光周期敏感不育水稻中激素的二阶导数卷积伏安法研究

二阶导数卷积伏安法应用于水稻中痛量雌雄激素的检测，具有快速，灵敏，干扰少的特点。本文以光周期敏感核不育水稻农垦５８Ｓ为材料，以农垦５８作对照，了叶焉和穗中雌，雄性激素的含量，研究了不同光周期条件下两类激素的变化。     

Convolution of discrete measures on linear groups

Let p,q∈R such that 1<p<2 and . Define

(∗)     

Increasing the polynomial reproduction of a quasi-interpolation operator

Quasi-interpolation is an important tool, used both in theory and in practice, for the approximation of smooth functions from univariate or multivariate spaces which contain , the d-variate polynomials of degree ≤m. In particular, the reproduction of Π_m leads to an approximation order of m+1. Prominent examples include Lagrange and Bernstein type approximations by polynomials, the orthogonal projection onto Π_m for some inner product, finite element methods of precision m, and multivariate spline approximations based on macroelements or the translates of a single spline.For such a quasi-interpolation operator L which reproduces and any r≥0, we give an explicit construction of a quasi-interpolant which reproduces Π_m+r, together with an integral error formula which involves only the (m+r+1)th derivative of the function approximated. The operator is defined on functions with r additional orders of smoothness than those on which L is defined. This very general construction holds in all dimensions d. A number of representative examples are considered.     

N=2^t点DFT的快速卷积算法

从所周知,循环卷积和离散富里叶变换(DFT)可以互相计算,只要得到其中一个的快速算法就可导出另一个的快速算法。循环卷积目前已有乘法量为O(N)的最佳算法(特别是当N较小时),为此关键是如何将DFT转化为循环卷积,当DFT的长度N=p(p为素数),Rader利用有限域GF(p)的乘法群是循环群就成功地将p点DFT转化为Q(p)(F(p)为户的Euler函数)点循环卷积;当N=p~e时,由于商环Z/(p~e)存在F(p~c)阶元素,人们也成功地将p~c点DFT转化为P(p~(c-1))一系列循环卷积,即一个y(p~c)点循环卷积,二个P(p~(c-1))点     

Generalizations of Non-Commutative Neutrix Convolution Products of Functions

The non-commutative neutrix convolution product of the functions x ^r cos_–(x) and x ^s cos₊(x) is evaluated. Further similar non-commutative neutrix convolution products are evaluated and deduced.     

Remarks on the r and Δ convolutions

In this paper we study the properties of the r–deformation introduced in [B1]. We observe that the associated convolution coming from the conditionally free convolution is associative only for r = 1 and r = 0. We give the realization of some r–Gaussian random variables and obtain Haagerup–Pisier–Buchholz type inequalities. We also study another convolution defined with the use of the r–deformation through a moment–cumulant formula [KY1] and show that it is associative and in general not positive. Partially sponsored with KBN grant no 2P03A00723 and RTN HPRN-CT-2002-00279.     

Spherical convolution operators in spaces of variable Hölder order

In this paper, we study the images of operators of the type of spherical potential of complex order and of spherical convolutions with kernels depending on the inner product and having a spherical harmonic multiplier with a given asymptotics at infinity. Using theorems on the action of these operators in Hölder-variable spaces, we construct isomorphisms of these spaces. In Hölder spaces of variable order, we study the action of spherical potentials with singularities at the poles of the sphere. Using stereographic projection, we obtain similar isomorphisms of Hö lder-variable spaces with respect to n-dimensional Euclidean space (in the case of its one-point compactification) with some power weights.     

Decompositions of the free additive convolution

We introduce and study a new type of convolution of probability measures, denoted μν and called the s-free additive convolution, which is defined by the subordination functions associated with the free additive convolution. We derive an alternating decomposition of μν for compactly supported μ and ν, using another convolution called orthogonal additive convolution. This decomposition leads to two types of ‘complete’ alternating decompositions of the free additive convolution μ?ν. More importantly, we develop an operatorial approach to the subordination property and introduce the associated notion of s-free independence. Moreover, we establish relations between convolutions associated with the main notions of noncommutative independence (free, monotone and boolean). Finally, our result leads to natural decompositions of the free product of rooted graphs.