Results 11 to 20 of about 1,291,137 (334)
When is a trigonometric polynomial not a trigonometric polynomial? [PDF]
The American Mathematical Monthly, 2011 As an application of B\'ezout's theorem from algebraic geometry, we show that the standard notion of a trigonometric polynomial does not agree with a more naive, but reasonable notion of trigonometric polynomial.Comment: 3 ...
Borzellino, Joseph E., Sherman, Morgan
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Limit key polynomials as p-polynomials [PDF]
Journal of Algebra, 2021 The main goal of this paper is to characterize limit key polynomials for a valuation $ $ on $K[x]$. We consider the set $ _ $ of key polynomials for $ $ of degree $ $. We set $p$ be the exponent characteristic of $ $. Our first main result (Theorem 1.1) is that if $Q_ $ is a limit key polynomial for $ _ $, then the degree of $Q_ $ is $p^r ...
Michael de Moraes, Josnei Novacoski
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Local polynomials are polynomials [PDF]
Studia Mathematica, 1995 Summary: We prove that a function \(f\) is a polynomial if \(G\circ f\) is a polynomial for every bounded linear functional \(G\). We also show that an operator-valued function is a polynomial if it is locally a polynomial.
Fong, C. K. +4 more
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The Dumont Ansatz for the Eulerian Polynomials, Peak Polynomials and Derivative Polynomials
Annals of Combinatorics, 2022 We observe that three context-free grammars of Dumont can be brought to a common ground, via the idea of transformations of grammars, proposed by Ma-Ma-Yeh. Then we develop a unified perspective to investigate several combinatorial objects in connection with the bivariate Eulerian polynomials. We call this approach the Dumont ansatz.
Chen, William Y. C., Fu, Amy M.
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Nonnegative Polynomials and Circuit Polynomials
SIAM Journal on Applied Algebra and Geometry, 2022 21 ...
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Extremal Polynomials Connected with Zolotarev Polynomials [PDF]
Vestnik St. Petersburg University, Mathematics, 2020 In this paper, the authors deal with the following extremal problem: Using the notation \(P_{n}(x,t)=x_{0}t^{n}+x_{1}t^{n-1}+\dotsb+x_{n}\) for a polynomial of degree not greater than \(n\), \(n\ge 2\) and given real parameters \[ a>1,\quad b0,\quad A \] maximize the magnitude of \(P_{n}(x,b)\) at the following constraints \[ |P_{n}(x,t)|\le M\quad ...
Agafonova, I. V., Malozemov, V. N.
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Entropy, 2023 In this paper, the radial basis function finite difference method is used to solve two-dimensional steady incompressible Navier–Stokes equations. First, the radial basis function finite difference method with polynomial is used to discretize the spatial ...
Liru Mu, Xinlong Feng
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Reasoning Method between Polynomial Error Assertions
Information, 2021 Error coefficients are ubiquitous in systems. In particular, errors in reasoning verification must be considered regarding safety-critical systems. We present a reasoning method that can be applied to systems described by the polynomial error assertion ...
Peng Wu +3 more
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Polynomial Time corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length [PDF]
, 2016 We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential equations with ...
Bournez, Olivier +2 more
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Tutte Polynomials and Link Polynomials [PDF]
Proceedings of the American Mathematical Society, 1988 We show how the Tutte polynomial of a plane graph can be evaluated as the "homfly" polynomial of an associated oriented link. Then we discuss some consequences for the partition function of the Potts model, the Four Color Problem and the time complexity of the computation of the homfly polynomial.
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