منابع مشابه
Lattice Points in High-Dimensional Spheres
A general principle, dating back to Gauss, that is widely used in estimating the number of integer lattice points in nice sets S in R is that this number equals the volume of S with a small error term [4,5,13]. This approach is very useful, and can be proved to be rigorous, for example, if one considers the number of lattice points in sets rT, where the dimension n is fixed, T is a given nice s...
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Given a sequence {Qn(x)}∞n=0 of symmetric orthogonal polynomials, defined by a recurrence formula Qn(x) = νn · x · Qn−1(x) − (νn − 1) · Qn−2(x) with integer νi’s satisfying νi ≥ 2, we construct a sequence of nested Eulerian posets whose ceindex is a non-commutative generalization of these polynomials. Using spherical shellings and direct calculations of the cd-coefficients of the associated Eul...
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Orthogonal polynomials on the standard simplex Σ in R are shown to be related to the spherical orthogonal polynomials on the unit sphere S in R that are invariant under the group Z2×· · ·×Z2. For a large class of measures on S cubature formulae invariant under Z2 × · · · × Z2 are shown to be characterized by cubature formulae on Σ. Moreover, it is also shown that there is a correspondence betwe...
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Orthogonal polynomials on the unit sphere in Rd+1 and on the unit ball in Rd are shown to be closely related to each other for symmetric weight functions. Furthermore, it is shown that a large class of cubature formulae on the unit sphere can be derived from those on the unit ball and vice versa. The results provide a new approach to study orthogonal polynomials and cubature formulae on spheres.
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In this paper we discuss a natural way to deene barycentric coordinates on general sphere-like surfaces. This leads to a theory of Bernstein-B ezier polynomials which parallels the familiar planar case. Our constructions are based on a study of homogeneous polynomials on trihedra in IR 3. The special case of Bernstein-B ezier polynomials on a sphere is considered in detail.
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ژورنال
عنوان ژورنال: Nonlinear Analysis
سال: 2019
ISSN: 0362-546X
DOI: 10.1016/j.na.2019.03.023