Arcs in a finite projective plane

The projective plane of order 11 is the dominant focus of this work. The motivation for working in the projective plane of order 11 is twofold. First, it is the smallest projective plane of prime power order such that the size of the largest (n, r)-arc is not known for all r ∈ {2,...,q + 1}. It is also the smallest projective plane of prime order such that the (n; 3)-arcs are not classified. Second, the number of (n, 3)-arcs is significantly higher in the projective plane of order 11 than it is in the projective plane of order 7, giving a large number of (n, 3)-arcs for study. The main application of (n, r)-arcs is to the study of linear codes. As a forerunner to the work in the projective plane of order eleven two algorithms are used to raise the lower bound on the size of the smallest complete n-arc in the projective plane of order thirty-one from 12 to 13. This work presents the classification up to projective equivalence of the complete (n, 3)- arcs in PG(2, 11) and the backtracking algorithm that is used in its construction. This algorithm is based on the algorithm used in [3]; it is adapted to work on (n, 3)-arcs as opposed to n-arcs. This algorithm yields one representative from every projectively inequivalent class of (n, 3)-arc. The equivalence classes of complete (n, 3)-arcs are then further classified according to their stabilizer group. The classification of all (n, 3)-arcs up to projective equivalence in PG(2, 11) is the foundation of an exhaustive search that takes one element from every equivalence class and determines if it can be extended to an (n′, 4)-arc. This search confirmed that in PG(2, 11) no (n, 3)-arc can be extended to a (33, 4)-arc and that subsequently m4(2, 11) = 32. This same algorithm is used to determine four projectively inequivalent complete (32, 4)-arcs, extended from complete (n, 3)-arcs. Various notions under the general title of symmetry are defined both for an (n, r)-arc and for sets of points and lines. The first of these makes the classification of incomplete (n; 3)- arcs in PG(2, 11) practical. The second establishes a symmetry based around the incidence structure of each of the four projectively inequivalent complete (32, 4)-arcs in PG(2, 11); this allows the discovery of their duals. Both notions of symmetry are used to analyze the incidence structure of n-arcs in PG(2, q), for q = 11, 13, 17, 19. The penultimate chapter demonstrates that it is possible to construct an (n, r)-arc with a stabilizer group that contains a subgroup of order p, where p is a prime, without reference to an (m < n, r)-arc, with stabilizer group isomorphic to ℤ1. This method is used to find q-arcs and (q + 1)-arcs in PG(2, q), for q = 23 and 29, supporting Conjecture 6.7. The work ends with an investigation into the effect of projectivities that are induced by a matrix of prime order p on the projective planes. This investigation looks at the points and subsets of points of order p that are closed under the right action of such matrices and their structure in the projective plane. An application of these structures is a restriction on the size of an (n, r)-arc in PG(2, q) that can be stabilized by a matrix of prime order p

Spinning in the NAPLAN ether: 'Postscript on the control societies' and the seduction of education in Australia

This paper applies concepts Deleuze developed in his ‘Postscript on the Societies of Control’, especially those relating to modulatory power, dividuation and control, to aspects of Australian schooling to explore how this transition is manifesting itself. Two modulatory machines of assessment, NAPLAN and My Schools, are examined as a means to better understand how the disciplinary institution is changing as a result of modulation. This transition from discipline to modulation is visible in the declining importance of the disciplinary teacher/student relationship as a measure of the success of the educative process. The transition occurs through seduction because that which purports to measure classroom quality is in fact a serpent of modulation that produces simulacra of the disciplinary classroom. The effect is to sever what happens in the disciplinary space from its representations in a luminiferous ether that overlays the classroom

Testing a Simplified Version of Einstein's Equations for Numerical Relativity

Solving dynamical problems in general relativity requires the full machinery of numerical relativity. Wilson has proposed a simpler but approximate scheme for systems near equilibrium, like binary neutron stars. We test the scheme on isolated, rapidly rotating, relativistic stars. Since these objects are in equilibrium, it is crucial that the approximation work well if we are to believe its predictions for more complicated systems like binaries. Our results are very encouraging.Comment: 9 pages (RevTeX 3.0 with 6 uuencoded figures), CRSR-107

Network-wide assessment of 4D trajectory adjustments using an agent-based model

This paper presents results from the SESAR ER3 Domino project. It focuses on an ECAC-wide assessment of two 4D-adjustment mechanisms, implemented separately and conjointly. These reflect flight behaviour en-route and at-gate, optimising given (cost) objective functions. New metrics designed to capture network effects are used to analyse the results of a microscopic, agent based model. The results show that some implementations of the mechanisms allow the protection of the network from ‘domino’ effects. Airlines focusing on costs may trigger additional side-effects on passengers, displaying, in some instances, clear trade-offs between passenger- and flight-centric metrics

Duration of Public Assistance Receipt: Is Welfare a Trap?

This paper uses data from the National Longitudinal Survey of Youth to answer two questions about the effects of the Aid to Families with Dependent Children (AFDC) program: (1) Does the length of time that one receives AFDC affect the likelihood of permanently leaving AFDC? (2) What personal and family characteristics are associated with the long-term receipt of AFDC? The answer to the first question is that the likelihood of permanently leaving AFDC decreases with the length of time that individuals receive benefits, after adjustments for other measured and unmeasured attributes of individuals and their families. The answer to the second question is that not having a high school diploma, never having married, having more than two children, and having little work experience are associated with long-term receipt. Many of the recipients who will reach the five-year limit imposed by the new federal legislation are in situations that make it difficult for them to support themselves and their families without public assistance.