Sentence examples for be given explicitly in from inspiring English sources

In many practical problems such as engineering design problems, criteria functions cannot be given explicitly in terms of design variables.

It must be noted that the maximal solution of (4) can only be given explicitly in a few special instances.

In fact, c n,i can be given explicitly in terms of the coefficients a i, although it is not necessary for programming numerically our expansions in any algebraic or numerical software.

The idea of this paper was illuminated by [6, 7]; however, the certain constant (L_{theta}) could not be given explicitly in [7] and η only equals (1/2) in [6].

Because the positive equilibrium proportions of the subpopulations in this model cannot be given explicitly in terms of the parameters, simulations are required to measure the effects of changes to the parameter values on the behavior of the system.

The result is given explicitly in terms of the Langlands parameters of X.

The number of iterations required to achieve minimal mass is given explicitly in closed form by a formula relating the chosen unit geometry and the material properties.

The Pontryagin Maximum Principle is applied to the problem and the optimal torques are given explicitly in Serret-Andoyer's variables and their adjoints.

The standard setting concerning vibrations of lumped parameter systems is based on the assumption that the mechanical response of the elements of the system is given explicitly in terms of kinematical variables.

First, the general conditions for crack closure are given explicitly in terms of the remote loading parameters, which delimit the applicability of the conventional traction-free model for both insulating and conducting cracks.

The fundamental hypothesis of the theory proposes a unified criterion for crack extension under monotonic and fatigue loading, so that the fatigue crack growth rate is given explicitly in terms of the total plastic dissipation per cycle and the monotonic plane stress or plane strain fracture toughness of the material.