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Finally, to get the expression of total stress tensor
of fiber polymer composites, the following Equation has been used [28, 29].
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R, S, Q & r being Christoffel Riemannian curvature tensor
, Ricci tensor
, Ricci operator and scalar curvature respectively.
In this example the second-order alignment tensor
of the flat distribution from Fig.
In Section 2, we briefly introduce the tensor
algebra basics and the tensor-based signal model of the bistatic MIMO radar.
In this situation as well validity of the above expression for all null vectors [l.sub.a], along with two times contracted Bianchi identity and covariant conservation of matter energy momentum tensor
, amounts to furnishing the ten components of Einstein's equations.
where the superimposed dot denotes differentiation with respect to t and A and [Y.sub.0] are given constant tensors
. The solution to system (1) is Y(f) = exp[(f - [t.sub.0])A] [Y.sub.0], and exp(x) is the tensor
Through the above literature, it can be seen that the existing recovery theories and methods for missing traffic data at random can be attributed to the form of vector, matrix, and tensor
, according to the combination of traffic data.
A = ([mathematical expression not reproducible]) is called a nonnegative tensor
if all of its entries [mathematical expression not reproducible] are nonnegative.
We compute Green's function matrix G for the full moment tensor
M inversion of the first P-wave arrival amplitudes (either positive or negative values--see Eisner et al., 2010 with example of real data picking strategy) for the surface vertical component array and shallow boreholes receivers with only vertical components array, and another matrix of both the first P- and first S-wave arrival amplitudes modeled for the dual borehole array.