维数

On the whole, we do as follows: Firstly, we list some conceptions and lemmas for later use. Secondly, we inducted the absolute value norm in the two-dimensional vector interspace, and also proved the two-dimensional vector interspace is a Banach Interspace. Thirdly, we define two-dimensional vector-valued functions on a interval by the definition of -fine partitions in part 1. Then, some sufficient and necessary conditions of integrabel are given, and discuss the property of the integral on two-dimensional vector-valued functions.

主要包括以下内容：在第一部分，我们介绍了本文所用到的几个基本概念和引理；第二部分，我们在二维向量空间中引入了绝对值范数，并且证明了二维向量空间是一个Banach空间；在第三部分中，通过第一部分关于-精细分划的定义，我们给出了在某区间上二维向量值函数积分的定义以及可积的充分必要条件，并讨论了二维向量值函数积分的一些性质。

The low-dimensional Galerkin method is generalized to solve the flow around arbi-trarily translating circular cylinder.Active control problems of wakes behind circularcylinders are numerically investigated by only small number of modes.The in-line andtransverse oscillation of a circular cylinder with proper frequency produce Karman vor-tex street successfully in some subcritical regime,vhereas the transverse oscillation of acircular cylinder with 1.8 times the natural shedding frequency can effectively suppressthe Karman vortex street at a slightly supercritical Re.

将低维Galerkin方法推广至可以求解任意平移运动圆柱的绕流问题，用较少的模数值研究了圆柱尾迹的主动控制问题，在亚临界Re数下圆柱以适当的频率沿流向和横向振动均成功地激发出Karman涡街；而在略高于临界Re数下圆柱以1.8倍自然脱涡频率沿横向振动明显地抑制了Karman涡街；再现了超临界Re数横向及流向振动圆柱绕流的频率锁定等复杂非线性现象。

For gas flow past cylinder, the characters of flow field in different Mach number and Knudsen number condition were investigated, and especially for low Knudsen number cases, the results were compared with calculating results of Euler's equation. It showed that they are correspondent by comparing the characters of bow shock and wake. The convergence rates of different high resolution and implicit schemes were also investigated. The convergence behavior of the implicit WENO scheme developed in this paper is better than others. For gas flow past NACA 0012 airfoil, the calculating results were compared with results of experiment. It showed that the results of WENO scheme are of higher accuracy for the case with angle of attack.

在圆柱流场时，我们探讨不同马赫数且不同纽森数时的流场特性，并在低纽森数时，与那维尔-史托克方程式的计算结果比较，我们比较了弓形震波及尾流附近的特性，其结果是相当符合的，同时我们也比较不同高解析隐式算则的收敛历程，从收敛历程图可得到，本文发展出来的隐式WENO算则有较佳的收敛效果；在NACA 0012翼形的流场中，我们将与实验结果做比较，发现利用WENO算则计算的结果，对於具有攻角的流场，亦有相当高的准确度。

In this paper, new classes of linear block codes over finite fields of the algebraicinteger ring of quadratic number fields Qd~(1/2 modulo irreducible elements with norm p or p~2 are presented. These codes can correct one error which takes from the cyclic subgroup of the multiplicative group of the finite fields. The results presented in this paper extend the corresponding results of previous papers.

在处理适用于二维信号的线性分组码时，我们考虑类数为1的有理数域二次扩域Qd~(1/2的代数整数环，利用范数为p或p~2的不可约元构造有限域，给出剩余类域的一组完全陪集代表元系，从而构造出一类有限域上的线性分组码，当错误取值于有限域乘法群的一个循环子群时，所得到的适用于二维信号的线性分组码可以纠单个错，推广了文[14-16]的结果。

The expansion coefficients Of aperture fields are Obtained after the three-dimensional arbitrary aperture fields have been represented by the sum of three-dimensional Gaussian function in the configuration-spatial wavenumber phase space.

本文利用Gabor原理把三维任意口面场表示成离散结构－波数相位空间中三维高斯基函数的叠加，将二维高斯基函数与相位空间谱双重正交的函数推广到三维，从而得到口面场展开函数。

My Cicero's Letters for instance: podgy volumes in parchment, with all the notes of Gronovius, Gronovius, and I know not how many other old scholars.

用羊皮纸印刷的短厚版本的《西塞罗信札》，书页上有葛来维斯、葛罗诺维斯，以及我数也数不清的其他老学者的注解。

In Chapter 4, A detailed comparison between the realization of Cholesky decomposition and OR method is given, a systolic/wavefront array made of general purpose DSP is used to realize the adaptive beamforming at a moderate speed, and a wavefront array to extract the adaptive weights which is necessary in some applications is designed. In Chapter 5, the author proposed a new structure to realize the space time adaptive processing. First 1~q using the FFr and the truncating infinite sequence and sone optimizing method, a much simpler architecture can be acquired in realizing the three portion of channel processing: quadrature sampling, pulse compression and adaptive equalization.

第五章研究并提出了用全通用DSP模块设计空时二维自适应信号处理机的新方案，首先用快速付立叶变换和对长序列截断处理的重叠保留法以大大减少的运算量完成了处理机通道处理部分的正交插值、脉压、自适应均衡三个功能块的长阶数线性卷积运算，接着对自适应波束形成提出了多种实现方案，分析了多种方案下的运算量和设备要求，指出在不同通道数、不同数据吞吐率、不同自适应要求时这几种方案有不同的可行度和实现难度，并针对实际要求确定了一种运算田N、的实现方案，对自适应波束合成部分的大量贝玉以良元组咸肋冈络结拘和处凰闺和羽凶挝娠昨了优化设计以威少设备复杂性，构成了设备量大夕父伯小、们g团回高、辜于生回阴田闩引愧快的空时二维自适囱戏升引毗四机。

This network's multidimensional wavelet basis function is built by substituting norm of the vector for that vector, not scalar product function of the vector, thus the cost of calculation of high dimensionalities is decreased nearly to the situation of one dimensionality.

此网直接用矢量的范数代替矢量来构造多维小波基函数，而不是采用通常的矢量的标量积函数的方法构造多维基函数，这样多维情况的运算量被降低到几乎和一维的情况基本相当的程度。

When the frequency is 15Hz and number of ampere turns is 20kA·turn, relative intracrytalline solubility of alloy elements (for Zn, Mg and Cu the solubility are 68.8%, 76.0% and 45.0％, respectively) is the highest; when the frequency is 15Hz and number of ampere turns is 20kA·turn, Vicker hardness is the highest of Hv160; when the frequency is 25Hz and number of ampere turns is 20kA·turn, ultimate tensile strength is the highest of 324MPa.

频率为15Hz，安匝数为20kA·turn时， Zn、 Mg和Cu元素相对溶质固溶百分数最高，分别为68.8%、 76.0%和45.0％；频率为15Hz，安匝数为20kA·turn时，锭坯维氏硬度最高为Hv160；频率为25Hz，安匝数为20kA·turn时，抗拉强度最高为324MPa。

The distributions of velocity, velocity gradient, shear stress, clongation stress, first normal stress difference and pressure of the flow of a power-law fluid in the profile die were analyzed. It indicates that for a power-law fluid only after a few iterations a good convergence can be reached, even though in the case of high extrusion velocity.

详细分析了聚合物口模挤出三维计算机模拟研究中的若干关键技术问题，如对异型材结构特点的分析、边界条件的确定、初始速度场的自动生成、罚数的求取、粘弹性流动模拟中的高We数问题、三维挤出胀大的自由界面更新等。

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。