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Zdeněk Martinec - One of the best experts on this subject based on the ideXlab platform.

  • shavel a program for the spherical harmonic analysis of a Horizontal Vector Field sampled in an equiangular grid on a sphere
    Computer Physics Communications, 2018
    Co-Authors: Zdeněk Martinec, David Einspigel
    Abstract:

    Abstract A method for performing a spherical harmonic analysis, using observed Horizontal components of a tangent Vector on a sphere, is presented. The Vector data samples are assumed to be provided in an equiangular grid, which essentially simplifies the least-squares analysis by making use of (1) the block diagonal structure of the normal equations of least squares, (2) the even–odd symmetry of the associated Legendre functions, and (3) the fast Fourier transform of mix-radix. The correct function of the program and its numerical precision is verified by applying it to a data set, derived by evaluating a given set of Vector spherical harmonic coefficients. That the program works correctly is demonstrated by the excellent agreement between the input and output spherical harmonic coefficients. Program summary Program Title: SHAVEL Program Files doi: http://dx.doi.org/10.17632/nppz4y7wg7.1 Licensing provisions: GPLv3 Programming language: Fortran 2003, Linux External routines: FFTPACK5.1, CPC program library SPHAN Classification: 4.9, 4.10, 4.11 Nature of problem: The least-squares analysis of Horizontal Vector Field sampled in an equiangular grid on a sphere in terms of Horizontal Vector spherical harmonics. Solution method: The Vector spherical harmonic coefficients of a Horizontal Vector Field are estimated by the method of least-squares adjustment of data samples distributed in an equiangular grid on a sphere. For such a regular grid the normal matrix is sparse and allows the system of the normal equations to be decomposed into a series of subsystems according to azimuthal order m . The solution of each subsystem is sought by the Gauss elimination. The fast Fourier transform of mix-radix is implemented in (i) setting up the right-hand sides of the normal equations, and (ii) performing the spherical harmonic synthesis where the series of spherical harmonics are summed.

David Einspigel - One of the best experts on this subject based on the ideXlab platform.

  • shavel a program for the spherical harmonic analysis of a Horizontal Vector Field sampled in an equiangular grid on a sphere
    Computer Physics Communications, 2018
    Co-Authors: Zdeněk Martinec, David Einspigel
    Abstract:

    Abstract A method for performing a spherical harmonic analysis, using observed Horizontal components of a tangent Vector on a sphere, is presented. The Vector data samples are assumed to be provided in an equiangular grid, which essentially simplifies the least-squares analysis by making use of (1) the block diagonal structure of the normal equations of least squares, (2) the even–odd symmetry of the associated Legendre functions, and (3) the fast Fourier transform of mix-radix. The correct function of the program and its numerical precision is verified by applying it to a data set, derived by evaluating a given set of Vector spherical harmonic coefficients. That the program works correctly is demonstrated by the excellent agreement between the input and output spherical harmonic coefficients. Program summary Program Title: SHAVEL Program Files doi: http://dx.doi.org/10.17632/nppz4y7wg7.1 Licensing provisions: GPLv3 Programming language: Fortran 2003, Linux External routines: FFTPACK5.1, CPC program library SPHAN Classification: 4.9, 4.10, 4.11 Nature of problem: The least-squares analysis of Horizontal Vector Field sampled in an equiangular grid on a sphere in terms of Horizontal Vector spherical harmonics. Solution method: The Vector spherical harmonic coefficients of a Horizontal Vector Field are estimated by the method of least-squares adjustment of data samples distributed in an equiangular grid on a sphere. For such a regular grid the normal matrix is sparse and allows the system of the normal equations to be decomposed into a series of subsystems according to azimuthal order m . The solution of each subsystem is sought by the Gauss elimination. The fast Fourier transform of mix-radix is implemented in (i) setting up the right-hand sides of the normal equations, and (ii) performing the spherical harmonic synthesis where the series of spherical harmonics are summed.

Cengizhan Murathan - One of the best experts on this subject based on the ideXlab platform.

  • Anti-invariant Riemannian Submersions from Kenmotsu Manifolds onto Riemannian manifolds
    arXiv: Differential Geometry, 2015
    Co-Authors: A. Beri, I. Küpeli Erken, Cengizhan Murathan
    Abstract:

    The purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. We proved that there do not exist (anti-invariant) Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds such that characteristic Vector Field {\xi} is a vertical Vector Field. We gave a method to get Horizontally conformal submersion examples from warped product manifolds onto Riemannian manifolds. Furthermore, we presented an example of anti-invariant Riemannian submersions in the case where the characteristic Vector Field {\xi} is a Horizontal Vector Field and an anti-invariant Horizontally conformal submersion such that {\xi} is a vertical Vector Field.

A. Beri - One of the best experts on this subject based on the ideXlab platform.

  • Anti-invariant Riemannian Submersions from Kenmotsu Manifolds onto Riemannian manifolds
    arXiv: Differential Geometry, 2015
    Co-Authors: A. Beri, I. Küpeli Erken, Cengizhan Murathan
    Abstract:

    The purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. We proved that there do not exist (anti-invariant) Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds such that characteristic Vector Field {\xi} is a vertical Vector Field. We gave a method to get Horizontally conformal submersion examples from warped product manifolds onto Riemannian manifolds. Furthermore, we presented an example of anti-invariant Riemannian submersions in the case where the characteristic Vector Field {\xi} is a Horizontal Vector Field and an anti-invariant Horizontally conformal submersion such that {\xi} is a vertical Vector Field.

Yılmaz Gündüzalp - One of the best experts on this subject based on the ideXlab platform.

  • On the Geometry of Conformal Anti-invariant $\xi^\perp-$ Submersions
    2018
    Co-Authors: Mehmet Akif Akyol, Yılmaz Gündüzalp
    Abstract:

    Lee [Anti-invariant $\xi^{\perp}-$ Riemannian submersions from almost contact manifolds, Hacettepe Journal of Mathematics and Statistic, 42(3), (2013), 231-241.] defined and studied anti-invariant $\xi^\perp-$ Riemannian submersions from almost contact manifolds.The main goal of this paper is to consider conformal anti-invariant $\xi^\perp-$ submersions (it means the Reeb Vector Field $\xi$ is a Horizontal Vector Field) from almost contact metric manifolds onto Riemannian manifolds as a generalization of anti-invariant $\xi^\perp-$ Riemannian submersions. More precisely, we obtain the geometries of the leaves of $\ker\pi_{*}$ and $(\ker\pi_{*})^\perp,$ including the integrability of the distributions, the geometry of foliations, some conditions related to totally geodesicness and harmonicty of the submersions. Finally, we show that there are certain product structures on the total space of a conformal anti-invariant $\xi^\perp-$ submersion.