The phrase "above exists" is not correct in standard written English.
It is unclear and lacks context, making it difficult to determine its intended meaning or usage.
Example: "The information mentioned above exists in the report."
Alternatives: "mentioned above" or "stated above".
whenever the inverse above exists.
Now, the problem is whether the p k defined above exists and whether it is globally optimal (when it exists) [35].
(16) Provided the integral above exists, it is so easy to see that ( Nf ) ( 1 v ) = ( Lf ) ( v ),qquad ( Nf ) ( u 1 ) = ( Sf ) ( u ), (17) where Sf and Lf are respectively the Sumudu and Laplace transforms of f.
According to Definitions 2.1 and 2.2, it is suitable to rewrite the problem (1.1) in the following equivalent integral equation: begin{aligned} x t) =&x_{0}+h(x)+frac{1}{Gamma q }int _{0}^{t} t-s)^{q-1} t-s[-Ax(s)+f bigl(s,x(s),Gx(s)bigr)+Bu(s)bigr],ds & +sum_{0< t_{k}< t}I_{k}bigl(x bigl(t_{k}^{q-1}bigl[-Ax sd tin[0, T], end{aligned} (2.1) provided that the integral above exists.
Also, the moresca (or morisca) (above) exists in some areas in the Americas that used to be Spanish colonies Mexico, for example.
Thus, we conclude that the error-threshold as defined above exists also with high lethality of mutants.
Unfortunately, no such universal standards exist for citing quantitative data, and so all the problems listed above exist now.
The pathways outlined above exist in essentially the same form in all organisms, but metabolism in plants does have certain unique features.
All of which is a reasonable summary of those peaks that came into one filmgoer's partial view, in the course of 2011, and the choices registered above exist, by definition, to be disputed.
And if the service described above existed, there is no question I would use it.
The five benefits listed above existed long before the internet, but with the rise of digital technology, each idea can be efficiently taken to new levels of personalization.
