Sentence examples for by introducing the generalized from inspiring English sources

This is made possible by introducing the generalized (2D) Hilbert transform, which is evaluated using the fast Fourier transform.

To avoid checkerboard patterns and generate edge-preserving results in topology optimization, a nonlinear diffusion technique is exploited by introducing the generalized interface energy into the objective function.

Explicit algorithms for estimating moment statistics of arbitrary order are derived, by introducing the generalized difference equation of Fokker-Planck type for the probability distribution function.

For plates with free edges, the effect of foundation medium beyond the edge of the plate has been considered by introducing the generalized shearing force concept in the analysis.

International Journal of Solids and Structures 39, 5173 5184.] is refined by introducing the generalized displacement vector and generalized stress vectors as the fundamental variables in which appropriate electrical variables are included.

We conclude this section by introducing the coupled generalized Riccati equation (GRE, for short), whose regular solvability will turn out to be necessary and sufficient for the closed-loop solvability of Problem (MF-LQ) in the next two sections.

By considering the transformations, introducing the generalized parameters, and employing a similarity parameter, comprehensive solutions are found to this problem; hence, the curves presented in the text are generic rather than specific.

We do so by introducing the notion of generalized mechanism.

By introducing the set of generalized pole directions as design parameters a compact parametric expression is derived for the closed loop denominator matrix parameterizing the state feedback controller in the frequency domain.

The authors of [25] proved some approximate fixed point theorems, by introducing the notion of generalized α-contractive maps.

We obtain the optimal order error estimates for the scalar unknown u (in (L^{2}(Omega))-norm), gradient σ (in ((L^{2}(Omega))^{2} -norm) and flux λ (in ((L^{2} -norm))^{2})-norm and (mathbflux}(operatorname{div},Omega))-norm) by introducing the Volterra-type generalized EMCVE projection.