Results 231 to 240 of about 15,351 (267)

Homogeneous polynomial identities

Israel Journal of Mathematics, 1982
PI-algebras are studied by attaching invariants to the homogeneous identities analogous to the invariants of the multilinear identities studied by Regev. Also, it is shown that every finitely generated PI-algebra is polynomially bounded.
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Homogeneous Polynomial Systems

2013
We finished the preceding chapter with a notion of approximate zero of a function and an algorithmic scheme to compute these approximate zeros, the adaptive homotopy.
Peter Bürgisser, Felipe Cucker
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Differentially homogeneous differential polynomials

Proceedings of the 1996 international symposium on Symbolic and algebraic computation - ISSAC '96, 1996
Let X be a differential field (characteristic zero) with a single derivation operator J (if a c Z we also write Ja = a’). Let y., yl, . . . . y~ be n+ 1 differential indeterminates over F and R = F{ y., . . . . yn ] be the differential polynomial ring over F. Finally, let t be a differential indeterminate over R. A differential polynomial (d.p.) P in R
Georg M. Reinhart, William Sit
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Non-Linear Homogeneous Differential Polynomials

Computational Methods and Function Theory, 2011
Let \(f\) be a transcendental meromorphic function in the complex plane, \[ u=f/f^{(k)} \] and \[ \phi=u^n+\sum_{j=0}^{n-2}c_ju^j, \] where \(c_j\) is a small meromorphic function in terms of \(u\). The author finds several conditions on \(f\), \(f^{(k)}\) and \(\phi\) such that \(f\) is of the form \(R\exp(P)\), where \(R\) is a rational function and \
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Elimination from Homogeneous Polynomials Over a Polynomial Ring

Canadian Journal of Mathematics, 1976
Let Ω be a field and Γ a parameter. We designate the set of all polynomials homogeneous in (X) = (X1, … , Xn) with coefficients in Ω [Γ] by H Ω Γ[X] and write such polynomials as F, F(X), or F(X, Γ). The degree of a polynomial in H Ω Γ [X] shall mean the degree in (X). Let I = (F1 … , Fr) be a fixed ideal in H Ω Γ [X] generated by F1 … , Fr.
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Linear Functionals on Homogeneous Polynomials

Canadian Mathematical Bulletin, 1968
The space Hm of homogeneous polynomials in n real variables x1, x2,…, xn of degree m may be considered as an inner product space with inner product ; where ds is the rotation-invariant measure on Sn-1 = {x ε Rn: |x| = 1}, . The problem solved in this paper is the following: given n-1 a linear functional ϕ on Hm, find Pϕ ε Hm so that ϕ(p) = (p, Pϕ) for ...
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Polynomial first integrals for quasi-homogeneous polynomial differential systems

Nonlinearity, 2002
Here, several results concerning first integrals of homogeneous polynomial systems of differential equations are generalized to quasi-homogeneous polynomial systems. Properties of such systems are characterized in terms of the eigenvalues of the associated Kowalevskaya matrix.
Llibre, Jaume, Zhang, Xiang
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Approximation by Homogeneous Polynomials

Constructive Approximation, 2006
Let \(K\subset\mathbb{R}^d\) be the boundary of a convex domain symmetric to the origin. The conjecture that any continuous even function can be uniformly approximated by homogeneous polynomials of even degree on K is proven in the following cases: (a) if d = 2; (b) if K is twice continuously differentiable and has positive curvature in every point; or
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Sign Definiteness of Quasi-Homogeneous Polynomials

Journal of Mathematical Sciences, 2001
The concept of quasihomogeneous polynomials is introduced. Criteria for quasihomogeneous polynomials to have a fixed sign in the space \(R^n\) and an arbitrary octant of this space are presented. Necessary and sufficient conditions for having this property are established.
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A Theorem on Homogeneous Differential Polynomials

Results in Mathematics, 2012
Let \(f(z)\) be a meromorphic function in the complex plane. The author considers the value distribution of a homogeneous differential polynomial in \(f\). The results in this paper are improvements of \textit{A. J. Whitehead}'s theorems appeared in his dissertation [Differential equations and differential polynomials in the complex plane.
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