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This paper is composed of the algorithm design of dual-tree binary coefficients complex wavelets,MGM algorithm for linear systems that can be diagonalized by generalized discrete Fourier transform and type-II discrete sine transform matrices, wavelet and MGM algorithms for Toeplitz systems and their applications in signal and image processing.

本文以多进制小波与对偶树二进制系数复数小波算法设计、三角变换对角化系统MGM算法、Topelitz系统的小波与MGM结合算法作为理论主线，以对偶树复数小波与扩散方程方法结合的图像去噪，信号与恢复作为应用背景展开讨论。

A systematic study on computing the integral curvature line on NURBS surface is presented. Discrete normal is used to simplify calculation of the second fundamental form of the surface, resulting in accelerating the Euler iteration process in solving the differential equation of curvature line. Discrete points on the curvature line are then obtained and approximated by an explicitly presented B-spline curve on the NURBS surface using singular mixed interpolation and capable of controlling the error within a given tolerance.

对NURBS曲面的曲率线的积分进行了系统的公式推导，并利用NURBS曲面的离散法向量有效地简化了曲面第二基本量的计算，加速了Euler法迭代求解曲率线微分方程的过程；在求得曲率线上的离散点集以后，应用奇异混合插值技术，在可控精度内把曲率线用显式直接表示为位于NURBS曲面上的B样条曲线。

And then, we gain some definitions that in relation to regular surfaces which include discrete Gauss curvature and discrete mean curvature.

由此获得了一系列的相对于光滑曲面的离散定义，如离散平均曲率，离散Gauss曲率等。

Applying this rule, we give a kind of definition of discrete Gauss curvature and mean curvature on the discrete parametric curves net.

应用这种加细方法，我们给出了一种针对由离散参数曲线网形成的四边形网格上任意顶点处的离散估计值的定义方法。

The dissertation focuses on performance gradient estimation and SRO algorithm of DES aswell as other related topics,such as modeling of DES and discrete event simulation,performancemeasure Hessian matrix estimation,Stochastic Approximationand so on.General Semi-Markov Processis adapted to describe behaviour of DES and discrete eventsimulation.A general result is obtained and applied to analyze strong consistency of performancegradient Perturbation Analysisestimator.Conditions for effectiveness of InfinitesimalPerturbation Analysisare also discussed.New PA algorithms,such as server PA,PA usingDirac generalized function,job sequence PA etc.,are proposed to deal with discreteparameters.Furthermore,strategies of combining PA algorithms with certain iterative rules areanalyzed widely in order to optimize DES parameters and some SRO algorithms are constructed toslove DES optimization problems.

论文将DES性能分析领域中性能梯度估计和单运行仿真优化作为主要的研究对象，探讨了与性能梯度估计有关的DES和离散事件仿真过程建模、高阶导数估计以及随机逼近等理论和方法；建立了具有一般性的DES和离散事件仿真的广义半Markov过程模型；获得了分析性能梯度估计量强相合性的理论结果和无穷小摄动分析算法应用的条件；提出了诸如服务台数目的摄动分析、奇异摄动分析、串联生产线和加工车间中工件加工序的摄动分析等一系列摄动的思想和算法，对连续参数和离散参数都进行了深入的研究；对摄动分析算法同优化规则结合实现仿真优化的策略也进行了广泛的分析，构造了新型的变界截尾的随机逼近算法，并用于DES的单运行仿真优化研究；最后，给出了DES性能分析方法的实证性研究结果。

Based on the study of a discrete chaotic system of numerical solution and graphical simulation, while for discrete time-delay chaotic system a numerical simulation procedure.

详细说明：摘要：基于研究了离散混沌系统的数值解法和图形仿真，同时针对离散时滞混沌系统给出了数值仿真的程序。

Using the Gray code, we obtain the relationship between the row of Hadamard matrix and discrete Walsh function. Because Hadamard matrix has good recursion, makes the construction of discrete Walsh function is simple and convenient.

通过Gray码给出了Hadamard矩阵的行和离散Walsh函数之间的关系，由于Hadamard矩阵具有良好的递推性，所以使得离散Walsh函数的构造简单方便。

We generalize the concepts of two kinds of discrete distance of interval-valued fuzzy sets based on Hausdorff metric, and introduce a new distance of discrete interval-valued fuzzy sets based on Hausdorff metric and study some properties.

同时我们分别举例说明全空间IF~*(R，d~*和IF~*(R，d_p~*不是完备的，IF~*(R，d~*和IF~*(R，d_∞~*不是可分的。我们还对区间值模糊数序列在这三种距离意义下的收敛性之间的关系进行了讨论，得到一些结果。

The method ofsolution for linear discrete Hilbert boundary value problem on the unit circleis illustrated and it is proved that,in case of the index〓,the solutionsof the discrete Hilbert problems are stongly convergent to the solution of theoriginal problem.

我们给出了单位圆上线性离散Hilbert边值问题的解法，并且证明了当问题的指标k=0时离散Hilbert边值问题的解强收敛于原Hilbert边值问题的解。

There are six points below serving as reasons: firstly, solvency report reveals company's solvency status at certain time point and discrete view regarding quarter as discrete accounting period is consistent with ideas of insurance surveillance and management; secondly, deferrals and withdrawals in advance of expenses in integral view make confirmed assets and liabilities inconsistent with definitions of admitted assets and ranking liabilities; thirdly, taking into account cost and expenses of the entire year also brings unnecessary troubles to accounting measurement; fourthly,"integral view" is more dependent on professional judgment and estimate by accounting personnel, which is likely to lead to incomparability of company's solvency reports; fifthly, it is consistent with provisions of enterprise accounting standards of our country, which is convenient for company to compile solvency report; sixthly, it is in compliance with methods adopted by most developed countries, which is helpful for international comparison.

其原因有以下六点：第一，偿付能力报告反映公司在某一时点上的偿付能力状况，"独立观"将季度视为独立的会计期间与保险监管的理念一致；第二，一体观下费用的递延和预提使确认的资产和负债不符合认可资产和认可负债的定义；第三，会计估计考虑全年的成本和费用也给会计计量带来不必要的麻烦；第四，"一体观"较多地依赖于会计人员的职业判断和估计，可能会导致不同公司的偿付能力报告不可比；第五，与我国的企业会计准则的规定一致，便于公司编制偿付能力报告；第六，与多数发达国家采用的方法一致，有利于国际比较。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。