title: Holomorphic Flows on Simply Connected Regions Have No Limit Cycles

authors: Broughan, Kevin A.

subjects: mathematics

abstract: The dynamical system or flow  = f(z), where f is holomorphic on C, is considered. The behavior of the flow at critical points coincides with the behavior of the linearization when the critical points are non-degenerate: there is no center-focus dichotomy. Periodic orbits about a center have the same period and form an open subset. The flow has no limit cycles in simply connected regions. The advance mapping is holomorphic where the flow is complete. The structure of the separatrices bounding the orbits surrounding a center is determined. Some examples are given including the following: if a quartic polynomial system has four distinct centers, then they are collinear.

text: Holomorphic Flows on Simply Connected Regions Have No Limit Cycles The dynamical system or flow  = f(z), where f is holomorphic on C, is considered. The behavior of the flow at critical points coincides with the behavior of the linearization when the critical points are non-degenerate: there is no center-focus dichotomy. Periodic orbits about a center have the same period and form an open subset. The flow has no limit cycles in simply connected regions. The advance mapping is holomorphic where the flow is complete. The structure of the separatrices bounding the orbits surrounding a center is determined. Some examples are given including the following: if a quartic polynomial system has four distinct centers, then they are collinear.

year: 2003

title: Anti-irrationalism in Izydora Dąmbska (1904-1983)

authors: Ulatowski, Joseph W.

subjects: Izydora Dąmbska

abstract: A summary of Polish philosopher Izydora Dąmbska's views on logistic anti-irrationalism.

text: Anti-irrationalism in Izydora Dąmbska (1904-1983) A summary of Polish philosopher Izydora Dąmbska's views on logistic anti-irrationalism.

year: 2023

title: Te Mauri o te Kaitiaki - Exploring Te Ao Māori in environmental relations and kaitiakitanga  in Aotearoa New Zealand

authors: Wareka, Mona-Lisa

subjects: Te Ao Māori

abstract: Indigenous environmental empowerment is on the rise as humans look at ways to slow the adverse effects of anthropogenic environmental degradation. In the context of Aotearoa New Zealand, the concept and practice of ‘kaitiaki’ and ‘kaitiakitanga’, respectfully, play a significant role in the co-existence of Māori with the natural world. Previous research shows the innate connections and responsibilities encompassed in being kaitiaki which extend beyond the human element to encompass nonhumans and spiritual manifestations. This research aims to illustrate how Māori use cultural values, concepts and practices in local-level conservational practices through ethnographic research in Matapōuri. I investigate the conflicts and convergences of a rāhui recently placed on two cultural significant areas to the local hapū, and through this, I analyse the practical and spiritual application of kaitiakitanga. Based on this ethnography, I discuss a model for relating environmental degradation with the wellbeing of Māori within Aotearoa New Zealand today. Here, I wish to highlight the ecological and cultural threats present from continuing in the current system. Lastly, I argue that the assertion of kaitiakitanga at the local-level is also an assertion of Indigenous autonomy for Māori and the environment.

text: Te Mauri o te Kaitiaki - Exploring Te Ao Māori in environmental relations and kaitiakitanga  in Aotearoa New Zealand Indigenous environmental empowerment is on the rise as humans look at ways to slow the adverse effects of anthropogenic environmental degradation. In the context of Aotearoa New Zealand, the concept and practice of ‘kaitiaki’ and ‘kaitiakitanga’, respectfully, play a significant role in the co-existence of Māori with the natural world. Previous research shows the innate connections and responsibilities encompassed in being kaitiaki which extend beyond the human element to encompass nonhumans and spiritual manifestations. This research aims to illustrate how Māori use cultural values, concepts and practices in local-level conservational practices through ethnographic research in Matapōuri. I investigate the conflicts and convergences of a rāhui recently placed on two cultural significant areas to the local hapū, and through this, I analyse the practical and spiritual application of kaitiakitanga. Based on this ethnography, I discuss a model for relating environmental degradation with the wellbeing of Māori within Aotearoa New Zealand today. Here, I wish to highlight the ecological and cultural threats present from continuing in the current system. Lastly, I argue that the assertion of kaitiakitanga at the local-level is also an assertion of Indigenous autonomy for Māori and the environment.

year: 2020