Sentence examples for denotes again from inspiring English sources

A discrete form of the characteristic equation (3) is given by, where denotes again the eigenvalues as in (3) and is the eigenvector, which is assumed to be the discretized eigenfunction.

And so, users of type 2 will get a rate equal to (βPP R + β(1 - P R ))c2 for y - 2 ( ( 1 - P R ) + P P R ) β y - 1 + β ( 1 - P R ) y - 2 + ( β + 1 ) R R y - 2 of the time where y - j, j = 1, 2, denotes, again, the mean number of users of each type in the system.

Denote again (a_{n}triangleq a hcdot f u_{n}))).

Denoting again According to the last assertion of Lemmas 2.7 and 2.2, we get that (3.18).

Let us denote again by (c_j) positive constants depending only on (K).

The compacity of implies that has a strongly convergent subsequence (we denote again by ) to.

Moreover, we can choose by Theorem 4.2 a convergent subsequence (denoted again by ) with in and in.

It follows from and which are bounded and Theorem 2.1 that contains a subsequence, denoted again by, such that (326).

Up to a subsequence, denoted again as the sequence, β ˜ n ( x ) → β ( x ) for a.a. x ∈ Ω.

Therefore, there exists a subsequence of ({u_{n}}) (for simplicity denoted again by ({u_{n}})) such that u_{n}rightharpoonup u quad mbox{in } W_{p,T}^{1,2}.

We also note that for simplicity we denote again by T 1 the value of the linear functional T 1 in (4.4).