English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The paper addresses a conjecture of Shapiro and Tater on the similaritybetween two sets of points in the complex plane; on one side is the values of$t\in \mathbb{C}$ for which the spectrum of the quartic anharmonic oscillatorin the complex plane $$\frac{{\rm d}^2 y}{{\rm d}x^2} - ( x^4 + tx^2 + 2Jx )y =\Lambda y, $$ with certain boundary conditions, has repeated eigenvalues. Onthe other side is the set of zeroes of the Vorob'ev-Yablonskii polynomials,i.e. the poles of rational solutions of the second Painlev\'e equation. Alongthe way, we indicate a surprising and deep connection between the anharmonicoscillator problem and certain degenerate orthogonal polynomials.

Exactly solvable anharmonic oscillator, degenerate orthogonal polynomials and Painleve' II