查询词典 algebraic

As an important algebraic subject, rings are the base on Algebraic Geometry and Algebraic Number Theory.

环作为一门重要的代数学科是代数几何和代数数论的基础，有许多其它相关学科领域都涉及到环。

We posed the concept of sufficient intersection about s(1≤s≤n) algebraic hypersurfaces in n-dimensional space and proved the dimension of polynomial space Pm(which denotes the space of all multivariate polynomials of total degree≤m) on the algebraic manifold S=s(f1,…, fs) where f1(X=0,…, f s=0denote s algebraic hypersurfaces of sufficient intersection, then gave a convenient expression for dimension calculation by using the backw ard difference operator.

给出了n维空间中s(1≤s≤n)个代数超曲面充分相交的概念，证明了n元m次多项式空间Pm在充分相交的代数流形S=s(f1，…， fs)（f1=0，…， fs=0表示s个代数超曲面）上的维数，并利用倒差分算子给出一个方便计算的表达式；构造了沿代数流形上插值适定结点组的叠加插值法；证明了在充分相交的代数流形上任意次插值适定结点组的存在性；给出代数流形上插值适定结点组的性质和判定条件。

In order to solvepiecewise algebraic varieties, we propose a new method to compute an algebraic varietyon a convex polyhedron by adding hyperplanes with the method of Groebner bases. Thus,the algebraic variety on the convex polyhedron is transformed to the positive solutionsof a system of polynomials. Besides, the minimal decomposition is also obtained.

通过添加超平面技巧将Groebner基方法应用到凸多面体内任意维代数簇的计算上，从而把凸多面体内的代数簇转化为另外一组多项式方程组的正解，并且得到了该代数簇在凸多面体内的极小分解。

We describe the algebraic characteristic of the public-key cryptosystems based on algebraic structures such as elliptic curves,bilinear pairings,as well as braid group s,with the emphasis on the difficulties of constructing public-key cryptosystems based on non-commutative algebraic structures.

通过分析基于椭圆曲线、双线性对以及基于辫子群的公钥密码体制的代数学特征，着重讨论了构建基于非交换代数的公钥密码体制所面临的困难。

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。

Moreover, multivariate splines are closely related with some topics in pure mathematics, such as, abstract algebraic, algebraic geometry and combinatorics.

另一方面，多元样条与基础数学的一些领域，如：抽象代数、代数几何、微分方程及组合数学等，亦有着密切关联。

Using the substitution-elimination method affine algebraic variety can be resolved to pure d-dimensional subvariety and expressed by an algebraic hypersurface on d+1-dimensional space with a sequence of elimination-polynomial systems. All 0-dimensional solution can be found, too.

利用变换消元法可以把代数簇分解成纯d维的子簇，并把代数簇表示为d+1维子空间上的超曲面形式和一系列的消元多项式组，且能求出全部孤立解，同时给出了算法及其在多项式因式分解中的应用。

The algebraic laws of InforSIB event algebra and its context consumption policy are discussed. Context consumption policy is very suitable for real-time monitoring applications and has good algebraic laws to ensure that the time and space complexity is bounded for composite event detection.

讨论了InforSIB事件代数的代数性质，提出的上下文策略非常适合用于实时监控等领域，且具有良好的代数性质，保证了复合事件检测的时间和空间复杂度是有界的。

The two-acre Dunbar Community Garden in Little Rock has served as a model for several years.

几年来，坐落于小石城，占地两英亩的邓巴社区菜园树立了一个标杆。

Jerry points to the jacket hanging in the bathroom. It's ruined, and unwearable What?

杰瑞指着洗手间里挂着的夹克，毁了，不能穿了）什么？