In order to carry out tensor analysis in a neighborhood of a reference surface,the principal-direction orthogonal basis accompanying with Lame s coefficients or general curvilinear coordinate systems are widely used.A...In order to carry out tensor analysis in a neighborhood of a reference surface,the principal-direction orthogonal basis accompanying with Lame s coefficients or general curvilinear coordinate systems are widely used.A novel kind of field theory termed as the nonholonomic theory of the Principal-Direction Orthonormal Basis(PDOB)is presented systematically in the present paper,in which the formal Christoffel symbols are related directly to the principal and geodesic curvatures with respect to the principal directions of the surface.Furthermore,a systematic and simple way to determine the curvatures of the surface are presented with some examples.It provides a way to recognize qualitatively the bending property of a surface.展开更多
The purpose of this paper is to extend the generation theorem of the general linear group GLn（F） over field F to the linear group GLn（R） over local ring R. When V is an n-dimensional R-space and σ is an element i...The purpose of this paper is to extend the generation theorem of the general linear group GLn（F） over field F to the linear group GLn（R） over local ring R. When V is an n-dimensional R-space and σ is an element in GLn（R）, in general, Q=（σ-1）V and M={x∈V|σx=x} are just R-submodules of V, but not always R-subspaces. Therefore, the展开更多
基金Project supported by the National Natural Science Foundation of China(11972120,11472082,12032016)。
文摘In order to carry out tensor analysis in a neighborhood of a reference surface,the principal-direction orthogonal basis accompanying with Lame s coefficients or general curvilinear coordinate systems are widely used.A novel kind of field theory termed as the nonholonomic theory of the Principal-Direction Orthonormal Basis(PDOB)is presented systematically in the present paper,in which the formal Christoffel symbols are related directly to the principal and geodesic curvatures with respect to the principal directions of the surface.Furthermore,a systematic and simple way to determine the curvatures of the surface are presented with some examples.It provides a way to recognize qualitatively the bending property of a surface.
文摘The purpose of this paper is to extend the generation theorem of the general linear group GLn（F） over field F to the linear group GLn（R） over local ring R. When V is an n-dimensional R-space and σ is an element in GLn（R）, in general, Q=（σ-1）V and M={x∈V|σx=x} are just R-submodules of V, but not always R-subspaces. Therefore, the
