多项式定理

For some special cases, the paper gives some important identical theorems, and then establishes a valuable relation between the uniformly almost periodic functions and the trigonometric polynomials.Secondly, on the basis of the identical theorem, the paper investigates the Fourier series of the uniformly B2 almost periodic functions, and further proves that the series is unique.Thirdly, the paper discusses the Parseval equation of the uniformly B2 almost periodic functions, which establishes the relation between these functions and the coefficients of their Fourier series; and next investigates an important approximation theorem-Riesc-Fischer theorem, about the uniformly B2 almost periodic functions and the trigonometric polynomials.

并给出了特殊情况下的几个重要的恒同定理，将一致概周期函数与有限三角多项式联系起来；第二，在恒同定理的基础上，给出了一致B~2概周期函数的Fourier级数，并且级数是唯一的；第三，讨论了一致B~2概周期函数的Parseval方程，建立了函数与其Fourier级数的系数之间的联系；接着给出了关于一致B~2概周期函数和三角多项式之间的一个重要近似定理—Riesc-Fischer定理。

Through the operation of formal power series, we set up the expansion of Ar, a popularizing of the common polynomial theorem, where r is a non-zero real number.

通过形式幂级数A的幂运算，建立了Ar的展开式，这里r为非零实数，这是常见的多项式定理的推广。

It is proved that all monic polynomials of order n with roots lying in some open region on the complex plane forms a simply connected set in the polynomial parameter space. Based on this result, Edge Theorems for D-stability of general polyhedrons of polynomials and Boundary Theorems for D-stability of compact sets of polynomials are obtained.

证明了其根位于复平面中某开域的所有n阶多项式的全体构成多项式参数空间中的一个单连通集，并基于这一结果进一步提出了关于一般多面体多项式族D-稳定性的棱边定理和关于一般多项式紧集D-稳定性的边界定理。

First interpret it combinatorially, and then derive it algebraically from the multinomial theorem.

先用组合方法阐述，然后从多项式定理利用代数方法推导。

First interpret it combinatorially, and th derive it algebraically from the multinomial theorem.

先用组合方法阐述，然后从多项式定理利用代数方法推导。

On the basic theory, some concepts are proposed, such as partial derivative of waveform polynomial, waveform polynomial vector, delay matrix, multiple valued Boolean process, conditional sensitization, waveform distance with crosstalk and three-dimentional Boolean process. And based on these concepts, a sensitization theorem for sequential circuits and the transition numbers theorems for waveform polynomial are proposed; the model and data structure for the representation and manipulation of waveform polynomial are proposed.

基础理论方面，提出波形多项式偏导、波形多项式向量、延时矩阵、多值Boolean过程、条件可敏化、考虑串绕的波形距离及三维Boolean过程等概念，并在此基础上提出时序电路的敏化定理、波形多项式描述跳变数的定理以及波形多项式的多项式符号表示与运算的模型和数据结构。

On the design of algorithms, a novel exact hierarchical delay analysis method for general circuits is proposed; based on the sensitization theorem for sequential circuits, an exact minimizing clocking method is proposed; based on Boolean process, a waveform simulation method considering interconnecting delay for logic circuit and a parallel waveform simulation method are proposed; a new method that transforms bit-level waveform polynomial to word-level polynomial model is proposed; a multiple valued synthesis algorithm based on multiple valued Boolean process and a wire-centered delay synthesis policy are proposed, in which timing planning, floorplanning, wire planning and optimal clock skew in early design are considered; a two-layers channel routing method for minimizing crosstalk under grid mode is proposed; based on the transition numbers theorems for waveform polynomial, a new method for generation of test with noise effects is proposed.

算法设计方面，提出了一种精确的通用电路层次化延时分析方法；基于时序电路的敏化定理提出时序电路最小时钟周期精确确定方法；提出基于Boolean过程论的考虑互连延迟的逻辑电路波形模拟方法，在分析了波形模拟适合并行化基础上，进一步提出一种并行波形模拟算法；提出一种将位级电路波形多项式描述转化成字级多项式描述的新方法；提出一种基于多值Boolean过程的多值电路综合算法以及一种将前期设计定时规划、前期设计的布局规划和线网结构化方法及低偏移的时钟分配等技术相结合的面向互连延时的综合策略；提出一种串绕最小化的网格模式下的双层通道布线方法；从波形多项式描述跳变数的定理出发提出了一种考虑噪声效应的测试生成新方法。

Then do carefully the construction of the auxiliary polynomial, beginning on mid-page 160, finally stating the Auxiliary Polynomial Theorem.

接着仔细讲辅助多项式的构造，从160页中间开始，最后讲辅助多项式定理。

Theoretical formula of powder homogenizing : H=N1/2 is deduced according to mathematical statistics and polynomial theorem.

根据数理统计、多项式定理推导出均化理论公式H=N1/2，并介绍了在Ф6m×18m圆库上运用此公式开发无动力粉料均化技术的实例。

II, Polynomial rings on a general field( on contrast of those over a number field): concepts of ring, ideals, field and several special rings as domains, principal ideal domains and unique factorization domains, the unique factorization theory of polynomial rings.

二、一般域上的多项式理论（是数域上多项式理论的推广）：学习环、域和几类特殊结构的环（整环、主理想环，唯一分解环等）的概念，多项式环的唯一分解定理；三、线性代数：讲述一般数域上的向量空间理论（是数域上向量空间理论的继续和推广），模的概念，主理想环上的模的结构及其线性变换的若当标准型等；四、一元多项式的解及域论：学习域扩张及其相关概念，伽罗瓦理论，用伽罗瓦定理判断根式解的存在性。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失