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A cosmological hydrodynamic code based on the piecewise parabolic method”, Monthly
 Notices of the Royal Astronomical Society, Blackwell Science
, 1998
"... We present a hydrodynamical code for cosmological simulations which uses the Piecewise Parabolic Method (PPM) to follow the dynamics of gas component and an N– body Particle–Mesh algorithm for the evolution of collisionless component. The gravitational ..."
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Cited by 5 (0 self)
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We present a hydrodynamical code for cosmological simulations which uses the Piecewise Parabolic Method (PPM) to follow the dynamics of gas component and an N– body Particle–Mesh algorithm for the evolution of collisionless component. The gravitational
Investigation of Qtubes stability using the piecewise parabolic potential
"... We analyse the classical stability of Qtubes — charged extended objects in (2 + 1)dimensional theory of complex scalar field. Explicit solutions were found analytically in the piecewise parabolic potential. Our choice of potential allows to construct a powerful method of the stability investigatio ..."
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We analyse the classical stability of Qtubes — charged extended objects in (2 + 1)dimensional theory of complex scalar field. Explicit solutions were found analytically in the piecewise parabolic potential. Our choice of potential allows to construct a powerful method of the stability
Submitted to the ApJ THE PIECEWISE PARABOLIC METHOD FOR MULTIDIMENSIONAL RELATIVISTIC FLUID DYNAMICS
, 2005
"... We present an extension of the Piecewise Parabolic Method to special relativistic fluid dynamics in multidimensions. The scheme is conservative, dimensionally unsplit, and suitable for a general equation of state. Temporal evolution is secondorder accurate and employs characteristic projection oper ..."
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We present an extension of the Piecewise Parabolic Method to special relativistic fluid dynamics in multidimensions. The scheme is conservative, dimensionally unsplit, and suitable for a general equation of state. Temporal evolution is secondorder accurate and employs characteristic projection
Mathematical Physics Quantisations of Piecewise Parabolic Maps on the Torus and their Quantum Limits
, 2008
"... Abstract: For general quantum systems the semiclassical behaviour of eigenfunctions in relation to the ergodic properties of the underlying classical system is quite difficult to understand. The Wignerfunctions of eigenstates converge weakly to invariant measures of the classical system, the socall ..."
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Abstract: For general quantum systems the semiclassical behaviour of eigenfunctions in relation to the ergodic properties of the underlying classical system is quite difficult to understand. The Wignerfunctions of eigenstates converge weakly to invariant measures of the classical system, the socalled quantum limits, and one would like to understand which invariant measures can occur that way, thereby classifying the semiclassical behaviour of eigenfunctions. We introduce a class of maps on the torus for whose quantisations we can understand the set of quantum limits in great detail. In particular we can construct examples of ergodic maps which have singular ergodic measures as quantum limits, and examples of nonergodic maps where arbitrary convex combinations of absolutely continuous ergodic measures can occur as quantum limits. The maps we quantise are obtained by cutting and stacking. 1.
Piecewise Parabolic Approximation of Plane Curves with Restrictions in ComputerAided Design of Road Routes
"... Approximation problems of plane curves, which are set as a sequence of points, arise in computeraided design of roads. Approximating curve consists of the elements: straightline and parabolas segments. The parameters of these elements are constrained. Moreover, the number of elements is unknown. ..."
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Approximation problems of plane curves, which are set as a sequence of points, arise in computeraided design of roads. Approximating curve consists of the elements: straightline and parabolas segments. The parameters of these elements are constrained. Moreover, the number of elements is unknown. This article deals with the problem of perelement approximation, in which the elements must meet to the restrictions of special kind. This problem arises in computeraided design of the longitudinal profile of road. The problem is solved by dynamic programming.
New tight frames of curvelets and optimal representations of objects with piecewise C² singularities
 COMM. ON PURE AND APPL. MATH
, 2002
"... This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges. Conceptually, the curvelet transform is a multiscale pyramid with many directions and positions at each length scale, and needleshap ..."
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Cited by 429 (21 self)
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shaped elements at fine scales. These elements have many useful geometric multiscale features that set them apart from classical multiscale representations such as wavelets. For instance, curvelets obey a parabolic scaling relation which says that at scale 2−j, each element has an envelope which is aligned along
The Contourlet Transform: An Efficient Directional Multiresolution Image Representation
 IEEE TRANSACTIONS ON IMAGE PROCESSING
"... The limitations of commonly used separable extensions of onedimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a “true” twodimensional transform that can capture the intrinsic geometrical structure t ..."
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Cited by 519 (20 self)
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link between the developed filter bank and the associated continuousdomain contourlet expansion via a directional multiresolution analysis framework. We show that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth
Adaptive Finite Element Methods For Parabolic Problems. VI. Analytic Semigroups
 SIAM J. Numer. Anal
, 1998
"... . We continue our work on adaptive finite element methods with a study of time discretization of analytic semigroups. We prove optimal a priori and a posteriori error estimates for the discontinuous Galerkin method showing, in particular, that analytic semigroups allow longtime integration without ..."
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Cited by 215 (3 self)
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with piecewise polynomial basis functions that are continuous in space and discontinuous in time. In [1], [2], [3], [4], [5] we proved optimal a priori and a posteriori error estimates for the dGmethod for parabolic problems, typically of the form: find u : [0; 1) ! H such that u(t) + Au(t) = f(t); t ? 0; u(0
Results 1  10
of
13,648