1,039,364 research outputs found
An Exact Interpretation of while
The behaviour and interaction of finite limits (products, pullbacks and equalisers) and colimits (coproducts and coequalisers) in the category of sets is illustrated in a âhands on â way by giving the interpretation of a simple imperative language in terms of partial functions between sets of states. We show that the interpretation is a least fixed point and satisfies the usual proof rule for loop invariants
Balancedness Conditions for Exact Games
We provide two new characterizations of exact games. First, a game is exact if and only if it is exactly balanced; and second, a game is exact if and only if it is totally balanced and overbalanced. The condition of exact balancedness is identical to the one of balancedness, except that one of the balancing weights may be negative while for overbalancedness one of the balancing weights is required to be non-positive and no weight is put on the grand coalition. Exact balancedness and overbalancedness are both easy to formulate conditions with a natural game-theoretic interpretation and are shown to be useful in applications. Using exact balancedness we show that exact games are convex for the grand coalition and that the classes of convex and totally exact games coincide. We provide an example of a game that is totally balanced and convex for the grand coalition, but not exact. Finally we relate classes of balanced, totally balanced, convex for the grand coalition, exact, totally exact, and convex games to one another.operations research and management science;
Strings, Loops, Knots and Gauge Fields
The loop representation of quantum gravity has many formal resemblances to a
background-free string theory. In fact, its origins lie in attempts to treat
the string theory of hadrons as an approximation to QCD, in which the strings
represent flux tubes of the gauge field. A heuristic path-integral approach
indicates a duality between background-free string theories and generally
covariant gauge theories, with the loop transform relating the two. We review
progress towards making this duality rigorous in three examples: 2d Yang-Mills
theory (which, while not generally covariant, has symmetry under all
area-preserving transformations), 3d quantum gravity, and 4d quantum gravity.
Yang-Mills theory in 2 dimensions has been given a string-theoretic
interpretation in the large- limit by Gross, Taylor, Minahan and
Polychronakos, but here we provide an exact string-theoretic interpretation of
the theory on for finite . The string-theoretic
interpretation of quantum gravity in 3 dimensions gives rise to conjectures
about integrals on the moduli space of flat connections, while in 4 dimensions
there may be connections to the theory of 2-tangles.Comment: 34 pages, LaTe
The spatial stability of a class of similarity solutions
The spatial stability of a class of exact similarity solutions of the NavierâStokes equations whose longitudinal velocity is of the form xfâ˛(y), where x is the streamwise coordinate and fâ˛(y) is a function of the transverse, crossâstreamwise, coordinate y only, is determined. These similarity solutions correspond to the flow in an infinitely long channel or tube whose surface is either uniformly porous or moves with a velocity linear in x. Small perturbations to the streamwise velocity of the form x^Îťgâ˛(y) are assumed, resulting in an eigenvalue problem for Îť which is solved numerically. For the porous wall problem, it is shown that similarity solutions in which fâ˛(y) is a monotonic function of y are spatially stable, while those that are not monotonic are spatially unstable. For the acceleratingâwall problem, the interpretation of the stability results is not unambiguous and two interpretations are offered. In one interpretation the conclusions are the same as for the porous problemâmonotonic solutions are stable; the second interpretation is more restrictive in that some of the monotonic as well as the nonmonotonic solutions are unstable
Quasiparticle Scattering Interference in High Temperature Superconductors
We propose that the energy-dependent spatial modulation of the local density
of states seen by Hoffman, et al [hoff2] is due to the scattering interference
of quasiparticles. In this paper we present the general theoretical basis for
such an interpretation and lay out the underlying assumptions. As an example,
we perform exact T-matrix calculation for the scattering due to a single
impurity. The results of this calculation is used to check the assumptions, and
demonstrate that quasiparticle scattering interference can indeed produce
patterns similar to those observed in Ref. [hoff2].Comment: RevTex4 twocolumn, 4 pages, 3 figures. Figs.2-3 virtually embedded
(bacause of too big size) while jpg files available in the postscript/source
package. Further polishe
New perspectives on constant-roll inflation
We study constant-roll inflation using the -function formalism. We
show that the constant rate of the inflaton roll is translated into a first
order differential equation for the -function which can be solved
easily. The solutions to this equation correspond to the usual constant-roll
models. We then construct, by perturbing these exact solutions, more general
classes of models that satisfy the constant-roll equation asymptotically. In
the case of an asymptotic power law solution, these corrections naturally
provide an end to the inflationary phase. Interestingly, while from a
theoretical point of view (in particular in terms of the holographic
interpretation) these models are intrinsically different from standard
slow-roll inflation, they may have phenomenological predictions in good
agreement with present cosmological data.Comment: 26 pages, 4 figure
Towards a physical interpretation for the Stephani Universes
A physicaly reasonable interpretation is provided for the perfect fluid,
sphericaly symmetric, conformally flat ``Stephani Universes''. The free
parameters of this class of exact solutions are determined so that the ideal
gas relation is identicaly fulfiled, while the full equation of state
of a classical monatomic ideal gas and a matter-radiation mixture holds up to a
good approximation in a near dust, matter dominated regime. Only the models
having spacelike slices with positive curvature admit a regular evolution
domain that avoids an unphysical singularity. In the matter dominated regime
these models are dynamicaly and observationaly indistinguishable from
``standard'' FLRW cosmology with a dust source.Comment: 17 pages, 2 figures, LaTeX with revtex style, submitted to General
Relativity and Gravitatio
Unveiling the significance of eigenvectors in diffusing non-hermitian matrices by identifying the underlying Burgers dynamics
Following our recent letter, we study in detail an entry-wise diffusion of
non-hermitian complex matrices. We obtain an exact partial differential
equation (valid for any matrix size and arbitrary initial conditions) for
evolution of the averaged extended characteristic polynomial. The logarithm of
this polynomial has an interpretation of a potential which generates a Burgers
dynamics in quaternionic space. The dynamics of the ensemble in the large
is completely determined by the coevolution of the spectral density and a
certain eigenvector correlation function. This coevolution is best visible in
an electrostatic potential of a quaternionic argument built of two complex
variables, the first of which governs standard spectral properties while the
second unravels the hidden dynamics of eigenvector correlation function. We
obtain general large formulas for both spectral density and 1-point
eigenvector correlation function valid for any initial conditions. We exemplify
our studies by solving three examples, and we verify the analytic form of our
solutions with numerical simulations.Comment: 24 pages, 11 figure
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