四阶直接控制系统绝对稳定的充分必要条件

本用用popov频率法，讨论了一类四阶直接控制系统dx/dt=Ax bf(σ），σ=c^Tx零解的绝对稳定性，获得了特征根均为负实数的一类四阶直接控制系统零解绝对稳定的充分必要条件．     

一类直接控制系统的绝对稳定性

利用线性代数理论中的厄米特二次型和若当标准形研究一类直接控制系统的绝对稳定性问题．进一步发展了控制系统稳定性理论中最近发展起来的一种新的研究方法──降维法．得到了用参数表示的代数形式的绝对稳定性的判别准则．     

Lurie型直接控制系统的绝对稳定性准则

本文对几类特殊的直接控制系统得到了绝对稳定的充要条件,讨论了控制系统第一标准型的绝对稳定性,所得结果改进了文[3]、[5]、[6]、[7]中的相应结果.     

变时滞退化Lurie控制系统的绝对稳定性

研究了变时滞退化Lurie控制系统的绝对稳定性问题.基于Lyapunov稳定性理论,利用线性矩阵不等式方法给出了系统绝对稳定的判别准则.讨论了变时滞退化Lurie直接控制系统和间接控制系统的绝对稳定性,得到绝对稳定性的充分条件仅依赖于时滞导数的大小,且时滞可以是无界函数：最后给出了实例说明本文结果的有效性.     

二阶直接控制系统绝对稳定性的充分必要条件

二阶直接控制系统的绝对稳定性,目前尚未见到充分必要条件。本文给出了二阶直接控制系统的绝对稳定性的充分必要条件,并且解决了各种临界情况的绝对稳定性,从而完全解决了二阶直接控制系统的绝对稳定性问题。研究二阶直接控制系统     

关于一类非线性控制系统绝对稳定性的研究

通过构造Liapunov函数讨论了一类非线性非定常控制系统并得出其零解绝对稳定性的条件,推广了相关结论.     

NFDE的Lurie型系统的绝对稳定性

1.引言 文[2]研究了一般的RFDE的Lurie型系统的绝对稳定性,推广了[5]、[7]的结果。E.N.Chukwu用Liapunov泛函研究了某一类NFDE的Lurie系统的绝对稳定性,其控制执行机构为一维情形。本文就m个非线性执行机构的情形,用POPOV频率特性方法讨论NFDE的Lurie型系统的绝对稳定性,并推广了[2]的某些结果。 我们考虑下列直接控制系统     

多非线性一般Lurie离散系统的绝对稳定性

本文应用Lyapunov函数方法,讨论了具有多个非线性项的一般Lurie离散控制系统的绝对稳定性问题,借助于关于变元σ绝对稳定性的概念,得出了上述系统绝对稳定的充要条件及一些简洁的充分条件。     

一类二阶广义控制系统的反馈控制与极点配置

应用泛函分析及算子理论讨论了Hilbert空间中一类二阶广义控制系统的反馈控制与极点配置问题，利用有界线性算子的广义逆给出了问题有解的一个充分条件，并在此条件下给出了解的构造性表达式，这对广义控制系统的稳定性及渐近稳定性研究具有重要的理论价值．     

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。     

A one parameter method for the matrix inverse square root

This paper is motivated by the paper [3], where an iterative method for the computation of a matrix inverse square root was considered. We suggest a generalization of the method in [3]. We give some sufficient conditions for the convergence of this method, and its numerical stabillity property is investigated. Numerical examples showing that sometimes our generalization converges faster than the methods in [3] are presented.     

Fatou theorems for parabolic equations

For elliptic parabolic operators with time dependent coefficients, bounded and measurable, the absolute continuity of the two caloric measures plus a Fatou theorem are shown to hold on the parabolic boundary of a smooth cylinder given a Carleson-type condition on the coefficients of the operators, and assuming one of the measures is a center doubling measure. Given a stronger Carleson condition, and no doubling assumption, another kind of Fatou theorem result holds. The method of proof follows that of Fefferman, Kenig and Pipher.

