Sentence examples for matrices and equations from inspiring English sources

In contrast to PH/PH(n)/C/C analytical queuing model [3], PH/PH(n)/C/C DES model eliminates the need to solve large matrices and equations systems to estimate the performance measures.

The definitions of the functions, vectors, matrices and equations (see Notation in Appendix S1) used for the simulations are given with the following additional assumptions: For t0 = 0 the initial state of the system is the reliability state R. The algorithm is applied until the system enters the maintenance state.

Due to the diploid/polyploid nature of most higher organisms, this will necessarily increase the size of transition matrices and equation systems to be analysed.

Consequently, (mathbf {I}_{Delta theta,hat {epsilon }_{m}}) is considered as an identity matrix and Equation 45 becomes widehat{{mathbf{h}}}_{Deltatheta_{m}} = left[mathbf{S}^{H}_{Deltatheta_{m}} mathbf{S}_{Deltatheta_{m}}+{sigma_{g}^{2}} mathbf{R_{h}^{-1}}right]^{-1} mathbf{S}^{H}_{Deltatheta_{m}} (mathbf{S}_{Delta theta_{m}}mathbf{h}) + mathbf{g}^{prime}, (46).

First of all, if there is a quadratic Lyapunov function such that nonlinear homogeneous systems are asymptotically stable, a matrix Lyapunov-like equation is obtained for a stable nonlinear homogeneous system using semi-tensor product of matrices, and Lyapunov equation of linear system is just its particular case.

The matrix storage and equation solution techniques for large-scale engineering structures are also considered.

Also, some applications were obtained, in particular when dealing with differential, matrix and integral equations (see, e.g., [5 7, 10]).

The system is modeled using homogeneous transformation matrices and loop closure equations.

The stiffness equation of individual flexure hinge is established firstly, and then the stiffness of the whole mechanism is modeled via assembling stiffness matrices and formulating constraint equations.

From Equation 30, we can see that U k, k=1,⋯,K are PSD matrices, and thus from Equation 27, U is PSD.

This is accomplished by representing the underlying control optimization problem in terms of a system of linear-matrix-inequality (LMI) constraints and matrix equations that are simultaneously solved.