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In view of this algorithm, the sufficient conditions ensuring that the bifurcated periodic solutions are orbitally asymptotically stable and unstable on the center manifold are obtained.

通过这一显式算法，给出了分支周期解在中心流形上轨道渐近稳定和不稳定的充分条件。

For general discrete bilinear system, this paper proposed a stability criteria which is sufficient for systems with linear feedback. The smallest attracting range is also obtained. Based on the criteria, a simple control law is proposed to guarantee the uniformly asymptotically stability of zero state.

对于一般离散双线性系统，本文提出了系统在线性反馈下的稳定性判据和最小吸引域，并给出了一种简单的控制方案，保证闭环系统在原点的一致渐近稳定性。

The return of a dishonoured Bill to the drawer or an indorser is, in point of form, deemed a sufficient notice of dishonour

这些名义上和形式上的肤浅事物都不能改变帝国实际上是希腊文化的这个事实。

The necessary and sufficient condition, which fundamental and total biorthogonal system in Banach spaces is Cesaro basis, is given.

利用BK空间的理论讨论了具有给定的完全双正交系的Banach空间X的乘子空间M的性质，给出了Banach空间X上基本完全的双正交系成为Cesaro基的充要条件。

Utilizing the theories of BK spaces and multiplier spaces, this paper discuss the necessary and sufficient condition which fundamental and total biorthogonal system in Banach spaces which don t contain copy of is unconditional basis.

利用BK空间的理论讨论了具有给定的完全双正交系的Banach空间X的乘子空间M的性质，给出了Banach空间X上基本完全的双正交系成为Cesaro基的充要条件。

Utilizing the theories of BK spaces and multiplier spaces, this paper discuss the necessary and sufficient condition which fundamental and total biorthogonal system in Banach spaces which don t contain copy of is unconditional basis .

本文利用BK空间和乘子空间的性质，讨论了在不含C0 的C0py的Banach空间上基本完全的双正交系成为无条件基的充要条件。

Concretely, starting from a short sequence primal masks possessing Hermite interpolation properties, a necessary and sufficient conditions such that primal masks satisfies the preassigned order of sum rules are established, then a dual masks with short support, symmetry and any preassigned order of sum rules is constructed, it follows that two multiscaling functions are obtained and then multiwavelets and dual multiwavelets are derived. From which, a general design framework is obtained for constructing biorthogonal multiwavelets system with multiplicity 2r associated with Hermite interpolation functions.

具体的，从具有Hermite插值性质的短序列尺度符号出发，首先建立它具有指定阶和规则的充要条件，然后构造出短支撑、对称的具有指定阶和规则的对偶尺度符号，从而得到一对对偶的尺度函数，再构造出相应的双正交多小波。

In this paper, we study a necessary and sufficient condition that complete bipartite graph exists factors.

讨论了完全偶图存在 [1，2 ]因子的充分必要条件，并给出了 [1，2 ]因子的计数

Applyingthe sufficient and necessary condition of biquadratic Bézier patch being non-negative,a method is presented to see whether two points are the closest points between twobiquadratic NURBS surfaces when the two points are respectively on the two surfaces. Based on the method, the surface split algorithm is improved while the surfaces arebiquadratic NURBS surfaces.

本文利用双二次 Bézier 曲面为非负的充要条件，提出了分别位于两张双二次 NURBS 曲面上的点是否为这两张曲面间距离最近的点的判别方法，并由此在双二次 NURBS 曲面的场合对计算最短距离的曲面分割法作了改进。

The general form of solution for the non symmetric matrix A is given, the expression of optimal approximation solution is presented, and an algorithm for solving the problem is described. The total least squares problem with symmetric and bisymmetry constraints is discussed respectively. A sufficient condition for existence of solution is derived by use of the theory of matrix Ricaati equation. The general form of solution is given if the problem has a solution, and the expression of optimal approximation solution is presented. Some numerical examples are given.

对矩阵A是非对称情形，给出了解的一般表达式，证明了最佳逼近问题解的存在唯一性，并给出了其解的表达式，描述了求解问题的算法；讨论了带对称和双对称约束的总体最小二乘问题，利用Ricaati矩阵方程的理论得到了解存在的一个充分条件，分别对对称矩阵和双对称矩阵两种情形，给出了解的一般表达式，证明了最佳逼近问题解的存在唯一性，给出了其解的表达式，提出了求解这些问题的算法，并给出了数值例子。

Consumer preference ; fuzzy partial ordering relation ; condorect function

消费者偏好；模糊偏序关系； condorect函数

And she doesn't have a cat, she has a Mexican hairless.

而且她不养猫，她养了一只墨西哥无毛犬。