Sentence examples for pair of solutions from inspiring English sources

Let and be a pair of solutions to the nonhomogeneous -harmonic equation (1.1) in a domain.

This means that the solutions y and x form a normalized pair of solutions of (SLλ).

Let and be a pair of solutions to (1.3) in a domain.

Let ( u, v ) be a pair of solutions of (1.2) up to a constant, then ( u, v ) satisfies (1.3).

Let and be a pair of solutions to the nonhomogeneous -harmonic equation (1.1) in a bounded domain.

A series of norm comparison theorems for a pair of solutions to (1.6) were established in [5].

Let and be a pair of solution to the conjugate -harmonic tensor in.

It is easy to see that ((u, v in C[0, 1]times C[0, 1]) is a pair of solution to the system (1) if and only if ((u, v)) is a pair of solution of the following nonlinear integral system: left { textstylebegin{array}l} u(t)=lambdaint_{0}^{1}G_{alpha}(t, s)f s, v s)),ds, v(t)=muint_{0}^{1}G_{beta}(t, s g s, u(s)),ds.

In this regard, these two algorithms may be considered as a complementary pair of solution tools that provide the system designer with more than one option for an appropriate trade-off between accuracy and complexity.

Remarkably, these six points lie on four lines, three points on each line; moreover, each line corresponds to the radical axis of a potential pair of solution circles.

Finding the same pole in C2 and C3 gives L2 and L3, respectively; thus, all six points can be located, from which one pair of solution circles can be found.