Results 1 to 10 of about 15,232 (148)
Triality for Homogeneous Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 Through the triality of SO(8,C), we study three interrelated homogeneous basis of the ring of invariant polynomials of Lie algebras, which give the basis of three Hitchin fibrations, and identify the explicit automorphisms that relate them.
Schaposnik, Laura P., Schulz, Sebastian
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Methods and algorithms for determining the main quasi-homogeneous forms of polynomials and power series [PDF]
MATEC Web of Conferences, 2022 Methods are proposed that allow one to determine the special forms of polynomials and power series used in solving a number of practical problems. The most important of them are the construction of necessary and sufficient conditions for an extremum for ...
Nefedov Viktor
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On (r; t; s)-nuclear polynomials
Moroccan Journal of Pure and Applied Analysis, 2022 In this work we extend the concept of (r; t; s)-nuclear operators presented by Lapresté in (Studia math., T. LVII. 1976, 47 – 83) to n-homogeneous polynomials. Factorization and inclusion properties are described.
Bougoutaia Amar +2 more
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Normality and uniqueness of homogeneous differential polynomials
Математичні Студії, 2023 The primary goal of this work is to determine whether the results from [19, 20] still hold true when a differential polynomial is considered in place of a differential monomial.
R. S. Dyavanal, S. B. Kalakoti
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Cubic homogeneous polynomial centers [PDF]
Publicacions Matemàtiques, 2021 Agraïments: The first author is partially supported by NSFC-11271027 and NSFC- 11171267. First, doing a combination of analytical and algebraic computations, we determine by first time an explicit normal form depending only on three parameters for all cubic homogeneous polynomial differential systems having a center. After using the averaging method of
Li, Chengzhi, Llibre, Jaume
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Reconstruction of a homogeneous polynomial from its additive decompositions when identifiability fails [PDF]
Arab Journal of Mathematical Sciences, 2021 Let X⊂ℙr be an integral and non-degenerate complex variety. For any q∈ℙr let rX(q) be its X-rank and S(X,q) the set of all finite subsets of X such that |S|=rX(q) and q ∈ 〈S〉, where 〈〉 denotes the linear span.
E. Ballico
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On Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball
Axioms, 2023 The paper gives an explicit representation of the Green’s function of the Dirichlet boundary value problem for the polyharmonic equation in the unit ball. The solution of the homogeneous Dirichlet problem is found.
Valery Karachik
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Orthogonal Homogeneous Polynomials
Advances in Applied Mathematics, 1999 These are stringent results on real homogeneous polynomials in several real variables: if the polynomials form a normalized biorthogonal system (with respect to a certain inner product, which is defined using partial derivatives of one of the components), then an addition theorem holds, and conversely: the addition property is sufficient for ...
Fryant, A. +2 more
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On Homogeneous Combinations of Linear Recurrence Sequences
Mathematics, 2020 Let (Fn)n≥0 be the Fibonacci sequence given by Fn+2=Fn+1+Fn, for n≥0, where F0=0 and F1=1. There are several interesting identities involving this sequence such as Fn2+Fn+12=F2n+1, for all n≥0. In 2012, Chaves, Marques and Togbé proved that if (Gm)m is a
Marie Hubálovská +2 more
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The set of forms with bounded strength is not closed
Comptes Rendus. Mathématique, 2022 The strength of a homogeneous polynomial (or form) is the smallest length of an additive decomposition expressing it whose summands are reducible forms. Using polynomial functors, we show that the set of forms with bounded strength is not always Zariski ...
Ballico, Edoardo +3 more
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