Sets with even partition functions and 2-adic integers

For P ? \(\mathbb{F}_2 \)[z] with _P(0) = 1 and deg(_P) ≥ 1, let \(\mathcal{A}\) = \(\mathcal{A}\)(P) (cf. [4], [5], [13]) be the unique subset of ? such that Σ _n≥0 p(\(\mathcal{A}\), n)z ⁿ ≡ P(z) (mod 2), where p(\(\mathcal{A}\), n) is the number of partitions of n with parts in \(\mathcal{A}\). Let p be an odd prime and P ? \(\mathbb{F}_2 \)[z] be some irreducible polynomial of order p, i.e., p is the smallest positive integer such that P(z) divides 1 + z ^p in \(\mathbb{F}_2 \)[z]. In this paper, we prove that if m is an odd positive integer, the elements of \(\mathcal{A}\) = \(\mathcal{A}\)(P) of the form 2 ^k m are determined by the 2-adic expansion of some root of a polynomial with integer coefficients. This extends a result of F. Ben Saïd and J.-L. Nicolas [6] to all primes p.     

IDEALS OF MINORS DEFINING GENERIC SINGULARITIES AND THEIR GRöBNER BASES

In this article, using the local parametric equations of a generic projection π of a smooth projective variety X, at an analytically irreducible singular point y of X′ = π(X), the defining ideals J and J′ of X′ and its singular locus at y are expressed as ideals of maximal and sub-maximal minors of certain Sylvester matrix @. The proof is obtained by a convenient reduction of @ to a “generic pluri-circulant matrix” P and the construction of minimal Gröbner bases for the ideal of t-minors of P and for the ideals J and J′. The depth of local rings of X′ and Sing (X′) at y are also computed in terms of the multiplicity at y.     

On the complexity of the multivariate resultant

The multivariate resultant is a fundamental tool of computational algebraic geometry. It can in particular be used to decide whether a system of n$n$ homogeneous equations in n$n$ variables is satisfiable (the resultant is a polynomial in the system’s coefficients which vanishes if and only if the system is satisfiable). In this paper, we investigate the complexity of computing the multivariate resultant.     

An Arithmetic Poisson Formula for the multi-variate resultant

In these pages we compute the expectation of several functions of multi-variate complex polynomials. The common thread of all our outcomes is the basic technique used in their proofs. The used techniques combine essentially the unitary invariance of Bombieri–Weyl’s Hermitian product and some elementary Integral Geometry. Using different combinations of these techniques we compute the expectation of the logarithm of the absolute value of an affine polynomial and we compute the expected value of Akatsuka Zeta Mahler’s measure. As main consequences of these results and techniques, we show a probabilistic answer to question (d)$\left(d\right)$ in Armentano and Shub (2012)  [2], concerning the complexity of one point homotopy, and an Arithmetic Poisson Formula for the multi-variate resultant. These two last statements and bounds are related to the complexity of algorithms for polynomial equation solving.     

电能测量综合误差的分析及减少措施

通过对电能测量装置综合误差分析 ,找出电能测量装置产生误差的综合因素 ,提出减少综合误差的措施 ,提高电能测量装置的准确度     

基于插值法计算Dixon结式

在经典方法中，计算Dixon多项式和结式都要涉及到行列式的计算。由于行列式中的元素通常是符号化的，即其中每个元素都是关于变元(或参数)的多项式，从而导致行列式展开时的中间计算过程膨胀(甚至爆炸)。对此，提出在结式计算过程中将符号计算数值化，即对变元选择不同的插值点，将行列式中的元素数值化。然后，求出在不同插值点下行列式的值。最后，根据Zippel多变元插值法或其他相关插值算法计算出Dixon多项式和结式。采用插值方法有效克服了经典算法的中间计算过程膨胀问题。     

空间任意力系平衡的充分性判据

本文较简单地得到了空间任意力系平衡的一些充分性判据,並提出了选取各种平衡方程的力矩轴和投影轴的若干方法。     

MATLAB在运动学中的应用

仿真处理了著名的PASCAL摆线问题,并求解了摆线的运动学参数(以矩阵形式输出);仿真一个很难凭空想象其绝对运动轨迹的点的合成运动,并用编制的通用程序探索它的美妙轨迹;仿真了椭圆尺规机构的运动过程.仿真结果可作为教学演示,使抽象的力学生动活泼起来.     

THREE-DIMENSION INTERACTIONS OF CIRCULAR CRACK IN TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES

Exact solutions in form of elementary functions were derived for the stress and electric displacement intensity factors of a circular crack in a transversely isotropic piezoelectric space interacting with various stress and charge sources: force dipoles, electric dipoles, moments, force dilatation and rotation. The circular crack includes penny-shaped crack and external circular crack and the locations and orientations of these resultant sources with respect to the crack are arbitrary. Such stress and charge sources may model defects like vacancies, foreign particles, and dislocations. Numerical results are presented at last.     

横观各向同性压电空间中圆裂纹与合成点源的三维相互作用

研究了横观各向同性压电空间中的圆裂纹与包括力偶极子、电偶极子、点力矩、力张和力旋这些常见合成点源的相互作用．用初等函数的形式给出了在任意位置和方向的合成点源作用下,裂纹尖端3种应力强度因子和电位移强度因子的三维解．其中圆裂纹包括币形裂纹和外圆裂纹．这一系列的力电合成点源不仅其自身在工程中普遍存在,而且在某些情形下还可以模拟诸如微裂纹、空洞、夹杂和位错等缺陷．