Here it may be pointed out that the different terms, namely, uniformly k-Lipschitzian semigroups of self mappings, uniformly G1-Lipschitzian semigroups of self mappings, uniformly G2-Lipschitzian semigroups of self mappings, uniformly G3-Lipschitzian semigroups of self mappings, and uniformly k-Lipschitzian semigroups of self mappings are adopted to facilitate the statements of our results.
In summary, the models facilitate quantitative statements about the spacer dynamics of microbial communities.
He threatens the owners of newspapers with reprisals by the federal government, talks of changing libel laws to facilitate lawsuits for statements which affront him, proposes revoking FCC licenses for media which ruffle him.
In such cases, accurate quantification of uncertainty to allow discriminating among treatments is vital to facilitate realistic probabilistic statements about, say, cost-effectiveness relative to the alternative treatments.
At the other extreme, the invention of category theory facilitated the statement and proof of very general results about algebraic structures that automatically apply to a whole range of such.
The proposed results are generalized for two- and three-dimensional filtration models in reservoir engineering using vertical and horizontal wells, which greatly facilitates the statement and development of simulation and optimal control methods for reservoir engineering in general (see Akhmetzyanov (2008a,b)).
(It is actually conventional to assume the row degrees are in ascending order; however, the difference is immaterial, and the choice of descending order facilitates the statement of certain results later).
The weekly evaluation finally included half-standardized interviews in order to clarify the former statements and facilitate their explication in a content analysis – described in detail below.
To map a docking calculation onto a GPU, we had to write several CUDA kernel functions, which describe the processes executed on the GPU, as well as adding statements to facilitate data transfer between the host and the accelerator.
The ranking of individual opinions about the statements facilitates the formation of individual viewpoints about the overall subjective question to which the sample statements referred.
