Sentence examples for present the first theorem of from inspiring English sources

Now we present the first theorem of this article.

Now we are ready to present the first theorem by using the classical representation of solution (2) derived by Khusainov et al. [2].

The strict mathematical conditions of the first theorem of welfare economics never hold in practice.

The first theorem presents conditions for the validity of inequality (6) for only non-negative sequences.

The following theorem presents the second inner bound.

Before we can present the proof of Theorem 2, we need the following auxiliary result.

□ In this final section we present the proof of Theorem 3.

For the first incompleteness theorem, Q is sufficient; for the standard proofs of the second theorem, something like PRA, at a minimum, is needed.

We present the following theorem showing the privacy property of Algorithm 1. Theorem 3 Algorithm 1 guarantees ϵ -differential privacy.

Now, we will give the first main theorem of the present paper on the stability of difference scheme (2).

A description of strategies, a high-level description of the algorithms, a description of the applications to operator, matrix, and linear system engineering theory, and a description of how one would use a strategy to "discover" four different theorems are presented in the first part of the paper.