title: Propagating action potentials and the regeneration of acetabularia mediterranea: a pilot study

authors: Lertsithichai, Somak

abstract: A study of the relationship between the cell membrane electrical activity and the observed polar regeneration in anucleate isolated stalk segments of Acetabularia may help answer the question of how a single cell can ‘break symmetry’ and establish a definite polarity. Such studies have been carried out extensively by Novak and Bentrup and their colleagues since 1972, but their results contain unresolved inconsistencies and although their experimental technique overcomes the problems arising from conventional microelectrode techniques, it gives a restricted and electrically perturbative environment for the cell.
In an attempt to overcome these limitations the work in this thesis describes the development of a new technique for measuring the electrical activity of the cell membrane with minimum perturbation from the measuring system. In addition it gives more precise and detailed information about the region of action potential initiation and subsequent propagation. 
The results of measurements using this technique on a variety of intact cells and various cell segments, including anucleate stalk segments are presented and discussed. The results provide strong evidence for the hypothesis that the region of action potential initiation is strongly correlated with the region of current growth. They do not however appear to provide any support for the suggestion of Novak and Bentrup that propagating action potentials are an essential component of the mechanism for ‘symmetry breaking’ in initially unpolarised anucleate stalk segments.

text: Propagating action potentials and the regeneration of acetabularia mediterranea: a pilot study A study of the relationship between the cell membrane electrical activity and the observed polar regeneration in anucleate isolated stalk segments of Acetabularia may help answer the question of how a single cell can ‘break symmetry’ and establish a definite polarity. Such studies have been carried out extensively by Novak and Bentrup and their colleagues since 1972, but their results contain unresolved inconsistencies and although their experimental technique overcomes the problems arising from conventional microelectrode techniques, it gives a restricted and electrically perturbative environment for the cell.
In an attempt to overcome these limitations the work in this thesis describes the development of a new technique for measuring the electrical activity of the cell membrane with minimum perturbation from the measuring system. In addition it gives more precise and detailed information about the region of action potential initiation and subsequent propagation. 
The results of measurements using this technique on a variety of intact cells and various cell segments, including anucleate stalk segments are presented and discussed. The results provide strong evidence for the hypothesis that the region of action potential initiation is strongly correlated with the region of current growth. They do not however appear to provide any support for the suggestion of Novak and Bentrup that propagating action potentials are an essential component of the mechanism for ‘symmetry breaking’ in initially unpolarised anucleate stalk segments.

year: 1980

title: Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras

authors: Escobar Ruiz, Mauricio A.

subjects: Science & Technology

abstract: Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by Bôcher contractions of the conformal Lie algebra ${\mathfrak{so}}(4,\mathbb {C})$ to itself. In this paper we give a precise definition of Bôcher contractions and show how they can be classified. They subsume well known contractions of ${\mathfrak{e}}(2,\mathbb {C})$ and ${\mathfrak{so}}(3,\mathbb {C})$ and have important physical and geometric meanings, such as the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. We also classify abstract nondegenerate quadratic algebras in terms of an invariant that we call a canonical form. We describe an algorithm for finding the canonical form of such algebras. We calculate explicitly all canonical forms arising from quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces. We further discuss contraction of quadratic algebras, focusing on those coming from superintegrable systems.

text: Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by Bôcher contractions of the conformal Lie algebra ${\mathfrak{so}}(4,\mathbb {C})$ to itself. In this paper we give a precise definition of Bôcher contractions and show how they can be classified. They subsume well known contractions of ${\mathfrak{e}}(2,\mathbb {C})$ and ${\mathfrak{so}}(3,\mathbb {C})$ and have important physical and geometric meanings, such as the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. We also classify abstract nondegenerate quadratic algebras in terms of an invariant that we call a canonical form. We describe an algorithm for finding the canonical form of such algebras. We calculate explicitly all canonical forms arising from quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces. We further discuss contraction of quadratic algebras, focusing on those coming from superintegrable systems.

year: 2017

title: The Māori language curriculum for New Zealand schools: Spiral lesson/ lesson sequence design

authors: Johnson, Diane

subjects: Māori language teaching

abstract: A draft curriculum document for the teaching and learning of te reo Māori as a subject in mainstream schools in New Zealand (that is, in schools other than Kura Kaupapa Māori schools) was designed and trialled in 2004 and 2005. That draft is currently being reworked in line with the advice of those who trialled the document as well as that of a team of advisers set up by the Ministry of Education. The revised curriculum document will be submitted to the Ministry of Education in May 2006. As is the case with all new curriculum documents, the implementation phase will be critical. The extent to which this flexible, outcomes-focused curriculum document will genuinely inform new approaches to teaching and learning will depend not only upon the good will of teachers and communities, but also upon their ability to interpret the curriculum and to use it in a way that informs the design of language programmes, including the planning of units of work and of lessons and lesson sequences. In balancing language development and language practice, a communicative core and spiral approach is recommended, an approach in which there are core lessons (where the focus is language development) and spiral lessons (where the focus is language practice). In an earlier issue of this Journal (Johnson, 2003), one of us discussed core lesson design. Here, the design of spiral lessons is discussed and exemplified in the context of an outcomes-based curriculum.

text: The Māori language curriculum for New Zealand schools: Spiral lesson/ lesson sequence design A draft curriculum document for the teaching and learning of te reo Māori as a subject in mainstream schools in New Zealand (that is, in schools other than Kura Kaupapa Māori schools) was designed and trialled in 2004 and 2005. That draft is currently being reworked in line with the advice of those who trialled the document as well as that of a team of advisers set up by the Ministry of Education. The revised curriculum document will be submitted to the Ministry of Education in May 2006. As is the case with all new curriculum documents, the implementation phase will be critical. The extent to which this flexible, outcomes-focused curriculum document will genuinely inform new approaches to teaching and learning will depend not only upon the good will of teachers and communities, but also upon their ability to interpret the curriculum and to use it in a way that informs the design of language programmes, including the planning of units of work and of lessons and lesson sequences. In balancing language development and language practice, a communicative core and spiral approach is recommended, an approach in which there are core lessons (where the focus is language development) and spiral lessons (where the focus is language practice). In an earlier issue of this Journal (Johnson, 2003), one of us discussed core lesson design. Here, the design of spiral lessons is discussed and exemplified in the context of an outcomes-based curriculum.

year: 2005