Sentence examples for problems equations from inspiring English sources

Otherwise, let n:=n+1 and go to step 2. Since the dimensions of b k and f l are N sk d and (N_{textit {rl}}^{2}), respectively, the computational complexity of solving the QCQP problems (Equations 38 and 39 to 41) is ({mathcal O}left ((N_{textit {sk}}d)^{3}right)) and ({mathcal O}left (N_{textit {rl}}^{6}right)), respectively.

In fact, the gap functions are widely applied in optimization problems, equation problems, variational inequalities problems and others.

Note that while equation (4) is based on the heuristic CME and therefore inherits all its problems, equation (8) has no such problems: it is derived from the CME of the full network of elementary reactions, which is fundamentally correct.

The optimization problem (Equations 24 to 25) is a quadratically constrained quadratic programming (QCQP) problem [13].

The eigenvalues of the problem (Equations 1 to 5) consist of the zeros of function ω.

Then, the eigenvalues of the problem (Equations 1 to 5) are analytically simple.

The real eigenvalues of the problem (Equations 1 to 5) are bounded below.

Now, we can rewrite the considered problem (Equations 1 to 5) in the operator form as AF = λF.

The paper is organized as follows: we will describe first the problem equations as well as the CFD simulations procedure.

In particular, the problem (Equations 24 to 25) can be solved by the CVX MATLAB toolbox for disciplined convex programming [14].

Analytical sensitivities of the objective function are required and the calculation of discrete derivatives based on the differentiation of the discrete problem equations is considered.