多维空间

College of Guandong Business, Guanzhou 510320, China）Abstract: Since large-scale vertical quench furnace is voluminous, whose working condition is a typically complex process with distributed parameter, nonlinear, multi-inputs/multi-outputs, close coupled variables, etc, dynamically decoupling control algorithm of temperature distributed parameter system in the furnace was presented, by which the whole system was decoupled to several subsystems and the implementation of controller was simplified. With finite difference approximation, the space and time step size was solved to ensure the convergency of finite difference approximation. After decoupling, the subsystems were controlled with self-learning PID control algorithm. The results show that the temperature control precision and homogeneity are improved; the overshoot and process in temperature rising period are reduced simultaneity.

摘 要：针对大型立式淬火炉体积庞大，工况复杂，炉内温度分布呈本征非均匀性，具有多输入/多输出、非线性、强耦合等特性，难以实现炉内温度高精度高均匀性控制目标等问题，提出一种温度分布参数系统动态解耦控制算法，其原理是：采用有限维逼近方法将对象解耦为多个独立的子系统，简化控制器的实现过程；通过分析有限维逼近方法的收敛性，获得保证收敛性的空间和时间步长应满足的条件；解耦后的子系统采用自学习PID控制算法，实现炉内温度高精度和高均匀性控制以及升温过程的快速性和小超调。

It is shown that many of the existing integral transforms (including their logically equivalents) such as chirplet transform, dispersion transform, wavelet transform, chirp-Fourier transform, short-time Fourier transform, Gabor transform, Fourier transform, cosine transform, sine transform, Hartley transform, Laplace transform, z transform, Mellin transform, Hilbert transform, autocorrelation function, cross-correlation function, and the energy and mean of a signal, can each be considered as a special case of the FMmlet transform with specific parameters. In fact, an inventory of subspaces of FMmlet transform runs into countless numbers. The subspaces mentioned above are merely a few among a zoo of subspaces. They are essentially obtained by cutting the transform space of FMmlet transform at different positions, and can be likened to the computed tomography in medical diagnosis. Through these subspaces we actually see different slices or profiles of the FMmlet transform.

将现有诸多变换置于统一的 FMmlet 变换中加以审视，发现 chirplet 变换、频散变换、小波变换、 chirp-Fourier 变换、短时 Fourier 变换、 Gabor 变换、 Fourier 变换、余弦变换、正弦变换、 Hartley 变换、 Laplace 变换、变换、 Mellin 变换、 Hilbert 变换、自相关函数、互相关函数、能量和均值等，均为 FMmlet 变换在其参数取特定值时的特例；上述诸变换之间的差别，主要在于变换空间的维数有别，以及在不同空间维上取值的不同；这些变换有如医学诊断中的 CT，均由压缩 FMmlet 变换域空间所致，可以说我们通过这些变换看到的，是 FMmlet 变换的不同剖面。

In chapter 2, first of all,we characterize subspace V_0 of multiresultion analysis {V_j}_~ based on invariant subspace. Subsequently, we consider the equivalent conditions among orthogonal multiwavelet Ψ=(Ψ_1,Ψ_2,...Ψ_r)~T, subspace, basis and dimension of subspace, properties of filter function matrix P are dealt with.

第二章讨论了多尺度分析{V_j}_~中子空间V_0的性质，进而讨论了多尺度分析生成的多重正交小波Ψ=(ψ_1，ψ_2，…，ψ_r)~T和子空间V_0以及基和维数之间的等价关系，分析了滤子函数矩阵P的性质，最后给出了r阶矩阵函数P生成尺度函数Φ的充分条件。

Then through solving that equation, a set of nonnegative linear independence weight vectors of principal components was obtained, by which a low-dimensional spectral space was spanned.

针对经典主成分分析法进行多光谱图像数据降维会使重构光谱反射比出现负值的问题，提出一种非负主成分分析法，并用该法构造低维光谱空间，实现高维多光谱数据与低维光谱空间的转换。

Firstly, a two-dimension tensor product space is constructed, in which reproducing kernel exists. Secondly a multiresolution analysis is constructed in the reproducing kernel space. Then an orthonormal basis in is obtained. Thus,the reproducing kernel space can be expressed by wavelets spaces. Wavelets approximation formula and sampling formula can also be obtained in the space. Besides, the wavelets approximation formula is simple and easy for calculation. That completes the theory of multiresolution analysis in finite interval fully and provides theoretical base and algorithm for application.

