查询词典 newton formula

With the idea of smoothing Newton method, we propose a new class of smoothing Newton methods for the nonlinear complementarity problem based on a class of special functions. In this paper, complementarity problem is converted into a series of smoothing nonlinear equations and a modified smoothing Newton algorithm is used to solve the equations. We use Newton direction and Gradient direction together in the algorithm which guarantees that our method is globally convergent. Also using another smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented, we use the modified smoothing Newton algorithm in generalized nonlinear complementarity problems, under mild hypothesis, a global convergence is proved.

本文一方面基于现有的各种光滑Newton法的思想和半光滑理论，利用著名的F-B互补函数的光滑形式，首先将互补问题的求解转化为求解一系列光滑的非线性方程组，然后给出了一种修正的光滑Newton法，该方法不仅放宽对函数F的要求，在Newton方程不可解时引入初始效益函数的最速下降方向，而且光滑因子的选择也比较简单可行，同时在适当的条件下，证明了其算法具有全局收敛性；另一方面，借助另一种F-B光滑函数，将多面体锥上的广义互补问题转化为一种光滑形式，讨论了优化问题的稳定点与广义非线性互补问题的解之间的理论关系，并将这种修正的光滑Newton法用于求解广义非线性互补问题中，在适当的条件下，该算法同样具有全局收敛性。

At the same time , we discuss the determinism and nondeterminism of formula-clock automata and the closure propertied under Boolean operation of the language which is accepted by formula-clock automata. We also prove the expressive equivalence between the deterministic formula-clock automata and the nondeterministic formula-clock automata. This means that every nondeterministic formula-clock automata can be transformed to a deterministic formula-clock automata which exactly accept the timed language identified by the fomer.We also extend timed words to infiniteness and define the formula-clock Buchi automata and the formula-clock Muller automata. At last, we show its application in formal verification and modeling of real-time system.

然后讨论了公式时钟自动机的确定性和非确定性，公式时钟自动机识别的语言类在并、交、补运算下的封闭性；并证明了确定的公式时钟自动机和非确定的公式时钟自动机表达能力的等价性，这意味这每一个非确定的公式时钟自动机都能转换为一个与之识别相同时间语言的确定的公式时钟自动机；我们将时间字扩展为无穷的，从而定义了公式时钟Buchi自动机与公式时钟Muller自动机；最后给出了用它进行实时系统的形式化验证方面及对实时系统建模的应用。

In this paper, Newton iteration formula for computing normal depth and critical depth was put forward by mathematical transformation of uniform flow equation and critical flow equation of circular section tunnel. Then, the relationship between the corresponding central angle and the introduced parameters was analyzed. An approximate formula for angle was obtained according to optimal uniform approximation principle. Using this approximate formula as initial value of iteration formula, a direct formula for calculating normal depth and critical depth of circular section tunnel was established after its first iterative.

该文通过对圆形断面均匀流方程与临界流方程的数学变换，分别得到其正常水深与临界水深的牛顿迭代公式，同时，通过对正常水深与临界水深对应的中心角与引入参数之间关系的分析及数值计算，利用最优一致逼近原理分别得到了正常水深与临界水深对应中心角的近似计算式，并以此近似计算式为初值，用迭代方程进行一次迭代得到了圆形断面均匀流水深与临界流水深的直接计算公式。

The algorithm has following properties: Although the merit function has the form of least squares of a system of overdetermined equations, in the Newton equation of our algorithm, only the coefficient matrix of the system of overdetermined equations is used instead of its product as in Guass-Newton method for solving the least squares problems. That is, our Newton method is more like that for the system of nonlinear equations rather than that for LSPs. The global convergence is obtained for VLCP with vertical block P_0 + R_0 matrix; The local quadratic convergence rate is proved under the condition that the solution is BD-regular; Although there is only a Newton equation in our algorithm, the finite convergence property can be shown if matrix is vertical block P— matrix (without the hypotheses of strict complementarity).

