In this paper, we provide simple and explicit formulas for computing Riemannian curvatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in IRk...In this paper, we provide simple and explicit formulas for computing Riemannian curvatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in IRk with k > 3.展开更多
In this work, a recently developed method based on the change of distance between collinear indents is used to evaluate different states of residual stress, which were generated in samples of AA 6082-T6 and AA 7075-T6...In this work, a recently developed method based on the change of distance between collinear indents is used to evaluate different states of residual stress, which were generated in samples of AA 6082-T6 and AA 7075-T6 aluminium alloys milled at high speed. One of the advantages of this method, which needs a universal measuring machine, is not requiring neither the use of specific equipment nor highly skilled operators. Also, by integrating an indentation device to the mentioned machine, the absolute error of measurement can be reduced. In results obtained in samples subjected to different cutting conditions it is observed a correlation between the stress values and the depth of cut, showing the AA 6082-T6 alloy higher susceptibility to be stressed. Furthermore, the high sensitivity of the method allowed detecting very small differences in the values reached by different normal components in the zones corresponding to climb and conventional cutting. It is important to note that these differences were similar for both evaluated alloys. Finally, the directions associated with the principal components of residual stress, where maximum local plastic stretching occurs, were found to be strongly dependent on the rolling direction prior to machining.展开更多
A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scali...A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum.展开更多
In this paper. we give a decomposition depending on p(1≤p≤n-2) orthonormaldirections assigned for nonsingular linear transformation F on a n-dimension (n≥3)Euclidean space En, and then prove foal there exist q(q=n-...In this paper. we give a decomposition depending on p(1≤p≤n-2) orthonormaldirections assigned for nonsingular linear transformation F on a n-dimension (n≥3)Euclidean space En, and then prove foal there exist q(q=n-p) quasi-Principaldirections.for F depending on the preceding p orthonormal directions. As applicance ofthe preceding result, we derive that there exist at least two orthonormal principaldirections of strain in arbitrary plane of body which is in homogeneous deformation,and strain energy density is.function of 5 real numbers under arbitrary quasi-principalbase.for the preceding nonsingular linear transformation.展开更多
基金The first author was supported in part by NSF (10241004) of ChinaNational Innovation Fund 1770900+2 种基金 Chinese Academy of Sciencesthe second author was supported in part by NSF grants CCR 9732306KDI-DMS-9873326.
文摘In this paper, we provide simple and explicit formulas for computing Riemannian curvatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in IRk with k > 3.
文摘In this work, a recently developed method based on the change of distance between collinear indents is used to evaluate different states of residual stress, which were generated in samples of AA 6082-T6 and AA 7075-T6 aluminium alloys milled at high speed. One of the advantages of this method, which needs a universal measuring machine, is not requiring neither the use of specific equipment nor highly skilled operators. Also, by integrating an indentation device to the mentioned machine, the absolute error of measurement can be reduced. In results obtained in samples subjected to different cutting conditions it is observed a correlation between the stress values and the depth of cut, showing the AA 6082-T6 alloy higher susceptibility to be stressed. Furthermore, the high sensitivity of the method allowed detecting very small differences in the values reached by different normal components in the zones corresponding to climb and conventional cutting. It is important to note that these differences were similar for both evaluated alloys. Finally, the directions associated with the principal components of residual stress, where maximum local plastic stretching occurs, were found to be strongly dependent on the rolling direction prior to machining.
文摘A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum.
文摘In this paper. we give a decomposition depending on p(1≤p≤n-2) orthonormaldirections assigned for nonsingular linear transformation F on a n-dimension (n≥3)Euclidean space En, and then prove foal there exist q(q=n-p) quasi-Principaldirections.for F depending on the preceding p orthonormal directions. As applicance ofthe preceding result, we derive that there exist at least two orthonormal principaldirections of strain in arbitrary plane of body which is in homogeneous deformation,and strain energy density is.function of 5 real numbers under arbitrary quasi-principalbase.for the preceding nonsingular linear transformation.
