Sentence examples for mean square where from inspiring English sources

The item fit is evaluated based on the infit (weighted mean square), where values near 1 are desirable (OECD 2012).

In other words, the solution is exponentially stable in mean square, where the Lyapunov exponent is −γ.

The purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that, for all admissible interval uncertainties and nonlinear disturbances, the closed-loop system is asymptotically stable in the mean square, where the stability criteria are dependent on the length of the time delay and therefore less conservative.

then the zero solution of Equation (4.1) is exponentially stable in the mean square, where q = max i ∈ S, 1 ≤ k < + ∞ d i k + d ̄ i k e λ τ ≥ 1. Next, we apply Corollaries 4.1 and 4.2 to establish some very useful criteria in terms of M matrix which can be verified much more easily.

then the zero solution of Equation (4.1) is exponentially stable in the mean square, where α 1 = min 1 ≤ i ≤ N r i, α 2 = max 1 ≤ i ≤ N r i, q = 1 max i ∈ S, 1 ≤ k < + ∞ d i k + d ̄ i k e λ τ > 1. Corollary 4.2.

(ii) inf 1 ≤ k < + ∞ t k - t k - 1 ≥ μ ; (iii) for all i ∈ S, ζ i - ζ ̄ i q α 2 2 e λ τ α 1 2 - λ > ln q μ, then the zero solution of Equation (4.1) is exponentially stable in the mean square, where q = max i ∈ S, 1 ≤ k < + ∞ d i k + d ̄ i k e λ τ ≥ 1. Proof.

The variance of components 5 10 were estimated as weighted sums of the variances of the appropriate mean squares, where the variance of a mean square is given by (Ref [ 49], equ. A1.10c): VAR = (2 MS) / (N + 2)     (3) in which MS represents the mean square of the term of interest and N is the number of blocks.

The prediction coefficients are time varying and updated by minimizing the mean square error where (12).

The cost function for optimization is the normalized mean square error where the normalization factor is the multiple window spectrogram.

In the latter case, if is a pilot symbol of user with zero mean and, and represents the observations at receiver, then given by (17) minimizes the mean square error over, where is a normalizing constant chosen such that, in the minimum,.

In addition, the cell mass centroid position measurements are used to calculate the mean square displacements, MSD, where | r (t + τ ) − r (t ) | is the mean distance travelled by the cell over the time interval τ and angular brackets denote time averaging.