Sentence examples for inclusion matrix from inspiring English sources

This note calculates the rank of a special set inclusion matrix and then solves the above problem.

For a v-set X, W23 v) is a (v2)×(v3) inclusion matrix where rows and columns are indexed by pairs and triples of X, respectively, and for row T and column K, W23 v)(T,K)="1 if T⊆K and zero otherwise.

We consider equilibrium problems for an inhomogeneous plate with a crack situated at the inclusion-matrix interface.

One of the key issues to be addressed by such models is the surface-stresses arising at the inclusion-matrix boundary, due to its high curvature.

The behaviors of both the inclusion and the matrix are described by Biot's equations (1941) with standard conditions of Deresiewicz and Skalak (1963) at the inclusion-matrix interface.

To further achieve an accurate and efficient RVE modeling, local refinement for the background mesh is introduced near the inclusion-matrix interfaces.

To overcome the mathematical challenges imposed by the complex geometries of inclusion-matrix interface and matrix boundary, the inclusion is replaced with an arbitrarily-sided polygon, which enables 1) the shape of inclusion to be closely approximated and 2) the gap function on the inclusion-matrix interface to be evaluated by Cauchy integrals performed on the straight edges.

The split hexahedral elements around the inclusion-matrix interfaces correspond to polyhedral elements, while the background hexahedral elements remain inside the inclusions and matrices.

This is ascribed to the pre-existing thermal GND zone at the inclusion-matrix interface that provides a more uniform stress distribution around a fine equiaxed inclusion compared to its coarser counterpart.

A general scheme for calculating the second-order moments of the random elastic fields in the case of a composite of inclusion-matrix type using perturbation approach is presented, for example, in (Buryachenko 2007).

This is done by considering the probability of inclusion-matrix debonding and the fatigue crack initiation potency of partially-debonded inclusions for a given load ratio and stress amplitude.