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A policy response to the e-commerce revolution: the case of betting taxation in the UK
Several environmental changes in the 1990s – including the introduction of a national lottery, the rise of Internet gambling, and the reduction of trade barriers within the EU – induced the UK government to initiate a large-scale review of betting duty. As a result of this review, the government recently announced a significant reduction in betting taxes. They also decided to replace the current general betting duty (GBD), levied as a proportion of betting stakes, with a gross profits tax (GPT), based on the net revenue of bookmakers. We examine the economic rationale behind these decisions and demonstrate how these tax changes have broad implications regarding optimal levels of taxation for other sources of government revenue
Subcritical Superstrings
We introduce the Liouville mode into the Green-Schwarz superstring. Like
massive supersymmetry without central charges, there is no kappa symmetry.
However, the second-class constraints (and corresponding Wess-Zumino term)
remain, and can be solved by (twisted) chiral superspace in dimensions D=4 and
6. The matter conformal anomaly is c = 4-D < 1. It thus can be canceled for
physical dimensions by the usual Liouville methods, unlike the bosonic string
(for which the consistency condition is c = D <= 1).Comment: 9 pg., compressed postscript file (.ps.Z), other formats (.dvi, .ps,
.ps.Z, 8-bit .tex) available at
http://insti.physics.sunysb.edu/~siegel/preprints/ or at
ftp://max.physics.sunysb.edu/preprints/siege
Lie Superalgebra Stability and Branes
The algebra of the generators of translations in superspace is unstable, in
the sense that infinitesimal perturbations of its structure constants lead to
non-isomorphic algebras. We show how superspace extensions remedy this
situation (after arguing that remedy is indeed needed) and review the benefits
reaped in the description of branes of all kinds in the presence of the extra
dimensions.Comment: Talk given at the conference ``Brane New World and Non-commutative
Geometry'', held in Torino, October 2000. To appear in the proceedings by
World Scientific. 10 pages, 1 figur
A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem
A computational procedure that allows the detection of a new type of
high-dimensional chaotic saddle in Hamiltonian systems with three degrees of
freedom is presented. The chaotic saddle is associated with a so-called
normally hyperbolic invariant manifold (NHIM). The procedure allows to compute
appropriate homoclinic orbits to the NHIM from which we can infer the existence
a chaotic saddle. NHIMs control the phase space transport across an equilibrium
point of saddle-centre-...-centre stability type, which is a fundamental
mechanism for chemical reactions, capture and escape, scattering, and, more
generally, ``transformation'' in many different areas of physics. Consequently,
the presented methods and results are of broad interest. The procedure is
illustrated for the spatial Hill's problem which is a well known model in
celestial mechanics and which gained much interest e.g. in the study of the
formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys
Abelian link invariants and homology
We consider the link invariants defined by the quantum Chern-Simons field
theory with compact gauge group U(1) in a closed oriented 3-manifold M. The
relation of the abelian link invariants with the homology group of the
complement of the links is discussed. We prove that, when M is a homology
sphere or when a link -in a generic manifold M- is homologically trivial, the
associated observables coincide with the observables of the sphere S^3. Finally
we show that the U(1) Reshetikhin-Turaev surgery invariant of the manifold M is
not a function of the homology group only, nor a function of the homotopy type
of M alone.Comment: 18 pages, 3 figures; to be published in Journal of Mathematical
Physic
Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium
The paper deals with the problem of existence of a convergent "strong" normal
form in the neighbourhood of an equilibrium, for a finite dimensional system of
differential equations with analytic and time-dependent non-linear term. The
problem can be solved either under some non-resonance hypotheses on the
spectrum of the linear part or if the non-linear term is assumed to be (slowly)
decaying in time. This paper "completes" a pioneering work of Pustil'nikov in
which, despite under weaker non-resonance hypotheses, the nonlinearity is
required to be asymptotically autonomous. The result is obtained as a
consequence of the existence of a strong normal form for a suitable class of
real-analytic Hamiltonians with non-autonomous perturbations.Comment: 10 page
Acceleration of bouncing balls in external fields
We introduce two models, the Fermi-Ulam model in an external field and a one
dimensional system of bouncing balls in an external field above a periodically
oscillating plate. For both models we investigate the possibility of unbounded
motion. In a special case the two models are equivalent
Non-ideal artificial phase discontinuity in long Josephson 0-kappa-junctions
We investigate the creation of an arbitrary -discontinuity of the
Josephson phase in a long Nb-AlO_x-Nb Josephson junction (LJJ) using a pair of
tiny current injectors, and study the formation of fractional vortices formed
at this discontinuity. The current I_inj, flowing from one injector to the
other, creates a phase discontinuity kappa ~ I_inj. The calibration of
injectors is discussed in detail. The small but finite size of injectors leads
to some deviations of the properties of such a 0-kappa-LJJ from the properties
of a LJJ with an ideal kappa-discontinuity. These experimentally observed
deviations in the dependence of the critical current on I_inj$ and magnetic
field can be well reproduced by numerical simulation assuming a finite injector
size. The physical origin of these deviations is discussed.Comment: Submitted to Phys. Rev. B (12 figures). v 2: refs updated, long eqs
fixed v 3: major changes, fractional vortex dynamics exclude
Green-Schwarz Formulation of Self-Dual Superstring
The self-dual superstring has been described previously in a
Neveu-Schwarz-Ramond formulation with local N=2 or 4 world-sheet supersymmetry.
We present a Green-Schwarz-type formulation, with manifest spacetime
supersymmetry.Comment: 11 pg., (uuencoded dvi file) ITP-SB-92-5
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