We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much ...We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much simpler.展开更多
In this article, we study the steady, shrinking, and expanding Kahler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that, under this condition, the Ricci solitons must have constant holomorphic sectional...In this article, we study the steady, shrinking, and expanding Kahler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that, under this condition, the Ricci solitons must have constant holomorphic sectional curvature.展开更多
The multispectral remote sensing image(MS-RSI)is degraded existing multi-spectral camera due to various hardware limitations.In this paper,we propose a novel core tensor dictionary learning approach with the robust mo...The multispectral remote sensing image(MS-RSI)is degraded existing multi-spectral camera due to various hardware limitations.In this paper,we propose a novel core tensor dictionary learning approach with the robust modified Gaussian mixture model for MS-RSI restoration.First,the multispectral patch is modeled by three-order tensor and high-order singular value decomposition is applied to the tensor.Then the task of MS-RSI restoration is formulated as a minimum sparse core tensor estimation problem.To improve the accuracy of core tensor coding,the core tensor estimation based on the robust modified Gaussian mixture model is introduced into the proposed model by exploiting the sparse distribution prior in image.When applied to MS-RSI restoration,our experimental results have shown that the proposed algorithm can better reconstruct the sharpness of the image textures and can outperform several existing state-of-the-art multispectral image restoration methods in both subjective image quality and visual perception.展开更多
In the theory of general relativity, the finding of the Einstein Field Equation happens in a complex mathematical operation, a process we don’t need any more. Through a new theory in vector analysis, we’ll see that ...In the theory of general relativity, the finding of the Einstein Field Equation happens in a complex mathematical operation, a process we don’t need any more. Through a new theory in vector analysis, we’ll see that we can calculate the components of the Ricci tensor, Ricci scalar, and Einstein Field Equation directly in an easy way without the need to use general relativity theory hypotheses, principles, and symbols. Formulating the general relativity theory through another theory will make it easier to understand this relativity theory and will help combining it with electromagnetic theory and quantum mechanics easily.展开更多
We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold.The expressions of Meigenvalues and M-eigenvectors are presented in this paper.As a special case,M-e...We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold.The expressions of Meigenvalues and M-eigenvectors are presented in this paper.As a special case,M-eigenvalues of conformal flat Einstein manifold have also been discussed,and the conformal the invariance of M-eigentriple has been found.We also reveal the relationship between M-eigenvalue and sectional curvature of a Riemannian manifold.We prove that the M-eigenvalue can determine the Riemann curvature tensor uniquely.We also give an example to compute the Meigentriple of de Sitter spacetime which is well-known in general relativity.展开更多
In this paper, a new Ricci flow is canonically introduced in Finsler Geometry and, under the variance of Finsler-Ehresmann form, conformal changes of Finsler metrics are studied. Some existence conditions of this Fins...In this paper, a new Ricci flow is canonically introduced in Finsler Geometry and, under the variance of Finsler-Ehresmann form, conformal changes of Finsler metrics are studied. Some existence conditions of this Finslerian Ricci flow on a compact manifold which preserves the conformal class of the initial metric are obtained as an application.展开更多
A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of...A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of nearly-Khlerian structures in terms of Kirichenko tensors is also given.展开更多
To denoise the diffusion weighted images （DWls） featured as multi-boundary, which was very important for the calculation of accurate DTIs （diffusion tensor magnetic resonance imaging）, a modified Wiener filter was...To denoise the diffusion weighted images （DWls） featured as multi-boundary, which was very important for the calculation of accurate DTIs （diffusion tensor magnetic resonance imaging）, a modified Wiener filter was proposed. Through analyzing the widely accepted adaptive Wiener filter in image denoising fields, which suffered from annoying noise around the edges of DWIs and in turn greatly affected the denoising effect of DWIs, a local-shift method capable of overcoming the defect of the adaptive Wiener filter was proposed to help better denoising DWIs and the modified Wiener filter was constructed accordingly. To verify the denoising effect of the proposed method, the modified Wiener filter and adaptive Wiener filter were performed on the noisy DWI data, respectively, and the results of different methods were analyzed in detail and put into comparison. The experimental data show that, with the modified Wiener method, more satisfactory results such as lower non-positive tensor percentage and lower mean square errors of the fractional anisotropy map and trace map are obtained than those with the adaptive Wiener method, which in turn helps to produce more accurate DTIs.展开更多
基金supported by National Natural Science Foundation of China(11301191)supported by MOST(MOST107-2115-M-110-007-MY2)
文摘We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much simpler.
