title: Completely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spaces

authors: Boyer, C.P.

subjects: Mathematics

abstract: The Hamilton–Jacobi and Laplace–Beltrami equations on the Hermitian hyperbolic space HH(2) are shown to allow the separation of variables in precisely 12 classes of coordinate systems. The isometry group of this two-complex-dimensional Riemannian space, SU(2,1), has four mutually nonconjugate maximal abelian subgroups. These subgroups are used to construct the separable coordinates explicitly. All of these subgroups are two-dimensional, and this leads to the fact that in each separable coordinate system two of the four variables are ignorable ones. The symmetry reduction of the free HH(2) Hamiltonian by a maximal abelian subgroup of SU(2,1) reduces this Hamiltonian to one defined on an O(2,1) hyperboloid and involving a nontrivial singular potential. Separation of variables on HH(2) and more generally on HH(n) thus provides a new method of generating nontrivial completely integrable relativistic Hamiltonian systems.

text: Completely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spaces The Hamilton–Jacobi and Laplace–Beltrami equations on the Hermitian hyperbolic space HH(2) are shown to allow the separation of variables in precisely 12 classes of coordinate systems. The isometry group of this two-complex-dimensional Riemannian space, SU(2,1), has four mutually nonconjugate maximal abelian subgroups. These subgroups are used to construct the separable coordinates explicitly. All of these subgroups are two-dimensional, and this leads to the fact that in each separable coordinate system two of the four variables are ignorable ones. The symmetry reduction of the free HH(2) Hamiltonian by a maximal abelian subgroup of SU(2,1) reduces this Hamiltonian to one defined on an O(2,1) hyperboloid and involving a nontrivial singular potential. Separation of variables on HH(2) and more generally on HH(n) thus provides a new method of generating nontrivial completely integrable relativistic Hamiltonian systems.

year: 1983-08

title: An algorithm for compositional nonblocking verification of extended finite-state machines

authors: Mohajerani, Sahar

abstract: This paper describes an approach for compositional nonblocking verification of discrete event systems modelled as extended finite-state machines (EFSM). Previous results about finite-state machines in lock-step synchronisation are generalised and applied to EFSMs communicating via shared variables. This gives rise to an EFSM-based conflict check algorithm that composes EFSMs gradually and partially unfolds variables as needed. At each step, components are simplified using conflict-equivalence preserving abstraction. The algorithm has been implemented in the discrete event systems tool Supremica. The paper presents experimental results for the verification of two scalable manufacturing system models, and shows that the EFSM-based algorithm verifies some large models faster than previously used methods.

text: An algorithm for compositional nonblocking verification of extended finite-state machines This paper describes an approach for compositional nonblocking verification of discrete event systems modelled as extended finite-state machines (EFSM). Previous results about finite-state machines in lock-step synchronisation are generalised and applied to EFSMs communicating via shared variables. This gives rise to an EFSM-based conflict check algorithm that composes EFSMs gradually and partially unfolds variables as needed. At each step, components are simplified using conflict-equivalence preserving abstraction. The algorithm has been implemented in the discrete event systems tool Supremica. The paper presents experimental results for the verification of two scalable manufacturing system models, and shows that the EFSM-based algorithm verifies some large models faster than previously used methods.

year: 2014

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