منابع مشابه
On Spherical Designs of Some Harmonic Indices
A finite subset Y on the unit sphere Sn−1 ⊆ Rn is called a spherical design of harmonic index t, if the following condition is satisfied: ∑ x∈Y f(x) = 0 for all real homogeneous harmonic polynomials f(x1, . . . , xn) of degree t. Also, for a subset T of N = {1, 2, · · · }, a finite subset Y ⊆ Sn−1 is called a spherical design of harmonic index T, if ∑ x∈Y f(x) = 0 is satisfied for all real homo...
متن کاملSome rigid Steiner 5-designs
Hitherto, all known non-trivial Steiner systems S(5, k, v) have, as a group of automorphisms, either PSL(2, v − 1) or PGL(2, v−2 2 ) × C2. In this paper, systems S(5, 6, 72), S(5, 6, 84) and S(5, 6, 108) are constructed that have only the trivial automorphism group.
متن کاملSome Indecomposable t-Designs
The existence of large sets of 5-(14,6,3) designs is in doubt. There are five simple 5-(14,6,6) designs known in the literature. In this note, by the use of a computer program, we show that all of these designs are indecomposable and therefore they do not lead to large sets of 5(14,6,3) designs. Moreover, they provide the first counterexamples for a conjecture on disjoint t-designs which states...
متن کاملComputational existence proofs for spherical t-designs
Spherical t-designs provide quadrature rules for the sphere which are exact for polynomials up to degree t. In this paper, we propose a computational algorithm based on interval arithmetic which, for given t, upon successful completion will have proved the existence of a tdesign with (t + 1)2 nodes and will have computed narrow interval enclosures which are known to contain these nodes with mat...
متن کاملOn Tight Spherical Designs
Let X be a tight t-design of dimension n for one of the open cases t = 5 or t = 7. An investigation of the lattice generated by X using arithmetic theory of quadratic forms allows to exclude infinitely many values for n.
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ژورنال
عنوان ژورنال: Memoirs of the Faculty of Science, Kyushu University. Series A, Mathematics
سال: 1992
ISSN: 0373-6385
DOI: 10.2206/kyushumfs.46.169