Sentence examples for first we remark that from inspiring English sources

First, we remark that for, (2.15) follows from Doob's inequality.

First, we remark that there exists a wide literature on capacity allocation issues in railway.

First we remark that as a straightforward extension of Lemma 2 the following lemma holds.

First, we remark that, by Theorem 2.2, inequality (2.23) is always satisfied under the conditions of our theorem.

First, we remark that inequality (4.2) becomes ∥ f n ( x ) − ∑ i = 0 n 1 i ! m i ( x ) ∥ ≤ Φ ( x ).

First we remark that if a module (M) is isomorphic to all its non-zero submodules, then (M) must be uniform.

First of all, we remark that (R_{2}(xi,eta)=1/2), by definition.

We remark that our first algorithm, while unable to provide any approximation guarantee in the general case, does yield an (O(1),O(1))-approximation for a wide set of instances.

The two networks N1, N2 are adapted from networks (a) and (b) in Jin et al. (2007b) (Fig. 10) (where we have substituted the actual names of the species by integers identifying them); we remark that the third one in the aforementioned paper and figure is isomorphic to the first one.

We remark that since the first singular function is in the space (Y_{delta}^), the second singular function imposes its order of convergence because it is the worst.

We remark that the second term on the right-hand side of the conclusion (I) vanishes when β = γ = 0.