首先，构造二维张量积空间，并证明该空间具有再生核；其次在再生核空间中，建立多尺度分析，获得该空间的一个标准正交基，使得再生核空间可以由小波空间来刻画，进而得到小波级数和相应的采样公式，而且给出的小波级数形式简单易于数值分析，进一步完善了有限区间上的多尺度分析方法，也为实际应用提供了良好的理论基础和算法。

Our idea of easy dimensional driving includes mainiy:(1) a driving mechanism of construction constraints and dimensional constraints,(2) automatic graphic recognition of constraints,(3) a bothway cross dimensional linked list for storing dimension sparse matrices and for recalling them,(4) a reasonable method of constraint consistence checking,(5) the linking of movement of 2D views,(6) a method for creating a sequence graphic library.

随着二维与三维设计技术的交叉发展，目前的参数化设计主要有两个分支：①面向纯二维的图形参数化，其特点是二维图形为多拓扑环的复杂图形；②面向三维的基于CSG特征造型的参数化，用于拉伸扫描的单拓扑环的二维图形参数化及空间任意曲面的参数化是其特点。

By time-varying filtering, we realize the signal selectivity and interference suppression, especially for the signals with time-varying power spectrum. It is shown herein that conventional eigenstructure based methods are lower dimensional special case of the time-frequency subspace fitting method. The closed-form array response estimation algorithms for blind source separation in wireless communication is also developed in the dissertation by exploiting the data structure of second-order statistics of the array output in the presence of multipath. The proposed method achieves array response estimation with little constraint on signal property and propagation environment such as scatters or angular spread. Moreover, the array utilized here can be of arbitrary geometry and even uncalibrated. Since the closed-form solution is obtained, no misconvergency may occur and large amount of computation can be saved. The equivalent feed model and corresponding optimization designation are proposed to realize the downlink multi-user selective transmission. By coherent and non-coherent superposition of the electromagnetical field, multiple beams can be formed using a single array, so that each co-channel user signal is transmitted in each beam and will not interfered with each other. The proposed system scheme implements the digital beamforming and the channel allocation in the base band, therefore is suitable for the utilization of the radio software technology. The feasibility and effectiveness of the proposed model are proved by the RF experiment.

在窄带条件下，GSC－SSF方法还可以提高阵列的虚拟孔径，从而提高估计的性能；可以证明，Cyclic DOA 和SC-SSF方法可看作该方法的特例或近似； 3、提出了二维GSC－SSF方法和宽带谱相关DOA矩阵方法，利用信号的循环平稳特性解决了宽带条件下二维 DOA 估计问题，并具有阵元数少、计算量较小的特点； 4、提出了时频子空间拟合和宽带时频DOA估计算法，将联合时频分析的理论和方法引入到阵列信号的空间谱估计研究中，利用时变滤波实现信号选择性测向和干扰抑制，特别适合于谱时变信号；可以证明传统特征结构法可看作是时频子空间拟合方法的特例； 5、提出了多用户环境下阵列响应的估计方法——CARE方法，该方法对信号结构和传播参数（主要是散射源分布与角度散布）的约束较少，适用于各种几何结构的阵列甚至未校准的阵列，能够直接得到阵列响应的闭式解，因此计算量小、稳健性好，不存在收敛问题； 6、提出了针对多用户下行选择性发送的阵列等效激励模型、优化设计方法及其系统实现方案，通过空间场的相干叠加与非相干叠加使得单一阵列能够形成多个波束，并保证各波束内的用户信号各不相同且相互干扰最小；其系统方案具有在基带实现数字波束成形、信道分配并便于软件无线电实现的特点，其有效性已得到外场实测数据的证实。

Although any unimodality type partially expresses limited semantics less or more, video semantics are fully manifested only by interaction and integration of any unimodal. Video data comprises plentiful semantics, such as people, scene, object ,event and story, etc. A great deal of research has been focused on utilizing multi-modality features for better understanding of video semantics. Proposed in this paper is a new approach to detect semantic concepts in video using co-occurrence data embedding, SimFusion, and locality preserving projections from temporal associated co-occurring multimodal media data in video.

该方法对所提取视频镜头的多模态底层特征，根据共生数据嵌入(co-occurrence data embedding)和相似度融合进行多模态子空间相关性传递而得到镜头之间的相似度关系，接着通过局部不变投影(locality preserving projections)对原始数据进行降维以获得低维语义空间内的坐标，再利用标注信息训练分类模型，从而可对训练集外的测试数据进行语义概念检测，实现视频语义信息挖掘。

The nonlinear characteristic of 2-D PSD is checked in a long collimating distance of 78 meters.

利用多层前馈神经网络建立了入射光实际位置与二维PSD输出坐标以及准直距离间的空间三维映射关系，进而对PSD的空间三维非线性进行修正。

According to the distribution feature of floral envelope, the distance between petals to calculate translucent shadow distribution was used. 3-D space question was changed to 2-D space question thought many times mapping and many buffer zone.

花瓣的间距基于图像空间实现，通过多次投影将三维空间的运算转化为二维问题，使用多缓冲区记录花瓣间的关系，最终实现半透明花朵的可视化三维图形。

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。