Moscow Mathematical Journal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mosc. Math. J.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Moscow Mathematical Journal, 2021, Volume 21, Number 3, Pages 613–637
DOI: https://doi.org/10.17323/1609-4514-2021-21-3-613-637
(Mi mmj807)
 

This article is cited in 3 scientific papers (total in 3 papers)

Grassmann convexity and multiplicative Sturm theory, revisited

Nicolau Saldanhaa, Boris Shapirob, Michael Shapiroc

a Departamento de Matemática, PUC-Rio R. Mq. de S. Vicente 225, Rio de Janeiro, RJ 22451-900, Brazil
b Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden
c Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA
Full-text PDF Citations (3)
References:
Abstract: In this paper we settle a special case of the Grassmann convexity conjecture formulated by the second and the third authors about a decade ago. We present a conjectural formula for the maximal total number of real zeros of the consecutive Wronskians of an arbitrary fundamental solution to a disconjugate linear ordinary differential equation with real time. We show that this formula gives the lower bound for the required total number of real zeros for equations of an arbitrary order and, using our results on the Grassmann convexity, we prove that the aforementioned formula is correct for equations of orders 4 and 5.
Key words and phrases: disconjugate linear ordinary differential equations, Grassmann curves, osculating flags, Schubert calculus.
Bibliographic databases:
Document Type: Article
MSC: Primary 34B05; Secondary 52A55
Language: English
Citation: Nicolau Saldanha, Boris Shapiro, Michael Shapiro, “Grassmann convexity and multiplicative Sturm theory, revisited”, Mosc. Math. J., 21:3 (2021), 613–637
Citation in format AMSBIB
\Bibitem{SalShaSha21}
\by Nicolau~Saldanha, Boris~Shapiro, Michael~Shapiro
\paper Grassmann convexity and multiplicative Sturm theory, revisited
\jour Mosc. Math.~J.
\yr 2021
\vol 21
\issue 3
\pages 613--637
\mathnet{http://mi.mathnet.ru/mmj807}
\crossref{https://doi.org/10.17323/1609-4514-2021-21-3-613-637}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85109946714}
Linking options:
  • https://www.mathnet.ru/eng/mmj807
  • https://www.mathnet.ru/eng/mmj/v21/i3/p613
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Moscow Mathematical Journal
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024