The system equations can be expressed in matrix notation as [varvec{M}]{varvec{textit{"{r}}}(t)} + [varvec{C}(t)]{dot{varvec{r}}(t)} + [varvec{K}(t)]{varvec{r}(t)} = {varvec{F}(t)}, (17 where {r(t)} = {z 1 t), z 2 t) q 1 (t), q 2 t)…, q n (t)}T is the response vector, {F t)} is the generalized stochastic force vector.
This indicates that the solutions to the S-system equations can depict time-transient behaviors analogous to the time-series data, even when arbitrary constant values are used for the kinetic orders, implying that the behavior of the metabolite concentrations is strongly governed by the network structure of a metabolic reaction system.
As stated in [14], for the traditional SG-based single machine infinite bus system, the system characteristic equation can be obtained according to the Phillips-Heffron model, as shown in (20).
The system of linear equation can be rewritten as N T N P = Q (11) P = N T N − 1 Q (12).
The scattering problem for the array of point dipoles, represented by the system of linear equation, can be solved with arbitrary accuracy.
The states and system coefficients equations can then be summarized as: (4) The last two equations determine the current system coefficients, which will be appended to the system state.
A system of equations can be established in order to reflect the ionic influence: 7 8 By solving the system of Equations (7) and (8), using the previously determined constants (a, b and A, B), donor and acceptor numbers for neat ionic liquids can be obtained.
Then, by appraising the nonlinear terms of the given systems, a dynamic equation can be delicately constructed.
A system of equations can be expressed elegantly using a coefficient matrix and column vectors.
