Sentence examples for basis of solutions of from inspiring English sources

It is easy to check that,,, form a basis of solutions of.

It is easy to check that x0 t), x1 t), x2 t), and x3 t) form a basis of solutions of L[x] = 0.

where m = - k 2. It is easy to check that x0 t), x1 t), x2 t), and x3 t) form a basis of solutions of L[x] = 0.

Applying the similar method to prove case 1 in Theorem 2.4, we conclude that x 0 ( t ) = e - 3 π 2 t cos π 2 t, x 1 ( t ) = e - 3 π 2 t sin π 2 t, x 2 ( t ) = e - 3 π 2 t cos π 2 t, x 3 ( t ) = e - 3 π 2 t sin π 2 t. form a basis of solutions of L[x] = 0.

This method consists of the construction of a basis of solutions for different values of this parameter.

Preliminary assignments were carried out on the basis of solution chemical shifts and on the basis of the computed shielding constants obtained for the fully optimized structures of (1) and (2), as described in §2.3 point (i).

On the basis of positivity of solutions in Theorem 1, we have frac{partial u x,t)}{partial t}-d_{1}Delta u x,t leq u x,t) bigl( 1-u x,t) bigr)quad mbox{for } (x,t)inOmegatimes[0,+infty). Then we can estimate the upper limit of (u(x,t)) due to the standard comparison principle: limsup_{trightarrow+infty} u(x,t) leq 1-u x

This concept is, in fact, the basis of separation of solution components by using equilibrium dialysis.

In their study, the researchers asked eight advanced physics doctoral students classified as "experts"—and eight undergraduates who had completed an introductory course in mechanics classified as "novices"—to sort 24 physics problems on the basis of similarity of solution.

Results are presented in terms of pressures, strains and loads and an interpretation of the measured data on the basis of theoretical solutions of the problem is provided.

Values of k1 and k−1=k1Keq−1 are determined on the basis of numerical solutions of both the Smoluchowski equation and the classical diffusion equation coupled to a jump condition.