离散问题

The text introduces the probability of random events and issues of counter-examples; discrete random variables related to the distribution and continuous random variable distribution of counter-examples; independence and related issues in the Phase capacitive on the counter-examples; number of characteristics of the random variable The counter-examples of; parameters estimates and assumptions in the anti-testing case of problems.

该文主要介绍了随机事件及其概率问题中的反例；有关离散型随机变量分布和连续型随机变量分布中的反例问题；独立性与相关性相容性问题中的反例介绍；有关随机变量数字特征的反例探讨；有关参数估计与假设检验中的反例问题。

Based on the ICMmethod,the discrete topological optimization problem about spot-weld's existence or not is transformed into the continuous optimization problem on[0,1].The optimization model is founded with maximizing the structural stiffness as objective and structural strength as constraints.The problem of multi-objectives and multi-constraints is transformed into the problem of single-objective and single-constraint with the K-S function.The displacement and stress are transformed into the explicit function of design variables with the Response Surface Methodology.The optimization model is solved with Sequential Quadratic Program.

基于ICM（Independent Continuous Mapping，即独立、连续、映射）方法，将焊点有无的离散拓扑优化问题转化为[0，1]区间上的连续优化问题；建立了以结构刚度最大为目标、结构强度为约束的连续拓扑优化模型；采用K-S函数将多目标和多约束问题转化为单目标和单约束问题；运用响应面方法将位移和应力转化为设计变量的显式函数，采用序列二次规划方法求解优化模型。

Based on the proposed ORPF models, the quadratic optimal models of minimizing the total load curtailment are established to identify power flow unsolvability for AC and AC-DC power systems, and can be further used to identify system voltage instability with the modal analysis method.

算例表明：当离散内点法不存在收敛问题时，启发式混合离散内点法能快速地获取优化解，反之，则要使用启发式混合随机优化算法来保证解的质量，但需要牺牲部分计算速度。

Firsdy, using the linear matrix inequality method and the concept of finite-time boundness, some sufficient conditions of finite-time boundedness for the linear discrete systems with uncertain exogenous disturbance were derived.

针对一类不确定线性离散系统有限时间观测器最优设计问题，利用线性矩阵不等式方法以及有限时间有界的概念，给出了具有不确定外部扰动输入的线性离散系统有限时间有界的充分条件。

Insection 4.3, semi-discrete and fully discrete Fourier spectral and pseudo-spectral schemes are constructed. The convergence and stability for the schemes are proved, and the error estimates are obtained.Chapter 5, consider the damped coupled generalized nonlinear wave equations. In section 5.2, by coupled a priori estimates and Galerkin method, prove the existence and uniqueness of the global smooth solution for the periodic initial value problem and obtain the existence of global attractors.

第四章，考虑一类具耗散的广义KdV方程组的周期初值问题，在第二节中证明了整体光滑解的存在性和唯一性，得到整体吸引子；在第三节中构造了半离散和全离散的Fourier谱格式和拟谱格式，在整体光滑解存在的条件下，证明了这些格式解的收敛性，并得到了误差估计。

In the first part, first of all, we have a priori estimate for solution of the reaction-diffusion equation with initial condition and Dirichret boundary conditions. Then, we construct a semidiscrete Legendre pseudospectral scheme, and have a priori estimate for approximate solution. We discuss the asymptotic stability of approximate solution. At last, we get a error estimation on large time for solution of the semidiscrete system.

首先，对此类方程初边值问题的解进行了先验估计；然后建立方程半离散的Legendre拟谱格式，并对近似解进行了先验估计，讨论了近似解的渐近稳定性；最后，得到了半离散系统解的长时间误差估计。

Many new detection techniques are proposed, that include: To overcome the faults of cross-terms and short unambiguity range for the common Wigner-Ville Distribution , short-time Fourier transform and Gabor transform are applied to SAR moving target detection. To improve the detection performance of WVD in noise environment, a new technique based on the Cross-WVD is proposed. The application of fractional Fourier transform to chirp signal detection is analyzed and extended to SAR moving target detection. To eliminate the restriction of chirp-Fourier transform, a new modified definition is proposed and applied to SAR moving target detection. To detect multiple moving targets whose scattering intensities are different heavily, the CLEAN technique is combined with the above techniques and the ideal detection performance is achieved. At last, the whole dissertation is concluded.

具体的研究成果如下：针对常用的Wigner-Ville分布在多目标情况下存在交叉项，并且多普勒不模糊范围小的缺点，提出将短时Fourier变换和Gabor变换应用于SAR运动目标检测，分析了其优势所在；为进一步提高Wigner-Ville分布低信噪比条件下的信号检测能力，提出基于互Wigner-Ville分布的运动目标检测方法；分析了分数阶Fourier变换在线性调频信号检测中的应用，提出基于分数阶Fourier变换的运动目标检测算法；对离散Chirp-Fourier变换的定义进行了修正，提出修正的离散Chirp-Fourier变换，克服了限制其应用的约束条件，并用于SAR运动目标检测当中；强度相差较大的多运动目标检测历来是机载SAR技术的一个重点和难点，我们将CLEAN思想融入上述多种算法当中，良好地解决了该问题。

Using the random field frame element, discretization process of random fields and finite elements can be done independently.

解决了传统方法中随机场离散过程与有限元离散过程相互耦联的问题。

By detailed comparion, it is shown that false scattering and ray effect exact not only in discrete ordinates method, but also in zone method,discrete transfer method,etc,and the influence of false scattering and ray effect on solution accuracy of radiative transfer eqution

离散坐标法由于可以很方便地处理入射散射项，因此离散坐标法在计算有散射的辐射问题方面要优于现有的其它方法，且易与流动方程联立求解。

Though historically there is a discernible break between Jewish law of the sovereign state of ancient Israel and of the Diaspora (the dispersion of Jewish people after the conquest of Israel), the spirit of the legal matter in later parts of the Old Testament is very close to that of the Talmud, one of the primary codifications of Jewish law in the Diaspora.

尽管在历史上古代以色列主权国家的犹太法和离散时期的犹太法存在着明显的断裂，旧约后部分的一些法律问题的精神与塔木德经－一种离散时期犹太法的主要经籍－的非常相近。

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。