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We prove that the minimizer in the Nédélec polynomial space of some degree $p\ge 0$ of a discrete minimization problem performs as well as the continuous minimizer in $H({\bf curl})$, up to a constant that is independent of the polynomial degree $p$. The
Chaumont-Frelet, Théophile +2 more
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Constant terms in powers of a Laurent polynomial
The following is a conjecture of O. Mathieu: Let \(K\) be a connected real compact Lie group. Let \(f\) and \(g\) be \(K\)-finite functions on \(K\). Assume for all \(n \geq 1\) that the constant term of \(f^{n}\) vanishes, i.e. \[ \int_{K} f^{n}(k) \;dk = 0 .
Duistermaat, J.J., Kallen, W. van der
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Problems on multivariate reliability polynomial
The original results include: (i) homogenization of a reliability polynomial; (ii) compact hypersurfaces attached to homogeneous polynomials; (iii) an affine diffeomorphism that preserves a reliability polynomial; (iv) duality of networks via a ...
Constantin Udriste +2 more
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An Elementary Approach to Polynomial Optimization on Polynomial Meshes
A polynomial mesh on a multivariate compact set or manifold is a sequence of finite norming sets for polynomials whose norming constant is independent of degree.
Marco Vianello
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Edit Distance with Block Deletions
Several variants of the edit distance problem with block deletions are considered. Polynomial time optimal algorithms are presented for the edit distance with block deletions allowing character insertions and character moves, but without block moves.
Dana Shapira, James A. Storer
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Degree estimates for polynomials constant on a hyperplane
The study of proper rational mappings between balls in complex Euclidean spaces naturally leads to the relationship between the degree and imbedding dimension of such a mapping. The special case for monomial mappings is equivalent to the question discussed in this paper. Estimate the degree $d$ of a polynomial in $n$ real variables, assumed to have non-
D'Angelo, John +2 more
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A Jacobi Dual-Petrov-Galerkin Method for Solving Some Odd-Order Ordinary Differential Equations
A Jacobi dual-Petrov-Galerkin (JDPG) method is introduced and used for solving fully integrated reformulations of third- and fifth-order ordinary differential equations (ODEs) with constant coefficients.
E. H. Doha, A. H. Bhrawy, R. M. Hafez
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The best constant of Sobolev inequality corresponding to anti-periodic boundary value problem
In this paper we establish the best constant of $\mathcal{L}^{p}$ Sobolev inequality for a function with anti-periodic boundary conditions. The best constant is expressed by $\mathcal{L}^q$ norm of $(M-1)$-th order Euler polynomial.
Jozef Kiseľák
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On the Sidon constant for Dirichlet polynomials
Minor ...
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Square-rich fixed point polynomial evaluation on FPGAs [PDF]
Polynomial evaluation is important across a wide range of application domains, so significant work has been done on accelerating its computation. The conventional algorithm, referred to as Horner's rule, involves the least number of steps but can lead to
McLoughlin, Ian V. +5 more
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