High-precision tephrostratigraphy : tracking the time-varying eruption pulse of Mt. Taranaki, North Island, New Zealand : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Earth Science, Massey University, Palmerston North, New Zealand

In this research it was proposed that a more robust record of volcanic activity for Mt. Taranaki (New Zealand) could be derived from tephras (pyroclastic fall deposits) within cores from several lakes and peatlands across a 120o arc, NE-SE of the volcano, covering a range of prevailing down-wind directions. These data were integrated with previous tephrochronology studies to construct one of the longest and most complete volcanic eruption history records ever developed for an andesitic stratovolcano. Using 44 new radiocarbon dates, electron microprobe analysis of glass shard and titanomagnetite chemical composition, along with whole-rock chemistry, a chrono- and chemostratigraphy was established. The new record identifies at least 272 tephraproducing eruptions over the last 30 cal ka BP. Six chemo-stratigraphic groups were identified: A (0.5 – 3 cal ka BP), B (3 – 4 cal ka BP), C (4 – 9.5 cal ka BP), D (9.5 – 14 cal ka BP), E (14 – 17.5 cal ka BP), and F (23.5 – 30 cal ka BP). These were used to resolve previous stratigraphic uncertainties at upper-flank (proximal) and ring-plain (medial) sites. Several well-known “marker tephras” are now recognized as being ~2000 years older than previously determined (e.g., Waipuku, Tariki, and Mangatoki Tephra units) with the prominent Korito Tephra stratigraphically positioned above the Taupo-derived Stent Tephra. Further, new markers were identified, including the Kokowai Tephra unit (~4.7 cal ka BP), at a beach-cliff exposure, 40-km north-east of the volcano. Once age-models were established for each tephra, units were matched between sites using statistical methods. Initial statistical integration showed that the immediate past high-resolution tephrochronological record suffered from a distinctive “old-carbon” effect on its ages (Lake Rotokare). This had biased the most recent probabilistic forecasting and generated artificially high probability estimates (52-59% eruption chance over the next 50 years). Once the Rotokare record was excluded and chemostratigraphy constraints were applied, a reliable multi-site tephra record could be built only for the last ~14 ka BP. The new data confirms a highly skewed distribution of mainly (98% of cases) short intervals between eruptions (mode of ~9 years and average interval ~65 years). Long intervals (up to 580 years) as seen in earlier records were reduced to 2% of the record, but can now be considered real, rather than missing data. The new data confirm a cyclic pattern of varying eruption frequency (with a five-fold range in annual frequency) on a period of ~1000-1500 years. The new time-varying frequency estimates suggest a lower probability for a new eruption at Mt. Taranaki over the next 50 years of 33-42%. The newly established chemostratigraphy was further used to investigate time-related compositional changes. Whole-lapilli analyses highlighted that a specific very evolved Ca-rich and Fe-poor composition was only found within the easterly and south-easterly depositional sites. This was explained by eruption of a stratified magma reservoir, which holds greater modal proportions of plagioclase and lower proportions of pyroxene within low-density, gas-rich upper conduit regions. During the most explosive phases of eruptions, when plumes reach the stratospheric jetstream, the lowest-density pumice is thus dispersed by high-level stable westerly winds. Further, two distinct evolutional trends were seen in the long and new tephrochronological record; from 17.5 to 3 cal ka BP and <3 cal ka BP; with wholelapilli, glass, and titanomagnetite compositions overall evolving over time. The former compositional trend indicates a crystallising and cooling magma source in the deep crust, with multiple, spatially separated magma source regions forming, each generating magmas (i.e., magma batches) with unique titanomagnetite compositions. This trend is interrupted by a distinct shift towards less-evolved compositions and the initiation of a second parasitic vent (Fanthams Peak at the southern flank of Mt. Taranaki)

Bounding the distance from a reachable/controllable equisingular switched linear system to the set of non-reachable/uncontrollable ones