     

Periodic solutions of a derivative nonlinear Schrödinger equation: Elliptic integrals of the third kind

The nonlinear Schrödinger equation (NLSE) is an important model for wave packet dynamics in hydrodynamics, optics, plasma physics and many other physical disciplines. The ‘derivative’ NLSE family usually arises when further nonlinear effects must be incorporated. The periodic solutions of one such member, the Chen-Lee-Liu equation, are studied. More precisely, the complex envelope is separated into the absolute value and the phase. The absolute value is solved in terms of a polynomial in elliptic functions while the phase is expressed in terms of elliptic integrals of the third kind. The exact periodicity condition will imply that only a countable set of elliptic function moduli is allowed. This feature contrasts sharply with other periodic solutions of envelope equations, where a continuous range of elliptic function moduli is permitted.     

A problem for the Helmholtz equation outside cuts on the plane with the dirichlet condition and the oblique derivative condition on opposite sides of the cuts

We consider a boundary value problem for the Helmholtz equation outside cuts on the plane. The Dirichlet condition is posed on one side of each cut, and an oblique derivative condition with pure imaginary coefficient of the tangential derivative is posed on the other side. We prove the uniqueness of the solution. The solvability of the problem is proved for the case in which the above-mentioned pure imaginary coefficient is less than unity in absolute value. In this case, we obtain an integral representation of the solution of the problem in the form of potentials. The densities of the potentials are found from a system of Fredholm integral equations of the second kind, which is uniquely solvable. The boundary value problem considered here generalizes the mixed Dirichlet-Neumann problem.     

Tensor absolute value equations

This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems and is a generalization of the well-known absolute value equations in the matrix case. We prove that tensor absolute value equations are equivalent to some special structured tensor complementary problems. Some sufficient conditions are given to guarantee the existence of solutions for tensor absolute value equations. We also propose a Levenberg-Marquardt-type algorithm for solving some given tensor absolute value equations and preliminary numerical results are reported to indicate the efficiency of the proposed algorithm.     

求解对称张量绝对值方程问题的非光滑牛顿法

提出一类对称张量绝对值方程问题,给出了求解此类问题的一类非光滑牛顿法,并且在一般的假设条件下,给出了算法的局部收敛性.最后给出相关的数值实验表明了算法的有效性.     

合数是绝对假素数的充要条件

利用正整数模的特征数这一新概念给出了合数是绝对假素数的充要条件。以此为据，证明了绝对假素数是奇数，它无异于1的平方因数，并且至少是三个互异的奇素数的乘积；还给出了两个绝对假素数或两个大于1的奇数的乘积是绝对假素数的充要条件。     

Minimum-weight design with piecewise constant specific stiffness

Much of the literature on minimum-weight design is concerned with structures with continuously varying dimensions. Structures of this kind achieve an absolute minimum of weight and thereby provide a useful standard of comparison, but their manufacturing cost is prohibitive in most applications. As a step toward the establishment of optimality conditions for more practical structures, the present paper discusses optimal design of sandwich beams and frames with segmentwise constant cross sections. Optimality is shown to require that the mean square stress in the face sheets has the same value for all segments. The use of the optimality condition is illustrated by examples.This research was supported by the Advanced Research Projects Agency, Project DEFENDER, and was monitored by the US Army Research Office-Durham, Contract No. DA-31-124-ARO-D-257.     

Uniform partial regularity of quasi minimizers for the perimeter

Quasi minimizers for the perimeter are measurable subsets G of such that for all variations of G with and for a given increasing function such that . We prove here that, given , G a reduced quasi minimizer, and , there are , with , and , homeomorphic to a closed ball with radius t in , such that for some absolute constant . The constant above depends only on n, and . If moreover for some , we prove that we can find such a ball such that is a dimensional graph of class . This will be obtained proving that a quasi minimizer is equivalent to some set which satisfies the condition B. This condition gives some kind of uniform control on the flatness of the boundary and then criterions proven by Ambrosio-Paolini and Tamanini can be applied to get the required regularity properties. Received: July 12, 1999 / Accepted: October 1, 1999     

Absolute summability of orthogonal series by Euler’s method

We have obtained a sufficient condition for the absolute summability of an orthogonal series by the (E, 1) method. We have proved that if the coefficients of the orthogonal series decrease monotonically in absolute value, then the condition we have found is exact. We have shown that for coefficients decreasing not necessarily monotonically the condition given is not exact. Translated from Matematicheskie Zametki, Vol. 21, No. 1, pp. 51–56, January, 1977.