Moyal Brackets in M-Theory

The infinite limit of Matrix Theory in 4 and 10 dimensions is described in terms of Moyal Brackets. In those dimensions there exists a Bogomol'nyi bound to the Euclideanized version of these equations, which guarantees that solutions of the first order equations also solve the second order Matrix Theory equations. A general construction of such solutions in terms of a representation of the target space co-ordinates as non-local spinor bilinears, which are generalisations of the standard Wigner functions on phase space, is given.Comment: 10 pages, Latex, no figures. References altered, typos correcte

Representing Carbon Property Rights

The reduction of carbon emissions is considered fundamental in the mitigation of a global rise in temperature and severe climate change events. A market approach has been adopted by several countries to efficiently reduce national carbon emissions and fulfil Kyoto Protocol obligations, and emergent sequestration rights in carbon have gained distinction from the archaic bundle of rights metaphor. In this respect, rights in carbon follow rights in water and biota as emerging property rights that must be independently managed, measured and represented visually. The distinction of carbon from rights in land, biota and water does not preclude the necessity of managing all land system rights as interdependent entities. We suggest that key to managing land and property rights holistically is an adequate representation of the relationships and interdependencies between land elements, the rights, obligations and restrictions, and the multiple stakeholders with an interest. Existing methods, such as Geographic Information Systems (GIS), fail to display systems holistically and comprise only visual elements with limited interactivity that risk compromising understanding and uptake by amateur users. In addressing the above, this paper will first explore areas of contested meaning significant to the unbundling of rights in real property and the management of land at the system level. These areas comprise land and property, representation and visualisation, and property rights themselves. We will then introduce the key requirements and base design of our proposed virtual representation of complex real property rights, specifically designed for a better interpretation of carbon property rights. This research is a work in progress, and is presented as a merging of ideas and concepts to provoke thought and cooperation on a subject that is integral to climate change discussions

Hyper-elliptic Nambu flow associated with integrable maps

We study hyper-elliptic Nambu flows associated with some $n$ dimensional maps and show that discrete integrable systems can be reproduced as flows of this class.Comment: 13 page

Integrable Generalisations of the 2-dimensional Born Infeld Equation

The Born-Infeld equation in two dimensions is generalised to higher dimensions whilst retaining Lorentz Invariance and complete integrability. This generalisation retains homogeneity in second derivatives of the field.Comment: 11 pages, Latex, DTP/93/3

Self-dual Yang-Mills fields in pseudoeuclidean spaces

The self-duality Yang-Mills equations in pseudoeuclidean spaces of dimensions $d\leq 8$ are investigated. New classes of solutions of the equations are found. Extended solutions to the D=10, N=1 supergravity and super Yang-Mills equations are constructed from these solutions.Comment: 9 pages, LaTeX, no figure

Behind the GATE Experiment: Evidence on Effects of and Rationales for Subsidized Entrepreneurship Training

Theories of market failures and targeting motivate the promotion of entrepreneurship training programs and generate testable predictions regarding heterogeneous treatment effects from such programs. Using a large randomized evaluation in the United States, we find no strong or lasting effects on those most likely to face credit or human capital constraints, or labor market discrimination. We do find a short-run effect on business ownership for those unemployed at baseline, but this dissipates at longer horizons. Treatment effects on the full sample are also short-term and limited in scope: we do not find effects on business sales, earnings, or employees. (JEL I26, J24, J68, L25, L26, M13) </jats:p

The Moyal bracket and the dispersionless limit of the KP hierarchy

A new Lax equation is introduced for the KP hierarchy which avoids the use of pseudo-differential operators, as used in the Sato approach. This Lax equation is closer to that used in the study of the dispersionless KP hierarchy, and is obtained by replacing the Poisson bracket with the Moyal bracket. The dispersionless limit, underwhich the Moyal bracket collapses to the Poisson bracket, is particularly simple.Comment: 9 pages, LaTe

Properties of the Scalar Universal Equations

The variational properties of the scalar so--called ``Universal'' equations are reviewed and generalised. In particular, we note that contrary to earlier claims, each member of the Euler hierarchy may have an explicit field dependence. The Euler hierarchy itself is given a new interpretation in terms of the formal complex of variational calculus, and is shown to be related to the algebra of distinguished symmetries of the first source form.Comment: 15 pages, LaTeX articl

On infinite walls in deformation quantization

We examine the deformation quantization of a single particle moving in one dimension (i) in the presence of an infinite potential wall, (ii) confined by an infinite square well, and (iii) bound by a delta function potential energy. In deformation quantization, considered as an autonomous formulation of quantum mechanics, the Wigner function of stationary states must be found by solving the so-called \*-genvalue (``stargenvalue'') equation for the Hamiltonian. For the cases considered here, this pseudo-differential equation is difficult to solve directly, without an ad hoc modification of the potential. Here we treat the infinite wall as the limit of a solvable exponential potential. Before the limit is taken, the corresponding \*-genvalue equation involves the Wigner function at momenta translated by imaginary amounts. We show that it can be converted to a partial differential equation, however, with a well-defined limit. We demonstrate that the Wigner functions calculated from the standard Schr\"odinger wave functions satisfy the resulting new equation. Finally, we show how our results may be adapted to allow for the presence of another, non-singular part in the potential.Comment: 22 pages, to appear in Annals of Physic