Particularly, when the dimension of input space of the column reduced interval polynomial fraction model is one, the result can be reduced to the well-known Box theorem in robust control.
为了使这种模型更接近于实际系统，文中分别采用了范数有界的加性扰动和乘性扰动以及Gap度量来反映系统的非结构扰动部分。
Secondly, for the slider crank mechanism with given dimensions and having a constant crank speed, the analytical form of the acceleration angle of the coupler is developed. Then, according to the theorem that the angle between the acceleration vector of any point on the coupler plane and the line joining the point to the acceleration pole is equal the acceleration angle, the polynomial equations of the loci of acceleration poles described on the fixed and coupler planes are derived, respectively.
其次，针对曲柄滑件机构，当已知曲柄滑件机构尺寸，且曲柄为等速转动时，先求出耦杆的加速度角之解析式，再根据加速度极心和耦杆上任何一点的连线与该点之加速度向量所夹的角度均等於加速度角的观念，推导曲柄滑件机构之加速度极心轨迹，分别推导出描绘在固定平面及耦杆平面上之多项式方程式。
We can associate - graphs with trees from this theorem. So combined with the O time algorithm to solve the k-terminal cut problem in trees, we propose an polynomial exact one to solve the same problem with the same time-complexity as in the tree, when there are not less than 2 terminals on P_c.
在充分考虑图结构特点的基础上，本文给出了它的一个重要性质，即：当最小k-终端割中包含有P_c(n，n图中唯一的基本回路上边时，一定包含P_c上的最小加权边。
Therefore, the definition, theorem, properties of kernel and some practical kernel functions, such as polynomial kernel, Gaussian radial basis function, are discussed in detail.
因此，有关核函数的定义、定理、相应的性质，以及一些实用的核函数，诸如多项式核、Gauss径向基函数，都在这里进行了详细的讨论。
Some theoretical extensions are first made in this paper, with the following concepts, theorems and models presented-Partial derivative and high-order partial derivative of waveform polynomial for describing the relation between input transitions and output transitions and redefining circuit sensitization; The concept of waveform polynomial vector for describing a circuit with multiple inputs and outputs, especially for the unified description of circuit modules; A sensitization theorem for sequential circuits for the purpose of exact timing; Theorems for transition numbers in circuits used to solve problems on noise, power consumption and etc; waveform polynomial description for sequential circuits used to give a unified form for the function and timing behavior of a sequtial circuit; And a data structure of generalized list for the representation and manipulation of waveform polynomial.
波形多项式偏导和高阶偏导的新概念，用来精确描述输出跳变与输入跳变之间的关系，并在本文中用来重新定义了电路的敏化和冒险；波形多项式向量的概念，用于形式化描述实际中的多输入多输出的电路，特别是用于统一描述电路模块的功能及定时行为；时序电路的敏化定理，用于时序电路精确定时分析；波形多项式描述跳变及跳变数的定理，用于噪声、功耗等问题的描述；时序电路的完整波形多项式描述，用于时序电路功能和定时行为的统一描述；波形多项式的多项式符号表示和运算的模型以及数据结构，用来实现对波形多项式比较有效的描述和运算。
It included Karaji's binomial theorem and rules of the arithmetic polynomial operations and developed Karaji's theory of polynomial.
其中保存了凯拉吉的关於二项式定理的工作以及多项式的运算法则，并进一步发展了凯拉吉的多项式理论。
This book included Karaji`s binomial theorem and rules of the arithmetic polynomial operations and it developed Karaji`s theory of polynomial.
算术珍本》中保存了凯拉吉的关于二项式定理的工作以及多项式的运算法则，并进一步发展了凯拉吉的多项式理论。
Besides, in order to estimate the parameters of HMMs defined in the above schemes the prerequisites of Baum-Eagon theorem are relaxed to nonnegative parameters of polynomial, and homogeneity is unnecessary.
同时，为了估计上述定义下的模型参数，通过严格证明，作者将Baum-Eagon定理的先决条件放宽为多项式系数非负，而齐次多项式的约束是不必要的。
For the case that the eigenstrains is in the form of linear function of Cartesian coordinates of the points of the inhomogeneity, the solution for the stress and strain fields is analytically derived based on the polynomial conservation theorem, the complex function method and conformal transformation together with the principle of minimum strain energy.
对于夹杂的特征应变为线性分布的情况，基于多项式保守定理，运用复解析函数法、保角变换和最小势能原理，获得了问题的封闭形式的解析解。
This paper by means of set theory, presents a modified suboptimal subset polynomial regression algorithm based on abstract algebra. In the paper, most of contents for regression process are adequately described and discussed in mathematics, one important theorem and corollary are given.
提出以集合论为工具建立在抽象代数理论基础上的修正次优子集多项式回归法，对回归过程的主要内容进行了充分的数学描述和讨论，给出了一个重要的定理和推论。
By means of the sufficient and necessary condition of the second order polynomial system's integrability and the division theorem of polynomial functions in two variables in the complex domain, we obtain some criterion for the non_existence of Brusselator equation algebraic curve solution.
依据管克英、雷锦志在IntegrabilityofSecondOrderAutonomousSystem一文中给出的二阶多项式自治系统可积的充要条件，通过复域上二元多项式函数整除定理，判定了Brusselator方程不存在代数曲线解。
This paper investigates the integral valued polynomial and its identity factors, also gives a new proof for Fermat's little theorem.
探讨整值多项式及其恒因子，并给出费马小定理的一种证明方法。
Inchapt 3, we study construction of the invariant polynomial ring oftrace map associated with substitution. We solve this problem whensubstitution is invertible, give a basic theorem.
第三章研究结合代换的迹映射的不变多项式所形成的环，解决了代换为可逆的情形的环的结构问题，并给出了有关的基本定理。
In the literature [6], combining the Polya counting theorem and the chromatic polynomial together, Professor Du Qingyan introduced the notion of the chromatic orbit polynomial, and gives its expressions and its calculation methods.
在文[6]中，杜清晏教授结合Polya计数定理和色多项式，提出色轨道多项式的概念，并给出了它的表达式及其计算方法。
Polynomial Function with Rational Exponent Power and Theorem of Its Roots
有理指数幂多项式函数及其根的定理
Polynomial Interpolation and Rolle's Theorem
多项式插值与Rolle定理
Based on the fuzzy Lagrange polynomial interpolation, we introduce the fuzzy New-ton interpolation formula and it's suitability theorem, Also, we give a method for com-puting the Newton interpolation polynomial.
本文在模糊Lagrange插值的基础上，引进了模糊牛顿插值公式及其适定性定理和求法。
Using the similarity between polynomial ring and integer ring the paper establishes Sunse's Theorem in the polynomial ring in number field, and offers its brief learning and practice.
利用数域上一元多项式环与整数环相似的性质，建立数域上一元多项式环中的孙子定理，并给出它的简单应用。
In this paper, we generalize Eisenstein's Discriminatory Method and give another theorem and its five important inferences for discriminating the irreducibility of intergral polynomial over the rational number field.
对Eisenstein判别法作了进一步推广，给出了判定整系数多项式在有理数域上不可约的又一定理及其5个重要推论。
The paper introduces the property theorem about roots of polynomial and the derivate limit theorem, by which we can study the derived number of a break point of piecewise function.
介绍了用多项式根的性质与导数极限定理求分段函数在分界点的导数的简单方法。