基金supported by the National Natural Science Foundation of China under the grant numbers 11126073the Fundamental Research Funds for the Central Universities of SCUT under the grant number 2012ZB0017
文摘In this article, we study the steady, shrinking, and expanding Kahler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that, under this condition, the Ricci solitons must have constant holomorphic sectional curvature.
基金This work was supported by the Project of Shandong Province Higher Educational Science and Technology Program[KJ2018BAN047,Geng,L.]National Natural Science Foundation of China[61801222,Fu,P.]+2 种基金Fundamental Research Funds for the Central Universities[30919011230,Fu,P.]Science and Technology Innovation Program for Distributed Young Talents of Shandong Province Higher Education Institutions[2019KJN045,Guo,Q.]Shandong Provincial Key Laboratory of Network Based Intelligent Computing[http://nbic.ujn.edu.cn/].
文摘The multispectral remote sensing image(MS-RSI)is degraded existing multi-spectral camera due to various hardware limitations.In this paper,we propose a novel core tensor dictionary learning approach with the robust modified Gaussian mixture model for MS-RSI restoration.First,the multispectral patch is modeled by three-order tensor and high-order singular value decomposition is applied to the tensor.Then the task of MS-RSI restoration is formulated as a minimum sparse core tensor estimation problem.To improve the accuracy of core tensor coding,the core tensor estimation based on the robust modified Gaussian mixture model is introduced into the proposed model by exploiting the sparse distribution prior in image.When applied to MS-RSI restoration,our experimental results have shown that the proposed algorithm can better reconstruct the sharpness of the image textures and can outperform several existing state-of-the-art multispectral image restoration methods in both subjective image quality and visual perception.
文摘In the theory of general relativity, the finding of the Einstein Field Equation happens in a complex mathematical operation, a process we don’t need any more. Through a new theory in vector analysis, we’ll see that we can calculate the components of the Ricci tensor, Ricci scalar, and Einstein Field Equation directly in an easy way without the need to use general relativity theory hypotheses, principles, and symbols. Formulating the general relativity theory through another theory will make it easier to understand this relativity theory and will help combining it with electromagnetic theory and quantum mechanics easily.
基金the National Natural Science Foundation of China(Grant No.11771099)supported by the Hong Kong Research Grant Council(Grant Nos.PolyU 15302114,15300715,15301716,15300717)supported by the Innovation Program of Shanghai Municipal Education Commission。
文摘We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold.The expressions of Meigenvalues and M-eigenvectors are presented in this paper.As a special case,M-eigenvalues of conformal flat Einstein manifold have also been discussed,and the conformal the invariance of M-eigentriple has been found.We also reveal the relationship between M-eigenvalue and sectional curvature of a Riemannian manifold.We prove that the M-eigenvalue can determine the Riemann curvature tensor uniquely.We also give an example to compute the Meigentriple of de Sitter spacetime which is well-known in general relativity.
文摘In this paper, a new Ricci flow is canonically introduced in Finsler Geometry and, under the variance of Finsler-Ehresmann form, conformal changes of Finsler metrics are studied. Some existence conditions of this Finslerian Ricci flow on a compact manifold which preserves the conformal class of the initial metric are obtained as an application.
文摘A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given.A characterization of nearly-Khlerian structures in terms of Kirichenko tensors is also given.
基金Project(2009AA04Z214) supported by the National High Technology Research and Development Program of ChinaProject(07JJ6133) supported by the Natural Science Foundation of Hunan Province, China
文摘To denoise the diffusion weighted images （DWls） featured as multi-boundary, which was very important for the calculation of accurate DTIs （diffusion tensor magnetic resonance imaging）, a modified Wiener filter was proposed. Through analyzing the widely accepted adaptive Wiener filter in image denoising fields, which suffered from annoying noise around the edges of DWIs and in turn greatly affected the denoising effect of DWIs, a local-shift method capable of overcoming the defect of the adaptive Wiener filter was proposed to help better denoising DWIs and the modified Wiener filter was constructed accordingly. To verify the denoising effect of the proposed method, the modified Wiener filter and adaptive Wiener filter were performed on the noisy DWI data, respectively, and the results of different methods were analyzed in detail and put into comparison. The experimental data show that, with the modified Wiener method, more satisfactory results such as lower non-positive tensor percentage and lower mean square errors of the fractional anisotropy map and trace map are obtained than those with the adaptive Wiener method, which in turn helps to produce more accurate DTIs.
