Differentiable spaces that are subcartesian

We show that the differential structure of the orbit space of a proper action of a Lie group on a smooth manifold is weakly reflexive. This implies that the orbit space is a differentiable space in the sense of Smith, which ensures that the orbit space has an exterior algebra of differential forms, that satisfies Smith’s version of de Rham’s theorem. Because the orbit space is a locally closed subcartesian space, it has vector fields and their flows.     

Anzahl theorems of matrices over the residue class ring modulo psqt and their applications

Let $h=p^s{q}^t$ be its decomposition into a product of powers of two distinct primes, and ${\mathbb{Z}}_h$ be the residue class ring modulo h. In this paper, we determine the Smith normal forms of matrices, compute the number of the orbits of $m\times n$ matrices under the action of the group $G{L}_m({\mathbb{Z}}_h)\times G{L}_n({\mathbb{Z}}_h)$ and the length of each orbit over ${\mathbb{Z}}_h$. As applications, we determine the clique number, the independence number and the chromatic number of the bilinear forms graph, construct a family of association schemes by using $1\times n$ matrices and compute the intersection numbers and the character table over ${\mathbb{Z}}_h$ for $s=t=1$.     

Deficiencies of smooth manifolds

Being given a closed manifold Mⁿ, there are involutions (X²ⁿ, T) on closed manifolds of twice the dimension having fixed point set M. Kulkarni defined the deficiency of M for a class of involutions to be $\text{min}\text{(}\text{1}\text{2}\text{{}\text{dim}\text{H}{}^1\text{(X;Z}{}_{\mathrm{<mtext>2</mtext>}}\text{)?}\text{dim}\text{H}{}^1\text{(M;Z}{}_{\mathrm{<mtext>2</mtext>}}\text{)})}$ for all involutions (X, T) in the class. This paper exhibits manifolds for which the deficiency is positive for all involutions and studies the deficiencies for other classes.     

Spectral factorization of two-variable para-Hermitian polynomial matrices

This paper presents an algorithm for the so-called spectral factorization of two-variable para-Hermitian polynomial matrices which are nonnegative definite on thej axis, arising in the synthesis of two-dimensional (2-D)passive multiports, Wiener filtering of 2-D vector signals, and 2-D control systems design. First, this problem is considered in the scalar case, that is, the spectral factorization of polynomials is treated, where the decomposition of a two-variable nonnegative definite real polynomial in a sum of squares of polynomials in one of the two variables having rational coefficients in the other variable plays an important role (cf. Section 4). Second, by using these results, the matrix case can be accomplished, where in a first step the problem is reduced to the factorization of anunimodular para-Hermitian polynomial matrix which is nonnegative definite forp=j , and in a second step this simplified problem is solved by using so-called elementary row and column operations which are based on the Euclidian division algorithm. The matrices considered may be regular or singular and no restrictions are made concerning the coefficients of their polynomial entries; they may be either real or complex.     

测试转台温控箱的计算机控制

本文针对测试转台温控箱系统的大滞后特性，设计了一种带Ｓｍｉｔｈ预估器的ＰＩ校正器，并采用了基于８０９８单片机的计算机控制实现。仿真和实验均表明，文中的控制算法能够有效克服纯大滞后对控制系统稳定性的影响，具有良好的鲁棒性及控制性能，而且实现简单，可靠性好。     

Differential Posets and Smith Normal Forms

We conjecture a strong property for the up and down maps U and D in an r-differential poset: DU + tI and UD + tI have Smith normal forms over . In particular, this would determine the integral structure of the maps U, D, UD, DU, including their ranks in any characteristic. As evidence, we prove the conjecture for the Young-Fibonacci lattice Y F studied by Okada and its r-differential generalizations Z(r), as well as verifying many of its consequences for Young’s lattice Y and the r-differential Cartesian products Y ^r .     

非最小相位系统的复杂控制算法研究

针对非最小相位系统右半平面零点所造成的负调问题,文中以抑制非最小相位系统的负调和时滞问题为目的,将两步PID参数整定法与Smith预估控制器相融合,提出了一种复杂控制算法。该算法通过调整系统前置系数和PID参数,达到抑制非最小相位负调的作用,并将其作用于Smith预估控制结构中,达到提升系统响应时间的目的。利用MATLAB软件中的Simulink对典型二阶控制系统建立仿真模型。仿真结果表明,该复杂控制算法在消除系统负调的同时也提升了系统的响应时间,验证了该复杂控制算法的有效性和鲁棒性。     

高速电路中电容的分析及其EMC设计

在高速数字电路设计中,电容的正确选用及配置对系统的正常工作及其电磁兼容性起着至关重要的作用.本文对电容在电路系统中的高频特性进行了详细的分析,进而对电容的选择、放置及容值的计算进行了研究,提出了具有一定工程意义的去耦电容的选取方案.     

A compound matrix algorithm for the computation of the Smith form of a polynomial matrix

In the present paper is presented a numerical method for the exact reduction of a singlevariable polynomial matrix to its Smith form without finding roots and without applying unimodular transformations. Using the notion of compound matrices, the Smith canonical form of a polynomial matrixM(s)^nxn[s] is calculated directly from its definition, requiring only the construction of all thep-compound matricesC _p (M(s)) ofM(s), 1<pn. This technique produces a stable and accurate numerical algorithm working satisfactorily for any polynomial matrix of any degree.