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It is evident from the correlation that gas hold-up is strongly function of modified gas Reynolds number and independent of liquid Reynolds number.
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If is a strongly sublinear function, then (2.1).
If is a strongly superlinear function, then every solution of (1.1) oscillates if and only if.
If is a strongly sublinear function, then every solution of (1.1) oscillates if and only if.
Then, is a strongly pseudoinvex function with respect to the same and on.
Thus, is a strongly pseudoinvex function with respect to the same and on.
(d) If is a strongly sublinear function, then every solution of (1.1) oscillates if and only if .
(b) If is a strongly superlinear function, then every solution of (1.1) oscillates if and only if .
Recall the generator of a solution operator if there exist and a strongly continuous function such that and,,.
Let I be some interval of real numbers and let (fin C^{1} [Itimes I, I]) be strongly increasing function.
Let denote the class of strongly convex functions, which satisfies.
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