1,721,144 research outputs found
2-norm effective isotropic Hookean solids
No full textWe discuss effective isotropic Hoekean solids with distance measured in the 2-nrom
On Certain Configurations of Points which are Univsolvent for Polynomial Interpolation
No full textWe give configurations of points which are proven to be univsolvent for polynomial interpolation
Some Remarks on the Fejer Problem for Lagrange Interpolation in Several Variables
No full textWe discuss when the sum of the squares of the Lagrange polynomials can be bounded by 1
Bounding the Lebesgue function for Lagrange interpolation in a simplex
No full textWe give bounds for the Lebesgue function for polynomial interpolation at points in a simplex
SICs and the elements of order three in the Clifford group
No full textFor over a decade, there has been intensive work on the numerical and analytic construction of SICs (d(2) equiangular lines in C-d) as an orbit of the Heisenberg group. The Clifford group, which consists of the unitary matrices which normalise the Heisenberg group, plays a key role in these constructions. All of the known fiducial (generating) vectors for such SICs are eigenvectors of symplectic operations in the Clifford group with canonical order 3. Here we describe the Clifford group and the subgroup of symplectic operations in terms of a natural set of generators. From this, we classify all its elements of canonical order three. In particular, we show (contrary to prior claims) that there are symplectic operations of canonical order 3 for d 6 mod 9, which are not conjugate to the Zauner matrix. It is as yet unknown whether these give rise to SICs
On the Calculuation of Approximate Fekete Points: the Univariate Case
No full textWe discuss some theoretical aspects of the univariate case of the method recently introduced by
Sommariva and Vianello for the calculation of approximate Fekete points for polynomial
interpolation
Application of modified Leja sequences to polynomial interpolation
No full textWe discuss several applications of the Leja point method for univariate polynomial interpolation. First weshow how more or less arbitrary interpolation points sets can be stabilized by adding some points fromthe Leja sequence generated beginning with the given set. We then show how the Leja point idea can beused to generate good point sets for Hermite–Lagrange polynomial interpolation. Then we discuss aversion of Leja sequences for the interval [−1, 1] that are constrained to be symmetric sets. Finally wediscuss the extension of Leja stabilization to several variables
On the relation between ray theory and the banana-doughnut formulation
No full textWe discuss the relationship between ray theory and the banana-doughnut formulation in geophysics
Weighted Splines as Optimal Interpolants
No full textWe give optimality properties for weighted splines
Sobolev-Gagliardo-Nirenberg and Markov Type Inequalities on Subanalytic Domains
No full textWe show existence and give equivalences for various types of calssical inequalities
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