Several examples illustrate that this spectral inclusion may be considerably tighter than the one by the usual numerical range or by perturbation theorems, both in the non-self-adjoint case and in the self-adjoint case.
In the proof of Theorem 3.1, a new integral inequality, called a Wirtinger-based inequality, is employed to bound the derivative of LKF, which was proposed in [6] and was shown to be tighter than the one employed in [26].
This bound is therefore tighter than the one found employing μ analysis or global/hybrid optimization methods.
Numerical examples are given to illustrate the effectiveness of the obtained results, and reachable set bound is tighter than the ones in [1 4, 6 8].
From Tables 1 and 2, we know that the proposed result in Theorem 2 is tighter than the ones in references [22, 27].
Namely, as long as the actual consecutive study design ensures large enough overlapping (7 years out of 10 in the current example) that the re-sampling confidence intervals are significantly tighter than the ones resulting from the traditional approach, the proposed method may be regarded as meaningful and preferred.
"Tight, Dan, tight," one man yelled.
CONS: The second bedroom would make a lovely child's bedroom, but might feel tight for more than one child.
To apply the QP method, Eq. 16 is changed to linear inequality constraints that are tighter than the original one as follows.
Parameter γ is small enough so that the σ reset mechanism is not entirely completed: σ starts increasing again from a value much greater than σ 0. Hence, a second episode of synchronization occurs few minutes later (at minute 23) and the corresponding synchronization is tighter than the preceding one, with the calcium peaks occurring in a time interval of 25 second length.
