The lower semicontinuity says that begin{aligned} P_n overset{s}{rightarrow } P_infty Rightarrow dim {mathrm{ran}}, P_infty le liminf dim {mathrm{ran}}, P_n end{aligned} (3.31 Kato was well aware that equality might not hold on the right side of (3.31) for examples of relevance to physics—a main example that he mentions is the Stark effect where the right side is infinite.
I now give some typical examples of relevance to the study of aging.
As an example of the relevance of northern studies for the 21st century, Senkpiel cites the American government's current plans to open up 1.5m acres of the coastal plain of the Arctic National Wildlife Refuge to oil and gas leasing and exploration.
No one can deny that Vogue is a vivid example of maintaining relevance in print, with great writing and a monthly display of the visual power of the medium.
This large offset is a strong example of the relevance of temperature-dependent thermal conductivity.
There is doubt expressed in the literature as to whether this sequence does converge strongly (cf. [[27], Example 4]) for an interesting example of possible relevance.
This example of industrial relevance will serve to evidence the progress made in computer modeling in recent years, but also to bring up aspects that need to be further improved, such as the use of LBM to simulate efficiently turbulent flow and heat and mass transfer in this type of structured catalytic reactors.
We now present numerical results assessing the performance of HCoSaMP in reconstructing signals characterized by the NAP; we both investigate the case of signals compressible in the DWT domain and the interesting case of signals compressible in the so-called graph-based transform domain, among which the texture images stand as an example of paramount relevance.
But this is only one example of the relevance of fantasy to the modern world -- and how strange I should find myself defending the importance of stories about dystopias and the evils of power gone wrong at a time when the American government has shut down over the question of whether or not, in essence, the poor deserve to have access to affordable healthcare.
Cigarette smoking represents a good example of the relevance of an environmental toxin to mitochondrial function.
