查询词典 prime formula

Using the elementary methods, we studied the hybrid mean value involving Smarandache function and the least prime divisor function, and gave an asymptotic formula.

用初等的方法研究了一个Smarandache函数与最小素因子的均值，并得到一个渐近公式。

In his speech at Lianhe Zaobao's 75th anniversary gala dinner on September 6, Prime Minister Goh Chok Tong said: In Singapore, we have evolved our own unique formula of a multi-racial, multi-cultural society.

9月6日晚，在《联合早报》75周年报庆晚宴上，吴作栋总理在致词里提及：在新加坡，我们已经为多元种族、多元文化的社会发展出自己的一套独特的方程式。

The main contributions of the paper are listed as follows:(1) Propose methods of key-locks, such as equations set, Newton's interpolation formula, and the prime factor decomposition theorem, to implement access control.

论文的主要研究成果为：(1)提出了利用方程组、牛顿插值公式和素因子分解因式等钥—锁配对法来实现一般的访问控制。

The main contributions of the second part of this dissertation are focused on the cryptographic properties of logical functions over finite field, with the help of the properties of trace functions, and that of p-polynomials, as well as the permutation theory over finite field: The new definition of Chrestenson linear spectrum is given and the relation between the new Chrestenson linear spectrum and the Chrestenson cyclic spectrum is presented, followed by the inverse formula of logical function over finite field; The distribution for linear structures of the logical functions over finite field is discussed and the complete construction of logical functions taking on all vectors as linear structures is suggested, which leads to the conception of the extended affine functions over finite field, whose cryptographic properties is similar to that of the affine functions over field GF (2) and prime field F〓; The relationship between the degeneration of logical functions and the linear structures, the degeneration of logical functions and the support of Chrestenson spectrum, as well as the relation between the nonlinearity and the linear structures are discussed; Using the relation of the logical functions over finite field and the vector logical functions over its prime field, we reveal the relationship between the perfect nonlinear functions over finite field and the vector generalized Bent functions over its prime field; The existence or not of the perfect nonlinear functions with any variables over any finite fields is offered, and some methods are proposed to construct the perfect nonlinear functions by using the balanced p-polynomials over finite field.

重新定义了有限域上逻辑函数的Chrestenson线性谱，考察了新定义的Chrestenson线性谱和原来的Chrestenson循环谱的关系，并利用一组对偶基给出了有限域上逻辑函数的反演公式；给出了有限域上随机变量联合分布的分解式，并利用随机变量联合分布的分解式对有限域上逻辑函数的密码性质进行了研究；给出了有限域上逻辑函数与相应素域上向量逻辑函数的关系，探讨了它们之间密码性质的联系，如平衡性，相关免疫性，扩散性，线性结构以及非线性度等；讨论了有限域上逻辑函数各类线性结构之间的关系，并给出了任意点都是线性结构的逻辑函数的全部构造，由此引出了有限域上的"泛仿射函数"的概念；考察了有限域上逻辑函数的退化性与线性结构的关系、退化性与Chrestenson谱支集的关系；给出了有限域逻辑函数非线性度的定义，利用有限域上逻辑函数的非线性度与相应素域上向量逻辑函数非线性度的关系，考察了有限域上逻辑函数的非线性度与线性结构的关系；利用有限域上逻辑函数与相应素域上向量逻辑函数的关系，揭示了有限域上的广义Bent函数与相应素域上的广义Bent函数的关系，以及有限域上的完全非线性函数与相应素域上向量广义Bent函数之间的关系；给出了任意有限域上任意n元完全非线性函数存在性与否的完整证明，并利用有限域上平衡的p-多项式的性质给出了有限域上完全非线性函数的一些基本构造方法。

One kind is using the particular solution of the indefinite equation, which can be obtained by the property of the prime number , and the foundation system of solution of its corresponding homogeneous equation ,obtains its solution formula. Another kind is under the foundation of the matrix primary line transformation, and with the aid of some knowledge of numeral theory, obtains its solution formula.

一种是利用该不定方程的一个特解和其相对应的齐次方程的一个基础解系，得出该不定方程的求解公式，而这个特解可以由素数性质得到；另一种是在矩阵的初等行变换基础上，借助一些数论知识，得出该不定方程的求解公式。

In chapter 4, the prime reasons for the ill-posed inversion are analyzed at first and then the remedy method is described. The basic formula of stochastic inversion method tor impedance with broarband constraint of well log is deduced from basic level.

第二章首先将信号分析中的MA过程的定阶问题引入到地震子波的提取中，发展了利用地震记录的高阶累积量矩阵的特征值的变化估计地震子波的有效长度的方法。

For over 2000 years, the mathematicians tried to find a universal formula for prime number.

这给我们学生学习质数留下了许多困难。

The formula for creating prime numbers is 6n + 1where n is any number and + 1 is symbolic of unity or the original cause.

获得素数的公式是6n +1，N是任意数字，+1是统一体的符号或者是最原始的原因。

The structure of prime submodules of free modules is depicted and a calculable formula about prime dimensions of free modules is given.

对自由模的素子模是进行了刻画，给出了自由模的素子模的结构为(PF，u1，u2，…，us)，且给出了自由模的素维数的计算公式D=dimA+rankF-1。

In prime number distributed research process,and through established one kind of new sieve method and the stair theory,this article obtained about three group of prime number distribution recurrence formula: The 1st is not bigger than x the prime number integer recurrence formula;The 2nd is not bigger than x the twin prime integer recurrence formula;The(3rd Recurrence) formula.

在研究素数分布过程中，通过创立一种新的筛法与台阶理论，得到关于素数分布的三组递推公式：不大于x的素数个数与孪生素数对数量的递推公式；不大于x的孪生素数个数的递推公式；任意偶数x≥6表为两个奇素数之和与孪生素数对数量对数的递推公式。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。