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The Complexity of Approximating the Matching Polynomial in the Complex Plane [PDF]
ACM Transactions on Computation Theory, 2021 We study the problem of approximating the value of the matching polynomial on graphs with edge parameter γ, where γ takes arbitrary values in the complex plane. When γ is a positive real, Jerrum and Sinclair showed that the problem admits an FPRAS on general graphs.
Bezáková, Ivona +3 more
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The complexity of separating points in the plane [PDF]
Proceedings of the twenty-ninth annual symposium on Computational geometry, 2013 We study the following separation problem: given n connected curves and two points s and t in the plane, compute the minimum number of curves one needs to retain so that any path connecting s to t intersects some of the retained curves. We give the first polynomial (O(n3)) time algorithm for the problem, assuming that the curves have reasonable ...
Cabello, S., Giannopoulos, P.
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Probability density in the complex plane [PDF]
Annals of Physics, 2010 38 pages ...
Bender, CM +3 more
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Burgers’ equation in the complex plane
Physica D: Nonlinear Phenomena, 2023 Burgers' equation is a well-studied model in applied mathematics with connections to the Navier-Stokes equations in one spatial direction and traffic flow, for example. Following on from previous work, we analyse solutions to Burgers' equation in the complex plane, concentrating on the dynamics of the complex singularities and their relationship to the
Daniel J. VandenHeuvel +4 more
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The Dynamics of Twisted Tent Maps [PDF]
, 2012 This paper is a study of the dynamics of a new family of maps from the complex plane to itself, which we call twisted tent maps. A twisted tent map is a complex generalization of a real tent map.
Chamblee, Stephen Joseph
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Infinite Radicals in the Complex Plane [PDF]
Proceedings of the American Mathematical Society, 1961 is called an infinite radical. The numbers aj are the elements of the infinite radical, and the uj are called partial radicals. Throughout this paper a'12 will mean that square root whose real part is positive or zero. If a is a negative real number, a"/2 will be defined to be on the positive imaginary axis.
W. J. Thron, Georgellen Schuske
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The Complexity of Hyperplane Depth in the Plane [PDF]
Discrete and Computational Geometry, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Langerman, Stefan, Steiger, William W.
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Point-curve incidences in the complex plane [PDF]
, 2017 We prove an incidence theorem for points and curves in the complex plane. Given a set of $m$ points in ${\mathbb R}^2$ and a set of $n$ curves with $k$ degrees of freedom, Pach and Sharir proved that the number of point-curve incidences is $O\big(m ...
Sheffer, Adam +2 more
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Hybrid inflation in the complex plane
Journal of Cosmology and Astroparticle Physics, 2014 Supersymmetric hybrid inflation is an exquisite framework to connect inflationary cosmology to particle physics at the scale of grand unification. Ending in a phase transition associated with spontaneous symmetry breaking, it can naturally explain the generation of entropy, matter and dark matter.
Buchmüller, W. +3 more
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On resolution complexity of plane curves [PDF]
Kodai Mathematical Journal, 1995 The authors show that any isolated plane curve singular point can be resolved in a sequence of toroidal blowing-ups. They prove that the minimal number of required toroidal blowing-ups is a topological invariant depending on the number of local branches and number of Puiseux pairs of each branch.
Lê, Dũng Tráng, Oka, Mutsuo
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