Sentence examples for using this formulation we from inspiring English sources

Using this formulation, we present explicit formulas of curves for both smooth and discrete cases.

Using this formulation, we prove the local in time existence and uniqueness of strong solutions.

Using this formulation, we have integrated the geometric parameters of the orifice and the physical properties of the fluids into the expression of εjet to establish an optimization methodology of the droplet formation in the orifice-shaped micromixer.

That is, using this formulation, we give implicit time integration methods that have no high order time step stability constraint associated with surface tension and are explicit in Fourier space.

Using this formulation, we define adjacency matrix ({{mathbf {W}}}=left( w_{ij}^{rs}right)), where begin{aligned} w_{ij}^{rs} = {left{ begin{array}{ll} 0 &quad i=j, r=s, g_{ij}^{rs}+ g_{ji}^{sr} & quadhbox {otherwise.} end{array}right.

Using this formulation, we obtain formulations for the outer and inner bounds on the SPCGS rate region using the approaches described in Section 4. The rate region for this scenario lies in a 4-dimensional space, which can be rather difficult to visualize.

By using this formulation strategy, we have successfully complexed CD22ΔE12-siRNA CD22ΔE12-siRNA polymer of PVBLG-8 to prepare a nanoscale formulation of CD22ΔE12-siRNA (Fig. 7D).

It is probably less familiar to people than Hill functions, which are generally used to describe gene regulation, but one of the advantages we found using this formulation is that it explicitly describes binding affinity of transcription factors and also has a very simple description for when you have several inputs integrated into the regulation of the gene.

Moreover, we calculate the expression for the second curvature coefficient, extending previous results using this formulation.

Very rapid simulations are achieved using this formulation.

We also present the topology optimization formulation, and some examples of optimal topologies that are obtained using this formulation.