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This is because the problem of estimating particle size and shape (aspect ratio) from signals provided by in-line measuring tools is often ill posed, and therefore it calls for appropriate constraints to be imposed on the problem.
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The solution of this integrated optimization problem requires sensitivity analysis implying computing the derivatives of the constraints imposed on the optimization problem with respect to the design variables.
The constraints imposed on the optimization problem are shown as follows: {P}_{min}le P t)le {P}_{max } (14 where P t) is the rated active power of the BESS (MW), P min is the allowed minimum rated active power, and P max is the allowed maximum rated active power of the BESS.
This leading edge vibration can be interpreted as the inhomogeneous boundary conditions imposed on the fluid dynamic problem, and gives rise to an acoustic wave in the test duct.
A sufficient condition on the parameter λ to guarantee the existence and uniqueness of the solution is introduced by using the fixed point theorem, also a condition is imposed on the domain of the problem in order to prove the existence and uniqueness of solution for any λ.
By interpreting the solution of the scheduling problem new constraints can be imposed on the previous multi-blend problem.
Thus, we establish the sufficient optimality conditions for a proper efficiency in the multitime multiobjective variational problem under univexity assumptions imposed on the functionals constituting such vector variational problems.
The conditions are obtained as the two-scale homogenization limit of a standard acoustic problem imposed on the layer perforated by a sieve-like obstacle with a periodic structure.
The nonlinear equality constraints of the optimization problem are imposed on the condensed harmonic balance equations.
In this context, there are three factors that should be considered in formulating the numerical problem: constraints imposed on the experimental study, limitations on the data collected, and accurate replication of boundary conditions and parameterizations.
Therefore, devising network null models, carefully tailored to the topological and biochemical constraints imposed on the network, remains an important computational problem.
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