不可约元素

It is precisely this incommensurability of these elements of life that gives them the right not to he compared with any particular equivalent and that gives to life an irreplaceable charm and wealth.

恰恰是这些生活元素的不可相互化约性给予自身不能与任何特定等价物相比较的权利，并由此给予了生活一种无可替代的魅力与财富。

The asymptotic synchronization in a lattice of x-coupled nonidentical Lorenz equations is considered, the external coupling matrix is an n×n irreducible symmetric real matrix having zero row sums and nonpositive off-diagonal elements.

考虑外部耦合格式为n×n阶实对称不可约，行和为零且对角线以外的元素非正的矩阵，内部耦合格式为仅有x-分量参与耦合的非恒同Lorenz格点系统的渐近同步。

If ris also irreducible in Z_nand f~n~κ≡fmodn,r(xfor all f∈Z_nthen we call n a Carmichael number of orderκmodulo r.Denote the set of all such numbers by C_κ,r(x.Define C_κ=∪_r(xC_κ,r(x,where rpasses through all monic irreducible polynomials over Z of degreeκ.We call elements of the set C_κCarmichael numbers of orderκ.ZHU and SUN[Journal of Sichuan University,42;1(2005), 47-51]first gave a necessary condition for Carmichael numbers of order 3.Then they gave a sufficient condition for Carmichael numbers of order 3,but did not find any such numbers less than 10~8 satisfying the sufficient condition.At last,they asked three questions;1.is the necessary condition also sufficient?

f∈Z_n，就称n是模r的κ阶Carmichael数，用C_κ，r(x表示所有这种数的集合，定义C_κ=∪_r(xC_κ，r(x，这里r跑遍Z中所有κ次首一不可约多项式，C_κ里面的元素就称为κ阶Carmichael数，C_κ称为κ阶Carmichael数集，朱文余和孙琦[四川大学学报，42；1(2005)，47-51]首先给出了3阶Carmichael数的一个必要条件；然后又给出了这种数的一个充分条件，并发现10~8内没有满足此充分条件的这种数；最后他们提出三个问题；一、问必要条件是否也是充分的？

Chapter 2 is devoted to the discussion of the asymptotic synchronization of par-tially coupled Lorenz systems with the external coupling matrices being n×n irreduciblesymmetric real matrices having zero row sums and nonpositive off-diagonal elements.

在第二章我们讨论了当外部耦合矩阵是n×n阶实对称不可约，行和为零且对角线以外的元素非正的矩阵时部分耦合非恒同Lorenz方程格点系统的渐近同步问题。

Under the conditions that the external coupling matricesare n×n irreducible symmetric real matrices with zero row sums and nonpositive off-diagonal elements, asymptotic synchronization occurs if the coupling strength exceedsa critical value.

第三章主要讨论非恒同的单摆振子系统，讨论了外部耦合格式矩阵是n×n阶实对称不可约，行和为零且对角线以外的元素非正的矩阵时系统的解的渐近同步性。

In Chapter 3, we discuss the synchronization of coupled dynamical systems on condition that the external coupling matrices are n × n irreducible symmetric real matrices with zero row sum and nonnegative off-diagonal elements and internal coupling matrices are m × m asymmetric matrices.

在第三章我们讨论了耦合动力系统中，当外部耦合矩阵是n×n阶实对称不可约，行和为零且对角线以外的元素非负的矩阵，内部耦合矩阵是m×m阶非对称矩阵时耦合系统的同步问题。

Chapter 2 is devoted to the discussion of the synchronization of coupled dynamical systems with the external coupling matrices being n × n irreducible circulant real matrices having zero row sum and nonnegative off-diagonal elements and internal coupling matrices being m × m symmetric positive definite matrices.

在第二章我们讨论了耦合动力系统中，当外部耦合矩阵是n×n阶实循环不可约，行和为零且对角线以外的元素非负的矩阵，内部耦合矩阵是m×m阶对称正定矩阵时耦合系统的同步问题。

In order to determine the solution set of the equation , by the means of meet-irreducible element and irredundant finite meet-decomposition, we first obtain the maximal solutions to the simple equation in the case that b has an irredundant finite meet-decomposition, and then consider the relation between the equation and the equation , based on this, we obtain the maximal solutions to the equation in the case that each element of the matrix B has an irredundant finite meet-decomposition and so determine its solution set completely.

为了确定方程的解集，本文利用交既约元与不可缩短的有限交分解等工具，同样地先求出简单形式的型矩阵方程的所有极大解，然后讨论方程与方程之间的关系，在此基础上，在B的每个元素均有不可缩短的有限交分解的情况下，求出了方程的所有极大解，从而完全确定了方程的解集。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失