矩阵系统的稳定与条件稳定

一个矩阵对应一种状态变换 .一系列的矩阵构成矩阵序列系统 .任一微小的扰动都会破坏伪逆的精确性 ,即状态的最后结果 .本文证明 :若矩阵系统是广义各态历经的 ,则系统是稳定的 ;若矩阵系统是普真的 ,则系统是条件稳定的 .     

Stability and Asymptotic Stability of Functional-Differential Equations

We investigate asymptotic behaviour of solutions of the functional-differentialequation where f and g arelocally Lipschitz functions, C is a continuous matrix and thesmooth lag function obeys 0 (t) t for t 0. We transformthe equation into a delay equation with an infinity of delaysand use a theorem of Söderlind to derive sufficient conditionsfor stability and for asymptotic stability in the case lim_t (t) = . The situation is qualitatively different when lim_t (t) = * < and we outline stability conditions for thatcase by employing direct techniques.     

Stability Functions

In this article we discuss the role of stability functions in geometric invariant theory and apply stability function techniques to various types of asymptotic problems in the Kähler geometry of GIT quotients. We discuss several particular classes of examples, namely, toric varieties, spherical varieties and the symplectic version of quiver varieties.     

扰动系统的Lipschitz稳定性和指数渐近稳定性

本文给出若干扰动微分系统的零解是一致Ｌｉｐｓｃｈｉｔｚ稳定和指数渐近稳定，以及第五个解渐近地趋于零的一些充分条件。     

Volterra系统全局稳定、扇形稳定及关联稳定的一些新判据

Stability of Volterra systems are discusses by subpositive definite matrix, and some new criterions for Volterra systems on overall situation stability, sector stability and connection stability are acquired. These results expand or improve some existing criterions.     

差分系统的渐近稳定性定理及渐近稳定性区域

本文首先给出了一个利用构造Liapunov函数来判别差分系统渐近稳定性的定理,此定理改进了已有结论[1]且在应用上更为方便.然后,给出了对于自治差分系统,求其渐近稳定区域或吸引区域的几个定理.     

金融机构的稳定性

用系统的观点分析金融稳定性问题,先简介了金融系统的有关概念,比较了金融稳定性和生态学稳定性概念以及金融生态环境与金融系统稳定性的关系,讨论了与金融稳定性有关的问题,论证了金融机构确定模型和随机模型以及具有下临界点L的金融机构模型的稳定性,构建并论述了金融群落、金融群落层级结构系统的稳定性.     

Stability preservation theorems

The basic result of the paper is the main theorem worded as follows. Let {ie155-01} be a valued field such that {ie155-02} has characteristic p > 0 and let {ie155-03} be an extension of valued fields satisfying the following conditions: (i) there exists a set {ie155-04} for which {ie155-05} is a separating transcendence basis for a field {ie155-06} over F_R; (ii) Γ _R is p-pure in {ie155-07}, i.e., {ie155-08} does not contain elements of order p; (iii) there exists a set B₁ ⊂ F₀^× such that the family {ie155-09} is linearly independent in the elementary p-group {ie155-10}; (iv) F₀ is algebraic over F(B₀ ⋃ B₁). Then the property of being stable for {ie155-11} implies being stable for {ie155-12}. Supported by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-344.2008.1) and by RFBR (grant No. 08-01-00442-a). __________ Translated from Algebra i Logika, Vol. 47, No. 3, pp. 269–287, May–June, 2008.     

Stability of peakons

The peakons are peaked solitary wave solutions of a certain nonlinear dispersive equation that is a model in shallow water theory and the theory of hyperelastic rods. We give a very simple proof of the orbital stability of the peakons in the H¹ norm. © 2000 John Wiley & Sons, Inc.     

Limit Cycle Stability

A method for determining the stability of limit cycles in non-linearsystems is presented. It is based on the describing functionmethod used in engineering, and is especially suitable for usewith single-loop feedback systems, though it can be used inits present form with autonomous sets of ordinary differentialor difference equations which can be transformed to single-loopfeedback form. The stability test uses a successive approximationmethod which is shown to be convergent; explicit error boundsare not given but a feature of the method is that it is apparentwhen a sufficiently high order approximation is being used.From a practical point of view, the stability criterion's mainadvantage appears to be that the nonlinear part of the systemis not greatly restricted—discontinuities and multiplebranches cause no difficulties, as evidenced by an example givenwhere the nonlinearity is a relay with hysteresis. Unlike earlierlimit cycle stability tests using describing functions, thisone includes its own reliability guide and allows a better approximationto be used if the current one is not good enough.     

Marginal Material Stability

Marginal stability plays an important role in nonlinear elasticity because the associated minimally stable states usually delineate failure thresholds. In this paper we study the local (material) aspect of marginal stability. The weak notion of marginal stability at a point, associated with the loss of strong ellipticity, is classical. States that are marginally stable in the strong sense are located at the boundary of the quasi-convexity domain and their characterization is the main goal of this paper. We formulate a set of bounds for such states in terms of solvability conditions for an auxiliary nucleation problem formulated in the whole space and present nontrivial examples where the obtained bounds are tight.     

Stability of g-frames

g-Frames are natural generalizations of frames which cover many other recent generalizations of frames, e.g., bounded quasi-projectors, frames of subspaces, outer frames, oblique frames, pseudo-frames and a class of time-frequency localization operators. Moreover, it is known that g-frames are equivalent to stable space splittings. In this paper, we study the stability of g-frames. We first present some properties for g-Bessel sequences. Then we prove that g-frames are stable under small perturbations. We also study the stability of dual g-frames.     

Stability and D-stability

In this paper, we prove a new sufficient condition for D-stability of a matrix. We then use it to show that (i) a nonderogatory stable matrix A has a Schwarz canonical form which is D-stable, and (ii) a nonderogatory stable matrix A has a Routh-canonical form which is totally stable.     

Stability of multipeakons

The Camassa–Holm equation possesses well-known peaked solitary waves that are called peakons. Their orbital stability has been established by Constantin and Strauss in [A. Constantin, W. Strauss, Stability of peakons, Comm. Pure Appl. Math. 53 (2000) 603–610]. We prove here the stability of ordered trains of peakons. We also establish a result on the stability of multipeakons.     

Stability and Conditional Stability of Time-dependent Difference Equations in Banach Spaces

Using methods parallel to those of ordinary differential equations,stability of time-dependent difference equations in Banach spacesis examined. Asymptotic stability, instability and conditionalstability properties are especially studied.     

Equivariant Sufficiency and Stability

An equivariant version of Tougerone’s finite determinacy theorem along with a criterion for stability of an invariant germ are proved.     

Stability has many names

A list of 22 definitions of stability of a functional equation and 5 definitions of stability of the alternation of two functional equations is given as well as some simple examples.     

X-调和映射的稳定性

在一般调和映射基础上定义了X-调和映射和次椭圆调和映射，得到了X-调和映射的稳定性定理，它是Leung一般调和映射及其稳定性定理的推广．