Sentence examples for provided for the case from inspiring English sources

For illustration, detailed calculations are provided for the case of two (n = 2) contact zones.

An algebraic proof is provided for the case of arbitrary number of connections.

Experimental validation of the predictions is provided for the case of zero mean flow.

Specialized conditions are provided for the case of time-dependent quadratic IDSs with prescribed resetting times.

The specific theoretical results are provided for the case of generalized Gaussian host and noise.

The analysis of equations has been provided for the case of discontinuous axial magnetic field on flex's boundary.

Asymptotic estimations of the main solution elements are provided for the cases of small and large toughness.

Special contact conditions are also provided for the cases where the triple junction mobility is infinite and/or in the case of one of the grain boundaries having zero mobility.

Furthermore, optimal controls were obtained and studied over each information class, while simulation and numerical results are provided for the cases where user interest is low and diffusion needs boosting to improve the efficiency of useful information spreading.

The general methods used to complete measurements of human exposures are identified and illustrations are provided for the cases of indirect and direct methods used for exposure analysis.

Theoretical results, based on one-dimensional elastic wave theory, are provided for the general case as well as for cases of piecewise constant characteristic impedance.