1,281 research outputs found
Regular Expression Subtyping for XML Query and Update Languages
XML database query languages such as XQuery employ regular expression types
with structural subtyping. Subtyping systems typically have two presentations,
which should be equivalent: a declarative version in which the subsumption rule
may be used anywhere, and an algorithmic version in which the use of
subsumption is limited in order to make typechecking syntax-directed and
decidable. However, the XQuery standard type system circumvents this issue by
using imprecise typing rules for iteration constructs and defining only
algorithmic typechecking, and another extant proposal provides more precise
types for iteration constructs but ignores subtyping. In this paper, we
consider a core XQuery-like language with a subsumption rule and prove the
completeness of algorithmic typechecking; this is straightforward for XQuery
proper but requires some care in the presence of more precise iteration typing
disciplines. We extend this result to an XML update language we have introduced
in earlier work.Comment: ESOP 2008. Companion technical report with proof
Compact Three Dimensional Black Hole: Topology Change and Closed Timelike Curve (minor changes)
We present a compactified version of the 3-dimensional black hole recently
found by considering extra identifications and determine the analytical
continuation of the solution beyond its coordinate singularity by extending the
identifications to the extended region of the spacetime. In the extended region
of the spacetime, we find a topology change and non-trivial closed timelike
curves both in the ordinary 3-dimensional black hole and in the compactified
one. Especially, in the case of the compactified 3-dimensional black hole, we
show an example of topology change from one double torus to eight spheres with
three punctures.Comment: 20 pages revtex.sty 8 figures contained, TIT/HEP-245/COSMO-4
Generating derivative structures: Algorithm and applications
We present an algorithm for generating all derivative superstructures--for
arbitrary parent structures and for any number of atom types. This algorithm
enumerates superlattices and atomic configurations in a geometry-independent
way. The key concept is to use the quotient group associated with each
superlattice to determine all unique atomic configurations. The run time of the
algorithm scales linearly with the number of unique structures found. We show
several applications demonstrating how the algorithm can be used in materials
design problems. We predict an altogether new crystal structure in Cd-Pt and
Pd-Pt, and several new ground states in Pd-rich and Pt-rich binary systems
The Black Hole in Three Dimensional Space Time
The standard Einstein-Maxwell equations in 2+1 spacetime dimensions, with a
negative cosmological constant, admit a black hole solution. The 2+1 black hole
-characterized by mass, angular momentum and charge, defined by flux integrals
at infinity- is quite similar to its 3+1 counterpart. Anti-de Sitter space
appears as a negative energy state separated by a mass gap from the continuous
black hole spectrum. Evaluation of the partition function yields that the
entropy is equal to twice the perimeter length of the horizon.Comment: This version is the one that appeared in PRL (1992), and has
important improvements with respect to the one previously submitted to the
archive. 13 pages, latex, no figure
Unitary Equivalence of the Metric and Holonomy Formulations of 2+1 Dimensional Quantum Gravity on the Torus
Recent work on canonical transformations in quantum mechanics is applied to
transform between the Moncrief metric formulation and the Witten-Carlip
holonomy formulation of 2+1-dimensional quantum gravity on the torus. A
non-polynomial factor ordering of the classical canonical transformation
between the metric and holonomy variables is constructed which preserves their
classical modular transformation properties. An extension of the definition of
a unitary transformation is briefly discussed and is used to find the inner
product in the holonomy variables which makes the canonical transformation
unitary. This defines the Hilbert space in the Witten-Carlip formulation which
is unitarily equivalent to the natural Hilbert space in the Moncrief
formulation. In addition, gravitational theta-states arising from ``large''
diffeomorphisms are found in the theory.Comment: 31 pages LaTeX [Important Revision: a section is added constructing
the inner product/Hilbert space for the Witten-Carlip holonomy formulation;
the proof of unitary equivalence of the metric and holonomy formulations is
then completed. Other additions include discussion of relation of canonical
and unitary transformations. Title/abstract change.
