, and has the potential to reproduce. These characteristics mean that the number of modules in a bryozoan colony, and hence its size, is a reasonably accurate measure of the colony’s ability to both capture resources and to produce sexually developed larvae. Size is therefore a more appropriate measure of colony demography than age, the criterion traditionally used for unitary organisms. However, processes that can complicate the demography of modular organisms such as colony damage, fission or fusion also mean that the age structure of the component modules in a colony or fragment remains an important predictor of colony functioning, interacting with the effects of colony size. (For complete abstract open document)

Thesis (M. Phil.)--University of Hong Kong, 2008. / Also available in print.