模运算

IGMs are a kind of experimentally new-identified optical mode, standing with apparent potential in design and application. However, the mathematical expression of IGMs under Elliptic Cylindrical coordinates, preventing us from understanding IGMs instinctively, stands a formidable challenge in application. The pure mathematical expressions of IGMs are composed by a great deal of calculation, which also bids us no help in common use. I am, therefore, prompted to build an easier mathematical approach in this study.

Ince- Gaussian modes为在实验中可见的一种崭新型态的光学模态，对於我们在应用和设计上的实现，拥有许多潜力；然而，由於IGMs是在椭圆圆柱座标系下的数学来表示，造成了我们无法直觉的去了解，也成了我们在使用上的一大考验； IGMs的不易亲近，也让我们无从进一步去了解其物理特性，若纯粹以数学出发，又包含了庞大的运算，无法达到普遍的运用，是故我希望能在这篇论文使用简单的数学描述来达成对IGMs较平易近人的理解。

In this paper, we describe the history of Mizar system and the method to use theMizar system. Then we give the definition of quaternion numbers, module, algebrastructre etc, and then we prove its properties.

本文首先介绍了Miza(来源：ABC论文61网www.abclunwen.com)r系统的计算机操作原理和使用方法，给出了在Mizar语言系统下四元数、四元数的运算、共轭、内积、模等代数结构理论的证明，所做结论都通过了Mizar系统的验证，发表在波兰的《Formalized Mathematics》杂志上，并被收录到MML数据库中。

A new blind audio watermarking algorithm based on modular arithmetic is presented.

提出了一种全新的基于模数运算的盲检测音频水印算法。

Java novice when a practice that, the realization of complex arithmetic and the angle of depression for the modular arithmetic.

java初学时的一个练习题，实现复数的加减乘除以及求模求俯角的运算。

The author mainly realized the method of generating the large random numbers and judging the prime number using Lehmann means,then three pairs of secure key with different lengths (256 bits,512 bits,1024 bits) was generated to meet the demand of different security grade. In encryption module,modular multiplication arithmetic of large number was realized adopting addition chaining. In decryption module,extended Euclid was used to get inverse,and the Chinese remainder theorem was used to realize decryption,which increased the speed of decryption greatly.

作者主要实现了大随机数的生成、采用整除小素数和勒曼测试法判定素数，可以生成三种不同长度的密钥对(256位、512位、1024位)来满足不同的加密安全等级的需求；加密模块中，选用了二进制序列的乘法方法，实现了大数模幂乘运算；解密模块中，引用了扩展的欧几里德法求逆元，并采用中国剩余定理实现解密过程，大大提高了解密速度。

It is also the base of structure optimization.According to main object characteristics of structural dynamics design,structuraleigenveetor sensitivity computation is,first,be studied.A Neumann series expansionmethod is proposed in accordance with the modal method and is developed to agreewith the structure with rigid body modes.A rapid Neumann series expansion methodfor eigenvector sensitivity is formed;it may greatly improve the efficiency ofcomputing eigenvector derivation.

本文根据结构动力学设计的主要目标特性，首先进行了结构特征向量灵敏度分析研究：形成了计算特征向量灵敏度的Neumann级数展开法，并将其扩展到适用于具有刚体模态的结构特征向量灵敏度分析；研究出计算特征向量灵敏度的快速Neumann级数展开法，该方法大大提高了特征向量灵敏度分析的效率；建立了无需K-1运算的结构特征向量灵敏度分析的共轭梯度迭代法。

Particularly, large numbers generating,primality testing and Modular computing,which directly affect the speed of RSA were analyzed and discussed.These provided a comprehensive theoretical basis for this subject.

认真分析了直接影响RSA速度的关键因素--大数生成、素性检测和大数模乘运算等，为开展课题研究奠定了理论基础。

A bstract: This paper focus on virtual instrument design of modal parameters identification with curve fitting theory based on rational fraction orthogonal polynomials. Using Forsythe orthogonal polynomials solves the coefficient equation instead of normal power polynomials in order to decrease the morbidity of it, making the orders of coefficient equation reduce to half and increasing computing efficiency.

本文基于有理分式正交多项式曲线拟合理论对振动系统的模态参数辨识进行了虚拟仪器的设计，为了减少系数矩阵的病态，采用 Forsythe 正交多项式代替普通的幂多项式进行求解，使系数矩阵阶次降低近一半，提高了运算速度。

The space-like hypersurfaces with constant scalar curvature in a de Sitter space were studied and a pinching theorem on the square of the norm of the second fundamental form was obtained.

研究de Sitter空间中具有常数量曲率的类空超曲面，将Cheng-Yau的自共轨运算元口作用在对称张量T上，得到了这类超曲面关於第二基本形式模长平方的一个拼挤定理，加强了已有的相应结果。

The Difference Amplifier 差分放大器: The difference amplifier is the complement of the summing amplifier and allows the subtraction of two voltages or, as a special case, the cancellation of a signal common to the two inputs.

电路见图5，这种电路在运算电路中相当有用，比如差分对单端的转换，抑制共模信号。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。