title: Infinite order symmetries for two-dimensional separable Schrödinger equations

authors: Kalnins, Ernie G.

subjects: mathematics

abstract: Consider a non-relativistic Hamiltonian operator H in 2 dimensions consisting of a kinetic energy term plus a potential. We show that if the associated Schrödinger eigenvalue equation admits an orthogonal separation of variables, there is a calculus to describe the (in general) infinite-order differential operator symmetries of the Schrödinger equation. The calculus is formal but can be made rigorous when all functions in the eigenvaue equation are analytic. The infinite-order calculus exhibits structure that is not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. We go further and extend the calculus to the situation where the Schrödinger equation admits a second-order symmetry operator, not necessarily associated with orthogonal separable coordinates.

text: Infinite order symmetries for two-dimensional separable Schrödinger equations Consider a non-relativistic Hamiltonian operator H in 2 dimensions consisting of a kinetic energy term plus a potential. We show that if the associated Schrödinger eigenvalue equation admits an orthogonal separation of variables, there is a calculus to describe the (in general) infinite-order differential operator symmetries of the Schrödinger equation. The calculus is formal but can be made rigorous when all functions in the eigenvaue equation are analytic. The infinite-order calculus exhibits structure that is not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. We go further and extend the calculus to the situation where the Schrödinger equation admits a second-order symmetry operator, not necessarily associated with orthogonal separable coordinates.

year: 2004

title: The construction of Karen Karnak: The multi-author function

authors: Snake-Beings, Emit

abstract: The context of this article is the changes in authorship that have occurred within the comparatively recent developments of Web 2.0 and the emergence of interactive WikiMedia. The mode of authorship within a Read/Write culture, compared with that of a Read/Only tradition, is that the role of the audience has become merged with the author, and as such represents new functions and attributes. Modes of multi-authorship, demonstrated in the use of the pseudonyms Karen Karnak and Karen Eliot, represent declarative authors whose names signify multiple origins, while concurrently indicating a distinct body of work. The function of these names forms an important tool of deconstruction involving an experimental mode of multi-authorship utilising WikiMedia technology in the creation of a collective multi-author pseudonym, Karen Karnak. The article ends with a discussion of the implications of multi-authorship on the concept of the body of work, ownership and copyright.

text: The construction of Karen Karnak: The multi-author function The context of this article is the changes in authorship that have occurred within the comparatively recent developments of Web 2.0 and the emergence of interactive WikiMedia. The mode of authorship within a Read/Write culture, compared with that of a Read/Only tradition, is that the role of the audience has become merged with the author, and as such represents new functions and attributes. Modes of multi-authorship, demonstrated in the use of the pseudonyms Karen Karnak and Karen Eliot, represent declarative authors whose names signify multiple origins, while concurrently indicating a distinct body of work. The function of these names forms an important tool of deconstruction involving an experimental mode of multi-authorship utilising WikiMedia technology in the creation of a collective multi-author pseudonym, Karen Karnak. The article ends with a discussion of the implications of multi-authorship on the concept of the body of work, ownership and copyright.

year: 2013

title: 'Waitangi and indigenous rights: Revolution, law and legitimacy' by F.M. Brookfield

authors: Melbourne, Hirini

subjects: indigenous rights

abstract: 'Waitangi and Indigenous Rights: Revolution, Law and Legitimacy' book review by Hirini Melbourne.

text: 'Waitangi and indigenous rights: Revolution, law and legitimacy' by F.M. Brookfield 'Waitangi and Indigenous Rights: Revolution, Law and Legitimacy' book review by Hirini Melbourne.

year: 2000-10