Sentence examples for main proofs based from inspiring English sources

This entails main proofs based on a false result, which invalidates all statements.

The inequalities (4) are the base of the main proof, and we will obtain a solution of (4) in an explicit form.

The proofs of main theorems are based on the Schauder fixed point theorem (Theorem 3.1) and on the discrete Bihari-type inequality (Theorem 4.1).

In this study, a boiler turbine unit simulation model is first built in order to verify the algorithm; then the L1 adaptive control approach is presented followed by its main results and proof; only based on one group of the equilibrium working point data, the L1 adaptive controller is designed for the overall working range of the boiler turbine unit.

The proofs of the main results are based on the quadrature method and variational techniques.

The proofs of the main results are based upon the Brouwer degree theory.

The proofs of our main results are based on the Guo-Krasnosel'skiĭ fixed point theorem [28].

The proofs of our main results are based upon bifurcation theory.

The proofs of our main results are based on the following fixed point, which can be found in [10].

The proofs of our main results are based upon disconjugate operator theory and the global bifurcation techniques.

The proofs of our main results are based on the monotone iterative technique, which we present now.