Sentence examples for solution boundary from inspiring English sources

The nonexistence of a positive solution boundary value problem for a class nonlinear fractional difference equations with 3 < α ≤ 4 is considered in terms of parameter.

The semi-suspended bio-carrier caused three different mass transfer zones occurring in the bioreactor, including the zones of bulk solution, boundary layer and biofilm, in which, the boundary layer zone had an obvious higher mass transfer resistance.

The proposed method operates on a dataset of scattered nodes that are placed within the solution domain and on the solution boundary, forming a small RBF collocation system around each internal node.

Depending on the precise situation and on the regularity required of the solution, boundary conditions at just one or both endpoints of the free surface need to be imposed.

Fig. 4 a Formation of nanowires at solution boundary, b entrapment of nanowires through activation of donut-shaped clamp, c close-up of trapped nanowire under donut clamp, d nanowires stay in position after careful deactivation of clamp under non-flowing conditions, e highlighting different sizes of nanowire bundles achievable by use of various clamp shapes.

The methods discussed in [ 37] and [ 38] assess the curvature of the solution boundary, which is used in an analytical correction formula to estimate the magnitude of the shifted bootstrap distribution.

This procedure runs until all solutions are located in solution boundaries.

The extended picture in (a) depicts the bubble-solution boundary indicating the process by which fine particles were attracted to the bubble surface.

Therefore, previous studies mainly focus on the one-electron reduction reactions between different oxidation states of transition metals to avoid modeling of an electrode-solution boundary [18 20].

Furthermore, the dependence of precipitation rates on ion transport across the solid-solution boundary should also be a function of the ion ratio.

The partial solutions (boundaries) are exchanged using built-in functions of the MPI.