Sentence examples for in the first relation from inspiring English sources

With respect to the parity of power in the first relation, we obtain by a sign discussion of terms in the other relation a set of conditions equivalent to (20) as | a h | < 1, b > 0, a < − b, a h < − 1, b > 0, b h < 1 (21).

The commutator in the first relation gives an automorphic mapping in time of the operators: A ˆ (t, x ˆ, p ˆ ) = A ˆ (x ˆ (t ), p ˆ (t ) ) exactly as in the classical case, Eq. (4).

In addition, the first relation of (3.4) directly yields that H ⊂ H 00 ∗.

and hence, since is bounded in and converges pointwise in to the trivial function, we deduce, from the second relation in(2.23) and(2.24), that which contradicts the first relation in(2.23).

Proof 1 If then due to the last relation in Equation 5 and according to the first relation in Equation 5: (7).

and, hence, the first relation in Eq. (19), where k is substituted by k + 1, is proved.

The substitution of the first relation (2.12). in the second of (2.11) gives (2.13).

Let us now consider the second relation in (19).

From the second relation in, we obtain that (3.17).

By the definition of, the second relation in (4.23), and, we get (425).

Analogously, it is obvious that the second relation in (4.15) holds.