Sentence examples for surfaces is expanded from inspiring English sources

To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials.

To solve the dual integral equations, the jumps of the displacement across the crack surfaces are expanded in a series.

To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials.

The radiation characteristics of simulator are improved and the optimized effectively irradiation surface is expanded up to 81.6%.

To solve the dual integral equations, the jump of the displacement components across the crack surface is expanded in a series of Jacobi polynomial.

The longer sonication alters the surface polymer coating of nanotubes, and as a result of this treatment, the access of water molecules to the nanotube surface is expanded.

The observed red shift of the bands in the emission and absorption spectra of nanotubes indicates that longer sonication alters the surface polymer coating of nanotubes and as a result of this treatment, the access of water molecules to the nanotube surface is expanded.

The cranial surface is expanded dorsally and rounded medially.

However, the Sobol' indices can be computed very efficiently when the distribution of the output measure or response surface is expanded into a series of orthogonal polynomials, the Polynomial Chaos Expansion (PCE) [ 33, 34].

Numerical examples are provided To solvethe effects of material properties on the stress anduale electrintegralacequationsensithefactors.

A new trigonometric shear deformation theory for isotropic and composite laminated and sandwich plates was developed recently in Mantari et al. (2012), El and Chulkov (1973), where displacements of the middle surface were expanded in terms of tangential trigonometric functions of the thickness coordinate, and the transverse displacements were assumed to be constant across the thickness.