Sentence examples for for wide class from inspiring English sources

It is well-known that for wide class of of fractional-order derivatives the integration by parts transforms the left-sided derivatives into the right-sided and vice versa.

For example, the Grünwald-Letnikov derivatives coizncide with Marchaud derivatives for wide class of functions (see Sections 20.2 and 20.3 in [23]), and the Marchaud derivatives are connected with the Liouville derivatives (see Section 5.4 in [23]).

For wide class of functions φ r,t) from the Lizorkin space [11] for example, Eq. (27) can be represented in the form rho, {D^{2}_{t}} varphi (textbf{r},t) + sum^{N}_{j=1} A_{j},^{RT}mathbb{D}^{alpha_{j}}_{j} varphi (textbf{r},t) = - frac{partial V varphi)}{partial varphi}.

Moreover, new results on the robust global exponential state predictor design problem are provided, for wide classes of nonlinear systems.

Representations or predictions of stiffness variations for wide classes of polymers (thermosets, thermoplastics, amorphous, semi-crystalline, filled, unfilled, linear, crosslinked, etc).

The parameters of response distributions can themselves be parameterized to provide dependence on explanatory variables, thus leading to regression formulations for wide classes of models.

The theory may provide a basis for developing a group-contribution method of estimating thermodynamic properties for wide classes of adsorbed mixtures from limited experimental data, similar to familiar methods for liquid solutions.

In this paper we obtain essentially sharp generalized Keller Osserman conditions for wide classes of differential inequalities of the form Lu⩾b(x f u ℓ(|∇u|) and Lu⩾b(x f u ℓ(|∇u|)−g u h(|∇u|) on weighted Riemannian manifolds, where L is a non-linear diffusion-type operator.

The examples above describe general grammatical rules that hold for wide classes of word pairs.

The IRKHSM is very powerful and accurate in obtaining approximate solutions for wide classes of the problem.

This can be remedied by hybridization, that is, hybridization of modal logics enables the formulation of uniform tableau, Gentzen, and natural deduction systems for wide classes of logics.