Sentence examples for matrix then the from inspiring English sources

The classical Mori Tanaka method is first used to analyze the porous polymer matrix, then the Mori Tanaka method for piezoelectric composites is used to analyze the porous polymer matrix with embedded piezoceramic fibers.

It is proved that, if the noise variance is larger than a threshold, which depends on the unknown parameters and on the extended design matrix, then the proposed estimator of the original parameters dominates the least-squares estimator, in the sense of the mean square error.

In 1995, Lasserre showed [18] the following given any matrix then the following.

If A = C 1, the Cesaro matrix, then the definition reduces to ( B Λ μ ) n -statistical convergence.

Let be a circulant and symmetric matrix, then the eigenvalue decomposition of is [15, pages 201-202] (8).

(i) If A = I (the unit matrix), then the statistical ( A, λ ) -summability is reduced to the λ-statistical convergence.

A matrix A is called an M-matrix if there exist a nonnegative matrix B and a real number s > ρ ( B ) such that A = s I − B, where ρ ( B ) is the spectral radius of B. It is well known that A is an H-matrix if and only if μ ( A ) is an M-matrix, and if A is an M-matrix, then the Schur complement of A is also an M-matrix and det A > 0 (see [3]).

If there is a constant (alpha>0) such that (G alpha)) is a nonsingular M-matrix, then the solution (X t)) of system (1.3) satisfies liminf_{ttoinfty}frac{ln x t)}{ln t}geq-frac{1}{alpha},qquad liminf_{ttoinfty}frac{ln y(t)}{ln t}geq-frac{1}{alpha},qquad liminf_{ttoinfty}frac{ln z(t)}{ln t}geq-frac{1}{alpha}quad textit{a.s.}.

If are exchange matrixes, then the matrix is called difference matrix, and the substitution is difference substitution, where, and.

Breakdown of the extracellular matrix then allows the cells to invade the surrounding tissue and enter the bloodstream or lymphatic system.

The matrix, then, is the site of creativity.