Sentence examples for a weak trace from inspiring English sources

In [13], a weak trace on ∂ Ω of the normal component of z ∈ X p is defined.

Furthermore, in Figure 2a, a weak trace of secondary phases was observed for the sintered specimen with the Bi0.5Na0.5Zr0.7Ti0.3O3 composition.

Using a frequency trippler and appropriate external filters, we extract the third harmonic (355 nm) which is the main PL exciting component, although a weak trace of the second harmonic (532 nm) remains present in the beam.

As can be seen clearly, the diagonal elements vanish more and more as divergence grows, but a weak trace remains even at a divergence level of 85 percent.

We prove higher order perturbation formulaτ(f(H+V)−∑j= 0n−11j!djdtjf(H+tV)|t= 0)="∫Rf(n)(t dmn(t), where τ is a trace on the weak trace class ideal and mn is a finite measure that is not necessarily absolutely continuous.

Such a description provides a simple explanation of the weak trace the particles leave, Vaidman 2013.

Nevertheless, it is possible that some instances of inattentional deafness in our task involved a failure to encode the sound into memory or to consolidate a weak memory trace over the short delay incurred by preparing and making a task response, rather than a failure to perceive the sound in the first place (see, e.g., Moore, 2001).

For real valued f, when x↦∥(∇f)(x)∥d2 is integrable, there exists a constant cd>0 such that for every continuous normalised trace φ on the weak trace class L1,∞ we have φ(|[sgn(D ,1⊗Mf]|d)="cd∫Rd‖(∇f)(x)‖2ddx.

After heat treatment at 300 °C, some weak trace of porous structure on the surface of the samples could be observed.

Let H, V be self-adjoint operators such that V belongs to the weak trace class ideal.

This result extends the first and second order perturbation formulas of Dykema and Shripka, who generalised the Krein and Koplienko trace formulas to the weak trace class ideal.