查询词典 algebraic expression

In the four section, from the interpolationdimension of an algebraic curve and an algebraic surface,using theoryand method of algebraic geometry, we get some interpolation of analgebraic curve and an algebraic surface, and we prove the reasonableof the interpolation dimension of an algebraic curve and an algebraicsurface.

第四章我们从沿代数曲线曲面空间的插值维数出发，利用代数几何理论与方法，给出了代数曲线曲面上的基本插值结构，并证明了我们长期应用的其上的插值维数公式的合理性。

This article starts with a review of the history of the "Expression" conception in the Occident literature tradition,from which to conclude the base connotation of modern "Expression" conception in occident.Relying on this springboard,we analyses the history of the occidental modern plastic arts gradually ,then the naissance and development of the occidental modern plastic arts may boil down to a going-deep course driven by the "Expression" conception:the impressionism which had been pursuing sensual reality brought out a turning point from Representation to expression;Faurism accomplished the consciousness of Expression based on inheriting and criticizing Post-Impressionisme, and resisted the suppressant on Expression by Physical Image; the German Expressionism and Surrealism uplifted Expression at the same time they resisted Physical Image by "Nugatory Physical image"; From the apocalypse of Cubism,Suprematism and De Stijl tended towards Pure Plastic which excluded Physical Image completely,meaning that it had realized absolute Expression in the range of plastic;After WW II,artsists in western detected that Pure Plastic had actually suppressed Expression newly,as a result of Abstract-Expressionism and Mirnirnaliam Art,Expression broke away from Pure Plastic gradually to seek some new possibilities other than plastic.

本文从对西方文艺传统中的"表现"观念的历史考察着手，归纳出西方现代"表现"观念的核心内涵，以此为基点来逐步分析西方现代造型艺术史，进而将西方现代造型艺术的产生与发展归结为在"表现"观念驱动下不断递进的历史进程：印象主义对感觉真实的追求为造型艺术由再现走向表现打开了缺口；野兽派在继承和批判后印象主义的基础上首次实现了表现的自觉，并在艺术中反抗物象对表现的压迫；德国表现主义与超现实主义以不彻底的"否定性物象"来张扬表现反抗物象；至上主义、风格派等则在立体主义的启示下走向完全排斥物象的纯粹造型，在造型的范围内实现彻底的表现；二战后的西方艺术家们察觉到纯粹造型已经掉转头来形成新的对表现的压制；经由抽象表现主义、最低限艺术，表现逐步摆脱了纯粹造型，寻求造型之外的新的表现可能。

This article starts with a review of the history of the "Expression" conception in the Occident literature tradition,from which to conclude the base connotation of modern "Expression" conception in occident.Relying on this springboard,we analyses the history of the occidental modern plastic arts gradually ,then the naissance and development of the occidental modern plastic arts may boil down to a going-deep course driven by the "Expression" conception:the impressionism which had been pursuing sensual reality brought out a turning point from Representation to expression;Faurism accomplished the consciousness of Expression based on inheriting and criticizing Post-Impressionisme, and resisted the suppressant on Expression by Physical Image; the German Expressionism and Surrealism uplifted Expression at the same time they resisted Physical Image by "Nugatory Physical image"; From the apocalypse of Cubism,Suprematism and De Stijl tended towards Pure Plastic which excluded Physical Image completely,meaning that it had realized absolute Expression in the range of plastic;After WW II,artsists in western detected that Pure Plastic had actually suppressed Expression newly,as a result of Abstract-Expressionism and Mirnirnaliam Art,Expression broke away from Pure Plastic gradually to seek some new possibilities other than plastic.

