查询词典 multiplication theorem

Finally, after defining an evaluation module of the corresponding Loop superalgebra (Section 4), two major results of the paper -Theorem 4.land Theorem 4.2 are proved: Theorem 4.1 reduces the irreducibility of the tensor product of finitely many evaluation modules to the irreducibility of the tensor product of finitely many irreducible modules of a nilpotent Lie superalgebra; Theorem 4.2 gives a criterion for the tensor product of such modules to be irreducible.

第4节在定义了相应的Loop超代数的赋值模之后，证明了本文的两个主要结论：定理4.1和定理4.2。定理4.1将有限多个赋值模其张量积的不可约性归结为一幂零李超代数的限多个不可约模其张量积的不可约性；定理4.2利用不可约指标给出了一幂零李超代数的限多个不可约模其张量积仍不可约的判别准则。

It includes luol theorem, Lagrange theorem and cauchy theorem, Taylor theorem.

它包括罗尔定理、拉格朗日定理、柯西定理、泰勒定理。

The use of Differential Mean Value Theorem (Rolle theorem, Lagrange's theorem, Cauchy's theorem) to solve a number of derivative and limit the problem.

利用微分中值定理（罗尔定理，拉格朗日定理，柯西定理）解决一些导数和极限的问题。

Chapter 2 deals with some refinements of the central limit theorem for a class of non-uniformly hyperbolic dynamical systems called Young\'s system, such as local central limit theorem and so-called Berry-Esseen theorem giving the rate of convergence in the central limit theorem.

在第二、三章中，我们考虑一类重要的非一致双曲动力系统的统计性质-中心极限定理，及其进一步的精细结果如局部中心极限定理，带有收敛速度的中心极限定理。

On the other hand , illuminated by close relation between harmonic maps and sumanifold theory, we have also researched in-depth about some relative problems in submanifolds theory which include: the estimate of heat kernel and eigenvalue and it geometric application of submanifolds with or without boundary; many kinds of pinching problem of submanifolds which include the rigidity theorem, topological sphere theorem, differential sphere theorem and topological finite theorem.

另外，鉴于调和映照与子流形之间的密切关系，我们还要深入研究子流形几何中与之相关的一些问题，主要包括：带边与不带边子流形的热核与特征值估计及其几何应用；子流形的刚性定理、拓扑球定理、微分球面定理、拓扑有限性定理等各类Pinching问题。

The positive periodic solution of functional differential equation with infinite delay is deeply concentrated these years, some scholars study this subject by means of Lyapunov theorem, Schauder fixed point theorem, and cone extending and compression theorem (from thesis -[5]), and they obtain the existence theorem of positive periodic solution.

近年来，无穷时滞泛函微分方程的周期解问题受到广泛关注，一些学者应用Lyapunov泛函方法，Schauder不动点方法，以及非线性泛函分析中的锥拉伸锥压缩方法(见[1]-[5])，研究了无穷时滞泛函微分方程的周期解的存在性问题。

In addition, by utilizing Jacobi two square numbers theorem and Lagrange four square numbers theorem and some theta function identities, we also prove the known results of number theory: two triangular number theorem, four triangular number theorem, and the number of representations of a positive integer by various quadratic forms in terms of divisor functions

包括Jacobi二平方数定理，Lagrange四平方数定理等，然后利用这些结果结合几个theta函数恒等式，我们获得了把任意一个正整数表示成两个三角数或四个三角数的和以及其他的二次形式的方法数，这些方法数都是用因子函数来表示的。

And guided by Schur theorem, many of the Schur theorem inference arises, formed a complete theoretical system Schur theorem. Schur theorem and put many of its reasoning applied to the unitary matrix and the similarity matrix eigenvalue of proof onto.

在Schur定理的指导下，许多关于Schur定理的推论便产生了，并且形成了一个完整的Schur定理理论体系，把Schur定理和它的许多推论推广到了酉矩阵的相似和矩阵的特征值的证明上来。

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。

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 quality of both red and white wine depends very much on the wine maker talent and on the quality of the grapes.

他的红酒和白酒的品质，根据酿造者的能力和葡萄的质量，各有差异。

No, I don't want to get drunk before my next match.

" "不，我不想让我的下一场比赛前喝醉了。