关于模N的原根与它的逆的差的奇数幂及其推广

本文研究了模ｎ的原根ａ与它的逆ａ差的奇数幂分布性质，并给出了(?)的一个渐近公式．     

轨迹成型法加工球面光学零件面形精度分析

分析了轨迹成型法加工球面时影响零面形精度的多种因素，其中包括：工件回转轴与摆动轴不共面误差，工件回转轴与砂轮轴不共面误差，工件回转轴径向跳动、摆动误差，轴向窜动工件摆动轴的径向跳动以及砂轮的振动等因素对工件面形精度的影响。为了提高工件面形精度，首先应提高各回转轴和移动件的制造精度和减少配合误差，使其静刚度和动刚度提高，这是保证面形精度的最重要和基本的条件。     

Bounds for the expectation of the kth root of a random variable

Exact bounds for the mean value of a fractional moment, such as the sample standard deviation, are considered. These bounds are compared with those found by summation techniques applied to computer extended series. An expansion involving an arbitrary parameter is introduced, and now best bounds are found by optimization. There are applications to bounds for a certain class of quadrature problem.     

关于正则图直径上界的加强

设G为n阶κ正则简单连通图（κ≥2)，λ是图G的次根，d(G)是图G的直径，如果G不是二部图，且d(G)≠2，则d(G)≤[log(n-1)/log(κ/λ)]，并且当G≌时，这一上界可达．     

一般多项式零点的新估计

本文给出了一般多项式根的上下界估计,所得结果与文[1～4]中给出的估计式互不包含     

Computing the real roots of a polynomial by the exclusion algorithm

We describe a new algorithm for localizing the real roots of a polynomialP(x). This algorithm determines intervals on whichP(x) does not possess any root. The remainder set contains the real roots ofP(x) and can be arbitrarily small.     

Is the rigid-body assumption reasonable?: Insights into the effects of dynamics on the electrostatic analysis of barnase-barstar

Electrostatically-driven association of proteins is important to many biological functions, and understanding which amino acid residues contribute to these interactions is crucial to protein design. Theoretical calculations that are used to elucidate the role of electrostatics in association are typically based on a single experimentally determined protein structure, while an underlying rigid-body assumption is adopted. The goal of this study was to investigate the role of conformational fluctuations on electrostatic interaction energies, as applied to the electrostatic analysis of barnase-barstar. For our calculations, we apply theoretical alanine-scan mutagenesis to introduce charge perturbations by replacing every ionizable residue with alanine, one at a time. Electrostatic clustering and free energy calculations based on the Poisson-Boltzmann method are used to evaluate the effects of each perturbation. Molecular dynamics simulations are performed for the barnase-barstar parent complex and seven experimental alanine mutations from the literature, in order to introduce relaxation before and after mutation. We discuss the effects of dynamics, in the form of pre- and post-mutation relaxation, on electrostatic clustering and free energies of association in light of experimental data. We also examine the utility of nine electrostatic similarity methods for clustering of barnase alanine-scan mutants. Our calculations suggest that the rigid-body assumption is reasonable for electrostatic calculations of barnase-barstar.     

Efficient Computation of Roots in Finite Fields

We present an algorithm to compute rth roots in $\mathbb{F}_{q^m}We present an algorithm to compute rth roots in with complexity ?[(log m + r log q) m log q] if (m,q) = 1 and either (q(q−1),r) = 1 or r|(q−1) and ((q−1)/r,r) = 1. This compares well to previously known algorithms, which need O(r m³ log³ q) steps. Paulo S. L. M. Barreto: Supported by Scopus Tecnologia S. A. José Felipe Voloch: Supported by NSA grant MDA904-03-1-0117.     

On the Abel Basis Property of the System of Root Vector-Functions of Degenerate Elliptic Differential Operators with Singular Matrix Coefficients

We establish completeness and summability in the Abel-Lidskii sense for the system of root vector-functions of nonselfadjoint elliptic matrix operators A generated by noncoercive forms with the Dirichlet-type boundary conditions. An operator A + βE is positive for a sufficiently large β > 0 but not strongly positive in general. We obtain estimates for the eigenvalues and resolvent of A. Also, we study the resolvent of the extension $A$ of A to the corresponding negative space.