Results 11 to 20 of about 661,613 (288)
Linearizability conditions for 1:-5 Lotka-Volterra two-dimensional complex quartic systems
上海师范大学学报. 自然科学版, 2017 In this paper we investigate the linearizability problem for the planar Lotka-Volterra complex quartic systems which are 1:-5 linear systems perturbed by homogeneous polynomials of degree 4, that is to say, we consider systems of the form ẋ = x(1 ...
Hu Zhaoping, Zhang Chao
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Automorphisms of algebras and Bochner`s property for discrete vector orthogonal polynomials [PDF]
, 2016 We construct new families of discrete vector orthogonal polynomials that have the property to be eigenfunctions of some difference operator. They are extensions of Charlier, Meixner and Kravchuk polynomial systems.
Horozov, Emil
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Polynomial systems with few real zeroes [PDF]
, 2005 We study some systems of polynomials whose support lies in the convex hull of a circuit, giving a sharp upper bound for their numbers of real solutions. This upper bound is non-trivial in that it is smaller than either the Kouchnirenko or the Khovanskii ...
Bertrand, Benoit +2 more
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On the first fall degree of summation polynomials
Journal of Mathematical Cryptology, 2019 We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.
Kousidis Stavros, Wiemers Andreas
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Solving parametric polynomial systems
Journal of Symbolic Computation, 2007 The authors present a new algorithm for solving constructible or semi-algebraic systems in the indeterminates \([U,X]\) where \(U=[U_1,\dots ,U_d]\) is the set of parameters and \(X=[X_{d+1},\dots,X_n]\) the set of unknowns. To this end, they study the characterization of open subsets in the parameter space over which the number of solutions is ...
Lazard, Daniel, Rouillier, Fabrice
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RESOLUTION OF POLYNOMIAL SYSTEMS [PDF]
Computer Mathematics, 2000 In this talk, the state of the art of solving polynomial system by algebraic methods is sketched, and the main directions where future work is needed are indicated.
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MultiRegeneration for polynomial system solving [PDF]
ACM Communications in Computer Algebra, 2020 We demonstrate our implementation of a continuation method as described in [7] for solving polynomials systems. Given a sequence of (multi)homogeneous polynomials, the software multiregeneration outputs the respective (multi)degree in a wide range of cases and partial multidegree in all others.
Crowley, Colin +3 more
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Bifurcation of critical periods of a quartic system
Electronic Journal of Qualitative Theory of Differential Equations, 2018 For the polynomial system $\dot x = ix + x \bar x ( a x^2 + b x \bar x + c \bar x^2)$ the study of critical period bifurcations is performed. Using calculations with algorithms of computational commutative algebra it is shown that at most two critical ...
Wentao Huang +3 more
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Rigid continuation paths II. structured polynomial systems
Forum of Mathematics, Pi, 2023 This work studies the average complexity of solving structured polynomial systems that are characterised by a low evaluation cost, as opposed to the dense random model previously used.
Peter Bürgisser +2 more
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Limit Cycles of Polynomially Integrable Piecewise Differential Systems
Axioms, 2023 In this paper, we study how many algebraic limit cycles have the discontinuous piecewise linear differential systems separated by a straight line, with polynomial first integrals on both sides.
Belén García +3 more
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