Sentence examples for and the first relation from inspiring English sources

Remark 3.1 H = ( H 00 J ∗ = ( H 0 J ∗ follows from (3.3) and the first relation of (3.8) in the special case that a = − ∞ and b = + ∞.

Since the even part of an odd function is equal to zero, using (2.3) and the first relation of (2.4) and Lemma 2.3 we get a_{20}=0,qquad b_{11}+a_{02}=0.

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

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

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).

Suppose that (3.5), the first relation of (3.2) and the second relation of (3.8) are satisfied.

The octave and the fifth relation tests are similar, the only difference among them is the relation between the notes involved and the thresholds.

It follows from (8) and the second relation of condition (7) that all the eigenvalues of D F ( O ) have absolute values larger than 1 in norm.

end{aligned} (3.3) By the invertibility of B, the first relation of (3.3) implies (y=nu B^{-1}x-B^{-1}Ax), and inserting it into the second relation yields begin{aligned} nu^{2} B^{-1}x- nu B^{-1}Ax+A^ bigl(nu B^{-1}x-B^{-1}Ax bigr -Cx=0.

So, the first relation of (3.4) holds.

The first relation immediately follows from (10.1) with Definition 8.1.