Sentence examples for given explicitly for from inspiring English sources

A second trustee, Michael L. Faltischek, the managing partner of Ruskin, Moscou, Evans & Faltischek, a Mineola law firm, said that Nassau officials had demanded the $20 million but that the trustees had agreed only after insisting that it be given explicitly for energy conservation.

A discrete solution is given explicitly for the inviscid Bürgers equation and the oscillatory nature of the shock profiles is determined according to the scheme order and to the shock location with respect to the mesh.

The solution to this heterogeneous problem is given explicitly, for arbitrary singularities, as a rapidly convergent Laurent series, whose coefficients are expressed in terms of those of the complex potential of a corresponding homogeneous problem with the same singularities.

The dynamic stiffness is given explicitly for uniform beams of symmetric cross-section with one bending stiffness being taken as infinite and with negligible warping stiffness, a follower external axial end force and a follower external bending end moment about the stiff cross-sectional axis.

Position arguments r, r ′, etc. are given explicitly where required for clarity, but omitted otherwise.

In order to faciliate a decomposition by pencil-and-paper, the determining systems for the coefficients of a component have been given explicitly in Sect. 2 for low values of K because they occur frequently in applications.

We present another system for which the linear evolution is given explicitly, and so all the coefficients for the conditions of the obtained results can be estimated properly.

Then, the elements,, and for, are given explicitly by using Corollary 3.5, as follows: (4.18).

In all cases, sufficient conditions for stability are given explicitly.

Although d is given explicitly, the monotonicity of it required for the existence of the inverse function is a rather general fact and can be verified as in [18, Theorem 2.1], where the continuous case was considered.

The stresses on the interface for monoclinic bimaterial are also given explicitly.