Sentence examples for many linear and from inspiring English sources

The main revolution in the existence theory of many linear and non-linear operators happened after the Banach contraction principle.

The main revolution in the existence theory of many linear and nonlinear operators happened after the Banach contraction principle [1].

For this reason, many linear and nonlinear methods for vector size reduction are applied (PCA, LDA, ICA,...).

The variational iteration method (VIM) can be usefully applied for solving many linear and nonlinear scientific and engineering problems.

Variational inequalities have become important methods to analyze many linear and nonlinear problems; see [1] and [2], such as linear complementarity problems in [3], convex optimization in [4], imaging problems in [5], etc. Classical variational inequalities were introduced by Hartman and Stampacchia in the 1960s; see [6] and [7].

Although many linear and non-linear non-increasing functions can be chosen as f(x i ), considering the practicality of the proposed method, we used f(x i ) = 1/| β i |, where β i is an importance index of variable x i.

TIRs appear to be a common characteristic not only of mitochondrial genomes but of many linear eukaryotic and bacterial plasmids as well (Meinhardt et al. 1990 , 1997 and have been proposed to be a solution to the end-replication problem for linear mitochondrial molecules (Dinouel et al. 1993; Vahrenholz et al. 1993).

Many linear alkanes and four trimethylsilylated metabolites, which had retention times of 10.68, 13.19, 15.33 and 18.07 min were identified as 1, 2-benzenediol, benzoic acid, 1,2-benzenedicarboxylic acid and phthalic acid, respectively (Fig. 7).

The linear wave equation represents the basis of many linear electromagnetic and acoustic propagation problems.

The "Boat" is a kind of image which contains many linear edges and curve singularities.

The results of many linear, nonlinear and heuristic techniques that can enhance design ability to minimize the total cost of road construction using many different variables are well acknowledged.