The self-affine measure associated with an expanding matrix and a finite digit set is uniquely determined by the self-affine identity with equal weight. The spectral and non-spectral problems on the self- affine measu...The self-affine measure associated with an expanding matrix and a finite digit set is uniquely determined by the self-affine identity with equal weight. The spectral and non-spectral problems on the self- affine measures have some surprising connections with a number of areas in mathematics, and have been received much attention in recent years. In the present paper, we shall determine the spectrality and non-spectrality of a class of self-aiffine measures with decomposable digit sets. We present a method to deal with such case, and clarify the spectrality and non-spectrality of a class of self-affine measures by applying this method.展开更多
The purpose of this paper is to survey the construction of orthogonal arrays of strength two by using difference sets. Some methods for constructing difference set D(2p.2p,p,2), where p is a prime or a prime power, ar...The purpose of this paper is to survey the construction of orthogonal arrays of strength two by using difference sets. Some methods for constructing difference set D(2p.2p,p,2), where p is a prime or a prime power, are given. It is shown that the Kronecker sum of a difference set D(λ1p, k1, p, 2) and an orthogonal array(λ2p2, k2, p, 2) leads to another orthogonal array (λ1λ2p3 .k1k2+1 ,p, 2). This enables us to construct orthogonal arrays[2p(n+1)、1+2(p+p2 +…+pn),p,2],[4p(n+2),1+2p+4(p2+p3+…+p(n+1)),p, 2],and [8p(n+3),1+2P+4p2+8(p3+p4+…+p(n+2)),p,2]where p is a prime or a prime power.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.10871123,11171201)
文摘The self-affine measure associated with an expanding matrix and a finite digit set is uniquely determined by the self-affine identity with equal weight. The spectral and non-spectral problems on the self- affine measures have some surprising connections with a number of areas in mathematics, and have been received much attention in recent years. In the present paper, we shall determine the spectrality and non-spectrality of a class of self-aiffine measures with decomposable digit sets. We present a method to deal with such case, and clarify the spectrality and non-spectrality of a class of self-affine measures by applying this method.
文摘The purpose of this paper is to survey the construction of orthogonal arrays of strength two by using difference sets. Some methods for constructing difference set D(2p.2p,p,2), where p is a prime or a prime power, are given. It is shown that the Kronecker sum of a difference set D(λ1p, k1, p, 2) and an orthogonal array(λ2p2, k2, p, 2) leads to another orthogonal array (λ1λ2p3 .k1k2+1 ,p, 2). This enables us to construct orthogonal arrays[2p(n+1)、1+2(p+p2 +…+pn),p,2],[4p(n+2),1+2p+4(p2+p3+…+p(n+1)),p, 2],and [8p(n+3),1+2P+4p2+8(p3+p4+…+p(n+2)),p,2]where p is a prime or a prime power.