Sentence examples for matrix and implies from inspiring English sources

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where is a column vector with elements, is an matrix, and implies the Hermitian transpose, where (5) corresponds to the HNN energy function in (2).

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Thus, a reduction of this coefficient, often under critical conditions such as joint large immobilization periods of time [ 38, 39] entails a decrease of fluid flow into the cartilage porous matrix and therefore implies smaller deformations.

This value is lower than that controlling the stabilization of the martensite with respect to the β phase matrix of 97 kJ/mol, and implies that the mechanism which is responsible for the rubber like behaviour is different from that for stabilization.

A great difference is also, of course, that C is a 17 × 17 matrix leading to 17 eigenvalues and implying that analytic solutions are impossible in practice.

The occurrence of extension veins that are confined to sandstone blocks and do not propagate into the surrounding matrix implies that the shale matrix was ductile, and a competence contrast existed between the sandstone blocks and the shale matrix, as described above.

In conclusion, chondrocyte death leads to acellularity and fibril network reorganization at the neocartilage/explant interface, and impacts the quality of cartilage repair as abnormal matrix remodeling implies.

Note that C z,n =C z,n I (identity matrix I) implies the elements of z n to be mutually statistically independent and of equal variance C z,n.

The continuous dependence of the determinant of a matrix on the elements of the matrix implies that all the above operations produce interval entities.

However, a high percentage of the positions coded by zero of the coding matrix, which implies a high sparseness degree, does not codify meta-class membership information.

In particular, we introduce a class of extensions to the directed graph corresponding to a given sparse matrix system, which when contains a stable sparse matrix system implies that the original system is stabilizable using periodic inputs.

In all cases, the use of a tensor product construction allows for efficient solution of the linear system involving the mass matrix, which implies optimal linear time solutions with respect to the number of degrees of freedom.

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