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Towards a Theory of Landscapes
, 1995
"... this paper), spanned by eigenvectors f` y g of the graph Laplacian, the familiar properties of Fourier series, such as Parseval's equation kfk ..."
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Cited by 65 (6 self)
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this paper), spanned by eigenvectors f` y g of the graph Laplacian, the familiar properties of Fourier series, such as Parseval's equation kfk
Physicochemical Properties of Molten KFK2NbF7Nb2O5 System
"... Molten KFK2NbF7Nb2O5 system has been determined from the point of phase equilibrium, density, viscosity and surface tension. In spite of narrow investigated concentration region, system has been studied only up to 20 mol % of the Nb2O5; in the system oxofluoroniobate compounds are formed. These ha ..."
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Molten KFK2NbF7Nb2O5 system has been determined from the point of phase equilibrium, density, viscosity and surface tension. In spite of narrow investigated concentration region, system has been studied only up to 20 mol % of the Nb2O5; in the system oxofluoroniobate compounds are formed
On global existence and scattering for the wave maps equation
 Amer. J. Math
"... Abstract. We prove global existence and scattering for the wavemaps equation in n + 1 dimensions, n = 2, 3, for initial data which is small in the scaleinvariant homogeneous Besov space ˙B 2,1 n=2 ˙B 2,1 n=21. This result was proved in an earlier paper by the author for n 4. ..."
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Cited by 71 (8 self)
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Abstract. We prove global existence and scattering for the wavemaps equation in n + 1 dimensions, n = 2, 3, for initial data which is small in the scaleinvariant homogeneous Besov space ˙B 2,1 n=2 ˙B 2,1 n=21. This result was proved in an earlier paper by the author for n 4.
Hypoelliptic Regularity in Kinetic Equations
, 2003
"... We establish new regularity estimates, in terms of Sobolev spaces, of the solution f to a kinetic equation. The righthand side can contain partial derivatives in time, space and velocity, as in classical averaging, and f is assumed to have a certain amount of regularity in velocity. The result ..."
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Cited by 43 (2 self)
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We establish new regularity estimates, in terms of Sobolev spaces, of the solution f to a kinetic equation. The righthand side can contain partial derivatives in time, space and velocity, as in classical averaging, and f is assumed to have a certain amount of regularity in velocity. The result
Rough solutions for the wave maps equation
 Amer. J. Math
"... Abstract. We consider the wave maps equation with values into a Riemannian manifold which is isometrically embedded in Rm. Our main result asserts that the Cauchy problem is globally wellposed for initial data which is small in the critical Sobolev spaces. This extends and completes recent work of ..."
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Cited by 38 (7 self)
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Abstract. We consider the wave maps equation with values into a Riemannian manifold which is isometrically embedded in Rm. Our main result asserts that the Cauchy problem is globally wellposed for initial data which is small in the critical Sobolev spaces. This extends and completes recent work
HYPERBOLIC EQUATIONS
"... Let us recall well{known results about linear and semilinear wave equations. We examine the Cauchy problems 2u = f(u) = NX ..."
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Let us recall well{known results about linear and semilinear wave equations. We examine the Cauchy problems 2u = f(u) = NX
Boundaryvalue problem for the Kortewegde VriesBurgers type equation
 NoDEA Nonlinear Differential Equations Appl
"... We consider the initial{boundaryvalue problem on the halfline for the Korteweg{ de Vries equation ut + uux + uxxx = 0; t> 0; x> 0; u(x; 0) = u0(x); x> 0; u(0; t) = 0; t> 0: 9>=>; We prove that if the initial data u0 2H0;21 \H0;3=22 and the norm ku0kH 0;21 + ku0kH 0;3=22 are su± ..."
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Cited by 5 (2 self)
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We consider the initial{boundaryvalue problem on the halfline for the Korteweg{ de Vries equation ut + uux + uxxx = 0; t> 0; x> 0; u(x; 0) = u0(x); x> 0; u(0; t) = 0; t> 0: 9>=>; We prove that if the initial data u0 2H0;21 \H0;3=22 and the norm ku0kH 0;21 + ku0kH 0;3=22 are su
On regular holonomic systems with solutions ramified along y k = x n
 PACIFIC J. MATH
, 2002
"... We classify the holonomic systems of (micro) differential equations of multiplicity one along the conormal of the hypersurface y k = x n. We show that their solutions are related to kFk−1 hypergeometric functions on the Riemann sphere. ..."
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Cited by 3 (2 self)
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We classify the holonomic systems of (micro) differential equations of multiplicity one along the conormal of the hypersurface y k = x n. We show that their solutions are related to kFk−1 hypergeometric functions on the Riemann sphere.
Time decay for the bounded mean oscillation of solutions of the Schrödinger and wave equations
"... : Let u(x; t) be the solution of the Schrodinger or wave equation with L 2 initial data. We provide counterexamples to plausible conjectures involving the decay in t of the BMO norm of u(t; \Delta). The proofs make use of random methods, in particular, Brownian motion. 1. Introduction Consider the ..."
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Cited by 20 (0 self)
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: Let u(x; t) be the solution of the Schrodinger or wave equation with L 2 initial data. We provide counterexamples to plausible conjectures involving the decay in t of the BMO norm of u(t; \Delta). The proofs make use of random methods, in particular, Brownian motion. 1. Introduction Consider
On Determining The Fundamental Matrix: Analysis Of Different Methods and . . .
, 1993
"... The Fundamental matrix is a key concept when working with uncalibrated images and multiple viewpoints. It contains all the available geometric information and enables to recover the epipolar geometry from uncalibrated perspective views. This paper addresses the important problem of its robust determ ..."
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Cited by 96 (15 self)
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The Fundamental matrix is a key concept when working with uncalibrated images and multiple viewpoints. It contains all the available geometric information and enables to recover the epipolar geometry from uncalibrated perspective views. This paper addresses the important problem of its robust determination given a number of image point correspondences. We first define precisely this matrix, and show clearly how it is related to the epipolar geometry and to the Essential matrix introduced earlier by LonguetHiggins. In particular, we show that this matrix, defined up to a scale factor, must be of rank two. Different parametrizations for this matrix are then proposed to take into account these important constraints and linear and nonlinear criteria for its estimation are also considered. We then clearly show that the linear criterion is unable to express the rank and normalization constraints. Using the linear criterion leads definitely to the worst result in the determination of the Fu...
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