No necessary and sufficient condition for reachability of switched linear singular systems has been found in general, but only in the case of the so-called “equisingular systems”. In this case, it is possible to obtain an upper bound for the distance between a controllable equisingular system and the set of uncontrollable onesPeer ReviewedPostprint (author's final draft

Klinikum 1: Hospital Cantonal de Basilea

Peer Reviewe

Some considerations about reachability of switched linear singular systems

No necessary and sufficient condition for reachability of switched linear singular systems has been found, exceptuating the case of the so-called “equisingular systems”. Such a condition is not valid in the general case, as examples show.Peer ReviewedPostprint (published version

Eigenvectors of permutation matrices

The spectral properties of special matrices have been widely studied, because of their applications. We focus on permutation matrices over a finite field and, more concretely, we compute the minimal annihilating polynomial, and a set of linearly independent eigenvectors from the decomposition in disjoint cycles of the permutation naturally associated to the matrix.Peer ReviewedPostprint (published version

D-stratification and hierarchy graphs of the space of order 2 and 3 matrix pencils

Small changes in the entries of a matrix pencil may lead to important changes in its Kronecker normal form. Studies about the effect of small perturbations have been made when considering the stratification associated with the strict equivalence between matrix pencils. In this work, we consider a partition in the space of pairs of matrices associated to regular matrix pencils, which will be proved to be a finite stratification of the space of such matrix pencils, called D-stratification. Matrix pencils in the same strata are those having some prescribed Segre indices. We study the effect of perturbations which lead to changes in the Kronecker canonical form, preserving the order of the nilpotent part. Our goal is to determine which DD-strata can be reached. In the cases where the order of the matrix pencils is 2 or 3, we obtain the corresponding hierarchy graphs, illustrating the DD-strata that can be reached when applying some small perturbationsPeer ReviewedPostprint (author's final draft

Re-examining Causal Relationship between Dividend Policies and Commercial Bank Performance: Evidence from 30 Sub-Saharan African Countries

Objective: This paper re-establishes the causality between two dividend policies (dividend payoutand dividend reinvestment plans) and financial performance (Return on Equity). Prior Work:Dividend policies issues have been continually debated around the world with mixed results, and yetto date, no definite conclusions have been reached. Approach: The study conveniently andpurposively used 250 commercial banks from 30 SSA countries over the period between 2006 and2015 to run long-run causality tests. Results: The results from the block exogeneity Wald test fromthe panel vector error correction model, and the pairwise Granger causality test shows that there is aunidirectional causality between return on equity and dividend payout ratio. Implications: Thisimplies no causality between dividend payout ratio/ retention ratio and banks&rsquo; return on equity overthe study period. Value: Hence, we conclude that the widely adopted model for the payment ofdividends in the SSA banking market is a win-lose game, as there is no causality between dividendpayment and bank performance. As such, we recommend that other dividend policies that canminimize future financing costs, increase bank assets, and improve the future growth prospects of theregion be explored

Nexus of Loan Re-payment Plans, Interest on Loans and the Sustainability of Small and Medium Enterprises in South Africa

This paper examined the influences of interest on loans and loan re-payment plans on the sustainability of small and medium enterprises (SMEs) in South Africa. A quantitative research design that adheres to the positivist paradigm was utilized for this study's methodology. The study targeted 103 SMEs operating in KwaZulu-Natal, South Africa using purposive sampling. A total of 103 surveys were administered, representing a participation rate of 100 percent. The analysis demonstrated a positive relationship between interest on loans and the SMEs’ sustainability and positive relationship between Loan re-payment plans and SMEs’ sustainability. The study recommended that financial institutions should examine loan re-payment plans for SMEs as necessary in order to minimize loan defaults by SMEs, and financial institutions should cut loan interest rates and the costs associated with loan approvals, which may be accomplished via automation and the utilization of online applications. Furthermore, the study suggested that financial institutions should design a flexible loan re-payment plan for SMEs that considers the nation's economic realities