Resolution of single-variable fuzzy polynomial equations and an upper bound on the number of solutions
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DOI: 10.1007/s00500-017-2790-5
Abstract: In this paper, the single-variable fuzzy polynomial equations are studied. We firstly define two solution types for the equations, called solution and r-cut solution. Then, sufficient and necessary conditions are proposed for existence of the… read more here.
Keywords: polynomial equations; variable fuzzy; number; solution ... See more keywords
Bezout-like polynomial equations associated with dual univariate interpolating subdivision schemes
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DOI: 10.1007/s10444-021-09912-4
Abstract: The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach for finding dual univariate interpolating subdivision schemes based on the solutions of certain associated polynomial equations. The proposed… read more here.
Keywords: dual univariate; polynomial equations; subdivision schemes; univariate interpolating ... See more keywords
Detecting tropical defects of polynomial equations
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DOI: 10.1007/s10801-019-00916-4
Abstract: We introduce the notion of tropical defects, certificates that a system of polynomial equations is not a tropical basis, and provide two algorithms for finding them in affine spaces of complementary dimension to the zero… read more here.
Keywords: defects polynomial; detecting tropical; tropical defects; polynomial equations ... See more keywords
Attasi nD Systems and Polynomial System Solving
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DOI: 10.1016/j.ifacol.2021.06.145
Abstract: Abstract Firstly it will be shown that, using the concept of monomial orderings, the classical 1D theory for linear systems generalizes in a very natural way to (autonomous) Attasi nD-systems, giving the Attasi-Hankel matrix, the… read more here.
Keywords: system; attasi systems; polynomial equations; attasi system ... See more keywords
PRIME SOLUTIONS TO POLYNOMIAL EQUATIONS IN MANY VARIABLES AND DIFFERING DEGREES
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DOI: 10.1017/fms.2018.21
Abstract: Let $\mathbf{f}=(f_{1},\ldots ,f_{R})$ be a system of polynomials with integer coefficients in which the degrees need not all be the same. We provide sufficient conditions for which the system of equations $f_{j}(x_{1},\ldots ,x_{n})=0~(1\leqslant j\leqslant R)$… read more here.
Keywords: polynomial equations; many variables; prime solutions; variables differing ... See more keywords
Quantum annealing for systems of polynomial equations
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DOI: 10.1038/s41598-019-46729-0
Abstract: Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct matrix inversion or iteratively… read more here.
Keywords: quantum annealing; systems polynomial; annealing systems; polynomial equations ... See more keywords
Rational limit cycles on generalized Bernouilli polynomial equations
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DOI: 10.1063/5.0015230
Abstract: We determine the maximum number of rational limit cycles of the generalized Bernouilli polynomial equations a(x)dy/dx = A(x)yn + B(x)y, where a(x), A(x), and B(x) are real polynomials with a(x)A(x) ≢ 0, n ≥ 3.… read more here.
Keywords: generalized bernouilli; polynomial equations; limit cycles; rational limit ... See more keywords
Galois theory for general systems of polynomial equations
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DOI: 10.1112/s0010437x18007868
Abstract: We prove that the monodromy group of a reduced irreducible square system of general polynomial equations equals the symmetric group. This is a natural first step towards the Galois theory of general systems of polynomial… read more here.
Keywords: system; systems polynomial; general systems; theory general ... See more keywords
Constructing Dixon Matrix for Sparse Polynomial Equations Based on Hybrid and Heuristics Scheme
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DOI: 10.3390/sym14061174
Abstract: Solving polynomial equations inevitably faces many severe challenges, such as easily occupying storage space and demanding prohibitively expensive computation resources. There has been considerable interest in exploiting the sparsity to improve computation efficiency, since asymmetry… read more here.
Keywords: computation; constructing dixon; polynomial equations; dixon matrix ... See more keywords