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116,309
Motion of hypersurfaces by Gauss curvature
 Pacific J. Math. 195
, 2000
"... We consider ndimensional convex Euclidean hypersurfaces moving with normal velocity proportional to a positive power α of the Gauss curvature. We prove that hypersurfaces contract to points in finite time, and for α ∈ (1/(n+ 2], 1/n] we also prove that in the limit the solutions evolve purely by h ..."
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Cited by 33 (2 self)
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We consider ndimensional convex Euclidean hypersurfaces moving with normal velocity proportional to a positive power α of the Gauss curvature. We prove that hypersurfaces contract to points in finite time, and for α ∈ (1/(n+ 2], 1/n] we also prove that in the limit the solutions evolve purely
Tensor product GaussLobatto points are Fekete points for the cube
 Math. Comp
, 2001
"... Abstract. Tensor products of GaussLobatto quadrature points are frequently used as collocation points in spectral element methods. Unfortunately, it is not known if GaussLobatto points exist in nontensorproduct domains like the simplex. In this work, we show that the ndimensional tensorproduct ..."
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Cited by 21 (3 self)
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Abstract. Tensor products of GaussLobatto quadrature points are frequently used as collocation points in spectral element methods. Unfortunately, it is not known if GaussLobatto points exist in nontensorproduct domains like the simplex. In this work, we show that the ndimensional tensor
Natural superconvergent points of equilateral triangular finite elements  A numerical example
"... Abstract. A numerical test case demonstrates that Lobatto and Gauss points are not natural superconvergent points for cubic and quartic finite elements under equilateral triangular mesh. ..."
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Cited by 1 (1 self)
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Abstract. A numerical test case demonstrates that Lobatto and Gauss points are not natural superconvergent points for cubic and quartic finite elements under equilateral triangular mesh.
Approximation of SturmLiouville problems by exponentially weighted LegendreGauss Tau Method
"... Abstract—We construct an exponentially weighted LegendreGauss Tau method for solving differential equations with oscillatory solutions. The proposed method is applied to SturmLiouville problems. Numerical examples illustrating the efficiency and the high accuracy of our results are presented. Keyw ..."
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. Keywords—Oscillatory functions, SturmLiouville problems, Legendre Polynomial, Gauss points. I.
Symmetric Uniformly Accurate GaussRungeKutta Method
"... Symmetric methods are particularly attractive for solving stiff ordinary differential equations. In this paper by the selection of Gausspoints for both interpolation and collocation, we derive high order symmetric singlestep GaussRungeKutta collocation method for accurate solution of ordinary di ..."
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Symmetric methods are particularly attractive for solving stiff ordinary differential equations. In this paper by the selection of Gausspoints for both interpolation and collocation, we derive high order symmetric singlestep GaussRungeKutta collocation method for accurate solution of ordinary
The Gauss map of minimal surfaces
 In Differential Geometry, Valencia 2001, Proceedings of the conference in honour of Antonio M. Naveira
, 2002
"... We give a new approach to the study of relations between the Gauss map and compactness properties for families of minimal surfaces in the Euclidean three space. In particular, we give a simple and unified proof of the curvature estimates for stable minimal surfaces and for minimal surfaces whose Gau ..."
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Cited by 12 (2 self)
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Gauss map image omits five points. The Gauss map of a minimal surface in the Euclidean space R3 is a conformal map. This fact has deep consequences in the behavior of these surfaces and has allowed a massive presence of complex variable techniques in the classical theory of minimal surfaces. In 1959
Improved fast Gauss transform
, 2003
"... The fast Gauss transform proposed by Greengard and Strain reduces the computational complexity of the evaluation of the sum of N Gaussians at M points in d dimensions from O(MN) to O(M + N). However, the constant factor in O(M + N) grows exponentially with increasing dimensionality d, which makes ..."
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Cited by 14 (5 self)
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The fast Gauss transform proposed by Greengard and Strain reduces the computational complexity of the evaluation of the sum of N Gaussians at M points in d dimensions from O(MN) to O(M + N). However, the constant factor in O(M + N) grows exponentially with increasing dimensionality d, which makes
Effect of Elements, Order of Approximation and Gauss Quadrature Points in Finite Element Method for Study of Rectangular Waveguides
"... Abstract — The main objective of this paper is to study the effect of number of elements, order of approximation and gauss quadrature points in finite element method for rectangular waveguide, which is the level at which the engineer is most interested in. By discretizing the crosssection of the wa ..."
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Abstract — The main objective of this paper is to study the effect of number of elements, order of approximation and gauss quadrature points in finite element method for rectangular waveguide, which is the level at which the engineer is most interested in. By discretizing the cross
GaussNewton Lines and Eleven Point Conics
"... Abstract. We give a projective version of the GaussNewton line for a complete quadrilateral and its extension for the complete quadrangle. 1. Projective form of GaussNewton Line The complete quadrilateral consists of the 6 intersection points on 4 given lines (quadrilateral). The diagonals are lin ..."
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Abstract. We give a projective version of the GaussNewton line for a complete quadrilateral and its extension for the complete quadrangle. 1. Projective form of GaussNewton Line The complete quadrilateral consists of the 6 intersection points on 4 given lines (quadrilateral). The diagonals
SHORT INCOMPLETE GAUSS SUMS AND RATIONAL POINTS ON METAPLECTIC
"... Abstract. In the present paper we investigate the limiting behavior of short incomplete Gauss sums at random argument as the number of terms goes to infinity. We prove that the limit distribution is given by the distribution of theta sums and differs from the limit law for long Gauss sums studied by ..."
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Abstract. In the present paper we investigate the limiting behavior of short incomplete Gauss sums at random argument as the number of terms goes to infinity. We prove that the limit distribution is given by the distribution of theta sums and differs from the limit law for long Gauss sums studied
Results 11  20
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116,309