The Magnus representation of the Torelli group

In this paper we consider the Magnus representation of the Torelli group. We prove that it is not faithful by showing a non-trivial element in the kernel of this representaion.

     

Efficient parallel exponentiation in using normal basis representations

Von zur Gathen proposed an efficient parallel exponentiation algorithm in finite fields using normal basis representations. In this paper we present a processor-efficient parallel exponentiation algorithm in GF(qⁿ) which improves upon von zur Gathen's algorithm. We also show that exponentiation in GF(qⁿ) can be done in O((log₂n)²/log_qn) time using n/(log₂n)² processors. Hence we get a processor-time bound of O(n/log_qn), which matches the best known sequential algorithm. Finally, we present an efficient on-line processor assignment scheme which was missing in von zur Gathen's algorithm.     

SL(2,R)上的Fourier变换的渐近性质的注记

该文借助于犛犔（２，犚）上李代数及其万有包络代数讨论了犛犔（２，犚）上函数的Ｆｏｕｒｉｅｒ变换在无穷远处下降的阶与函数的光滑性的关系，我们得到的结论较［６］中的结论好，并由此得到犆２犮（犌）中的Ｐｌａｎｃｈｅｒｅｌ定理．     

Sensitivity Analysis of M-Estimates of Nonlinear Regression Model: Influence of Data Subsets

Asymptotic representations of the difference of M-estimators of the parameters of nonlinear regression model for the full data and for the subsample of data are given for the following three situation: i) fix number of points excluded from data, ii) increasing number, however asymptotically negligible part of data excluded, and finally iii) asymptotically fix portion of data excluded. Asymptotic normality of the difference of estimators (for the two latter cases) is proved.     

Topologically Free Partial Actions and Faithful Representations of Crossed Products

We study the relationship between the topological freeness of partial actions of discrete groups and faithful representations of the corresponding crossed products.     

On the calculation of force constants using isotopic frequencies by parametric method: Application to systems of (3×3) order

A method is proposed for the determination of angle parameters for ONF, ONCl and ONBr, utilising the isotopic frequencies of two isotopically substituted molecules. The force constants, Coriolis coupling constants, inertia defect, mean amplitudes of vibration and rotational distortion constants were also calculated and compared with literature values.     

左删失右截断数据的分位数的固定宽度序贯置信区间估计

基于左截断右删失数据下的乘积限估计构造了分位数固定宽度序贯置信区间及其估计，研究了序贯置信区间估计的渐近性质。作为副产品，获得了分位数估计近邻点的Bahadur表示定理。这个表示定理是推导分位数固定宽度序贯置信区间估计渐近性质的重要基础。同时，在文中，进行了一些计算机模拟试验，证明了左截断右删失数据下分位数估计的序贯方法是效的和精确的。     

Wavelet bases in generalized Besov spaces

In this paper we obtain a wavelet representation in (inhomogeneous) Besov spaces of generalized smoothness via interpolation techniques. As consequence, we show that compactly supported wavelets of Daubechies type provide an unconditional Schauder basis in these spaces when the integrability parameters are finite.     

New Correlation Duality Relations for the Planar Potts Model

We introduce a new method to generate duality relations for correlation functions of the Potts model on a planar graph. The method extends previously known results, by allowing the consideration of the correlation function for arbitrarily placed vertices on the graph. We show that generally it is linear combinations of correlation functions, not the individual correlations, that are related by dualities. The method is illustrated in several non-trivial cases, and the relation to earlier results is explained. A graph-theoretical formulation of our results in terms of rooted dichromatic, or Tutte, polynomials is also given.