离散化

The method that combines the effective - field renormalization group with the discretized path - integral representation is extenged to study phase transition of the transverse Ising model in a quantum - spin system on the plane triangular lattice.

将离散路径积分表示下的有效场重整化群技巧推广应用于平面三角晶格上量子自旋横向Ising模型的相变研究，在这个方法中，注意区分了两种具有相同配位数而不同几何构形的晶体，并且考虑了起伏的影响，在二阶累积量近似下，得到了接近于精确解的临界值。

In the ***, all types and fundamental principles of Radon transform are summarized systematacially. This *** starts from the general linear Radon transform, and then researches how to use the damped least square method to find the solution of the forward transform. However, the least squares smoothing effect will lead to a certain degree of trails in the data of Radon domain, which led to the application\'s limitations. After that the implementation in Radon domain and relative merits of linear Radon transform, parabolic Radon transform and polynomial Radon transform which have time invariance are introduced, the conjugate gradient method that can solve numerical solution is also given. And then the high resolution Randon transform is discussed, it introduces the regularization theory and Bayes principle into inversion, which successfully remove the negative affect caused by discrete Radon transform. Finally, we introduce the optimal weighting similar coefficient Radon transform, which adapt to the time variant quality of hyperbolic Radon transform.

本文系统总结了Radon变换的各种类型及其基本原理，从τ- p变换(即一般线性Radon变换)出发，研究利用阻尼最小二乘平方法求解其正变换，但是最小平方法的平滑作用会导致Radon域数据存在一定程度的拖尾效应，给这种方法的应用带来了很大的局限性；然后先容了具有时不变性的线性、抛物和多项式Radon变换在频率域的实现及其优缺点，给出了求解其数值解的共轭梯度算法；接着讨论了高分辨率Radon变换，它把正则化思想和贝叶斯原理引进到了反演中，很好的克服了离散Radon变换产生的截断效应对结果的不利影响；最后先容了适应双曲Radon变换时变性质的高分辨率最优相似系数加权Radon变换。

Lastly, this paper discussed the invertibility of discrete nonlinear systems and the construction of ANN α-th order time-delay inverse system for the linearization and decoupling of discrete nonlinear system is proposed.

从逆系统理论的完整性出发，本文探讨了离散非线性系统的可逆性，并给出具有线性化和解耦能力的神经网络α阶时延逆系统的结构及其实现。

Based on the experiences in Computational Fluid Dynamics, the linear equation solver takes more than 60% CPU time of the whole process, therefore acceleration of the linear equation solver is a key element in enhancing the whole performance of CFD.

研究了基于非结构化网格通用输运方程的数值求解方法，包括输运方程的离散格式，边界条件处理方法，压力速度耦合SIMPLE求解方法，详细讨论了影响界面流量计算的重要因素。

Necessary and sufficient conditions for state feedback linearization of a class of nonlinear discrete-time systems is presented.

4给出并证明了一类多输入非线性离散系统状态反馈线性化的充要条件。

The every frame image was transformed by dyadic discrete wavelet and the characteristic of wavelet transform coefficient was analyzed. Low frequency coefficients were analyzed by fast principal component method which quoted Gram-Schmidt orthonormalization procedure in fixed-point algorithm then distilled principal component and reconstructed the low frequency coefficients. To suppress image noise, the high frequency coefficients were equated to zero.

该算法对热图像序列中的每帧图像进行二进制离散小波变换，提取出低频部分的系数；对低频系数进行改进PCA分析，通过固定点算法并引入Gram-Schmidt正交化过程求解特征向量；令高频系数为零，抑制图像的噪声。

Expert system, Discrete optimization, Parametrization, CAD

专家系统离散优化参数化 CAD

The constraints to the fluctuations of granular microstructure are also presented; and the intrinsic length scale parameter is discussed.

基于Hill-Mandel宏观均质化条件，给出了离散颗粒微结构波动场的边界条件，并且讨论了内部长度尺度参数的选择问题。

A compromise between the implicit and explicit models, known as discrete-continuum, cluster-continuum, semicontinuum, orsupermolecule-continuum model, is to include several solvent molecules around the solute into the QM part, but the rest bulk solvent is treated with the continuum theory.

结果表明：(1)，离散—连续组合模型既在从头算水平考虑了溶质分子和第一溶剂化层中溶剂分子间的短程作用，又包含了溶剂效应的长程静电作用；既包括了量子力学的精确性，又利用了连续场的高效性。

We use the boundary integral method to simulate the spherically symmetric collapse of a cavitation bubble, a free-surface potential problem having analytical solution. Evolving error curves are given in the thesis, and the influences of various discretization methods on the accuracy and the stability are compared.

我们使用边界积分法模拟空化气泡的球对称溃灭，一个具有分析解的自由面势流问题，给出了计算误差的演化曲线，比较了各种数值离散法对精度和稳定性的影响。

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。