Sentence examples for introduce the functional from inspiring English sources

In particular, we introduce the functional identities described in the introduction which are crucial in finding the functions used to express the L α. Throughout the paper, we will use the following conventions: N = { 0, 1, … } and N ∗ = { 1, 2, … } denote the nonnegative and positive integers, respectively.

Then, introduce the functional (3.10).

Let us introduce the functional as follows: (1.2).

Let us introduce the functional spaces where operators and equations are considered.

Then we introduce the functional principle of MUD and discuss MUD-based CLDs from the literature in Sect.

Under this circumstance, we introduce the functional (mathcal{J}_{lambda}:Xtomathbb {R}) by mathcal{J}_{lambda} u)=Phi u -lambdaPsi u).

In order to study problem (P), we introduce the functionals Φ, Ψ : X → R defined as follows: Φ ( u ) = 1 p ∥ u ∥ p and Ψ ( u ) = ∫ a b F ( x, u ( x ) ) d x, ∀ u ∈ X. (2.7).

To this end, this paper introduces the functional linear models and adapts it to hydrological forecasting.

This paper thus introduces the functional principle of electrically tunable lenses, setup arrangement for 3D laser microprocessing, computational simulation of system parameters and comparison with experimental results.

The mathematicians who introduced the functional, M. Fekete and G. Szegö [1], were able to bound the classical functional in the class S by 1 + 2 exp { − 2 μ 1 − μ }.

We then introduced the functional boxplots which provide bands which take into account the 'joint' distribution of the Minkowski functionals at different lags, by regarding them as continuous functions.