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For a general parametric curve/surface, we usually cannot compute its exact implicit form. Even though its exact implicit form can be computed, the curve/surface implicitization involves relatively complicated computation and the degree is higher. Moreover, it may have unexpected components and self-intersections. All these unsatisfied properties limit the applications of the exact implicitization. So finding curve/surface approximate implicitization has become a practical problem. In this paper, we present an algorithm to solve the approximate implicitization of a given parametric curve by using a quadratic algebraic spline curve.

由于精确隐式化过程不一定可以实现，即使可以实现隐式曲线曲面的阶数高计算复杂，并且具有不希望的自交点和奇异分支，从而限制了隐式化的运用，所以寻求参数曲线曲面的近似隐式化问题成为很实际又重要的问题，提出利用二次代数样条曲线来实现一般平面参数曲线近似隐式化的一种算法。

Considering the pitch deviation, pitch accumulative deviation, flank angle deviation and their combined influence on the pitch diameter, the authors present a complete differential optimal approximate model in this paper and use the ideal thread to approximate the actual thread radially and axially.

本文建立的螺纹中径当量全微分优化逼近模型，考虑了螺距偏差、螺距累积偏差和半角偏差本身及其相互间对中径的综合影响，并用理想螺纹在径向和轴向二维逼近实际螺纹。

In this paper, Galerkin method is employed. First, test functions to satisfy natural boundary conditions are selected. Then the approximate analytic formulations of the system frequency are derived. Meanwhile the approximate analytic formulation of the limit velocity is got.

采用直接法，首先选取满足自然边界条件的试函数，而后求出了系统固有频率的近似解析公式，同时也得到了极限流速的近似解析公式。

The relationship between transient response and shape design variables is highly non-linear, and the behavior of feasible domains is often not good, which may cause convergence difficulties. In order to improve convergence speed of iteration process, some algorithms the feasible domains adjusting, the adaptive move limit, the approximate line search and the approximate reanalysis, are adopted.

采用基于Newmark积分的直接求导法计算瞬态响应灵敏度，在序列二次规划算法中采用了可行域调整、近似—维搜索、自适应运动极限等改进技术，提高求解效率和收敛稳定性，以解决结构动态响应与设计变量的关系复杂、高度非线性，优化可行区域的性态不良等问题。

By the best approximation theory, it is first proved that the SISO (single-input single-output) linear Takagi-Sugeno fuzzy systems can approximate an arbitrary polynomial which, according to Weierstrass approximation theorem, can uniformly approximate any continuous functions on the compact domain.

借助于最优逼近理论，证明了线性SISO TS模糊系统可以逼近任意一个多项式，然后以Weierstrass逼近定理为桥梁，证明了该模糊系统可以以任意精度逼近一个任意的连续函数，从而得到了该模糊系统万能逼近性的一个新的充分条件。

If average values before or after catastrophe point when the pressure at both ends reduces exceed the threshold value, judging that there is leak and positioning: calculating approximate wavelet transformation coefficient of pressure data at both ends, initializing searching interval, calculating a signal time delay value corresponding to approximate wavelet transformation coefficient in the searching interval from maximal scale N; converting the time delay value under scale N to that under N-1 by geometric proportion relation; updating the searching interval, repeating above processes until the scale is 0 and positioning based on the time delay value.

若两端压力下降突变点前后的均值变化均超过阈值，判定有泄漏并进行定位：计算两端压力数据的近似小波变换系数，初始化搜索区间，从最大尺度N开始在搜索区间内计算对应近似小波变换系数的信号时延值，利用等比关系将尺度N下的时延估计值转换为N-1下时延估计值，以该值更新搜索区间，重复以上过程至尺度为0，以此时延估计值进行定位。

In the method, the symmetric positive semidefinite matrices are updated to approximate the Hessian matrices of the elemental objective functions and their sum to approximate the Hessian matrix of the objective function.

