Results 11 to 20 of about 15,351 (267)

Homogeneous p-differential polynomials

Journal of Algebra, 2003
The first author earlier showed that algebraic geometry may be enlarged by adjoining a ``Fermat quotient type operation'' and the resulting geometry was named as \(\delta\)-geometry. Later he with his kolleagues introduced certain graded rings that should be interpreted as rings of sections of appropriate line bundles on the corresponding orbit spaces ...
Buium, Alexandru, Zimmerman, Ken
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Homogeneous Formulas and Symmetric Polynomials [PDF]

computational complexity, 2011
We investigate the arithmetic formula complexity of the elementary symmetric polynomials S(k,n). We show that every multilinear homogeneous formula computing S(k,n) has size at least k^(Omega(log k))n, and that product-depth d multilinear homogeneous formulas for S(k,n) have size at least 2^(Omega(k^{1/d}))n.
Hrubeš, Pavel, Yehudayoff, Amir
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The algebraic curves of planar polynomial differential systems with homogeneous nonlinearities

Electronic Journal of Qualitative Theory of Differential Equations, 2021
We consider planar polynomial systems of ordinary differential equations of the form $\dot x = x + P_n(x,y)$, $\dot y = y + Q_n(x,y)$, where $P_n(x,y),\ Q_n(x,y)$ are homogeneous polynomials of degree $n$.
Vladimir Cheresiz, Evgenii Volokitin
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Ideals of Homogeneous Polynomials

Publications of the Research Institute for Mathematical Sciences, 2012
Given a surjective ideal of operators, we undertake a new general procedure to construct an ideal of polynomials. The relation with the ideal of polynomials obtained by the well-known method of composition is established.
Aron, Richard M., Rueda, Pilar
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Embedding of Unimodular Row Vectors

Mathematics, 2023
In this paper, we mainly study the embedding problem of unimodular row vectors, focusing on avoiding the identification of polynomial zeros. We investigate the existence of the minimal syzygy module of the ZLP polynomial matrix and demonstrate that the ...
Tao Wu, Jinwang Liu, Jiancheng Guan
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Polynomial programming using multi- homogeneous polynomial continuation

Journal of Computational and Applied Mathematics, 1992
In this note a polynomial programming problem of the type \(\min_ x\{\theta(x)\mid\) \(h(x)=0\}\), where \(\theta\), \(h\) are polynomial functions \(\theta: E^ n\to E\), \(h: E^ n\to E^ q\), is considered. Traditional constructions of the polynomial continuation approach need the computation of the complete list of geometrically isolated solutions of ...
Watson, Layne T., Morgan, Alexander P.
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New Solvable System of 2 First-Order Nonlinearly-Coupled Ordinary Differential Equations [PDF]

Open Communications in Nonlinear Mathematical Physics, 2022
In this short communication we introduce a rather simple autonomous system of 2 nonlinearly-coupled first-order Ordinary Differential Equations (ODEs), whose initial-values problem is explicitly solvable by algebraic operations.
Francesco Calogero, Farrin Payandeh
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Approximation Hierarchies for the Copositive Tensor Cone and Their Application to the Polynomial Optimization over the Simplex

Mathematics, 2022
In this paper, we discuss the cone of copositive tensors and its approximation. We describe some basic properties of copositive tensors and positive semidefinite tensors. Specifically, we show that a non-positive tensor (or Z-tensor) is copositive if and
Muhammad Faisal Iqbal, Faizan Ahmed
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FEEDBACK STABILIZATION OF HOMOGENEOUS POLYNOMIAL SYSTEMS [PDF]

IFAC Proceedings Volumes, 1995
The propose of this paper is to drive a simple necessary and sufficient stabilizability condition for a class of multi-inputs polnomial systems. This result represents a generalization of the main theorems of (Iggidr and Vivalda, 1992). The stabilizing feedbacks are explicitly given.
Iggidr, Abderrahman, Outbib, Rachid
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On the equivalence and differences of three plane-stress yield criteria for modelling orthotropic sheet metals with the tension-compression strength differential effect [PDF]

MATEC Web of Conferences
The plane-stress yield surface of a sheet metal exhibiting tension-compression asymmetry may be modelled by a single polynomial yield stress function consisting of both even and odd order stress terms.
Sheng Jie, Tong Wei
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