Improved fewnomial upper bounds from Wronskians and dessins d\u27enfant [PDF]
We use Grothendieck\u27s dessins d\u27enfant to show that if $P$ and $Q$ are two real polynomials, any real function of the form $x^α(1-x)^β P - Q$, has at most $°P +°Q + 2$ roots in the interval $]0,~1[$.
Hilany, Boulos El, Tavenas, Sébastien
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LACUNARY WRONSKIANS ON GENUS ONE CURVES
, 2008 . Let X be a nonsingular projective curve of genus one defined over an algebraically closed field of characteristic 0. Let D be a divisor of X of degree n> 1 and let O be a (closed) point of X. As is well known, there exists a unique morphism φD,O: X →
Greg W. Anderson
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A Remarkable Wronskian with Application to Critical Lengths of Cycloidal Spaces
, 2019 International audienceRecently, Carnicer et al. (Calcolo 54(4):1521–1531, 2017) proved the very elegant and surprising fact that half of the critical length of a cycloidal space coincides with the first positive zero of a spherical Bessel function. Their
Mazure, Marie-Laurence +2 more
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Wronskians as N-ary brackets in finite-dimensional analogues of sl(2)
The Wronskian determinants (for coefficients of higher-order differential operators on the affine real line or circle) satisfy the table of Jacobi-type quadratic identities for strong homotopy Lie algebras - i.e. for a particular case of L∞-deformations -
Kiselev, Arthemy V.
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On two dimensional Schrödinger operators
, 2023 Following the works of Berest, we compute explicitly Hadamard's coefficients for two dimensional Schrödinger operators.
Gaillard, Pierre
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From finite-gap solutions of KdV in terms of theta functions to solitons and positons
, 2010 We degenerate the finite gap solutions of the KdV equation from the general formulation in terms of abelian functions when the gaps tends to points, to recover solutions of KdV equations in terms of wronskians called solitons or positons.
Gaillard, Pierre
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Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions. [PDF]
Philos Trans A Math Phys Eng Sci, 2014 Berkolaiko G, Weyand T.
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Some integrability results for wronskians in gravity and supersymmetric gauge theories
In this thesis we study the Confluent Heun equation (CHE) with quantum integrability methods, with particular focus on the relevant wronskians solving it’s monodromy problem.
Nervo, Alessandro
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A geometric method for eigenvalue problems with low-rank perturbations. [PDF]
R Soc Open Sci, 2017 Anastasio TJ, Barreiro AK, Bronski JC.
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Laws of composition of Bäcklund transformations and the universal form of completely integrable systems in dimensions two and three. [PDF]
Proc Natl Acad Sci U S A, 1983 Chudnovsky DV, Chudnovsky GV.
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