We will consider new Weyl-type estimates for the counting function:NEc, ρ= {k∈N/|Ek−E|⩽ρℏ}.
We obtain estimates for the counting function of the Neumann Laplacian on a planar domain bounded by the graph of a lower semicontinuous L1-function.
To support efficient implementation, a computationally convenient hypergeometric approximation is developed for the counting distributions appropriate to our underlying stochastic model.
Although this detector was designed primarily for imaging applications [21, 22] and has an 11 × 11 anode readout scheme, it provides the large detection volume required for the counting application developed here.
This result, together with Berezin's inequality, allows us to obtain a refined version of the Li Yau estimate for the counting function of the Dirichlet Laplacian which implies the Li Yau estimate itself and, at the same time, the asymptotic results obtained by the variational method.
Additionally, a starting number of 400 was chosen for the counting task such that counting would happen in the range of three-digit numbers.
A Z-series Coulter Counter (Coulter Corp., Miami, FL, USA) was used for the counting.
For the MTT- and crystal violet assay, cells were treated in 24-well plates for 5 days, whereas for the counting cell numbers were determined at designated time points.
For determining the tumours cellularity and the counting of the number of cells expressing the cleaved caspase 3, three pictures were taken randomly from each sections and from each level and were used for the counting.
Implement national standards for the counting of provisional ballots.
This year the population gathered anxiously for the counting of the votes.
