Sentence examples for proved based on which from inspiring English sources

Some related mathematical theorems are proved, based on which the basic ideas of the generalized wavelet-Galerkin method are described in details.

It has been proved based on Besov space norm theory.

This growth mechanism is proven based on the EDS analysis results, which indicate that the surface of the pillar is composed of Cu2O (Table 1).

In order to establish the condition of existence of subharmonic solutions for (2.1), first, we will prove the following lemmas, based on which we can get results of Theorem 1.1 and Theorem 1.2.

For the second one, we design an orientation and prove that it is Pfaffian, based on which we derive a closed-form expression for the number of perfect matchings.

Below we present a range of lemmas, based on which we prove two main theorems.

Instead, it's just providing the technology to digital ad companies and agencies, allowing them create personalized ads and optimize campaigns based on which variations are proving most effective.

We prove a unique property of single-link distance, based on which an algorithm is designed for data clustering.

We start with a series of lemmas based on which Theorem 2.1 will be proved.

Based on which criteria?

Indeed, truth values play an essential role in applications of model-theoretic semantics in areas such as, for example, knowledge representation and theorem proving based on semantic tableaux, which could not be treated in the present entry.