本文从对西方文艺传统中的&表现&观念的历史考察着手，归纳出西方现代&表现&观念的核心内涵，以此为基点来逐步分析西方现代造型艺术史，进而将西方现代造型艺术的产生与发展归结为在&表现&观念驱动下不断递进的历史进程：印象主义对感觉真实的追求为造型艺术由再现走向表现打开了缺口；野兽派在继承和批判后印象主义的基础上首次实现了表现的自觉，并在艺术中反抗物象对表现的压迫；德国表现主义与超现实主义以不彻底的&否定性物象&来张扬表现反抗物象；至上主义、风格派等则在立体主义的启示下走向完全排斥物象的纯粹造型，在造型的范围内实现彻底的表现；二战后的西方艺术家们察觉到纯粹造型已经掉转头来形成新的对表现的压制；经由抽象表现主义、最低限艺术，表现逐步摆脱了纯粹造型，寻求造型之外的新的表现可能。

The paper applies algebraic geometry, computational geometry, approximation theory to study the following problems: the Nother type theory and the Riemann-Roch type theory of the piecewise algebraic curve; the number of real intersection points of piecewise algebraic curves; the real piecewise algebraic variety and the B-net resultant of polynomials.

本文应用代数几何，计算几何，函数逼近论等学科的基本理论，分别就分片代数曲线的Nother型与Riemann-Roch型定理；分片代数曲线的实交点数；实分片代数簇以及多项式的B-网结式进行研究。

Representation Theory and Higher Algebraic K-Theory is the first book to present higher algebraic K-theory of orders and group rings as well as characterize higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory and their relative generalizations.

代表理论和更高的代数学的K 理论是第一个书提出订货和组戒指的更高的代数学的K 理论，好和导致equivariant更高的代数学的K 理论和他们的有关的概括的麦基functors一样表现更高的代数学的K 的特性理论。

Algebraic K-theory is an important branch of algebra which has deep relationships with other branches of mathematics such as algebraic number theory, algebraic geometry and algebraic topology.

代数K-理论是代数学的一个重要分支，它与数学中代数数论，代数几何和代数拓扑等其它分支有深刻的联系。

The non-uniform algebraic codebook is determined by the non-uniform statistical properties of the algebraic codebook, and the part-searching-area is determined by the periodicity of the algebraic codebook excitation vector, which makes up the insufficient numbers of signed pulses in algebraic codebook at low bit rate.

非均匀代数码书由代数码书的脉冲非均匀统计特性确定，部分搜索域代数码书则由代数码书矢量的周期性确定，该方法有效地弥补了低比特率情况下代数码书中脉冲数不足的缺点。

Chapter 8: We discuss the acceleration of multigrid by Krylov subspace approaches, and recognize the reason for slow convergence of algebraic multigrid methods is that error reduction is significantly less efficient for some very specific error components which may cause a few eigenvalues of the algebraic multigrid iteration matrix to be considerably closer to 1 than all the rest. However, the eigenvectors belonging to the few isolated eigenvalues can be expected to be typically captured after only a few conjugate gradient iterations, which accelerate algebraic multigrid algorithms. Theoretical analysis and numerical results of some practical problems show the iterant recombination accelerates algebraic multigrid convergence.

第八章：先介绍用Krylov子空间迭代法加速一般多重网格方法收敛的基本框架，然后紧紧抓住引起代数多重网格方法收敛减慢的根本原因往往是误差减小对几个特别的误差分量不明显，这导致代数多重网格方法的迭代矩阵的几个特征值接近于1，而共轭梯度方法则能比较典型地捕捉属于孤立特征值的特征向量，从而推导出有效的共轭梯度加速算法和程序实现，不仅从一些具体的实际应用例子的数值结果去验证迭代复合加速收敛的效果，而且还从理论上分析了预处理共轭梯度法加速代数多重网格法收敛的机理。

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。

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。

Now she was hungry and angry.She began to smoulder.

现在她又饿又气，她开始流露难以抑制的怒火。

You have placed our iniquities before You, Our secret sins in the light of Your presence.

诗90：8 你将我们的罪孽摆在你面前、将我们的隐恶摆在你面光之中。