Sentence examples for for any modes from inspiring English sources

While the molecular vibrations span a wide energy range, we seek to understand whether strong electron phonon coupling exists for any modes having energy similar to the energy difference between peaks 1 and 2 (0.2 eV), as well as between peaks 2 and 3 (0.22 eV).

The solutions are valid for any mode of input perturbation with non-negative and constant initial conditions.

The solution is valid for any mode of input perturbation with non-negative and constant initial conditions, and for continuous and semi-batch operations.

The generalized force for any mode is formulated by assuming a distribution of the wind force power spectral density (PSD) along the structural height, and employing the base moments measured from HFBB wind tunnel tests.

There is no average energy flux from span to span for any mode defined by a real eigenvector, and we infer that zero-energy transfer between spans is a characteristic of the resonant response of the system to a stationary vibrating source located on some particular span.

However, the protocol guarantees complete flexibility to opt for any mode of communication.

Because all modes of operation specified by the IEEE-802.16e standard use the same intercarrier spacing [21], it follows that the curves in Figures 2 through 7 are in fact valid for any mode of mobile WiMAX transmission.

For any mode i ∈ S, the parameter uncertainties considered here are norm-bounded and of the following forms: ( Δ C i j ( t ) Δ D i j ( t ) ) = E i j F ( t ) ( H i j M i j ), ∀ i ∈ S.

For any mode i ∈ S, the parameter uncertainties considered here are norm-bounded and of the following forms: ( Δ C i j ( t ) Δ D i j ( t ) ) = E i j F ( t ) ( H i j M i j ), ∀ i ∈ S. (2.1).

where positive scalars α ̲ i, α ¯ i satisfy α ̲ i I ⩽ P i and α ¯ I ⩾ P i for any mode i ∈ S, scalars γ = 1 min i ∈ S { α ̲ i } ( max i ∈ S { α ¯ i } + λ max Q ) > 0, β > 0. Therefore, we can see by (3.13) and Definition 2.1 that system (1.6) is global stochastic exponential robust stability in the mean square.

For any mode r ( t ) = i ∈ S, we assume that C i j, D i j are real constant matrices of appropriate dimensions, and Δ C i j, Δ D i j are real-valued matrix functions which stand for time-varying parameter uncertainties, satisfying C i j ( t ) = C i j + Δ C i j ( t ), D i j ( t ) = D i j + Δ D i j ( t ).