模数

The content of this course is: analytic function (the definition of analytic function, elementary functions, etc.), conformal mapping (the definition if conformal mapping, fractional linear functions, elementary mappings, etc.), complex integration (Cauchy's integral formula, Cauchy's theorem, etc.), Series (Laurent Series, singularities, local property, etc.), residues and its applications (the Residues Theorem, integration by residues, the Argument Principle, the Maximum Principle, Schwarz's Lemma, etc.), analytic continuation and harmonic functions, etc.

本课程内容主要包括：解析函数(解析函数的定义、初等函数等)、共形映射(共形映射的定义、分式线性变换及初等映射等)、复积分(Cauchy 积分公式、 Cauchy 定理等)、级数(Laurent 级数、孤立奇点、局部映射等)、留数及其应用(留数定理、利用留数计算积分、幅角原理、最大模原理、 Schwarz 引理等)、解析开拓和调和函数等内容。

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。

The first 10 chapters study cohomolgy of open set in Euclidean space,treat smooth manifolds and their cohomology and end with integration on manifolds.

全书分四章：范畴与函子及其在模论中的应用；特殊模与相应的维数；环模复形的同调理论；谱序列。

Then we introduce the concept of(n,0)-projective dimension for modules and rings.It measures how far away a finitely generated module is from being n-presented,and how far away a ring is from being Noetherian.

然后，我们介绍环与模的(n，0)-投射维数，它可以衡量一个有限生成模与n-表现模的差距，以及衡量一个环与Noether环的差距。

So in chapter 2, we use P-flat and P-injective modules to characterize some important rings, like SF-rings, Von Neumann regular rings and Coherent rings, etc. In chapter 3, we introduce the homological dimension of P-flat and P-injective modules.

众所周知，正是由于研究各类模以及它们的同调维数，人们才能对环得到更深层次的性质的描述，所以在第二章中，我们就利用了P-平坦模与P-内射模来刻划几种重要的环，如SF环、Von Neumann正则环、凝聚环等。

If ris also irreducible in Z_nand f~n~κ≡fmodn,r(xfor all f∈Z_nthen we call n a Carmichael number of orderκmodulo r.Denote the set of all such numbers by C_κ,r(x.Define C_κ=∪_r(xC_κ,r(x,where rpasses through all monic irreducible polynomials over Z of degreeκ.We call elements of the set C_κCarmichael numbers of orderκ.ZHU and SUN[Journal of Sichuan University,42;1(2005), 47-51]first gave a necessary condition for Carmichael numbers of order 3.Then they gave a sufficient condition for Carmichael numbers of order 3,but did not find any such numbers less than 10~8 satisfying the sufficient condition.At last,they asked three questions;1.is the necessary condition also sufficient?

f∈Z_n，就称n是模r的κ阶Carmichael数，用C_κ，r(x表示所有这种数的集合，定义C_κ=∪_r(xC_κ，r(x，这里r跑遍Z中所有κ次首一不可约多项式，C_κ里面的元素就称为κ阶Carmichael数，C_κ称为κ阶Carmichael数集，朱文余和孙琦[四川大学学报，42；1(2005)，47-51]首先给出了3阶Carmichael数的一个必要条件；然后又给出了这种数的一个充分条件，并发现10~8内没有满足此充分条件的这种数；最后他们提出三个问题；一、问必要条件是否也是充分的？

As to arithmetic operations of fuzzy numbers,the arithmetic rules of fuzzynumbers based on generalized t-norms are introduced,which extend greatlythe implication of the arithmetic rules of noninteractive fuzzy numbers andgeneralize the arithmetic rules of fuzzy numbers of Dubois-Prade.

在模糊数算术运算方面，给出基于广义t-模的模糊数算术运算规则，该规则极大地拓展了非相互作用模糊数算术运算的范围与含义，对Dubois-Prade意义下的模糊数算术运算是一个很好的推广。

The phase tracking principle of source-contained homodyne detection is researched, the frame diagram for phase detection and experimental results are given.

介绍了一种新型的光纤电压传感器结构和工作原理，分析了系统中椭圆芯双模光纤的传输模式和模间相干光斑的变化，采用熔接的方式进行相干光接收来获得正交相位漂移信号，根据模间群折射率差与光程差的关系设计调整光纤的长度，依据石英晶体和空气的绝缘强度进行传感光纤匝数设计，讨论了含源零差探测法的相位跟踪原理，给出了相位检测框架图及实验结果，分析表明该设计方案能达到相位跟踪的目的。

We also propose program optimization technologies: removing integer DIV and MOD, upraising common code for reducing the complex array subscription effectively.

为此本文进一步研究了数据变换和重构手段，提出通过直接扩展数组范围、构造松弛数组范围和循环扭曲变换等技术，使数据变换后的数据规模尽量小；同时，通过采用整数模和整数除消除优化技术、代码上提优化等程序优化技术，简化了数组下标表示，有效地减少了数组下标计算开销。

The digital users signals comprising in-phase component and quadrature component are converted to analog baseband signals by digital-to-analog converters 104 and 114, which are followed by lowpass filters 106 and 116 for removing harmonics at unwanted frequencies.

包括同相分量和正交分量的数字用户信号通过数模转换器104和114转换成模拟基带信号，在数模转换器104和114的后面具有低通滤波器106和116，低通滤波器106和116用于去除在不期望频率处的谐波。

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。