多维空间

Aiming at the characteristic of degree of freedom in multiple input multiple output radars, a scheme for multitarget identification and localization using a monostatic MIMO radar system with L-shape arrays is proposed, as well as the MIMO-Capon method based on Capon waveformer is presented.

针对多输入多输出(multiple input multiple output， MIMO)雷达的自由度特性，提出了一种单基地L型阵列MIMO雷达的空间多目标分辨和定位方案和基于Capon波束形成器的MIMOCapon二维空间谱估计方法。

Multidimensional filtering and recursive filtering on Cartesian space can be transformed into onedimension space to process.

利用螺旋坐标系统可以把笛卡尔坐标空间中的多维滤波和递归滤波转化到一维空间中来处理。

In virtue of this,some properties of convex polyhedroid are studied and the definite values and extreme values of convex polygon in Euclidean plane are extended to the case in n-dimensional space.

提出n维欧氏空间中广义重心坐标的概念，建立了广义重心坐标下两点间的距离公式，并利用于研究凸多胞形的若干性质，将欧氏平面上凸多边形的一些定值与极值性质推广到n维空间。

Obviously, it's much easier to do the system analysis in a lower dimensional space.

显然，在一个低维空间做系统分析要比在高维空间容易得多。

In Chapter 3,the exponential stability and its algebraic criteria for a linear degenerate functional differential equation is discussed.

第二章在n维空间中讨论了中立型多时滞泛函方程的通解表示和指数稳定性，得到与一维空间中类似的结论。

The GKS stability theorem for one-dimensional model of hyperbolic initial and boundary value problem, Trefethen's explanation and extension based on the concept of group velocity are generalized firstly. Another possible high-frequency instability mechanism in numerical realization of MTF is pointed out based on his explanation and extension, namely, coupling effect of outgoing harmonic wave along one direction and node motion in the other directions can reverse the energy propagation in multi-dimensional discrete grids.

本文概述了—维双曲型偏微分方程组初边值问题数值稳定性的GKS定理及Trefethen基于群速度概念对这一定理的解释和推广；并应用Trefethen的解释和推广指出了MTF在数值实现中可能出现的另一种高频失稳机制，即在多维离散网格中，沿某一空间方向的外行简谐波，由于与其他空间方向节点运动的耦合效应可以使能量传播方向反向。

Prior to searching a multidimensional feature space populated with data objects, each dimension in the feature space is divided into a number of intervals.

在搜索数据对象组装的多维特征空间之前，该特征空间的每个维度被划分为多个间隔。

Each condition or resource which defines the niche of an organism contributes one dimension to the space in which the organism's niche, and is the multidimensional niche space, or'n-dimensional hypervolume'.

定义有机体生态位的每一个条件和资源，对于有机体能出现的空间提供一个维度。一起考虑所有维度，全面确定的有机体的生态位，是多维生态位空间，或&n-维超体积&。

Then, according to phase space reconstruct technique from one-dimensional and multi-dimensional time series, the quantitative criterion and rule of system chaos which combine neural network, analyses, computations and sort are conducted on EEG signals of five kinds of human consciousness activities. The author finds that statistic results of the determinism computation in time series indicate that chaos characteristic may lie in human consciousness activities, and central tendency measure is consistent with phase graph, so it may become one division way of attractor; approximate entropy of different subjects exists discrepancy; correlation dimension and Lyapunov exponent of different consciousness activities indicate that attractors of human activities are all fractional; nonlinear quantitative criterion and rule, which unites neural network, can distinguish different styles of consciousness activity in principle, and the result of sortation takes on that consciousness activity type of arithmetic is distinguished more easily than that of abstract.

采用一维与多维时间序列相空间重构技术和系统混沌的定量判据准则，结合神经网络，对五种思维作业方式的脑电信号进行了分析、计算与分类，发现确定性计算的统计结果表明人类的意识活动中可能蕴含混沌特性，中心趋向测量(Central Tendency Measure，CTM)与相图吻合较好，可作为EEG吸引子的区分方法之一；功率谱分析反映出单个受试者的各种意识形态的差异很小，但是不同意识活动谱中的活跃频段还是略有差异的；个体之间的近似熵存在差异，同种状态下近似熵大的人可能具有更好的创新性；关联维数和Lyapunov指数的计算结果表明大脑的运动落在具有分维的奇怪吸引子上；非线性量化方法与神经网络相结合，可对人脑思维活动进行较好的分类，并且从分类结果来看数理计算类思维活动较抽象类思维活动有着更好的区分度。

In this paper, the dynamic behavior of long-span space lattice structures subjected to multi-dimensional and multi-support excitation, as well as to multi-dimensional and simple-support excitation are thoroughly analyzed based upon time history method.

同时考虑地震动2个水平和1个竖直共3个平动分量，并考虑了地震动场的空间相关性，用时程分析法对大跨空间结构进行了多维多点输入和多维一致输入下的响应分析。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。