Results 21 to 30 of about 15,351 (267)
On composite abstract homogeneous polynomials [PDF]
Transactions of the American Mathematical Society, 1977 We study the null-sets of composite abstract homogeneous polynomials obtained from a pair of abstract homogeneous polynomials defined on a vector space over an algebraically closed field of characteristic zero. First such study for ordinary polynomials in the complex plane was made by Szegö, Cohn, and Egerváry and Szegö’s theorem was later generalized ...
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Problems on multivariate reliability polynomial
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2017 The original results include: (i) homogenization of a reliability polynomial; (ii) compact hypersurfaces attached to homogeneous polynomials; (iii) an affine diffeomorphism that preserves a reliability polynomial; (iv) duality of networks via a ...
Constantin Udriste +2 more
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New iterative codes for 𝓗-tensors and an application
Open Mathematics, 2016 New iterative codes for identifying 𝓗 -tensor are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor, i.e., an even-degree homogeneous polynomial form are given.
Wang Feng, Sun Deshu
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A Dichotomy for First-Order Reducts of Unary Structures [PDF]
Logical Methods in Computer Science, 2018 Many natural decision problems can be formulated as constraint satisfaction problems for reducts $\mathbb{A}$ of finitely bounded homogeneous structures. This class of problems is a large generalisation of the class of CSPs over finite domains. Our first
Manuel Bodirsky, Antoine Mottet
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Weights induced by homogeneous polynomials [PDF]
Pacific Journal of Mathematics, 1989 Let \(B\) be the unit ball and \(S\) the unit sphere in \({\mathbb{C}}^ n\) \((n\geq 2)\). Let \(\sigma\) be the unique normalized rotation-invariant Borel measure on \(S\) and \(m\) the normalized area measure on \({\mathbb{C}}.\) We first prove that if \(\Lambda\) is a holomorphic homogeneous polynomial on \({\mathbb{C}}^ n \)normalized so that ...
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A note on the integrability of exceptional potentials via polynomial bi-homogeneous potentials
Bulletin of Computational Applied Mathematics, 2021 This paper is concerned with the polynomial integrability of the two-dimensional Hamiltonian systems associated to complex homogeneous polynomial potentials of degree k of type $V_{k,l}=\alpha (q_2-i q_1)^l (q_2+iq_1)^{k-l}$ with $\alpha$ in C and l=0 ...
Primitivo B. Acosta-Humánez +2 more
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The Nearest Zero Eigenvector of a Weakly Symmetric Tensor from a Given Point
MathematicsWe begin with a degree m real homogeneous polynomial in n indeterminants and bound the distance from a given n-dimensional real vector to the real vanishing of the homogeneous polynomial.
Kelly Pearson, Tan Zhang
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On the growth of gap power series of homogeneous polynomials
Researches in MathematicsLet $f$ be an entire functions $f\colon \mathbb{C}^{p}\to\mathbb{C}$, represented by power series of the form $$f(z)=\sum\limits_{k=0}^{+\infty} P_k(z), z\in\mathbb{C}^p$$ where $P_0(z)\equiv a_{0}\in\mathbb{C}$, $P_k(z)=\sum\limits_{\|n\|=\lambda_k ...
A.I. Bandura +2 more
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Rigid Polynomial Differential Systems with Homogeneous Nonlinearities
MathematicsPlanar differential systems whose angular velocity is constant are called rigid or uniform differential systems. The first rigid system goes back to the pendulum clock of Christiaan Huygens in 1656; since then, the interest for the rigid systems has been
Jaume Llibre
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Positive Semi-Definite and Sum of Squares Biquadratic Polynomials
MathematicsHilbert proved in 1888 that a positive semi-definite (PSD) homogeneous quartic polynomial of three variables always can be expressed as the sum of squares (SOS) of three quadratic polynomials, and a psd homogeneous quartic polynomial of four variables ...
Chunfeng Cui, Liqun Qi, Yi Xu
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