The Dirichlet-to-Neumann map for the elliptic sine Gordon

We analyse the Dirichlet problem for the elliptic sine Gordon equation in the upper half plane. We express the solution $q(x,y)$ in terms of a Riemann-Hilbert problem whose jump matrix is uniquely defined by a certain function $b(\la)$, $\la\in\R$, explicitly expressed in terms of the given Dirichlet data $g_0(x)=q(x,0)$ and the unknown Neumann boundary value $g_1(x)=q_y(x,0)$, where $g_0(x)$ and $g_1(x)$ are related via the global relation $\{b(\la)=0$, $\la\geq 0\}$. Furthermore, we show that the latter relation can be used to characterise the Dirichlet to Neumann map, i.e. to express $g_1(x)$ in terms of $g_0(x)$. It appears that this provides the first case that such a map is explicitly characterised for a nonlinear integrable {\em elliptic} PDE, as opposed to an {\em evolution} PDE.

Boundary value problems for the elliptic sine-Gordon equation in a semi-strip

We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a substantial generalization of the inverse scattering transform and can be used for the analysis of boundary as opposed to initial-value problems. We first express the solution in terms of a 2 by 2 matrix Riemann-Hilbert problem whose \jump matrix" depends on both the Dirichlet and the Neumann boundary values. For a well posed problem one of these boundary values is an unknown function. This unknown function is characterised in terms of the so-called global relation, but in general this characterisation is nonlinear. We then concentrate on the case that the prescribed boundary conditions are zero along the unbounded sides of a semistrip and constant along the bounded side. This corresponds to a case of the so-called linearisable boundary conditions, however a major difficulty for this problem is the existence of non-integrable singularities of the function q_y at the two corners of the semistrip; these singularities are generated by the discontinuities of the boundary condition at these corners. Motivated by the recent solution of the analogous problem for the modified Helmholtz equation, we introduce an appropriate regularisation which overcomes this difficulty. Furthermore, by mapping the basic Riemann-Hilbert problem to an equivalent modified Riemann-Hilbert problem, we show that the solution can be expressed in terms of a 2 by 2 matrix Riemann-Hilbert problem whose jump matrix depends explicitly on the width of the semistrip L, on the constant value d of the solution along the bounded side, and on the residues at the given poles of a certain spectral function denoted by h. The determination of the function h remains open.

The elliptic sine-Gordon equation: a nonlinear elliptic integrable PDE

In this paper, we summarise this recent progress to underline the features specific to this nonlinear elliptic case, and we give a new classification of boundary conditions on the semistrip that satisfy a necessary condition for yielding a boundary value problem can be effectively linearised. This classification is based on formulation the equation in terms of an alternative Lax pair.

Interaction and Persuasion:An analysis of the use of rhetorical devices in Gordon Brown's speech to the Labour Party Conference, on September 25, 2006

This essay has identified and analysed rhetorical devices in Gordon Brown’s speech delivered at the Labour Party conference on September 25, 2006. The aim of the study was to identify specific rhetorical devices which are described as interactional resources, analyse their uses and discuss possible effects that they may have when included in a political speech. The results are based on my own interpretations but are supported by information provided in current literature by analysts and researchers of rhetoric use. The result findings could probably serve as evidence of the need for better understanding of the devices used by politicians in their relentless endeavours to influence audience decisions.

The Role of TAFE as an Equity Pathway to Social Inclusion, Employment, and to University : a submission from The Deakin University Social Work/Gordon TAFE Community Services Work, Geelong Based Project Team

Executive Summary

The Deakin University Social Work/Gordon TAFE Community Services Work Geelong Based Project Team (the Project Team) was assisted by Higher Education Partnership and Participation funding made available through Deakin University Participation and Partnerships Program (DUPPP) to carry out research and project work in 2012/13.

In the following submission to the House of Representatives Inquiry into the role of Technical and Further Education (TAFE) system and its operation, this Project Team seeks to establish a case for:

