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Remark (1) α 1 = α 2 = ⋯ = α d = 1 2 case: Let { X n, n ∈ Z + d } be a strictly stationary associated random field with E X 1 = 0 and E X 1 2 < ∞.
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As a novelty, the present research exploits the combination of time and frequency domain features, to deal with the inherent non-stationary associated to the electrical anomalies, with the goal to improve the performance of the ANN and to make feasible the integration in an smart meter.
For example, Xing et al. [4] consider a strictly stationary negatively associated sequence of random variables.
It is also shown that there is a unique stationary distribution associated with each admissible control.
To conclude this example, we calculate the stationary distributions associated with each of the two policies the uncoded and the coded one.
The steady state probability density function, the characteristic function and the second order moments of the stationary solution associated with an explicit invariant measure are explicitly constructed.
If (V_{2}=0), system (1.1) is the Kirchhoff equation, which is the stationary problem associated to the time-dependent problem, which models small vertical vibrations of an elastic string [2].
But, as the model is of hyperbolic type and the run of the characteristics crucially depend on the physical parameters, the existence regimes of the stationary solutions associated to certain boundary conditions turn out to be limited.
To test the hypothesis that the seismicity in each of the subareas is stationary Poissonian associated with time, we quantitatively evaluate the discrepancies between the observed frequency distribution and the expected Poissonian distribution by the ×2-test (e.g., Gardner and Knopoff, 1974; Wyss and Toya, 2000).
The flow of the components of stress fibers away from the stationary FAs associated with their tips suggests that stress fibers grow at these tips.
Black nodes represent stationary nodes associated with a location, and are included in this graph for illustrative purposes only.
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CEO of Professional Science Editing for Scientists @ prosciediting.com