The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Jean-pierre Gazeau - One of the best experts on this subject based on the ideXlab platform.
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Continuous wavelet transform on the Hyperboloid
Applied and Computational Harmonic Analysis, 2007Co-Authors: Iva Bogdanova, Pierre Vandergheynst, Jean-pierre GazeauAbstract:In this paper we build a Continuous Wavelet Transform (CWT) on the upper sheet of the 2-Hyperboloid $H_+^2$. First, we define a class of suitable dilations on the Hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to $SO_0(1,2)$, we define a family of hyperbolic wavelets. The continuous wavelet transform $W_f(a,x)$ is obtained by convolution of the scaled wavelets with the signal. The wavelet transform is proved to be invertible whenever wavelets satisfy a particular admissibility condition, which turns out to be a zero-mean condition. We then provide some basic examples and discuss the limit at null curvature.
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Wavelets on the 2-Hyperboloid
2004Co-Authors: Iva Bogdanova, Pierre Vandergheynst, Jean-pierre GazeauAbstract:We build wavelets on the 2-Hyperboloid. First, we define dilations on the Hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to $SO_0(1,2)$, we define a family of hyperbolic wavelets. The continuous wavelet transform (CWT)is obtained by convolution of the scaled wavelets with the signal. This wavelet transform is proved to be invertible whenever wavelets satisfy a particular admissibility condition. Finally, the Euclidean limit of this CWT on the Hyperboloid is considered.
A Genz - One of the best experts on this subject based on the ideXlab platform.
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approximation of multiple integrals over Hyperboloids with application to a quadratic portfolio with options
Computational Statistics & Data Analysis, 2008Co-Authors: Sadefo J Kamdem, A GenzAbstract:An application involving a financial quadratic portfolio, where the joint underlying log-returns follow a multivariate elliptic distribution, is considered. This motivates the need for methods for the approximation of multiple integrals over Hyperboloids. Transformations are used to reduce the Hyperboloid integrals to products of integrals which can be approximated with appropriate numerical methods. The application of these methods is demonstrated using some financial applications examples.
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Approximation of Multiple Integrals over Hyperboloids with Application to a Quadratic Portfolio with Options.
2003Co-Authors: Jules Sadefo Kamdem, A GenzAbstract:We consider an application involving a financial quadratic portfolio of options, when the joint underlying log-returns changes with multivariate elliptic distribution. This motivates the needs for methods for the approximation of multiple integrals over Hyperboloids. A transformation is used to reduce the Hyperboloid integrals to a product of two radial integrals and two spherical surface integrals. Numerical approximation methods for the transformed integrals are constructed. The application of these methods is demonstrated using some financial applications examples.
Weixing Shu - One of the best experts on this subject based on the ideXlab platform.
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wave propagation in an anisotropic metamaterial with single sheeted Hyperboloid dispersion relation
Applied Physics A, 2007Co-Authors: Hailu Luo, Zhongzhou Ren, Weixing ShuAbstract:We investigate the wave propagation in an anisotropic metamaterial with single-sheeted Hyperboloid dispersion relation. Based on boundary conditions and dispersion relations, we find that the opposite amphoteric refraction, such that E (or H)-polarized waves are positively refracted whereas H (or E)-polarized waves are negatively refracted, can occur at the interface associated with the anisotropic metamaterial. Under a certain condition, both E- and H-polarized waves can exhibit the same single-sheeted Hyperboloid or straight line dispersion relation, while the two polarized waves exhibit different propagation characteristics. We expect some potential device applications can be derived based on the unique amphoteric refraction properties.
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wave propagation in the anisotropic media with single sheeted Hyperboloid dispersion relation
arXiv: Optics, 2006Co-Authors: Hailu Luo, Zhongzhou Ren, Weixing ShuAbstract:We investigate the wave propagation in the anisotropic metamaterial with single-sheeted Hyperboloid dispersion relation. Based on boundary conditions and dispersion relations, we find that the opposite amphoteric refraction, such that E- (or H-) polarized waves are positively refracted whereas H- (or E-) polarized waves are negatively refracted, can occur at the interface associated with the anisotropic metamaterial. Under a certain condition, both E- and H-polarized waves can exhibit the same single-sheeted Hyperboloid or straight dispersion relation, while the two polarized waves exhibit different propagation characteristics. We expect some potential device applications can be derived based on based on the unique amphoteric refraction properties.
Iva Bogdanova - One of the best experts on this subject based on the ideXlab platform.
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Continuous wavelet transform on the Hyperboloid
Applied and Computational Harmonic Analysis, 2007Co-Authors: Iva Bogdanova, Pierre Vandergheynst, Jean-pierre GazeauAbstract:In this paper we build a Continuous Wavelet Transform (CWT) on the upper sheet of the 2-Hyperboloid $H_+^2$. First, we define a class of suitable dilations on the Hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to $SO_0(1,2)$, we define a family of hyperbolic wavelets. The continuous wavelet transform $W_f(a,x)$ is obtained by convolution of the scaled wavelets with the signal. The wavelet transform is proved to be invertible whenever wavelets satisfy a particular admissibility condition, which turns out to be a zero-mean condition. We then provide some basic examples and discuss the limit at null curvature.
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Wavelets on the 2-Hyperboloid
2004Co-Authors: Iva Bogdanova, Pierre Vandergheynst, Jean-pierre GazeauAbstract:We build wavelets on the 2-Hyperboloid. First, we define dilations on the Hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to $SO_0(1,2)$, we define a family of hyperbolic wavelets. The continuous wavelet transform (CWT)is obtained by convolution of the scaled wavelets with the signal. This wavelet transform is proved to be invertible whenever wavelets satisfy a particular admissibility condition. Finally, the Euclidean limit of this CWT on the Hyperboloid is considered.
Sadefo J Kamdem - One of the best experts on this subject based on the ideXlab platform.
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approximation of multiple integrals over Hyperboloids with application to a quadratic portfolio with options
Computational Statistics & Data Analysis, 2008Co-Authors: Sadefo J Kamdem, A GenzAbstract:An application involving a financial quadratic portfolio, where the joint underlying log-returns follow a multivariate elliptic distribution, is considered. This motivates the need for methods for the approximation of multiple integrals over Hyperboloids. Transformations are used to reduce the Hyperboloid integrals to products of integrals which can be approximated with appropriate numerical methods. The application of these methods is demonstrated using some financial applications examples.
