Sentence examples for order for solutions from inspiring English sources

Therefore, it is necessary that the function be well defined in order for solutions of (4.7) to exist.

In order for solutions to arise, we have to understand what causes this very human problem.

The extent of this challenge will still need to be assessed in order for solutions to be explored.

In order to calculate the hb border positions in solutions exhibited at the onset of gastrulation, we used spatial interpolation of first and third order for solutions in the shorted and full models, respectively.

Violating this principle, the linear and quadratic GCAs have the following shortcomings: (1) restrictive constraints on grid size when the viscosity is small; (2) susceptibleness to instability of a time-explicit formulation for strongly transient flows; (3) convergence deterioration to zeroth- or first-order for solutions with high-frequency modes.

Our new stabilized methods are L∞ stable, second order accurate for any smooth solution and with accuracy of order 2/3 for solutions with moving discontinuities.

In this paper, we investigate the growth of transcendental meromorphic solutions of some types of systems of complex functional equations and obtain the lower bounds for Nevanlinna lower order for meromorphic solutions of such equations.

But to prove such order of solutions for non-increasing g is an open problem.

Taking one of the solutions as an example, we compare the effects of fractional order for the solution.

In most cases the order for each solution is important.

In order for the solution to be acceptable, the exterior of the ROI has to be estimated.