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A grid generation algorithm was used to map the solution region onto a rectangle and an upwind finite difference scheme was then used to solve the Navier-Stokes equations in terms of stream function and vorticity.

The standard PSO algorithm basically involves the following steps [31]: (1) Construct the particle to map the solution of interest problem;   (2) Create the initial topology for swarm and parameters to initial the optimization;   (3) Calculate fitness value for each particle;   (4) Renew particle position;   (5) Return to (2) until the solution satisfies the requirement of interest problem.  .

Construct the particle to map the solution of interest problem; Create the initial topology for swarm and parameters to initial the optimization; Calculate fitness value for each particle; Renew particle position; Return to (2) until the solution satisfies the requirement of interest problem.

The first issue of building up the framework is whether we could map the solution space to the "environment".

However, when using an image based prior, such as the anisotropic diffusion prior, it is convenient to map the solution into a regular grid.

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end{aligned} For the convenience, we will use the abbreviated notations V, WV, S, and WS to denote the optimal value mapping, the weak optimal value mapping, the solution mapping and the weak solution mapping for problem (2.2), respectively.

If F is a hemicontinuous and strongly monotone mapping, the solution of VIP (1.2) is unique or not?

If F is a hemicontinuous and strongly monotone mapping, the solution of VIP (1.2) is unique or not?  .

Complemented by a parameter continuation method and stability analysis, the method is capable of mapping the solution space of the wetting states and computing the energy barriers of the wetting transitions.

When someone maps the solution to a global challenge, it makes it more problematic for it to remain unsolved.

For IMRT fluence map optimization, the solution is the vector of beamlet intensities x at each beam (gantry/couch pair) that is used in the solution.

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