Sentence examples for given the solutions of from inspiring English sources

Given the solutions of the steady state probabilities, we know that π p (T i ) is the stationary probability that the system is in state T i, and thus, it can be thought of as the expected long-run fraction of the time that the Markov chain spends in the state T i [32]: π p T i = lim τ → ∞ 1 τ ∫ 0 τ Pr T t = T i dt (36).

Once the autocorrelation function is given, the solution of the characteristic equation (3).

We note that for a given the solution of (12) can be computed numerically.

Cohen et al. [12] had given the solution of (3), that is, (4).

It is noted here that for a given the solution of (17) is uniquely determined (see proof of Theorem 1 in Section 4).

The problem is also formulated as a control Lyapunov function based feedback design when the Lyapunov function parameters are given, the solution of this problem can be obtained by solving a linear matrix inequality.

In this paper, we give the solutions of these problems.

Solving the simultaneous equations gives the solutions of the two sought-after estimators.

Let us give the solutions of this equation by integral equation representations.

In the next two columns formulas give the solutions of (V_{P}) and (V_{I}). in function of (theta _{P}).

Recently, Huang and Ychussie (see [7]) gave the solutions of the Dirichlet-Schrödinger problem with continuous data having slow growth in the boundary.