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For a small time step, each crack is extended in the direction of maximal hoop stress, and by a length set by the kinetic law.
To account for the orientation of lamellar blocks in the direction of maximal stresses and formation of micro-fibrils in the post-yield region of deformations (which is observed as strain-hardening of specimens) elastic moduli are assumed to depend on the principal invariants of the right Cauchy Green tensor for the viscoplastic flow.
The direction of maximal RSSI is determined as follows.
In particular, we can obtain posterior distributions for any such gradient, for the direction of maximal gradient, and for the magnitude of the maximal gradient.
It reduces a set of variables into a smaller set of orthogonal, and therefore independent, principal components (PCs) in the direction of maximal variation i.e. it reduces the dimensionality and retains the most significant information for further analysis.
We were interested in determining how well the self-selected postures aligned the direction of maximal endpoint stiffness with the orientation of the unstable haptic environments.
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The method makes use of the local structure of the normal stretching rates by projecting the dynamics onto the local directions of maximal stretching.
The basic idea of PCA is to project the data along the directions of maximal variances so that the reconstruction error can be minimized.
Many generalizations in various different directions of maximal element principle have been studied in the past; for example, see [2, 3, 6 10] and references therein.
Hence, while in PCR the eigenvectors of the data covariance matrix are used to span the solution space, in PLSR the directions of maximal covariance between data and the dependent variables are used.
The ICA calculates the directions of maximal independency of the pre-analysed data set.
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