Sentence examples for solutions is valid from inspiring English sources

Pellet sizes and reactor conditions under which one or more of these solutions is valid have been indicated.

The construction of these upper solutions is valid only in the case that corners are allowed in the definition.

These solutions are valid for both real and complex values of the invariants.

The cylindrical solutions are valid for an arbitrary geometry, but previous methods for computing the necessary coefficients were cumbersome.

The solutions are valid for any mode of input perturbation with non-negative and constant initial conditions.

What is new is that these solutions are valid for all values of the equation parameter q, no matter how large.

These solutions are valid when several or all species are initially present and, in the case of planar electrodes, when their diffusion coefficients are not necessarily equal.

The obtained ATET deflection solutions, verified by comparison with the numerical solutions, are valid for the entire beam length, and independently and efficiently adaptable for the very large loading conditions, and easily implementable for engineering analyses and syntheses.

Moreover, we show that the obtained approximate solutions are valid for the whole solution domain and the approximations are uniformly valid not only for small parameters, but also for very large parameters.

For this specimen SLF solutions are available only for bending with small tensile load (defined in Section 3.2.4) while classical upper bound solutions are valid for bending with large tensile load.

Physically, this restriction is due to forces between atoms in the falling body and atoms in the ground, but, as a practical matter, it is preferable to say that the solutions are valid only for z > 0 (where z = 0 is ground level).