Sentence examples for solution pairs from inspiring English sources

The structure of the set of solution pairs of (2.4) and of (2.5) has been studied in [8].

Hence p ( N + 1 ) → p. For the uniqueness, we assume that problem (1 -(4) has two solution pairs ( p, u ), ( q, v ).

When the entire protein was then placed in solution, pairs of the coils in different parts of the long protein were coded so that the weak interactions between amino acids in the coils would draw them together.

To prove the uniqueness we consider two smooth solution pairs, say u, p and v, p 1. Let their difference be w = u − v, with initial value w 0, and let p ˜ be the difference of the corresponding pressures.

From Tables 1 and 2, we find the GNIM and the CBSN are all effective methods whose solution pairs ((u^, w^)) are also displayed in the last column of tables.

Moreover, in [16], the authors consider the radial symmetry and uniqueness of positive solution pairs ( u, v ) of integral system u = G α ∗ u p ( y ) v q ( y ) | y | β, v = G α ∗ v p ( y ) u q ( y ) | y | β. (1.6).

Hence, system (4.1) has a unique solution pair on ([0,1]).

Assume that ((lambda, x)) is a solution pair of (2.1).

Obviously, z = ( u, v ) ∈ E is a nonnegative solution pair of (1.1).

The conditions assume the existence of a strong upper and lower solution pair.

Therefore, Problem IV has a unique solution pair ((u^{hk},v^{hk})in U_{hk}^{2}).