1,039,364 research outputs found

    An Exact Interpretation of while

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    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 “hands on ” 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

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    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

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    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. SU(N)SU(N) Yang-Mills theory in 2 dimensions has been given a string-theoretic interpretation in the large-NN limit by Gross, Taylor, Minahan and Polychronakos, but here we provide an exact string-theoretic interpretation of the theory on R×S1\R\times S^1 for finite NN. 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

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    The spatial stability of a class of exact similarity solutions of the Navier–Stokes equations whose longitudinal velocity is of the form xf′(y), where x is the streamwise coordinate and f′(y) is a function of the transverse, cross‐streamwise, 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^λg′(y) are assumed, resulting in an eigenvalue problem for λ which is solved numerically. For the porous wall problem, it is shown that similarity solutions in which f′(y) is a monotonic function of y are spatially stable, while those that are not monotonic are spatially unstable. For the accelerating‐wall 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 problem—monotonic 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

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    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

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    We study constant-roll inflation using the β\beta-function formalism. We show that the constant rate of the inflaton roll is translated into a first order differential equation for the β\beta-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

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    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 p=nkTp=n k T 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

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    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 NN 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 NN 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 NN 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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