谱几何

We will obtain that 0 is an eigenvalue of the operator corresponding to the model with geometric and algebraic multiplicity one.

第三节中研究对应于该排队模型主算子的谱特征，得到0是该主算子及其共轭算子几何重数与代数重数为1的特征值。

It obtains that the transport operator A has no complex eigenvalue s, and the spectrum of the transport operator A consists of finite real isolated eigenvalues which have a finite algebraic multiplicity in trip Pas.

本文研究了板几何中一类具各向异性、单能、均匀介质迁移算子A的谱，得出了该算子A在带域Pas中无复本征值和由有限个具有限代数重数的实离散本征值组成等结果。

We thorough search the stable conformers of aromatic amino acids and arginine and examine the properties of the stable conformers using ab initio and DFT methods. The properties examined include the characteristics of intramolecular interactions, IR and UV spectra, temperature dependent conformer distributions, electron attachment and ionization energies, protonation/deprotonation processes.

木论文对芳香型氨基酸和精氨酸进行了理论研究，研究的性质包括几何结构、电子结构、构刑分布、电离能和电子亲和势、质子化过程、红外谱、紫外谱以及分子内相互作用等方面。

At many occasions they arise quite natu-rally.For example,they appear in the Iwasawa decomposition of the isometry group ofa non-compact Riemannian symmetric space.Also,every connected homogeneous Rie-mannian manifold of non-positive sectional curvature can be represented as a connectedsolvable Lie group with a left-invariant Riemannian metric.

它们出现在非紧致黎曼对称空间的等距群的Iwasawa分解中；任一非正截面曲率的连通齐性和黎曼流形可以表为带有左不变黎曼度量的连通可解李群等，带有左不变黎曼度量的幂零及可解李群的微分几何，调和分析和谱几何是重要的研究课题。

And then, a window-type novel x-ray crystal spectrometer was put forward based on the elliptically curved crystal analyzer. It was coupled to an x-ray CCD camera, and a set of system had been designed and constructed. The spectrograph is useful in the experiments of x-ray diagnostics, for example in x-ray lasers, inertial confinement fusion, laser-matter interaction, and so on.

本论文从X射线晶体衍射和椭圆自聚焦几何光学原理出发，剖析追究了椭圆型弯曲X射线晶体谱仪在实际应用中产生问题的根源，率先从技术上提出解决目前椭圆型弯曲X射线晶体谱仪存在问题的思路，论证了其相应实施方案的可行性。

A geometric structure representation of images based on the angle between spectral coefficient vectors of Laplacian graph was proposed. Graph clustering of spectral features was also investigated.

提出一种用拉普拉斯图的谱系数夹角谱特征来描述图像几何结构的方法，同时研究了基于图的谱聚类系统。

Results reveal that the spatial correlation properties of MIMO channel are dependent on the PAS, the antenna pattern and the geometric configuration of the array. When the PASs at the base station and the mobile station are independent, the spatial correlation matrix of the MIMO channel is the Kronecker product of the spatial correlation matrix at the BS and the MS. The temporal correlation properties of the MIMO channel are determined by the PAS at the MS, antenna pattern and the traveling speed of the MS. Based on the analysis of the physical essence, the temporal correlation properties are equivalent to the spatial correlation properties at the MS. The joint spatio-temporal correlation properties at the BS and the MS are quite different. When the PASs at the BS and the MS are independent, the spatial correlation at the BS is independent on the temporal correlation, but this is not true for the spatial correlation at the MS.

分析与计算的结果表明，MIMO信道的空间相关特性由角度谱、阵元的方向图、阵元间距以及阵列几何结构决定，并且当发射端与接收端的空间统计特性相互独立时，MIMO信道的空间相关矩阵可以表示为发射阵列空间相关矩阵与接收阵列空间相关矩阵的Kronecker乘积：信道的时间相关仅与MS端的角度谱、阵元方向图以及MS的运动速度有关，通过对信道时间相关的物理本质的研究，说明了时间相关与MS端空间相关的等价性；MIMO信道的空-时联合相关特性在BS端和MS端具有不同的特点，当发射端与接收端的空间统计特性相互独立时，BS端的空间相关与时间相关是独立的，而由于信道的时间相关与MS端的空间相关具有相同的物理本质，MS端的空间相关与时间相关不是独立的。

In this thesis, we mainly study problems on global geometry and geometricanalysis of Riemannian submanifolds, including vanishing theorem for homologygroups, topological sphere theorem, L~2 harmonic 1-forms, finiteness of end andthe spectrum of the Laplacian. In 1973, by using the Federer-Fleming existence theorem and the techniquesfrom the calculus of variations in the geometric measure theory, H.

本文着重研究黎曼子流形上整体几何与几何分析的若干问题，主要内容包括子流形的同调群消没定理、拓扑球面定理、L~2调和1-形式、端的有限性和Laplace算子谱等问题。

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。

Based on the return map and the principle of closed vectors, a new method is proposed to extract unstable periodic orbits embedded in chaotic attractors. As examples, the UPOs embedded in chaotic attractors of Logistic, Hénon and Lorenz are extracted respectively by this method. And our results of Skewed Hénon map also be compared with Nusse's. These results suggest that this method is valid for unstable periodic orbits from period one to period infinite of arbitrary dimension chaotic system. The dynamic considerations of spiking and UPO coding for individual neuron and neural system under external periodic and chaotic exciting stimulus also be studied in this dissertation. A lot of spiking phenomena, such as synchronization, period, and chaos appear alternatively with the changing of the stimulus frequency. For the small stimulus frequency the neuron could completely convey the periodic signal in synchronous anti-phase into interspike intervals sequences. For the slow time–scale chaotic input, the output two ISI sequences are reciprocally related to input signals, and their oscillation wave shape in time course can be derived from that of the input signals variation, furthermore, the similar input sequence and order of UPOs, distribution of LES and value of KYD remain in attractors reconstructed from ISI sequences.

发现周期信号在单个神经元传递过程中，随着激励频率的改变，神经元输出的峰峰间期interspike interval时间序列呈现出周期、混沌和准周期的交错变化，特别当外加激励信号频率较低时，周期信号可以通过神经元ISI序列以反相同步的周期运动形式传递下去；同时无论是周期还是混沌激励信号，在神经系统中的传递均与其自身强度和神经元之间的耦合强度的大小密切相关；快变时间尺度的混沌激励信号在耦合的神经系统传递过程中，会造成大量基本信息的丢失；而慢变时间尺度的混沌激励信号在神经系统传递中，它的非线性特征信息，如混沌吸引子、不稳定周期轨道、Lyapunov指数谱和分形维数，会通过系统输出的ISI序列部分地重现出来，如与输入慢变时间尺度的混沌激励信号相比，神经系统输出的ISI序列具有：相似几何形状的混沌吸引子、相近的Lyapunov指数谱和分形维数、局部结构相同的不稳定周期轨道的排列方式。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。