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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.

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With a deterministic energy source, there will be no silent symbols; thus, the system equation can be expressed as textbf{y} = sqrt{E_{s}} textbf{s} + textbf{z} (20).

The system equation can be expressed in the matrix form as follows y [ m ] = H [ m ] T [ m ] b [ m ] + n [ m ], (2).

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.

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.

The last system of equations can be rewritten as (7).

A system of equations can be expressed elegantly using a coefficient matrix and column vectors.

This is why the following system of equations can be obtained relatively to : (28).

The basic system of equations can be reduced to the dispersion equation for the small-scale in transverse direction disturbances.

Once decoupling of the function is made, the system of equations can be connected in an approximate manner.

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