Sentence examples for evolution given by from inspiring English sources

Finally, the correspondence in damage evolution given by the experimental AE data at microscopic scale and a cumulated damage variable at macroscopic scale validates the ability of both approaches to quantify the damage degree in fiber-reinforced PMCs, and to identify a critical threshold for damage initiation.

Choosing our voltage and time units in such a way that C m = g L = 1, we can summarize our approximation to the stochastic differential equation model (1.1) as the evolution given by d V = ( − V + V L + μ c ) d t + σ C d B t (1.3).

(P) The effort control problem for sentimental dynamics: Assume feeling evolution given by Eq. (1), a utility structure as described in A3, initial feeling level x 0) = x0≫1, and denote the impatience factor by ρ>0.

We now show that the partial ordering defined in Lemma 4 is indeed preserved under the evolution given by Eqs.

However, information of resistance pattern evolution given by this early alert would remain occasional, and would not provide a representative sample of the infected population.

In Fig. 10(b) we show the evolution given by both the microscopic Hamiltonian (13) and the effective model (15)–on a single plaquette including the effect of qubit decay.

The tendencies indicated by the theoretical expressions account for the evolutions given by the experimental results.

The evolution operator is obtained in the interaction picture where time evolution is given by the interaction Hamiltonian, which is the integral over space of the second term in the Lagrangian density given above: V=e\int d^3x\bar\psi\gamma^\mu\psi A_\mu and so, one has U=T\exp\left[-\frac{i}{\hbar}\int_{t_0}^tdt'V(t')\right] where T is the time ordering operator.

Let A v) ∈ G X, 1, ω), v ∈ B r and U v (t, s), 0 ≤ s ≤ t ≤ T be the evolution system given by Lemma 2.2.

Using impulsive periodic evolution operator given by us, the -periodic PC-mild solution is introduced and suitable Poincaré operator is constructed.

Damage evolution was given by {d}_i=left{begin{array}{cc}hfill frac{{leftlangle sqrt{Y_i}-sqrt{Y_0}rightrangle}_{sqrt{Y_c}} hfill & hfill if {d}_i<1hfill hfill 1hfill & hfill otherwisehfill end{array}left(i=1,2right)right., (43 where Y 0 controls the damage initiation, Y c the damage evolution.