一类间接控制系统的绝对稳定性问题

利用厄米特二次型和若当标准形理论研究了一般间接控制系统的绝对稳定性问题,给出了绝对稳定性的代数形式的判别准则。所得到的结果是新的和有用的。     

关于正规Boole矩阵行空间的基数

称Ｂｏｏｌｅ矩阵Ａ是正规的，是指Ａ的行秩与列秩相等．本文主要得到两个结果．第一，推广了Ｊ．Ｋｏｎｉｅｃｚｎｙ在ＳｅｍｉｇｒｏｕｐＦｏｒｕｍ，ｖｏｌ．４４（１９９２）发表的论文Ｏｎｃａｒｄｉｎａ－ｌｉｔｉｅｓｏｆｒｏｗｓｐａｃｅｏｆＢｏｏｌｅａｎｍａｔｒｉｃｅｓ的主要结果．第二，若ｎ阶Ｂｏｏｌｅ矩阵的行空间基数大于２￣（ｎ－２）－２，则Ａ必是正规的．     

A Judging Method for Normal Family

ＡＪｕｄｇｉｎｇＭｅｔｈｏｄｆｏｒＮｏｒｍａｌＦａｍｉｌｙ￥ＺｈｕＺｈｅｎｘｉｎｇ（Ｄｅｐｔ．ｏｆＳｙｓｔｅｍＳｃｉｅｎｃｅａｎｄＭａｔｈ．，ＺｈｅｎｇｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｚｈｅｎｇｚｈｏｕ，４５００５２）Ａｂｓｔｒａｃｔ：Ｉｎ１９６４，Ｈ...     

Variables separated equations: Strikingly different roles for the Branch Cycle Lemma and the finite simple group classification

Davenport’s Problem asks:What can we expect of two polynomials,over Z,with the same ranges on almost all residue class fields? This stood out among many separated variable problems posed by Davenport,Lewis and Schinzel.By bounding the degrees,but expanding the maps and variables in Davenport’s Problem,Galois stratification enhanced the separated variable theme,solving an Ax and Kochen problem from their Artin Conjecture work.Denef and Loeser applied this to add Chow motive coefficients to previously introduced zeta functions on a diophantine statement.By restricting the variables,but leaving the degrees unbounded,we found the striking distinction between Davenport’s problem over Q,solved by applying the Branch Cycle Lemma,and its generalization over any number field,solved by using the simple group classification.This encouraged Thompson to formulate the genus 0 problem on rational function monodromy groups.Guralnick and Thompson led its solution in stages.We look at two developments since the solution of Davenport’s problem.Stemming from MacCluer’s 1967 thesis,identifying a general class of problems,including Davenport’s,as monodromy precise.R(iemann)E(xistence)T(heorem)’s role as a converse to problems generalizing Davenport’s,and Schinzel’s (on reducibility).We use these to consider:Going beyond the simple group classification to handle imprimitive groups,and what is the role of covers and correspondences in going from algebraic equations to zeta functions with Chow motive coefficients.     

A -normal, not densely normal Tychonoff space

We give an example of a -normal space which is not densely normal.

     

Essentially subnormal operators

An operator is essentially subnormal if its image in the Calkin algebra is subnormal. We shall characterize the essentially subnormal operators as those operators with an essentially normal extension. In fact, it is shown that an essentially subnormal operator has an extension of the form ``normal plus compact'.

The essential normal spectrum is defined and is used to characterize the essential isometries. It is shown that every essentially subnormal operator may be decomposed as the direct sum of a subnormal operator and some irreducible essentially subnormal operators. An essential version of Putnam's Inequality is proven for these operators. Also, it is shown that essential normality is a similarity invariant within the class of essentially subnormal operators. The class of essentially hyponormal operators is also briefly discussed and several examples of essentially subnormal operators are given.

     

纯正半群上的同余扩张(一)

刻划半群上的同余及其扩张是半群的代数理论中的一个非常重要的课题．本文讨论了带上的同余的正规性和不变性以及在其Ｈａｌｌ半群上的扩张，从同余扩张的角度刻划了带上的同余的性质，给出了扩张的极大、极小同余的描述．     

Hermite and Smith normal form algorithms over Dedekind domains

We show how the usual algorithms valid over Euclidean domains, such as the Hermite Normal Form, the modular Hermite Normal Form and the Smith Normal Form can be extended to Dedekind rings. In a sequel to this paper, we will explain the use of these algorithms for computing in relative extensions of number fields.

     

On the use of loss functions in the changepoint problem

Summary We consider a sequence of independent random variables whose densities depend on a parameter which is subject to a change at an unknown time point. A Bayesian decision-theoretic approach is used to obtain an optimal choice of changepoint. The exponential and multivariate normal models are analyzed, and some numerical examples are given.     

Scaled DFT Force Constants and Vibrational Spectrum of Cyclopropylamine

Abstract

The molecular structure and harmonic vibrational frequencies of cyclopropylamine have been calculated using the B3LYP density functional method with the 6‐31G(2d,2p) basis set. The scaled DFT force field gives very good reproduction of the experimental vibrational frequencies. Several of the vibrational fundamental modes assigned previously are reassigned on the basis of the B3LYP/6‐31G(2d,2p) method and the scaled force field calculations. The optimized scaling factors were used to scale the B3LYP/6‐31G(2d,2p) force field of cyclopropane and cyclopropylamine (–ND₂) molecules.