查询词典 algebraic integer

Using the concept of Boolean functions and combinatorics theory comprehensively, we investigate the construction on annihilators of Boolean functions and the algebraic immunity of symmetric Boolean functions in cryptography:Firstly, we introduce two methods of constructing the annihilators of Boolean functions, Construction I makes annihilators based on the minor term expression of Boolean function, meanwhile we get a way to judge whether a Boolean function has low degree annihilators by feature matrix. In Construction II, we use the subfunctions to construct annihilators, we also apply Construction II to LILI-128 and Toyocrypt, and the attacking complexity is reduced greatly. We study the algebraic immunitiy of (5,1,3,12) rotation symmetric staturated best functions and a type of constructed functions, then we prove that a new class of functions are invariants of algebraic attacks, and this property is generalized in the end.Secondly, we present a construction on symmetric annihilators of symmetric Boolean functions.

本文主要利用布尔函数的相关概念并结合组合论的相关知识，对密码学中布尔函数的零化子构造问题以及对称布尔函数代数免疫性进行了研究，主要包括以下两方面的内容：首先，给出两种布尔函数零化子的构造方法，构造Ⅰ利用布尔函数的小项表示构造零化子，得到求布尔函数f代数次数≤d的零化子的算法，同时得到通过布尔函数的特征矩阵判断零化子的存在性：构造Ⅱ利用布尔函数退化后的子函数构造零化子，将此构造方法应用于LILI-128，Toyocrypt等流密码体制中，使得攻击的复杂度大大降低；通过研究(5，1，3，12)旋转对称饱和最优函数的代数免疫和一类构造函数的代数免疫，证明了一类函数为代数攻击不变量，并对此性质作了进一步推广。

The sums may be from any one or combination of the following topics: pre-algebra, algebraic expressions, algebraic expansion (multiplication of binomials and trinomials), algebraic factors, simple equations,simultaneous equations and quadratic equations.

数学试题可能来自于下列主题之一或者其组合：学龄前数学，数学表达式，代数表达式，代数因数，简单等式，联立方程式和二次方程式。

Secondly, in a more generalized framestructrue--lattice-ordered monoids,the notion of lattice-valued Mealy-type automata is introduced,we traverse some algebraic properties of this automata and investigate the congruences and homomorphisms of this type automata.Our main results indicate that the algebraic properties of lattice-valued Mealy-type automata have Close links to the algebraic properties of lattice-ordered monoids which automata take values in.Futhermore we study the minimization of lattice-valued Mealy-type automata and provide an algorithm to achieve the minimal lattice-valued Mealy-type automata within finite steps.

其次，在更一般的框架—格半群意义下，提出具有输入和输出字符的自动机——格值Mealy自动机的概念，从代数角度出发较详细地研究了此类自动机具有的性质，同时研究了此类自动机的同余和同态，揭示了此类自动机的代数性质和格半群的紧密联系，最终研究了格值Mealy自动机的极小化问题，并给出了在有限步可实现此极小化的算法。

This article outlines the integer aliquot concept in the first primary theory of numbers, the basic nature, as well as some special integer divisible characteristics.

本文先概述初等数论中整数的整除概念、基本性质，以及一些特殊整数的可除性特征。

Carries on the classification to the question, analyzes each kinds of questions the explanation mentality, inquires and summarizes that it can 100 within the odd number aliquot aliquot characteristic, finally discovered that any integer can by the lowliest place digit be 1,3,7,9 aliquot integer characteristics according to the lowliest place numeric classification, each kind has certain rule.

对问题进行分类，分析各类问题的解答思路，探寻、总结出能被100以内奇数整除的整除特征，结果发现任何一个整数能被末位数字是1，3，7，9整除的整数特征可按末位数字分类，每一类都有一定的规律。

Finally, we obtain the solutions of the 0-1 Integer Programming problem. The most merit of the model is its automatization characteristic, and the model fits to solve arbitrary 0-1 Integer Programming problem having arbitrary variable element.

该模型的最大优点在于具有自动化的特点；同时，从理论上来讲，该模型适合含有任意变量的任意0-1整数规划问题的求解。

We studied the asymptotic properties of the integer part of the k-th root positive integer and gave an interesting asymptotic formula.

研究了一个关于正整数κ次根的整数部分序列的均值，并利用初等的方法得到了一个有趣的渐近公式： 3。

A verifier can be convinced that the committed number x is neither less than the integer a nor more than the integer baiter the protocol is operated only once, and hence the exact proof that x lies in the interval is achieved.

为了去掉这种方法上的重复性，通过联合运用两承诺值相等协议及CFT证明协议提出了一个证明承诺值位于特定区间的新协议，协议运行一次便可使验证者确信承诺值x位于区间中。

In the problem, there are m persons who are to be assigned to do n jobs, and the number of the persons who are assigned to do the jth job is bj, where bj is an unknown positive integer number to be calculated such that djbjej, dj and ej are known positive integer number (j=1,2,…,n) such that ∑nj=1bj=m and m≥n.

考虑一类较一般的最优指派问题：欲指派m个人做n项工作，要求每个人只做一项工作，第j项工作可以由bj个人共同去做，其中bj是待求未知数，满足dj≤bj≤ej(即ej，dj为第j项工作所需人数的上下限)及∑nj=1bj=m，dj，ej为已知常数，j=1，…，n。

In the thesis , we give combinatorial proof of some q-identities using integer partition.In the thesis some vital identities with binomial coefficient are given with their combinatorial proof, and the q-analogues of some identities are offered with corresponding combinatorial proof using integer partition.

本文给出了一些重要的二项式系数恒等式的组合证明或组合解释，并从分拆的角度给出了一些q-恒等式的组合证明，其中突出的成果是给出了平方和恒等式的一个直接的组合证明并给出了偶数平方和与奇数平方和的q-模拟及组合证明。

The shaping method of noncircular part and the tool holder's radial motion characters in noncircular turning process are discussed in detail in the thesis.

论文详细研究了非圆零件的成型方法和加工过程中刀架的径向运动规律。

I have not really liked him,I do not like his this kind of disposition.

我没有真的喜欢他，我不喜欢他的这种性格。