title: Towards a quantitative proxy of cave dripwater hydrology

authors: Hartland, Adam

abstract: Speleothems capture a wide range of geochemical signals related to hydroclimate variability. However, the quantification of climatic parameters (e.g. rainfall, temperature) using traditional proxies is hampered by the multitude of influencing factors.

text: Towards a quantitative proxy of cave dripwater hydrology Speleothems capture a wide range of geochemical signals related to hydroclimate variability. However, the quantification of climatic parameters (e.g. rainfall, temperature) using traditional proxies is hampered by the multitude of influencing factors.

year: 2018

title: Existence, mixing and approximation of invariant densities for expanding maps on Rr

authors: Murray, Rua

subjects: mathematics

abstract: This paper generalises Gora and Boyarsky’s bounded variation(BV) approach to the ergodic properties of expanding transformations, and analysies the convergence of Ulam’s method for the numerical approximation of absolutely continuous invariant measures. We first prove an existence theorem for BV invariant densities for piecewise expanding maps on subsets of Rr; the maps must be C2, but may have infinitely many branches and need not be Markov. Under and additional “onto” assumption, explicit bounds on the spectral gap in the associated Perron-Frobenius operator are proved. The corresponding contraction rates are in the BV norm, rather than a projective metric. With this quantitative information, we are then able to prove convergence and explicit upper bounds on the approximation error in Ulam’s method for approximating invariant measures. Because the BV approach is rather concete, the methods of this paper can be applied in practice; this is illustrated by an application of the main results to the Jacobi-Perron transformation on R2.

text: Existence, mixing and approximation of invariant densities for expanding maps on Rr This paper generalises Gora and Boyarsky’s bounded variation(BV) approach to the ergodic properties of expanding transformations, and analysies the convergence of Ulam’s method for the numerical approximation of absolutely continuous invariant measures. We first prove an existence theorem for BV invariant densities for piecewise expanding maps on subsets of Rr; the maps must be C2, but may have infinitely many branches and need not be Markov. Under and additional “onto” assumption, explicit bounds on the spectral gap in the associated Perron-Frobenius operator are proved. The corresponding contraction rates are in the BV norm, rather than a projective metric. With this quantitative information, we are then able to prove convergence and explicit upper bounds on the approximation error in Ulam’s method for approximating invariant measures. Because the BV approach is rather concete, the methods of this paper can be applied in practice; this is illustrated by an application of the main results to the Jacobi-Perron transformation on R2.

year: 2001

title: The relationship between Māori cultural identity loss & rangatahi Māori suicide

authors: Graham, Shaquille

subjects: Māori

abstract: This research explores the relationship between Māori cultural identity loss and rangatahi Māori suicide in Aotearoa. The McLachlan et al. (in press) Whiti Te Rā model of cultural identity was employed to frame the investigation with specific analysis into the six critical cultural ara of Whakapapa, Reo Māori, Taiao, Mahi-a-toi, Take pū whānau and Wairuatanga. A Kaupapa Māori research approach was utilised for cultural applicability and the promotion of Tino Rangatiratanga. Qualitative methodology guided data collection and analysis. Data collection involved (i) literature reviews and (ii) interviews with whānau members of rangatahi lost to suicide, seeking to understand the āhuatanga of the six cultural ara within the case studies (n=5). Interviews were governed by a semi-structured technique that looked to understand (i) the factors influencing the strength or weakness of each cultural ara; (ii) the state of health within each cultural ara; (iii) and identify causal relationships between cultural ara and wellbeing outcome. Reflexive thematic analysis showed that geographical location, generational knowledge transmission, and individual and whānau engagement were the global themes influencing either the diminishing or strengthening of cultural identity. Ngā Ara Wairua and Take pū whānau were also portrayed as the most compromised. The research suggests that optimal access to the three global themes potentiates rangatahi Māori to cultural flourishing and Mauri Ora; proposed as the most significant deterrent for suicidality. Contrastingly, suboptimal access to the three global themes is proposed as diminishing cultural ara as expressed in a state of Mauri Moe, where rangatahi Māori wellbeing is most vulnerable, and where suicidality has the greatest potentiation.

text: The relationship between Māori cultural identity loss & rangatahi Māori suicide This research explores the relationship between Māori cultural identity loss and rangatahi Māori suicide in Aotearoa. The McLachlan et al. (in press) Whiti Te Rā model of cultural identity was employed to frame the investigation with specific analysis into the six critical cultural ara of Whakapapa, Reo Māori, Taiao, Mahi-a-toi, Take pū whānau and Wairuatanga. A Kaupapa Māori research approach was utilised for cultural applicability and the promotion of Tino Rangatiratanga. Qualitative methodology guided data collection and analysis. Data collection involved (i) literature reviews and (ii) interviews with whānau members of rangatahi lost to suicide, seeking to understand the āhuatanga of the six cultural ara within the case studies (n=5). Interviews were governed by a semi-structured technique that looked to understand (i) the factors influencing the strength or weakness of each cultural ara; (ii) the state of health within each cultural ara; (iii) and identify causal relationships between cultural ara and wellbeing outcome. Reflexive thematic analysis showed that geographical location, generational knowledge transmission, and individual and whānau engagement were the global themes influencing either the diminishing or strengthening of cultural identity. Ngā Ara Wairua and Take pū whānau were also portrayed as the most compromised. The research suggests that optimal access to the three global themes potentiates rangatahi Māori to cultural flourishing and Mauri Ora; proposed as the most significant deterrent for suicidality. Contrastingly, suboptimal access to the three global themes is proposed as diminishing cultural ara as expressed in a state of Mauri Moe, where rangatahi Māori wellbeing is most vulnerable, and where suicidality has the greatest potentiation.

year: 2021