Sentence examples for a theorem based on from inspiring English sources

For 2,000 years following Euclid, mathematicians attempted either to prove the postulate as a theorem (based on the other postulates) or to modify it in various ways.

A theorem based on Routh–Hurwitz stability criterion is proposed that gives a triple inequality to determine the stability region of PD controller and consequentially, the stability of coning motion.

We prove that the expected value of the first return time is finite and, using a theorem based on return times, derive the upper part of claim \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b $$\end{documentt} (b ).

The stable design of Takagi Sugeno Kang fuzzy controllers is guaranteed by means of a stability theorem based on LaSalle's global invariant set theorem formulated for a class of multi input-multi output (MIMO) nonlinear processes.

By some spectral theorems and a continuation theorem based on coincidence degree, we not only obtain some new sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic solution but also estimate the exponentially convergent rate.

Some new sufficient conditions for ascertaining the existence and global exponential stability of the periodic solution of such BAM neural networks are obtained by using the properties of nonsingular M-matrix, integral inequality analysis and a continuation theorem based on coincidence degree.

Then, a chaotification theorem based on the snap-back repeller theory for maps is established.

By using a continuation theorem based on coincidence degree theory, they obtained sufficient criteria for the existence of periodic solutions for the system.

By using a continuation theorem based on coincidence degree theory, we obtain suffcient criteria for the existence of periodic solutions for the system.

In this paper, with the help of a continuation theorem based on Gaines and Mawhin's coincidence degree theory, we study the existence and multiplicity of periodic solutions of a ratio-dependent food chain model with exploited term(s).

We first present a universal function approximation theorem based on a fuzzy dynamic model.