Hence, there exist in and such that, and.
Then, is a decreasing and bounded below sequence, and hence there exist such that.
So is a Cauchy sequence in complete metric space, hence there exist such that.
Since is a generalized concave operator, hence there exist real numbers, such that.
To prove the necessity, let and let be defined by for all Let be such that Then and hence there exist and a neighborhood of in such that for all with.
We assume a maximal throwing range and a maximal lay-down time, hence there exist (y_{mathrm{max}}> 0) and (t_{mathrm{max}}>t_{mathrm{min}}> 0) such that p_{0} x,y,t) = 0 quad text{for } |y|> y_{mathrm{max}}, t notin[t_{mathrm{min}},t_{mathrm{max}}].
In this regard, the Tibeto-Burman speaking populations inhabiting the easternmost tip of northeast India, Arunachal Pradesh, (sharing the international border between India and Bhutan, Tibet, Myanmar) were hardly dealt with and hence there exist a dearth of population genetic studies in this region [21] [24].
In fact, when is sufficiently small and is sufficiently large, we have η k > 0; and when is sufficiently large and is sufficiently small, we have η k < 0. Hence, there exist, and such that η k and Z k have the same sign, regardless of Z k > 0 or Z k < 0. The proof for and is similar.
Hence, there exist interoperability problems among them.
Hence, there exist special compensation acts or constitutional clauses providing for compensation.
Hence, there exist N subintervals.
