Regularising Transformations for Complex Differential Equations with Movable Algebraic Singularities [PDF]
Mathematical physics, analysis and geometry, 2022 In a 1979 paper, Okamoto introduced the space of initial values for the six Painlevé equations and their associated Hamiltonian systems, showing that these define regular initial value problems at every point of an augmented phase space, a rational ...
T. Kecker, G. Filipuk
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Differential Equations for Approximate Solutions of Painlevé Equations: Application to the Algebraic Solutions of the Painlevé-III $({\rm D}_7)$ Equation [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2023 It is well known that the Painlevé equations can formally degenerate to autonomous differential equations with elliptic function solutions in suitable scaling limits.
R. Buckingham, P. Miller
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On the Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry [PDF]
, 2021 This paper presents the relationship between differential algebra and tropical differential algebraic geometry, mostly focusing on the existence problem of formal power series solutions for systems of polynomial ODE and PDE. Moreover, it improves an approximation theorem involved in the proof of the fundamental theorem of tropical differential ...
Boulier, François +3 more
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Elliptic K3 surfaces at infinite complex structure and their refined Kulikov models
Journal of High Energy Physics, 2022 Motivated by the Swampland Distance and the Emergent String Conjecture of Quantum Gravity, we analyse the infinite distance degenerations in the complex structure moduli space of elliptic K3 surfaces. All complex degenerations of K3 surfaces are known to
Seung-Joo Lee, Timo Weigand
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Smoothly splitting amplitudes and semi-locality
Journal of High Energy Physics, 2022 In this paper, we study a novel behavior developed by certain tree-level scalar scattering amplitudes, including the biadjoint, NLSM, and special Galileon, when a subset of kinematic invariants vanishes without producing a singularity.
Freddy Cachazo +2 more
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Algebraic aspects of hypergeometric differential equations [PDF]
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2020 We review some classical and modern aspects of hypergeometric differential equations, including A-hypergeometric systems of Gel′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{
Thomas Reichelt +3 more
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Weights and recursion relations for ϕ p tree amplitudes from the positive geometry
Journal of High Energy Physics, 2020 Recently, the accordiohedron in kinematic space was proposed as the positive geometry for planar tree-level scattering amplitudes in the ϕ p theory [1]. The scattering amplitudes are given as a weighted sum over canonical forms of some accordiohedra with
Ryota Kojima
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Notes on biadjoint amplitudes, Trop G(3, 7) and X(3, 7) scattering equations
Journal of High Energy Physics, 2020 In these notes we use the recently found relation between facets of tropical Grassmannians and generalizations of Feynman diagrams to compute all “biadjoint amplitudes” for n = 7 and k = 3.
Freddy Cachazo, Jairo M. Rojas
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Kinematic singularities of Feynman integrals and principal A-determinants
Journal of High Energy Physics, 2022 We consider the analytic properties of Feynman integrals from the perspective of general A-discriminants and A $$ \mathcal{A} $$ -hypergeometric functions introduced by Gelfand, Kapranov and Zelevinsky (GKZ).
René Pascal Klausen
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Differential-algebraic systems are generically controllable and stabilizable
MCSS. Mathematics of Control, Signals and Systems, 2021 We investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in ...
A. Ilchmann, Jonas Kirchhoff
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