算法用对称半正定矩阵作为元素目标函数的Hessian阵的近似，使得其和仍然保持目标函数的Hessian阵的某种稀疏性。

First of all,we have given some of the basic concepts of differential equations, described the constant coefficient linear ordinary differential equation solution, for a class of second-order variable coefficient linear ordinary differential equation initial value problem, an approximate solution, the method is first unknown function of a definition for N sub-interval, and then in between each district within a constant coefficient ordinary differential equations similar to the replacement, the solution has been the problem as similar to the original analytical solution, and then gives a detailed second-order change order coefficient of linear homogeneous ordinary differential equation solution examples, the examples of the approximate method proposed in this paper is valid.

首先给出了微分方程的一些基本概念，讲述了常系数线性常微分方程的解法，针对一类二阶变系数线性常微分方程初值问题，提出了一个近似解法，本方法是先对未知函数的一个定义区间作N等分，然后在每一个小区间内用一个常系数常微分方程近似替换，所得到的解作为原问题的近似解析解，随后详细给出了一个求二阶变系数齐次线性常微分方程的解的实例，该实例说明本文提出的近似方法是有效的。

At the same time, due to 2~1S_0、 3_1S_0 are the radical excitations of 1~1S_0,we can use Regge trajectory on the (n,M~2)-plane with the approximate same slope to describe the mass of isoscalar of 3~1S_0 nonet (1926MeV). The two results derive from different ways are approximate. 2 The mass of the isodoublet of 2~3S_1 nonet is analyzed in the quarkonium-quarkonium mixing scheme, the results (1584±16.7MeV) is far from the K~*(1410)(1414±15MeV). 3 Based on "glueball dominance" picture, we establish glueball-meson mass relations. For the 2~ glueball mass and 4~ glueball mass used as input parameters, these relations predict the mass of isoscalar of 1~3F_4(4~)(2076±19.66MeV).

的质量(1900±12MeV)；同时考虑到2~1S_0、3~1S_0为1~1S_0的径向激发态，在(n，M~2)雷吉轨迹图中应该具有近似相同的斜率，利用雷吉轨迹可以得到其对应质量为(1926MeV)，两种方法得到了两个十分自洽的结果。2在介子—介子混合框架下，对2~3S_1介子九重态中同位旋二重态的质量给出估计，得到(1584±16.7MeV)，这个结果相对于K~*(1410)=1414±15MeV有较大的偏离。3在胶球为主的图像下，利用介子—胶球质量关系，选择2~与4~胶球的质量作为输入参数，我们得到1~3F_44~(介子九重态中同位旋标量态？

Then, the relation between vibration and sound, the acoustic holography method, the indeterminacy and identifiability of BSS, the BSS algorithm are discussed in detail. Based on above researches, the dissertation is divided in following four sections. The first section investigates the BSS algorithm suitable to acoustic feature separation. The algorithm of the joint approximate diagonalization of eigen-matrices is proposed. The spectra or the time-frequency distributions of source signals are the interesting features in ABD and they are separated from mixing signals by JADE algorithm. Then, the convolutive mixing model is transformed into a high-dimension instantaneous mixing model, and the deconvolution of source signals is achieved by the joint approximate block diagonalization of eigen-matrices. The proposed algorithm has a global minimum, and it is unsensitive to noise interference.

论文首先概述国内外声学诊断研究进展与盲分离研究进展，给出机器噪声声场与盲分离的数学描述，讨论了声振辐射、声全息、盲分离模型、盲分离可解性、盲分离结果不确定性、分离算法等基本问题，在此基础上，论文的研究工作分为以下四个部分：第一部分研究适用于声学特征分离的盲分离算法，提出基于特征提取的联合近似对角化盲分离算法，该算法以频谱特征或时频特征作为分离目标，从混合信号中分离源信号频谱特征或时频特征，最大限度地保留了与声学特征提取有关的频谱特征或时频特征，采用模型变换把卷积混合模型变换为一个高维瞬时混合模型，通过联合近似分块对角化算法实现源信号频谱特征与时频特征的盲反卷积。

In this paper, the requirement analysis, design and implementation of the system are introduced in detail.

此论文详细介绍了系统的需求分析，系统设计和具体实现。

In the context of economic globalization is increasingly deepening, China's economy can not be spared.

在经济全球化日益加深的背景下，中国经济不可能做到独善其身。