We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors which leads to greater geometric insight and a higher degree of organization in analytical expressions. We demonstrate t...We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors which leads to greater geometric insight and a higher degree of organization in analytical expressions. We demonstrate the effectiveness of the approach by proving a number of integral identities with vector integrands. The presented approach may be aptly described as absolute vector calculus or as vector tensor calculus.展开更多
As an important part of water level warning in water conservancy projects,often due to the influence of environmental factors such as light and stains,the acquired water gauge images have sticky,broken and bright spot...As an important part of water level warning in water conservancy projects,often due to the influence of environmental factors such as light and stains,the acquired water gauge images have sticky,broken and bright spot conditions,which affect the identification of water gauges.To solve this problem,a water gauge image denoising model based on improved adaptive total variation is proposed.Firstly,the regular term exponent in the adaptive total variational equation is changed to an inverse cosine function;secondly,the differential curvature is used to distinguish the image noise points and increase the smoothing strength at the noise points;finally,according to the characteristics of the gradient mode and adaptive gradient threshold after Gaussian filtering,the New model can adaptively denoise in the smooth area and protect the edge area,so as to have the characteristics of both edge-preserving denoising.The experimental results show that the new model has a great improvement in image vision,higher iteration efficiency and an average increase of 1.6 dB in peak signal-to-noise ratio,and an average increase of 9%in structural similarity,which is more beneficial to practical applications.展开更多
We start recalling with critical eyes the mathematical methods used in gauge theory and prove that they are not coherent with continuum mechanics, in particular the analytical mechanics of rigid bodies (despite using ...We start recalling with critical eyes the mathematical methods used in gauge theory and prove that they are not coherent with continuum mechanics, in particular the analytical mechanics of rigid bodies (despite using the same group theoretical methods) and the well known couplings existing between elasticity and electromagnetism (piezzo electricity, photo elasticity, streaming birefringence). The purpose of this paper is to avoid such contradictions by using new mathematical methods coming from the formal theory of systems of partial differential equations and Lie pseudo groups. These results finally allow unifying the previous independent tentatives done by the brothers E. and F. Cosserat in 1909 for elasticity or H. Weyl in 1918 for electromagnetism by using respectively the group of rigid motions of space or the conformal group of space-time. Meanwhile we explain why the Poincaré duality scheme existing between geometry and physics has to do with homological algebra and algebraic analysis. We insist on the fact that these results could not have been obtained before 1975 as the corresponding tools were not known before.展开更多
The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in R^(n).They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several ge...The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in R^(n).They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several geometric properties of such hypersurfaces.In particular,they discover a class of non-compact rotational hypersurfaces with constant and negative Gauss-Kronecker curvature and finite volume,which can be seen as the higher-dimensional generalization of the pseudo-sphere.展开更多
Under the assumption that the normalized mean curvature vector is parallel in the normal bundle, by using the generalized ChengYau＇s self-adjoint differential operator, here we obtain some rigidity results for compac...Under the assumption that the normalized mean curvature vector is parallel in the normal bundle, by using the generalized ChengYau＇s self-adjoint differential operator, here we obtain some rigidity results for compact submanifolds with constant scalar curvature and higher codimension in the space forms.展开更多
为减少低剂量计算机断层扫描(computed tomography,CT)重建图像时出现的大量条形伪影,提出一种基于差分曲率自适应正则化的低剂量CT重建算法。将差分曲率应用到原有的投影域惩罚加权最小二乘法(penalized weight least square,PWLS)中,...为减少低剂量计算机断层扫描(computed tomography,CT)重建图像时出现的大量条形伪影,提出一种基于差分曲率自适应正则化的低剂量CT重建算法。将差分曲率应用到原有的投影域惩罚加权最小二乘法(penalized weight least square,PWLS)中,差分曲率对图像的边缘、平滑区域以及斜坡结构具有良好的检测性能,可有效地控制平滑区域和边缘区域的扩散程度,自适应地去除重建图像中的条形伪影。实验结果表明,该算法能有效抑制条形伪影的产生,较好保持图像的边缘和细节信息。展开更多
文摘We present a tensor description of Euclidean spaces that emphasizes the use of geometric vectors which leads to greater geometric insight and a higher degree of organization in analytical expressions. We demonstrate the effectiveness of the approach by proving a number of integral identities with vector integrands. The presented approach may be aptly described as absolute vector calculus or as vector tensor calculus.
文摘As an important part of water level warning in water conservancy projects,often due to the influence of environmental factors such as light and stains,the acquired water gauge images have sticky,broken and bright spot conditions,which affect the identification of water gauges.To solve this problem,a water gauge image denoising model based on improved adaptive total variation is proposed.Firstly,the regular term exponent in the adaptive total variational equation is changed to an inverse cosine function;secondly,the differential curvature is used to distinguish the image noise points and increase the smoothing strength at the noise points;finally,according to the characteristics of the gradient mode and adaptive gradient threshold after Gaussian filtering,the New model can adaptively denoise in the smooth area and protect the edge area,so as to have the characteristics of both edge-preserving denoising.The experimental results show that the new model has a great improvement in image vision,higher iteration efficiency and an average increase of 1.6 dB in peak signal-to-noise ratio,and an average increase of 9%in structural similarity,which is more beneficial to practical applications.
文摘We start recalling with critical eyes the mathematical methods used in gauge theory and prove that they are not coherent with continuum mechanics, in particular the analytical mechanics of rigid bodies (despite using the same group theoretical methods) and the well known couplings existing between elasticity and electromagnetism (piezzo electricity, photo elasticity, streaming birefringence). The purpose of this paper is to avoid such contradictions by using new mathematical methods coming from the formal theory of systems of partial differential equations and Lie pseudo groups. These results finally allow unifying the previous independent tentatives done by the brothers E. and F. Cosserat in 1909 for elasticity or H. Weyl in 1918 for electromagnetism by using respectively the group of rigid motions of space or the conformal group of space-time. Meanwhile we explain why the Poincaré duality scheme existing between geometry and physics has to do with homological algebra and algebraic analysis. We insist on the fact that these results could not have been obtained before 1975 as the corresponding tools were not known before.
基金Peking University for providing financial support for the first author
文摘The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in R^(n).They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several geometric properties of such hypersurfaces.In particular,they discover a class of non-compact rotational hypersurfaces with constant and negative Gauss-Kronecker curvature and finite volume,which can be seen as the higher-dimensional generalization of the pseudo-sphere.
文摘Under the assumption that the normalized mean curvature vector is parallel in the normal bundle, by using the generalized ChengYau＇s self-adjoint differential operator, here we obtain some rigidity results for compact submanifolds with constant scalar curvature and higher codimension in the space forms.
文摘为减少低剂量计算机断层扫描(computed tomography,CT)重建图像时出现的大量条形伪影,提出一种基于差分曲率自适应正则化的低剂量CT重建算法。将差分曲率应用到原有的投影域惩罚加权最小二乘法(penalized weight least square,PWLS)中,差分曲率对图像的边缘、平滑区域以及斜坡结构具有良好的检测性能,可有效地控制平滑区域和边缘区域的扩散程度,自适应地去除重建图像中的条形伪影。实验结果表明,该算法能有效抑制条形伪影的产生,较好保持图像的边缘和细节信息。
