The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

非受格动词及非作格动词研究

在“直接宾语限制”和“动词行为一致性”两个假设的基础上,利用致使型结果结构作为一种测试手段来区分现代汉语中的三种动词：非受格动词、非作格动词和及物动词,从而证明普尔马特曾提出的“非受格动词假设”在现代汉语中同样成立.     

《钢铁意志》女主人公的坚韧性格及其二元成因

《钢铁意志》作为美国女作家埃伦·格拉斯哥的中晚期作品,是她对其人类生存思想与女性主义创作思想的一次成熟表达。这部小说的女主人公埃达·芬卡斯特尔既独立自主又坚忍不拔,既是格拉斯哥所倡导的理想女性形象,也是其性格制胜生存法则的典型体现。格拉斯哥将埃达的坚毅性格归因于个体的内在遗传因素和社会外在环境因素的双重塑造作用。换言之,埃达的钢铁意志体现着家族血脉传承与新时代女性观念嬗变在其性格铸造方面的一种合力效应。     

多束非相干光迭加后光强分布的一点讨论

本文利用光的迭加原理,运用矢量合成的方法,推导出多束非相干光的合振幅,合光强计算公式,从而帮助学生加深对光的相干迭加和非相干迭加的理解。     

精密车床主轴回转误差的测试与补偿

文中介绍了精密车床主轴回转误差的一种补偿系统及补偿刀架结构,可以提高被加工件的圆度。实验表明,主轴转速为485 r/min 下,工件圆度误差由原来的1～1.7μm 减少到0.4～0.8μm,即补偿掉了40%～67%.文中还介绍了一种主轴回转误差的综合误关差计算机辅助测试系统,可绘制出径向、摆角、轴向3种回转误差的误差曲线图和误差频谱图,并打印出误差值、相关系数等。     

微分周形式与稀疏微分结式

代数周(Chow)形式和代数结式是代数几何的基本概念,同时还是消去理论的强大工具.一个自然的想法是在微分代数几何中发展相应的周形式和结式理论.但是由于微分结构的复杂性,在本文的研究工作之前,微分结式只有部分结果,而微分周形式与稀疏微分结式理论一直没有得到发展.本文的主要结果包括:第一,发展一般(generic)情形的微分相交理论,作为应用,证明一般情形的微分维数猜想.第二,初步建立微分周形式理论.对不可约微分代数簇定义微分周形式并证明其基本性质,特别地,给出微分周形式的Poisson分解公式,引入微分代数簇的主微分次数这一不变量并证明一类微分代数闭链的周簇和周坐标的存在性.作为应用,首次严格定义微分结式,证明其基本性质.第三,初步建立稀疏微分结式理论.引入Laurent微分本性系统的概念,定义稀疏微分结式,证明其基本性质,特别地,引入微分环面簇的概念,给出稀疏微分结式阶数和次数界的估计,并基于此给出计算稀疏微分结式的单指数时间算法.     

矢量合成移相器

描述一种可靠性、价格、能耗和体积诸方面都优于机械相位调节器的新型电控移相器，它的工作原理基于矢量合成，故定名为矢量合成移相器。并已在兰州重离子加速器相位稳定系统０号、４号、６号机柜中代替机械相位调节器，取得了令人满意的结果。     

Geometrically non-linear analysis of laminated composite structures using a 4-node co-rotational shell element with enhanced strains

To demonstrate the solutions of linear and geometrically non-linear analysis of laminated composite plates and shells, the co-rotational non-linear formulation of the shell element is presented. The combinations of an enhanced assumed strain (EAS) in the membrane strains and assumed natural strains (ANS) in the shear strains improve the behavior of 4-node shell element. To secure computational efficiency in the incremental non-linear analysis, the present element uses the form of the resultant forces pre-integrated through the thickness. The transverse shear stiffness of the laminates is defined by an equilibrium approach instead of the shear correction factor. Numerical examples of this study show very good agreement with the references.     

循环码译码的Dixon结式方法

针对纠错码译码就是非线性方程组的求解问题,提出利用Dixon结式方法对译码方程进行消元以得到接收数据中的错位多项式.首先,根据纠错码的纠错能力和接收数据得到伴随式矩阵并通过该矩阵的秩确定接收码字中错误位的个数.然后,根据错位个数和伴随多项式构造译码方程.译码时,将其中一个错位变元作为隐藏变元,利用Dixon结式方法进行消元.最后,得到的Dixon结式就是关于隐藏变元的多项式.该多项式去掉多余因子后就是错位多项式,利用Chien搜索法即可求解出错误位置.当错位较多时,采用逐次计算结式的方法以筛除计算过程中的多余因子和重因子.另外,根据不同错位个数得到的错位多项式,提出了构造一类循环码错位多项式符号解的猜想,该猜想可以大大提高译码效率.实验验证了结式理论在纠错码译码方面的应用是有效的且有助于降低对芯片性能的要求.