Sentence examples for be explicitly expressed as from inspiring English sources

Its solution can be explicitly expressed as follows: (43) (43) (43) (43).

In fact, can be explicitly expressed as (see, e.g., [35]): (5).

end{aligned} (7) All the other components of a given singular point can be explicitly expressed as functions of the (y_{0}) component.

The dual problem of (13) can be explicitly expressed as: begin{aligned} &mathop {max }limits_{y} hspace{5pt}{sumnolimits}_{i = 1}^{N} {{g_{i}} y)} &hspace{3pt} s.t y ge 0, end{aligned} (14).

After obtaining the threshold η i, the probabilities pi,jin (11) can be explicitly expressed as p i, j = ∫ η i - 1 η i f ( x | H j ) dx, i ∈ [ 1, …, M ], j = 0, 1. (16).

Therefore, the nature of the design is to find a set of optimal parameters of the rectangular periodic grating in order to get a minimum evaluated function F. However, P q is a multi-variables function and a numerical solution, which could not be explicitly expressed as a function of the parameters above.

It can be noted that the channel gain (5) has been explicitly expressed as a function of p −k,n.

To enable efficient tailoring to specific applications during the operation phase, the variation points are not implicitly hardcoded as traditionally, but are explicitly expressed as models.

The object of the present work is the development and application of a totally general approach to optimal design of composite laminates where all the required properties for the laminate are explicitly expressed as criteria of the optimisation process.

The stress state generated in each constituent material is explicitly expressed as a function of overall applied loads by making use of a bridging matrix that correlates the stress state in the fibers with that in the matrix.

However, with the archetype approach, concepts are explicitly expressed as archetypes and can be mapped to standalone tables.