Verb Tenses in Academic Writing

"In this paper we discuss a problem mentioned by Eliashberg in his paper [3]. He has asked if two completed Weinstein structures (X, λ ˆ0, φ0) and (X, λ ˆ1, φ1) on the same symplectic manifold (X, ωˆ) can be homotoped through Weinstein structures."

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"On Weinstein cobordisms a similar result has been proved in [7] although the Weinstein structures need to flexible."

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"The notations of recurrent, rigid and uniformly rigid operators were introduced and systematically investigated by G. Costakis, I. Parissis and A. Manoussos (cf. [5]–[6])."

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"... here, we are going to give some answers concerning this questions for C0-semigroups of operators."

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"This concept, in the context of topological dynamical systems, is known as the (uniform) rigidity, which was introduced by S. Glasner and D. Maon (see [14], [10] and [11])."

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"We will always assume that the sequences (kn) n∈N in the previous definitions satisfy lim n→+∞ kn = +∞."

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"It has been studied by many authors (see [2], [3], [12], [16], [17], [18] and [19])."

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"For the sake of brevity and better exposition, we will work only in the setting of Banach spaces." This future form states...

• a promise or fact.

• a plan.

• a deduction or prediction.

• a refusal.

"In [27] the authors showed that this minimum constraint is necessary for the finite element method (FEM) applied to the 1-dimensional acoustic Helmholtz equation."

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"Furthermore, in [27] it was shown that the H1 error bound for the solution of the FEM applied to the 1-d acoustic Helmholtz equation contains a term of the order k 3h 2 called the pollution term."

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