Sentence examples for the equivalent formulation from inspiring English sources

This technique is extended in this paper, to the response from ambient excitation tests based on the equivalent formulation between the free response and the correlation function of a linear mechanical system under stationary stochastic excitation.

Thus, we have the equivalent formulation.

By using the equivalent formulation, the existence and uniqueness theorems for solutions of the system are established.

This leads to the equivalent formulation u ( k + log a, t ) = 1 2 π ∫ − ∞ ∞ f ˆ h ( a ω ) e i ω t d ω. (12).

Since is the equivalent formulation of the price region where these conditions are satisfied, any would either lead to nonunique NE or to a unique NE without concurrent transmission.

Note that if the coefficients are in fact of class C 2 in each variable, then (4.11) has the equivalent formulation ∂ ¯ z Ω 0 ( w, z ) = − d w Ω 1 ( w, z ).

This corresponds to modeling a single neuron without inputs by the equivalent formulations { d v ϵ d t = − l z ϵ, d z ϵ d t = β 2 ( v ϵ − z ϵ ) ⇔ { d v ϵ d t = − l v ϵ ∗ g 2, where  g 2 ( t ) = β 2 e − β 2 t H ( t ).

We have proved the equivalence between the SGNMVID and the fixed point problem, and then by this equivalent formulation, discussed the existence and uniqueness of solution of the SGNMVID.

Then by using this equivalent formulation, the existence and uniqueness of solution of the problem of extended general nonlinear regularized nonconvex variational inequalities are discussed.

With these and given that the communication graph G is connected, we obtain the following equivalent formulation of (1) (see e.g., [13]): min ∑ i = 1 L f i ( x ( i ) ), s.t.

In this article, we use the following equivalent formulation (see [18] WCS X = inf lim n, m ; n ≠ m x n - x m.