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The first asymptotic approximation of the solutions describing stationary and no stationary behavior, in the regions around the two coupled resonances, is the principal result of the authors.
Describing stationary equilibrium states with several coexisting phases in a multicomponent system is a complicated task.
A standard mathematical approach to describing stationary probability distributions in growing systems is to normalize the histogram in question by the sum of its elements (∑ p N a (p) in our case).
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It is apt to describe stationary discharges such as microwave and radio frequency plasmas.
We also describe stationary cylindrical flames of finite-extent, or 2D burning spots.
All candidate covariance functions describe stationary processes, given the inherently limited state space of relative abundances, although they differ in their temporal dynamics and in their implications for the biological systems that generate these behaviours.
In the rest of the paper, Section 2 describes stationary wavelet transform (SWT); Sections 3 and 4 explains the threshold selection and the proposed method respectively.
The autoregressive (AR) model is a parametric model used to describe stationary time series, and it is also a popular tool for EEG analysis [38].
It should be pointed out that the explanation of the stationary process ( {mathbf{u}}({mathbf{x}} + {mathbf{v}}t + {mathbf{x}}_{{mathbf{0}}},t) ) is essentially different from the commonly described stationary process.
where Ω: = {x | x ∈ ℝ n, a < |x| < b}, a and b are positive real numbers, f ∈ C1 0, + ∞) × [0, + ∞)) and g : [0, + ∞) → ℝ is differentiable. Equation 1.1 describes stationary states for many reaction-diffusion equations.
In general, the mean function of a commonly described stationary process refers to the time average of the random process, while the mean in (112) is indeed interpreted as a spatial average of the random response.
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