Sentence examples for by solving the quadratic from inspiring English sources

The optimum values of the selected variables were found by solving the quadratic regression model and analyzing the response surface plots.

The optimum values of the selected variables were obtained by solving the quadratic regression model, as well as by analysing the response surface contour plots.

Calculation of the degree of crystallinity by solving the quadratic in the SAXS invariant gave good agreement with the WAXS result.

By solving the quadratic regression equation using appropriate statistic methods, the optimum concentration values for obtaining 876.32 μg extracellular polysaccharide per milliliter of cultivation medium were determined: yeast extract 6.0 g l−1, fructose 11.5 g l−1, magnesium sulfate 0.5 g l−1, maltose 9.6 g l−1, zinc chloride 38.6 mg l−1 and initial pH value 5.3.

By analyzing response surface plots and corresponding contour plots and by solving the quadratic equation, experimental values were shown to be significantly in agreement with predicted values, since the adjusted determination coefficient (R2Adj) was 0.9752 and the level of significance was P < 0.0001.

In the proposed controller design, process nonlinearities are accounted for by the set of local models obtained on-line by the JITL technique and the optimal control actions are obtained by solving the quadratic optimization problem formulated in the GPC design framework.

The feedback filter coefficients are then obtained by solving the constrained quadratic minimization problem (45) as (48).

The parameters of the optimal hyperplane and the optimal shifts can be found by solving the following quadratic programming problem: (13).

By solving the above quadratic programming problem, the SVM tries to maximize the margin between the data points in the two classes and to minimize the training errors simultaneously.

One may be able to get f by solving the following quadratic equation system F_{1} - F_{2} = left(s_{1} - s_{2}right)f + (r_{1}-r_{2})X = s^{prime}f^{prime} + r^{prime}X.

The coefficients α i are obtained by solving the following quadratic optimization problem: L α = ∑ i = 1 N α i − 1 2 ∑ i = 1 N ∑ j = 1 N α i α j y i y j K ( y i, y j ) (6). subject to two constraints given in (6) and (7):, i = 1, …, N (7) ∑ i = 1 N α i y i = 0 (8).