Complex joint probabilities as expressions of determinism in quantum mechanics
The density operator of a quantum state can be represented as a complex joint
probability of any two observables whose eigenstates have non-zero mutual
overlap. Transformations to a new basis set are then expressed in terms of
complex conditional probabilities that describe the fundamental relation
between precise statements about the three different observables. Since such
transformations merely change the representation of the quantum state, these
conditional probabilities provide a state-independent definition of the
deterministic relation between the outcomes of different quantum measurements.
In this paper, it is shown how classical reality emerges as an approximation to
the fundamental laws of quantum determinism expressed by complex conditional
probabilities. The quantum mechanical origin of phase spaces and trajectories
is identified and implications for the interpretation of quantum measurements
are considered. It is argued that the transformation laws of quantum
determinism provide a fundamental description of the measurement dependence of
empirical reality.Comment: 12 pages, including 1 figure, updated introduction includes
references to the historical background of complex joint probabilities and to
related work by Lars M. Johanse
Hamiltonian structure and quantization of 2+1 dimensional gravity coupled to particles
It is shown that the reduced particle dynamics of 2+1 dimensional gravity in
the maximally slicing gauge has hamiltonian form. This is proved directly for
the two body problem and for the three body problem by using the Garnier
equations for isomonodromic transformations. For a number of particles greater
than three the existence of the hamiltonian is shown to be a consequence of a
conjecture by Polyakov which connects the auxiliary parameters of the fuchsian
differential equation which solves the SU(1,1) Riemann-Hilbert problem, to the
Liouville action of the conformal factor which describes the space-metric. We
give the exact diffeomorphism which transforms the expression of the spinning
cone geometry in the Deser, Jackiw, 't Hooft gauge to the maximally slicing
gauge. It is explicitly shown that the boundary term in the action, written in
hamiltonian form gives the hamiltonian for the reduced particle dynamics. The
quantum mechanical translation of the two particle hamiltonian gives rise to
the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit
is given by the total energy of the system irrespective of the masses of the
particles thus proving at the quantum level a conjecture by 't Hooft on the two
particle dynamics. The quantum mechanical Green's function for the two body
problem is given.Comment: 34 pages LaTe
The Torus Universe in the Polygon Approach to 2+1-Dimensional Gravity
In this paper we describe the matter-free toroidal spacetime in 't Hooft's
polygon approach to 2+1-dimensional gravity (i.e. we consider the case without
any particles present). Contrary to earlier results in the literature we find
that it is not possible to describe the torus by just one polygon but we need
at least two polygons. We also show that the constraint algebra of the polygons
closes.Comment: 18 pages Latex, 13 eps-figure
Friction in inflaton equations of motion
The possibility of a friction term in the equation of motion for a scalar
field is investigated in non-equilibrium field theory. The results obtained
differ greatly from existing estimates based on linear response theory, and
suggest that dissipation is not well represented by a term of the form
.Comment: 4 pages, 2 figures, RevTex4. An obscurity in the original version has
been clarifie
Large Diffeomorphisms in (2+1)-Quantum Gravity on the Torus
The issue of how to deal with the modular transformations -- large
diffeomorphisms -- in (2+1)-quantum gravity on the torus is discussed. I study
the Chern-Simons/connection representation and show that the behavior of the
modular transformations on the reduced configuration space is so bad that it is
possible to rule out all finite dimensional unitary representations of the
modular group on the Hilbert space of -functions on the reduced
configuration space. Furthermore, by assuming piecewise continuity for a dense
subset of the vectors in any Hilbert space based on the space of complex valued
functions on the reduced configuration space, it is shown that finite
dimensional representations are excluded no matter what inner-product we define
in this vector space. A brief discussion of the loop- and ADM-representations
is also included.Comment: The proof for the nonexistence of the one- and two-dimensional
representations of PSL(2,Z) in the relevant Hilbert space, has been extended
to cover all finite dimensional unitary representations. The notation is
slightly improved and a few references are added
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