Sentence examples for form a fundamental set from inspiring English sources
They are also linearly independent and therefore form a fundamental set of solutions.
If the β-Wronskian of u and v is not zero, then u and v form a fundamental set of solutions.
It can easily be verified that x k j, k = 1, 2, j = 1, 2, form a fundamental set of solutions of L 2 [ x ] ( t ) = μ x ( t ), t ∈ I. (3.2).
Based on the above-mentioned note and Theorem 3.6, we get the following: if (psi_{1}(t),psi_{2}(t),ldots,psi_{n}(t)) form a fundamental set for (3.1) and (psi_{0}(t)) is a solution of equation (6.1), then, for any solution of equation (6.1), there are unique constants (c_{1},ldots,c_{n}inmathbb{X}) such that psi(t)=c_{1}psi_{1}(t)+ cdots+c_{n}psi_{n}(t)+psi_{0}(t).
Let (psi(t)) be any solution of equation (3.1) and ({psi_{j}, 1leq jleq n}) forms a fundamental set for equation (3.1) valid in J. Then there are unique constants (c_{j}inmathbb{X}) such that psi(t)=c_{1}psi_{1}(t)+ cdots+c_{n}psi_{n}(t quad forall tin J. (3.2).
From Theorem 3.1, it follows that, if, then (1.1) has a fundamental set of solutions with, and ; if, then (1.1) has a fundamental set of solutions with, and,.
Nanotechnology is assumed to be a fundamental setting in drug delivery system and human therapeutics.
Therefore, these functions form a fundamental system of solutions of equation (3) for (lambda=lambda_{sjn}).
Systematic reviews of diagnostic test accuracy form a fundamental part of evidence-based practice [ 1, 2].
Fatty acids occur in saturated and unsaturated forms, a fundamental feature of their physical properties.
