Sentence examples for above assertions from inspiring English sources

According to the strict convexity of f, we conclude the above assertions.

By the relationship of the derivative and the monotonicity, the above assertions obviously hold.

Since, we can replace by in the above assertions to obtain a minimal element in the sense, where ia defined here as (2.3).

Based on the above assertions, we have used SD = 1.2 to define the ceiling at which all of the hereditary variance has been explained in our simulation work.

Then, they analyse matrices (10) and (15) obtained after elementary row transformation from (9) and (14), respectively, to show that all the eigenvalues of (9) and (14) are negative from which they concluded the above assertions of their theorem.

Update: A representative of Blackstone contacted us to deny the above assertion that the Blackstone I.P.O. was a "cash-out".

It simply demonstrates that the data suggest that such a large tax increase will almost certainly cause private equity investment to fall relative to what it otherwise would have beenI am fine with the above assertion.

This proves the above assertion.

In this case, the above assertion holds.

From the above assertion, we know that (= has only isolated zeros for. As, we have, a contradiction with (4.2).

The slight increase in the lifetime of the dominant component further supports the above assertion that the excited state is somewhat stabilized through interactions with the Pluronic P123 molecules of the mesostructure (Figure 4).