Sentence examples for be a fundamental system from inspiring English sources

be a fundamental system of solutions of equation (3.14).

Let be a fundamental system of homogeneous equation (3.1).

Proof Let { w k ( x ) } be a fundamental system in H ( 0, 1 ), such that ( w k, w i ) = δ k, i = { 1, k = i, 0, k ≠ i.

What we have is a fundamental system problem, and it can't be solved by following the advice of business leaders and politicians and merely doing longer, harder, and with greater precision, what we've always done.

Proof Suppose that is a fundamental system of p-convex openneighborhoods of 0. Then, for any U ∈ U, there is V ∈ U for which V ⊆ V ¯ ⊆ U. Now, we claim that T C p ( V ¯ ) = T V ¯ is closed.

For linear equations this may be written as (y=C_1varphi _1(x)+C_2varphi _2(x)) where (varphi _1,varphi _2) are a fundamental system; the function field containing these basis elements is determined by the Galois group corresponding to the differential equation, details may be found in the book by Magid [15].

Hence B is a fundamental system to (3.2) and the determinant of the Wronskian matrix W ( x n ) is nonzero: det W ( x n ) = det ( v 1 ( x n ) ⋯ w m ( x n ) ⋮ ⋮ D n 2 m − 1 v 1 ( x n ) ⋯ D n 2 m − 1 w m ( x n ) ) ≠ 0 ( x n ∈ R ). (3.3).

Here, it is used that Φ−1 is a fundamental system for ϕ ˙ = − ∇ y fϕ which follows from Φ being a fundamental system for ϕ ˙ = + ∇ y fϕ.

Glycolysis is a fundamental system for energy metabolism in most organisms, and it plays an essential role in energy homeostasis and the support of cell survival [ 18].

In order to cope with greater demands on water, Asda says there needs to be a fundamental reform of systems governing land and water use but points to the difficulty of individual companies to influence complex global supply chains.

Unfortunately this may be a fundamental shortcoming of the system.