Results 11 to 20 of about 71,831 (301)
Polynomial Solutions of Equivariant Polynomial Abel Differential Equations [PDF]
Advanced Nonlinear Studies, 2018 Let a(x){a(x)} be non-constant and let bj(x){b_{j}(x)}, for j=0,1,2,3{j=0,1,2,3}, be real or complex polynomials in the variable x. Then the real or complex equivariant polynomial Abel differential equation a(x)y˙=b1(x)y+b3(x)y3{a(x)\dot{y}=b_{1}(
Llibre Jaume, Valls Clàudia
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Electronic Journal of Differential Equations, 2017 Let $A(\theta)$ non-constant and $B_j(\theta)$ for $j=0,1,2,3$ be real trigonometric polynomials of degree at most $\eta \ge 1$ in the variable x. Then the real equivariant trigonometric polynomial Abel differential equations $A(\theta) y' =B_1(\theta)
Claudia Valls
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Estimates of the asymptotic Nikolskii constants for spherical polynomials [PDF]
Journal of Complexity, 2021 Let $Π_n^d$ denote the space of spherical polynomials of degree at most $n$ on the unit sphere $\mathbb{S}^d\subset \mathbb{R}^{d+1}$ that is equipped with the surface Lebesgue measure $dσ$ normalized by $\int_{\mathbb{S}^d} \, dσ(x)=1$. This paper establishes a close connection between the asymptotic Nikolskii constant, $$ \mathcal{L}^\ast(d):=\lim_{n\
Feng Dai +2 more
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Asymptotics of Polynomial Interpolation and the Bernstein Constants [PDF]
Results in Mathematics, 2021 AbstractIt is well known that the interpolation error for $$\left| x\right| ^{\alpha },\alpha >0$$ x α , α > 0
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Learning Read-Constant Polynomials of Constant Degree Modulo Composites [PDF]
Theory of Computing Systems, 2011 Peer ...
Arkadev Chattopadhyay +3 more
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Decomposition of differential polynomials with constant coefficients [PDF]
Proceedings of the 2004 international symposium on Symbolic and algebraic computation, 2004 In this paper, we present an algorithm to decompose differential polynomials in one variable and with rational number as coefficients. Besides arithmetic operations, the algorithm needs only factorization of multi-variable polynomials and solution of linear equation systems. Experimental results show that our method is quite efficient.
Xiao-Shan Gao, Mingbo Zhang
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Constant term identities and Poincaré polynomials [PDF]
Transactions of the American Mathematical Society, 2015 In 1982 Macdonald published his now famous constant term conjectures for classical root systems. This paper begins with the almost trivial observation that Macdonald’s constant term identities admit an extra set of free parameters, thereby linking them to Poincaré polynomials.
Károlyi, Gyula +2 more
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Unconditional constants and polynomial inequalities
Journal of Approximation Theory, 2009 If \(P\) is a polynomial with real coefficients, \(|P|\) denotes the polynomial obtained from \(P\) replacing its coefficients by their absolute values. Inequalities between the norm of \(|P|\) and the norm of \(P\) on a convex subset are studied for some specific spaces of polynomials.
Bogdan C. Grecu +2 more
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Constant Terms of Near-Dyson Polynomials [PDF]
The Electronic Journal of Combinatorics, 2018 We formulate and prove a formula for the constant term for a certain class of Laurent polynomials, which include the Dyson conjecture and its generalizations by Bressoud and Goulden. Our method is explicit Combinatorial Nullstellensatz.
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Polynomial Optimization, Certificates of Positivity, and Christoffel Function
, 2023 International audienceWe briefly recall basics of the Moment-SOS hierarchy in polynomial optimization and the Christoffel-Darboux kernel (and the Christoffel function (CF)) in theory of approximation and orthogonal polynomials.
Lasserre, Jean-Bernard
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