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We establish an asymptotic Lipschitz homotopy invariance theorem for these K-homology groups and K-theory groups. We show that the asymptotic index maps are isomorphisms for the asymptotically scaleable spaces, which include Euclidean cones, simply connected complete Riemannian manifolds with nonpositive curvature.

我们证明了这些K-同调群和K-理论群具有渐近Lipschitz同伦不变性；对于渐近可标度的几何空间（包括欧氏锥、单连通非正曲率完备黎曼流形等），证明了渐近指标映射为同构。

We call L n=1-matrices for N_0~1-matrices. Meyer introduced the concept of the Perron complement of a nonnegative and irreducible matrix in 1989 and used it to construct an algorithm for computing the stationary distribution vector for Markov chains. We extend the Perron complements of nonnegative and irreducible matrices to the Perron complements of nonpositive and irreducible matrices.

我们这里是把Perron余的概念推广到了非正不可约矩阵，显然它也具有非负矩阵相类似的性质，逆N 01矩阵又是特殊的非负矩阵，我们证明了在一定条件下，逆N 01矩阵和N 02矩阵的广义Perron余的继承性，并给出了相关的不等试：逆N 01矩阵和N 02矩阵的广义Perron余逆矩阵的不等式；逆N 01矩阵的主子阵与其逆矩阵的不等式。

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。

When the target is of nonpositive curvature in the sense of Alexandrov, the noncharacteristic condition of the domain was removed and the uniqueness and local Holder continuity of energy minimizers were obtained.

当靶空间是非正曲率(Alexandrov意义下)空间时，定义域的非特征条件可以去掉，并可以得到能量极小解的唯一性和局部Hlder连续性。

In this paper, one sufficient condition for the global asymptotical stability of the three-dimensional cooperative system is derived using the nonpositive divergence and the properties of monotone flow.

利用非负散度和单调流性质推导出三维合作系统全局渐近稳定的充分条件，并将该条件应用到一些具体的三维合作系统系统的稳定性判定中，所得结果说明了Hirsch所提出的猜测的正确性，同时推广和改进了相关文献的已有研究成果。

In chapter three, in order to distinct N 0?matrices that defined by deferent references, we will use the following notions. A matrix is called N_0~2-matrix if the matrix is nonpositive and its all-principal minors are nonpositive.

不可约矩阵Perron余的Perron向量同原矩阵Perron向量有着继承性，另外非负矩阵的Perron余也可用于Perron根的估计，因此非负矩阵的Perron余的研究有着重要的理论价值。

In Chapter Ⅲ, by considering functions H k that may not have nonpositive partial derivative on s and employing integral averaging technique and Hardy inequality, the oscillation for a class of high order nonlinear differential equations and high order nonlinear damped differential equations is discussed, new oscillation criteria are established.

第二章利用广义Riccati技巧、积分平均技巧以及微分不等式理论，讨论了一类二阶非线性常微分方程的振动性，得到了若干新的振动准则，并讨论了该方程具有强迫项时解的渐近性态。

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。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。