title: Transition formulae for ranks of abelian varieties

authors: Delbourgo, Daniel

abstract: Let A/k denote an abelian variety defined over a number field k with good ordinary reduction at all primes above p, and let K∞ =∪n≥1 Kn be a p-adic Lie extension of k containing the cyclotomic Zp-extension. We use K-theory to find recurrence relations for the λ-invariant at each σ-component of the Selmer group over K∞, where σ : Gk → GL(V ). This provides upper bounds on the Mordell-Weil rank for A(Kn) as n → ∞ whenever G∞ = Gal(K∞/k) has dimension at most 3.

text: Transition formulae for ranks of abelian varieties Let A/k denote an abelian variety defined over a number field k with good ordinary reduction at all primes above p, and let K∞ =∪n≥1 Kn be a p-adic Lie extension of k containing the cyclotomic Zp-extension. We use K-theory to find recurrence relations for the λ-invariant at each σ-component of the Selmer group over K∞, where σ : Gk → GL(V ). This provides upper bounds on the Mordell-Weil rank for A(Kn) as n → ∞ whenever G∞ = Gal(K∞/k) has dimension at most 3.

year: 2015

title: Vibration analysis of cracked structures as a roving body passes a crack using the Rayleigh-Ritz Method

authors: Ilanko, Sinniah

subjects: cracked plate

abstract: The natural frequencies of a cracked plate with a roving mass were computed using the Rayleigh-Ritz Method for various sets of boundary condition. The obtained frequencies exhibit a sudden shift as a roving body crosses a crack. If the crack is only partial and continuity of translation is maintained, then the frequency shift occurs only when the body possesses a rotary inertia. If the crack is a complete one (through thickness) which permits differential translation to occur on either side of the crack, a particle having mass only (translatory inertia) is sufficient to cause a sudden shift. There is no need for a rotary inertia. This is potentially useful in detecting cracks in structures, as it is possible to track the changes in the natural frequencies of a structure as a test body such as a vehicle on a bridge moves and identify points where sudden frequency changes occur.

text: Vibration analysis of cracked structures as a roving body passes a crack using the Rayleigh-Ritz Method The natural frequencies of a cracked plate with a roving mass were computed using the Rayleigh-Ritz Method for various sets of boundary condition. The obtained frequencies exhibit a sudden shift as a roving body crosses a crack. If the crack is only partial and continuity of translation is maintained, then the frequency shift occurs only when the body possesses a rotary inertia. If the crack is a complete one (through thickness) which permits differential translation to occur on either side of the crack, a particle having mass only (translatory inertia) is sufficient to cause a sudden shift. There is no need for a rotary inertia. This is potentially useful in detecting cracks in structures, as it is possible to track the changes in the natural frequencies of a structure as a test body such as a vehicle on a bridge moves and identify points where sudden frequency changes occur.

year: 2018

title: The relevance of discourse analysis to the teaching and learning of te reo Māori: A text-centred example

authors: Greensill, Hine-iti-moana

subjects: Māori language

abstract: In this paper, I analyse a single text written in te reo Māori in terms of two different approaches derived from discourse analysis (discourse macro-patterning and discourse relations and their signalling) in order to demonstrate the importance of deriving a discourse-centred methodology for teaching learners of Māori what is involved in interpreting and creating coherent discourses.

text: The relevance of discourse analysis to the teaching and learning of te reo Māori: A text-centred example In this paper, I analyse a single text written in te reo Māori in terms of two different approaches derived from discourse analysis (discourse macro-patterning and discourse relations and their signalling) in order to demonstrate the importance of deriving a discourse-centred methodology for teaching learners of Māori what is involved in interpreting and creating coherent discourses.

year: 2007