title: The general legal principles of doing business in China

authors: Liao, Zhixiong (Leo)

subjects: law

abstract: By virtue of the New Zealand-China Free Trade Agreement, more and more New Zealand legal practitioners will have to consider some basic legal issues concerning business law in China when called upon to advise a corporate client with business connections to China. It is risky to assume that the related Chinese law is “basically similar” to its New Zealand “counterparts”.

text: The general legal principles of doing business in China By virtue of the New Zealand-China Free Trade Agreement, more and more New Zealand legal practitioners will have to consider some basic legal issues concerning business law in China when called upon to advise a corporate client with business connections to China. It is risky to assume that the related Chinese law is “basically similar” to its New Zealand “counterparts”.

year: 2012

title: Variable separation for Heat and Schrödinger equations

authors: Reid, Gregory John

abstract: All R-separable coordinate systems are classified for the equation
Δₘ Ψ + 2ε ∂/∂t Ψ = EΨ (*)
where Δₘ = ᵐΣ ᵤ₌₁ ∂²/(∂yᵘ)² and the variables t and yᵘ are real. An R-separable coordinate system for (*) is a coordinate system yᵘ = yᵘ (xᵏ), t = t (xᵏ) such that (*) admits a solution of form Ψ = eᴿ⁽ˣⁱ⁾ ᵐ⁺¹Πᵢ₌₁ Ψᵢ(xⁱ;c₁, ···, cₘ₊₁). For ε = ⁱ/₂ and ε = - ¹/₂, E = 0, (*) yields standardised versions of the Schrӧdinger and Heat equations respectively. Recognition of (*) as a symmetry-reduced version of the Helmholtz equation on m + 2 dimensional Minkowski space, for which there is a well developed theory of separation, is central to the solution of the classification problem. The solution is built from the case ε = 0 which has been solved by Kalnins and Miller in an article submitted to the Transactions of the American Mathematical Society.
We find the operators and separation equations for (*) and give a detailed treatment of the physically interesting case m =3. The operators are always in the enveloping algebra of the Schrӧdinger algebra. This means that much of the special function theory relating to the separated solutions can be reduced to problems in the representation theory of this algebra.
Various complex extensions of (*) are treated. In particular a class of systems is uncovered leading to nontrivial R-separation for the Hamilton-Jacobi equation corresponding to (*). A formula is derived for expressing the second order Killing tensors describing separation in flat spaces in terms of the enveloping algebra. This formula forms the basis of a program written in the symbolic language MACSYMA capable of producing all the time consuming details of separation.

text: Variable separation for Heat and Schrödinger equations All R-separable coordinate systems are classified for the equation
Δₘ Ψ + 2ε ∂/∂t Ψ = EΨ (*)
where Δₘ = ᵐΣ ᵤ₌₁ ∂²/(∂yᵘ)² and the variables t and yᵘ are real. An R-separable coordinate system for (*) is a coordinate system yᵘ = yᵘ (xᵏ), t = t (xᵏ) such that (*) admits a solution of form Ψ = eᴿ⁽ˣⁱ⁾ ᵐ⁺¹Πᵢ₌₁ Ψᵢ(xⁱ;c₁, ···, cₘ₊₁). For ε = ⁱ/₂ and ε = - ¹/₂, E = 0, (*) yields standardised versions of the Schrӧdinger and Heat equations respectively. Recognition of (*) as a symmetry-reduced version of the Helmholtz equation on m + 2 dimensional Minkowski space, for which there is a well developed theory of separation, is central to the solution of the classification problem. The solution is built from the case ε = 0 which has been solved by Kalnins and Miller in an article submitted to the Transactions of the American Mathematical Society.
We find the operators and separation equations for (*) and give a detailed treatment of the physically interesting case m =3. The operators are always in the enveloping algebra of the Schrӧdinger algebra. This means that much of the special function theory relating to the separated solutions can be reduced to problems in the representation theory of this algebra.
Various complex extensions of (*) are treated. In particular a class of systems is uncovered leading to nontrivial R-separation for the Hamilton-Jacobi equation corresponding to (*). A formula is derived for expressing the second order Killing tensors describing separation in flat spaces in terms of the enveloping algebra. This formula forms the basis of a program written in the symbolic language MACSYMA capable of producing all the time consuming details of separation.

year: 1984

title: Restoring Indigneous Law and Justice Traditions

authors: Cook, Michelle Lynn

subjects: Indigenous peoples

abstract: Restoring indigenous people's law and their ability to practice their justice traditions is a fundamental aspect of non-discrimination, decolonization, self-governance, self-determination, and social justice. The critical application and interpretation of indigenous people's law has revolutionary potentiality to transform, confront, and heal multiple forms of oppression such as environmental destruction, patriarchy, and the prison/criminal justice system. The sovereign jurisgenerative (law making) power of indigenous peoples is a site of profound hope for the revitalization of indigenous law and justice traditions restores legal principles and values of sacredness, harmony, balance, and interconnectivity within human relationships and with the natural world. Revitalizing indigenous law is a way to re-construct the self and society while also finding and re-connecting to new/old ways of being human. This thesis focuses on both Navajo and Māori practices and visions of law and justice; the challenges and, successes they have faced and the hopes they have of living by their law. Indigenous peoples, their ways of being, their wisdom, laws, and philosophies, must be respected, protected, and preserved not only because they contribute to humanity's richness and cultural diversity but also because they are living examples of  a more just, dignified, and ecologically sustainable society, which can serve all humanity.

text: Restoring Indigneous Law and Justice Traditions Restoring indigenous people's law and their ability to practice their justice traditions is a fundamental aspect of non-discrimination, decolonization, self-governance, self-determination, and social justice. The critical application and interpretation of indigenous people's law has revolutionary potentiality to transform, confront, and heal multiple forms of oppression such as environmental destruction, patriarchy, and the prison/criminal justice system. The sovereign jurisgenerative (law making) power of indigenous peoples is a site of profound hope for the revitalization of indigenous law and justice traditions restores legal principles and values of sacredness, harmony, balance, and interconnectivity within human relationships and with the natural world. Revitalizing indigenous law is a way to re-construct the self and society while also finding and re-connecting to new/old ways of being human. This thesis focuses on both Navajo and Māori practices and visions of law and justice; the challenges and, successes they have faced and the hopes they have of living by their law. Indigenous peoples, their ways of being, their wisdom, laws, and philosophies, must be respected, protected, and preserved not only because they contribute to humanity's richness and cultural diversity but also because they are living examples of  a more just, dignified, and ecologically sustainable society, which can serve all humanity.

year: 2010