1. Funding to enable TAFE to continue as:

a) an equity pathway to social inclusion, employment, and to university, particularly in regional areas.
b) an integral complement to the University education sector to deliver on the ambitious objectives of the Federal Government’s widening participation agenda, as a mechanism to deliver the skills, knowledge and workforce needed now, and in the future, in the Australian economy.
2. Increased resources for separate and joint sector development
a) Publicly funded TAFEs need funding to be restored and increased to enable them to maintain the high quality education they provide and to maintain their successful work in supporting communities, regions and disadvantaged individuals to gain skills, training and employment.
b) Universities need increased funding to increase staffing levels and therefore free up teaching staff to spend the necessary time to develop relationships with and provide support to students. This is important for the achieving the goals of the widening participation agenda of increasing access without increasing attrition at the same time.
c) TAFEs and Universities need funding to do the work required to further develop and formalise diploma-degree pathways so that disadvantaged individuals can exit into employment at the diploma level or be supported in an efficient and seamless way to undertake further study.
3. Active use of localised and nuanced partnership approaches by education institutions. This includes:
• Cross teaching by TAFEs and Universities in courses that can be articulated, such as professional practice diplomas and degrees
• Programs negotiated and designed according to the needs of students in each location. TAFEs and Universities need resources in order to do this work
• Focus on regional centres where there is a particular opportunity for government to make an impact on TAFE pathways to employment and/or further education
• Workforce development in regional areas due to new industries is a particular area of need
4. Recognise and capitalise on the complementary and symbiotic nature of each sector’s skills, strengths and capacities.
The submission responds to the second, third and fifth points of the Terms of Reference of the Inquiry and is based on the research work carried out by the Project Team in 2012/13.

We provide evidence of Gordon TAFE in Geelong working as an equity mechanism in the particular case of the welfare/ community services diploma to social work degree pathway. The project team considers that there is a strong case for additional resourcing of TAFE to enable it to continue what it does well. TAFE is the key training and education sectorthe ‘education and social hub’that can successfully attract, retain, and graduate people who may not otherwise access education due to one or more combinations of:

1. having a low SES current or past background;
2. living in regional areas;
3. receiving interrupted primary and secondary education;
4. having disabilities;
5. being sole parents;
6. being from refugee backgrounds;
7. having English as an additional language/culture;
8. retrenchment from employment in dying industries;
9. short, medium and long term unemployment;
10. past and/or current caring roles;
11. marriage/relationship breakdowns;
12. domestic violence;
13. gender, class, age, race/ethnicity and dis/ability discriminations; and
14. socialised expectations and fears.

The recommendations in this submission are based on research findings about important similarities and differences between Gordon TAFE welfare and Deakin University social work students in Geelong, and their respective institutional organisations and contexts. The two institutions employ a repertoire of diverse administrative, teaching, learning and support approaches to meet different mission goals, requirements and needs.

Dorothy Gordon

Perhaps due to her later fame as the newspaper columnist and controversial radio personality known as “Andrea,” the early film career of Dorothy Gordon has been largely overlooked. Certainly her significant celebrity in Australia in the 1 960s overshadowed her comparatively lesser achievements as a silent cinema extra, actor, screenwriter, and art director. The recognition of her contribution to the Australian film industry is further diminished by the loss of her major work as star of Raymond Longford’s Hills of Hate (1926). In addition, her reputation as an entertaining raconteur fond of telling tall stories, especially about herself, leav es much room for doubt about the recorded detail of her early career in both Holly wood and Australian silent films.

Klein-Gordon particles in mixed vector-scalar inversely linear potentials

The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the eigenfunctions which ensure that the effective Hamiltonian is Hermitian for all the points of the space. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist. (c) 2005 Elsevier B.V. All rights reserved.

A NEW HOST RECORD, PALAEMONETES CARTERI (GORDON, 1935) (DECAPODA, PALAEMONIDAE), FOR TELOTHA HENSELII (VON MARTENS, 1869) (ISOPODA, CYMOTHOIDAE)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Equivalence of many-photon Green's functions in the Duffin-Kemmer-Petiau and Klein-Gordon-Fock statistical quantum field theories

Using the functional integral formalism for the statistical generating functional in the statistical (finite temperature) quantum field theory, we prove the equivalence of many-photon Greens functions in the Duffin-Kennner-Petiau and Klein-Gordon-Fock statistical quantum field theories. As an illustration, we calculate the one-loop polarization operators in both theories and demonstrate their coincidence.

Conformal Klein-Gordon equations and quasinormal modes

Using conformal coordinates associated with conformal relativity-associated with de Sitter spacetime homeomorphic projection into Minkowski spacetime-we obtain a conformal Klein-Gordon partial differential equation, which is intimately related to the production of quasi-normal modes (QNMs) oscillations, in the context of electromagnetic and/or gravitational perturbations around, e.g., black holes. While QNMs arise as the solution of a wave-like equation with a Poschl-Teller potential, here we deduce and analytically solve a conformal 'radial' d'Alembert-like equation, from which we derive QNMs formal solutions, in a proposed alternative to more completely describe QNMs. As a by-product we show that this 'radial' equation can be identified with a Schrodinger-like equation in which the potential is exactly the second Poschl-Teller potential, and it can shed some new light on the investigations concerning QNMs.