Sentence examples for matrix relation from inspiring English sources

It is established that the procedure is determined by the dimension of the breakage matrix (relation between the number of input and output size fractions).

It is based on the derivation of a matrix relation which determines how an arbitrary but small perturbation at the beginning of a periodic solution propagates to the end of a response period.

Putting formula (3) into (1) and confining w to non-affine transformation, i.e., M 1 ′ T w = 0, it leads to a direct solution for d and w formed by the following matrix relation: w d = K ′ M r ′ M r ′ T 0 M i ′ 0 (4).

The general transfer matrix relation has been used, with the boundary conditions of zero shear stress and appropriate radiation loading on the two exposed surfaces, to evaluate the response of the plate to a given external pressure excitation on one of the faces.

Property (ii) follows since all the pairs ( A j n, B j n ) being controllable implies that the matrices of the closed-loop dynamics satisfy at the subsequence { j n } of samples the following matrix relation: M j n = A j n + B j n K j n = A j n + ∑ i = 1 q B j n ( i ) K j n ( i ) T ≈ [ 0 I p − 1 g j n T ], (3.10).

We substitute obtained matrix relations in the previous subsections given in Eqs.

The matrix relations between the injected waves and externally applied forces and moments are also derived.

Matrix relations in kinematics and dynamics of the Star parallel manipulator are established in this paper.

Then, based on Hamilton's principle and matrix relations, the reduced form of stiffness matrices is derived.

Recursive matrix relations for kinematics and dynamics analysis of a 2-DOF orienting gear train are established in this paper.

In [6], the authors used the matrix in relation to the recurrence relation (1) M = ( p − q 1 0 ).