查询词典 multiplication theorem

Applied with the holistic analysis method, based on the theorem of maximal probability multiplication and the principle of cannikin, the paper establishes a coordination model between the sub-systems (river, wetland, lake, city, dryland) within the ecological water allocation system of the river basin.

本文应用整体分析法，基于最大概率乘积定理和"木桶法则"，构造了流域生态用水分配系统的协调性评价模型，分析了各子系统生态用水分配的合理度，完善了流域生态用水分配合理性的评价内容和方法。

In this paper, we introduce the algorithm of Schoof-Elkies-Atkin to compute the order of elliptic curves over finite fields. We give out a fast algorithm to compute the division polynomial f〓 and a primitive point of order 2〓. This paper also gives an improved algorithm in computing elliptic curve scalar multiplication. Using the method of complex multiplication, we find good elliptic curves for use in cryptosystems, and implemented ElGamal public-key scheme based on elliptic curves. As a co-product, we also realized the algorithm to determine primes using Goldwasser-Kilian's theorem. Lastly, the elliptic curve method of integer factorization is discussed. By making some improvement and through properly selected parameters, we successfully factored an integer of 55 digits, which is the product of two 28-digit primes.

本文介绍了计算有限域上椭圆曲线群的阶的Schoof-Elkies-Atkin算法，在具体处理算法过程中，我们给出了计算除多项式f〓的快速算法和寻找2〓阶本原点的快速算法；标量乘法是有关椭圆曲线算法中的最基本运算，本文对[Koe96]中的椭圆曲线标量乘法作了改进，提高了其运算速度；椭圆曲线的参数的选择直接影向到椭圆曲线密码体的安全性，文中利用复乘方法构造了具有良好密码特性的椭圆曲线，并实现了椭圆曲线上ElGamal公钥体制；文中还给出了利用Goldwasser-Kilian定理和椭圆曲线的复乘方法进行素数的确定判别算法；最后讨论了利用椭圆曲线分解整数的方法并进行了某些改进，在PC机上分解了两个28位素数之积的55位整数。

The 2~ one is to reduce the area cost by reuse some field operation modules such as GF-MUL and GF-SQR. Fermat"s little theorem proves that inversion can be obtained by add and square operations, we needn"t design one more module for inversion on condition that inversion only needed for one time when Montgomery point multiplication method been used.

我们采用射影坐标系表示有限域上的元素，实现点乘只需一次求逆，因而只需要在现有的底层模块基础上，设计平方和乘法的控制电路来实现求逆，而不必设计专用的求逆运算模块。

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。

In this paper, introduces firstly a concept of polynomial coefficient matrix, and then the polynomial multiplication is masterly changed into the computing of matrix multiplication. Then a theorem is received. Throughout the process, the steps are very clear and the calculating is pretty simple.

该文首先引进了一个多项式系数矩阵的概念，然后巧妙地将多项式的乘法转变为矩阵乘法的运算，得到了一个定理，步骤清晰，计算简单。

The multiplication theorem and MVDR beamforming are introduced. Various broadband beamforming methods and methods of broadband constant beamwidth beamforming are studied. 3. The necessity and the importance to introduce beamforming of array with virtual elements had been analyzed, the main ideas and principle are studied deeply.

分析了束控和加权对波束形成的影响，给出了仿真实例，介绍了乘积定理和MVDR波束形成方法，并且系统研究了频域和时域宽带波束形成的结构和特点，最后导出了宽带波束形成的恒定束宽实现方法。

The basic idea of the method is as follows: an algebraic theorem is used to avoid computing the composition and multiplication of B-spline basis function by Blossom and Polar form, and to reduce the computation by solving linear equations.

基本思想是：运用代数基本定理避免通常B样条基函数复合所采用的极形式以及非常烦琐复杂的开花运算，把B样条基函数的复合、乘积运算转化为求解线性方程组。

A good use of the integer type, the biggest 9999990 to support the decimal integer, It can perform large integers, plus or minus, multiplication, addition and modular, with a big round of the largest factions, extended Euclidean algorithm, the Chinese remainder theorem algorithm, Miller - Rabin primality testing algorithm, random generation of arbitrary integer spaces such as libraries, This kind of dynamic library has been used for commercial software, the reliability and speed is affirmed.

一个很好用的大整数的类，最大可支持9999990位的十进制整数，可进行大整数的加、减、乘、除和取模运算，并带有求大整数的最大公因数、扩展Euclidean算法、中国剩余定理算法、Miller-Rabin素性测试算法、随机生成任意位的大整数等函数库，这个类的动态库曾用于商业软件之中，其可靠性和速度是得到确认的。

It is also known as one of the most poisonous naturally occurring substances.

它也被称为一个最自然发生的有毒物质。

The greatest stress is found at the location on the cross section where V is the largest.

最大应力出现在横截面上V为最大的地方。