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This paper presents an affirmative answer to the heretofore unresolved question as to whether an autonomous nonlinear system can always be synthesized to possess a finite number of prescribed singular points, as well as a prescribed set of eigenvalues associated with each singular point. The answer is given in the form of a new canonic nth-order nonlinear system containing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(3n-2)</tex> single-valued functions. In the case <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n=2</tex> the canonic system is shown to possess many nice general properties which are useful for determining aspects of the system's global qualitative behavior, such as global stability.
ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTRaman study of the preparation of silica- and alumina-supported titania from titanium tetramethoxide and nitric acidMark G. Reichmann and Alexis T. BellCite this: Langmuir 1987, 3, 4, 563–567Publication Date (Print):July 1, 1987Publication History Published online1 May 2002Published inissue 1 July 1987https://pubs.acs.org/doi/10.1021/la00076a022https://doi.org/10.1021/la00076a022research-articleACS PublicationsRequest reuse permissionsArticle Views89Altmetric-Citations4LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose Get e-Alerts