By calculating the corresponding principal tensile strains, normalized with respect to an appropriate reference value, and by assuming suitable stress strain relationships, the equilibrium and compatibility conditions are imposed.
In this way, it is possible to derive analytical expressions for the distribution along the cross-section of axial, hoop and shear strains and also proceed to their consistent superposition in order to obtain the corresponding principal and von Mises strains.
The principal curvature flow makes the images smooth in the corresponding principal direction.
The surface evolution equation using the principal curvature flows smooths and enhances the AFM images in the corresponding principal directions.
where v stands for the principal eigenvector of a matrix and λ is the corresponding principal eigenvalue.
As a procedure, scientists acquire digital data of interest from the corresponding principal investigators and make the plots by themselves.
For testing, a test image is projected on the PCS and then the corresponding principal component is classified using the trained SVM.
Here, we focus on hydrothermal fluids with similar Cl concentrations to seawater in providing a brief overview of the geological settings and corresponding principal characteristics of their hydrothermal environments.
Proof Let U = ( u 1, …, u n ) be a positive solution of (1.1), and let ( μ 1, u ∗ ) be the corresponding principal eigen-pair of (2.6) such that ξ i ∗ > 0 in Ω for any 1 ≤ i ≤ n.
Similar to the proof above, let ( μ 1, u ) be the corresponding principal eigen-pair of (2.1) such that ξ i > 0 in Ω for any i = 1, …, n.
After successful authentication, the security provider can map the subject to its corresponding principal and thus provide respective service providers with its roles for access control and external credentials for trust delegation.
