查询词典 compatible system of algebraic equations

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。

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。

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。

The basic idea is to set a continuous solution of the region with a finite number of discrete points instead of a grid consisting of, these discrete points called grid nodes the solution of a continuous area on a given function of continuous variables used in the definition of discrete grid variable function approximation the original equation and boundary conditions in the micro-business operators to approximate differential, integral with the points and to approximate, so the original differential equations and boundary conditions are replaced by algebraic equations near Side, that is, finite difference equations , solve this equation group can get the original problem in discrete points on the approximate solution.

基本思想是把连续的定解区域用有限个离散点构成的网格来代替，这些离散点称作网格的节点；把连续定解区域上的连续变量的函数用在网格上定义的离散变量函数来近似；把原方程和定解条件中的微商用差商来近似，积分用积分和来近似，于是原微分方程和定解条件就近似地代之以代数方程组，即有限差分方程组，解此方程组就可以得到原问题在离散点上的近似解。

By integral transformation of basic equations, the stress and displacement expressions with unknown coefficients of elastic and viscoelastic materials were obtained in Laplace domain respectively, and introducing dislocation density functions, the singular integral equations were got according to the boundary conditions and interface connection conditions, further adopting Gauss integration and Gauss-Jacobi integration formula, the problem was reduced to algebraic equations, then it can be solved with the method of collocation dots in Laplace domain. Finally, the time response of dynamic stress intensity factor was calculated with the inverse Laplace integral transformation.

采用积分变换方法，得到Laplace域内弹性和粘弹性材料的应力和位移的含未知系数的表达式；引入位错密度函数，并通过边界条件和界面连接条件，导出反映裂纹尖端奇异性的奇异积分方程组，采用Gauss积分，并运用Gauss-Jacobi求积公式化奇异积分方程组为代数方程组，利用配点法进行求解；最后经过Laplace逆变换，求得动态应力强度因子的时间响应。

Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcame. Finally, natural frequency is obtained by the existence condition of nontrivial solution of the discrete algebraic equations derived from the integral equations.

边界方程有多种选择，在选定一种边界方程的基础上，可以通过建立一个新的边界方程来表示问题的边界，以克服积分核的奇异性；最后由积分方程的离散化方程组有非平凡解的条件，求得固有频率。

Based on independent research and development, we successfully develop following research productions: Data Acquisition System, Radio Frequency Warehouse Management System, Digital Picking System, High-speed Document Autoscan Identification System, SMT Assembly Line Barcode Management System, Manufacturing Execution System. Meanwhile, various management systems in the field of ambulant operation are provided as well, such as Handheld Computer- Ambulant Operation System, Distribution Resource Planning Management System, Container Yard Wireless Operation Management System, Retail Wireless Operation Management System, Air Cargo- Ambulant Operation Management System, etc . In addition, programming interfaces service we provided, which are compatible with SAP, Oracle, Kingdee and UFIDA platform, have been applied into many fields including stock distribution, manufacturing, business chain, airport, container yard, transportation, tobacco, finance, telecom, post, public Utilities ,etc.

公司自主研发出先进的数据采集管理系统、生产制造执行系统、仓库无线作业管理系统、电子标签拣货系统、AutoScan高速单证扫描识别系统、SMT生产线条码管理系统；同时提供无线手持终端的移动业务系统、移动分销管理系统、堆场码头无线作业管理系统、零售无线作业管理系统、航空货运移动作业管理系统等信息系统；并且提供与SAP、Oracle、金蝶和用友等ERP系统的接口程序，广泛应用于仓储配送、生产制造、商贸连锁、航空机场、码头堆场、交通、烟草、金融、电信、邮政、政府公共事业等领域。

It is therefore not possible to provide a specific number of backwards compatible titles at this stage, but close to launch consumers will be able to check whether their titles are compatible with PS3 by looking at the list of compatible titles at http://faq.eu.playstation.com/bc.

所以就目前的数据我们无法提供准确的兼容游戏的列表或者受影响的程度。不过在邻近发售的时候消费者就可以在 http：//faq.eu.playstation.com/bc 查询他们手里的游戏是否可以在PS3上运行了。

Through analysis of bank ATM compatibility, some conclusions can be gotten. To manufacturers, producing compatible machine get more profits than that of uncompatible machine; to consumers, producing uncompatible machine get more values than that of compatible machine; to social welfare, producing compatible machine get more welfares than that of uncompatible machine.

最后通过银行ATM兼容性实例分析，得出以下结论：针对厂商来说，生产兼容机比生产不兼容机获利多；针对消费者来说，生产不兼容机比生产兼容机获取的效用多；针对社会福利来说，生产兼容机比生产不兼容机社会福利大。

More direct, directer ; most direct, directest

径直的，笔直的

Do you know how to use a chain saw?

你知道如何使用链锯吗？