title: Symmetries of the Hamilton–Jacobi equation

authors: Boyer, C.P.

subjects: Mathematics

abstract: We present a detailed discussion of the infinit esimal symmetries of the Hamilton-Jacobi equation (an arbitrary first order partial equation) Our presentation clucidates the role played by the characteristic system in determining the symmetries. We then specialize to the case of a free particle in one space and one time dimension, and study of local Lie group of point transformations locally isomorphie to O(3,2). We show that the separation of variables of the corresponding Hamilton-Jacobi equation n the form of a sum is related to orbits in the Schrödinger subalgebra of c(3,2). The remaining orbits of o(3,2) yield symmetry related solutions which separate in more complicated product forms. Finally some connections with the primordial equation of hydrodynamics (without force terms) are made.

text: Symmetries of the Hamilton–Jacobi equation We present a detailed discussion of the infinit esimal symmetries of the Hamilton-Jacobi equation (an arbitrary first order partial equation) Our presentation clucidates the role played by the characteristic system in determining the symmetries. We then specialize to the case of a free particle in one space and one time dimension, and study of local Lie group of point transformations locally isomorphie to O(3,2). We show that the separation of variables of the corresponding Hamilton-Jacobi equation n the form of a sum is related to orbits in the Schrödinger subalgebra of c(3,2). The remaining orbits of o(3,2) yield symmetry related solutions which separate in more complicated product forms. Finally some connections with the primordial equation of hydrodynamics (without force terms) are made.

year: 1977-05

title: Evaluating earthquake hazard and risk using liquefied volcanic-ash layers in lakes

authors: Lowe, David J.

subjects: tephra seismites

abstract: Liquefied volcanic-ash or tephra layers, for which we have coined a new term, ‘tephra seismites’, are preserved in lake sediments in numerous 20,000-year-old lakes in the Hamilton Basin in northern North Island. Up to five tephra layers in cores taken from the lakes show signs of liquefaction - the phenomenon seen during the Christchurch earthquakes - that include disrupted tephra layers, voids, and dykes (injectites). These features show that one or more of four newly-discovered ‘hidden’ faults in Hamilton (see map) were responsible for previously unrecognised prehistoric earthquakes within the past 20,000 years (Kleyberg et al., 2015). Around 30 lakes are scattered amidst the faults, and hence cores are being taken from almost all of these to build up a picture of which fault(s) may have been active in that time. We anticipate that lakes closest to faults that have been active will show more tephra seismites than those farther from the faults.

text: Evaluating earthquake hazard and risk using liquefied volcanic-ash layers in lakes Liquefied volcanic-ash or tephra layers, for which we have coined a new term, ‘tephra seismites’, are preserved in lake sediments in numerous 20,000-year-old lakes in the Hamilton Basin in northern North Island. Up to five tephra layers in cores taken from the lakes show signs of liquefaction - the phenomenon seen during the Christchurch earthquakes - that include disrupted tephra layers, voids, and dykes (injectites). These features show that one or more of four newly-discovered ‘hidden’ faults in Hamilton (see map) were responsible for previously unrecognised prehistoric earthquakes within the past 20,000 years (Kleyberg et al., 2015). Around 30 lakes are scattered amidst the faults, and hence cores are being taken from almost all of these to build up a picture of which fault(s) may have been active in that time. We anticipate that lakes closest to faults that have been active will show more tephra seismites than those farther from the faults.

year: 2021

title: Indigenous Rights Hollow Rights?

authors: Toki, Valmaine

abstract: The Declaration on the Rights of Indigenous Peoples (“the Declaration”) was the initiative of the Working Group on Indigenous Populations (“WGIP”). Established in 1982, the mandate of the WGIP was to develop international standards concerning Indigenous peoples’ rights. The Declaration was a manifestation of this mandate and a clear articulation of international standards on the rights of Indigenous peoples. It was not until 25 years later, in September 2007, that the final text was adopted by the General Assembly with a majority of 143 states in favour. Eleven states offered abstentions. Four states opposed adoption: Australia, Canada, the United States of America (“the United States”) and New Zealand.

text: Indigenous Rights Hollow Rights? The Declaration on the Rights of Indigenous Peoples (“the Declaration”) was the initiative of the Working Group on Indigenous Populations (“WGIP”). Established in 1982, the mandate of the WGIP was to develop international standards concerning Indigenous peoples’ rights. The Declaration was a manifestation of this mandate and a clear articulation of international standards on the rights of Indigenous peoples. It was not until 25 years later, in September 2007, that the final text was adopted by the General Assembly with a majority of 143 states in favour. Eleven states offered abstentions. Four states opposed adoption: Australia, Canada, the United States of America (“the United States”) and New Zealand.

year: 2011