Sentence examples for small parameters and from inspiring English sources

The approximate symmetry reduction approach can be used to search for similar results of other perturbed nonlinear differential equations with small parameters, and it is worthwhile to summarize a general principle for the perturbed nonlinear differential equations holding analogous results.

The multiscale noise tuning SR (MSTSR), which breaks the restriction of the requirement of small parameters and white noise in classical SR, has been applied to identify the characteristic frequency of a bearing.

First, we characterize the amplitude of the mismatch with large parameters and in order to characterize the deviation for the system setup described in Section 3. In a second step, we evaluate the end-to-end performance and the mismatch for small parameters and.

By expanding in these small parameters, and assuming Gaussian distributions for each source of variability, the authors obtain analytic expressions for the n-fold covariance of the voltages of each cell in the network, as well as (asymptotically) the covariances of the firing rates.

The variances of the random effects had an inverse Gamma prior with small parameters and a uniform prior was used for the fixed intercepts : p σ 2 ~ Γ - 1 ε, ε p β ∝ 1 ε = 0.001.

where,,,,, is a small parameter, and is a strictly increasing sequence such that.

where is a small parameter and has a desired smooth scalar function on its arguments.

(1.2) where α is the factor of influences, σ is a small parameter and (I_{c}) is a critical level.

Theorem 4.1 Let Y, X be Banach spaces, ε ∈ R be a small parameter and η ∈ R 2 d.

where x, y, z ∈ ℝ, μ ∈ ℝ is the bifurcation parameter, ε is a small parameter and f1, f2 and g are O(1) smooth functions.

The method proposed in this article does not depend on a small parameter and therefore can overcome the disadvantages and limitations of perturbation expansions with respect to the small parameter.