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The option of wave-undulator based FEL might provide a valid solution in the future.
Non-real numbers are not valid arguments for models and can cause non-convergence to a valid solution in simulators.
This special operation is a valid solution in single-exposure time sensors, but not in multiexposure time sensors.
Should we increase the cell by a factor of 2, the BZ will shrink (BZ→BZ'), placing the valley outside the new BZ boundary (past X'); however, a valid solution in any BZ must be a solution in all BZs.
These experimental results reveal that our approach, compared to other approaches based only on analytical estimation models or simulations guided by e.g. genetic algorithms, not only can explore a large design space and reach a valid solution in a time-efficient way, but also can provide solutions optimizing resource usage efficiency, system traffic and processor load balancing.
That is, the joint solution composed by X1 and X2 is a valid solution (in the simple, unweighted case, this is just a union of X1 and X2).
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In order to enforces the construction of a valid solution used in ACS a new algorithm called reinforcing Ant Colony System (RACS) it is elaborated with a new pheromone rule as in Pintea and Dumitrescu (2005) and pheromone evaporation technique as in Stützle and Hoos (1997).
To the extent that she's not doing her fair share of society's workload, we might be able to address this by drafting her to perform some community-service work every month; that's a perfectly valid solution in principle.
Parallel Computing represents a valid solution for reducing execution times in simulations of complex geological processes, such as lava flows, debris flows and, in general, of fluid-dynamic processes.
Note that a chromosome produced in this manner does not in general represent a valid solution as it may have more than n 'on' genes (but not fewer).
If so, boundedness of the Nikaido-Isoda function should be taken into account so that this algorithm to a valid solution, which according to the analysis in Section 4.1 is a Nash equilibrium point.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com