该算法具有下列特点：所构造的价值函数虽然具有超定方程组的最小二乘问题的形式，但在基此建立的Newton算法中，其Newton方程的形式更象非线性方程组的Newton法中的Newton方程，仅利用了超定方程组的系数矩阵本身的信息，避免了一般最小二乘问题的Guass-Newton法中必须计算系数矩阵的乘积的工作量；对竖块P_0+R_0矩阵的垂直线性互补问题，算法具有全局收敛性；在解是BD-正则条件下，证明了算法的局部二次收敛性；虽然算法只含一个Newton方程，但对竖块P-矩阵垂直线性互补问题，算法具有有限步收敛性。

It also makes analysis on the connection of Newton's prism experiments, and describes how Newton proved these propositions by taking advantage of these experiments in the article. As well the author makes analysis and generalization on the make of Newton's reflecting telescope and Newton's

首先，在对《光学》认真研读的基础上，首次对其光的颜色理论部分的大量棱镜实验之间的关系进行了分析，从而说明牛顿是如何利用这些实验证明这些命题的；其次，笔者在前人研究的基础上，对反射望远镜的制造和牛顿环理论进行分析和总结，力求描述得清楚全面；最后，鉴于国内外对牛顿光本性认识的研究存在分歧的情况，笔者对惠更斯和牛顿的相关著作进行了详细考察，对他们的光本性观点进行了系统的研究和比较，从而指出那种只因牛顿

After rectifying the family structure, and educational level of parents, the influencing factor of adaptability was formula mainly; intensity of reaction was breastfeeding duration for 4-6 months and breast milk mainly; rhythmicity was breastfeeding duration for 7-9 months and formula only; activity level was both breast milk an formula milk equally and breastfeeding duration for 7-9 months; quality of mood was formula only and duration of breastfeeding for 7-9 months; approach-withdrawal was breast milk mainly and both breast milk and formula milk equally; distractibility was formula milk mainly.

校正家庭结构、父母亲受教育水平等因素后，适应度的影响因素是主要喂奶粉；反应强度的影响因素是母乳喂养持续时间4~6个月和主要喂母乳；规律性的影响因素是母乳喂养持续时间7~9个月和只喂奶粉；活动水平的影响因素是母乳与奶粉等量和母乳喂养持续时间7~9个月；情绪本质的影响因素是只喂奶粉和母乳喂养持续时间7~9个月；趋避性的影响因素是主要喂母乳和母乳与奶粉等量；注意分散的影响因素是主要喂奶粉。

Tne paper systemically discusses the object-image relations in the thin-lens imasery with Newton Formula and the relative graphs,and new and deeper theoretical otplanations are given. Thin-lens imasery Newton Formula,graph velation

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Fist, comprehensive analysis on the current study on data processing is made, and characters of Newton methods about nonlinear surveying and mapping data processing are discussed, and then new solutions to parameters estimate with multi-sources, multi-types, multi-dimension, multi-precision bynonlinear least square are presented such as PSB algorithm, digital continuation and generalized digital continuation algorithm, cone model method, tensor analysis method, GCMA(mixed algorithm of gradient method and conjugate gradient method), combining algorithm based on Newton method and gradient method and confidence region and so on, and a new fast difference iterative algorithm is proposed towards parameters estimation containing random parameters in nonlinear models, and a new solutions to nonlinear least squares surveying and mapping adjustment by parameters estimation both considering the random and nonrandom parameters is presented after studying on nonlinear data processing in deformation monitoring, and at last primary analysis on error propagation of spatial data is made and approximate error propagation formula and error analysis formula to length and area are proposed.

首先比较全面分析了目前测量数据处理理论的研究现状，讨论了牛顿类方法在处理非线性模型参数估计方面的特点，研究并给出了求解多源、多类型、多维、多精度、非线性最小二乘测量平差参数估计的若干种新方法，这包括PSB算法、数值延拓及其广义数值延拓算法、锥模型法、张量分析法、基于最速下降法和牛顿法的组合算法、基于最速下降

Tne paper systemically discusses the object-image relations in the thin-lens imasery with Newton Formula and the relative graphs,and new and deeper theoretical otplanations are given. Thin-lens imasery Newton Formula,graph velation

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As research and extensive, gradually discovers that the seeastigmatism formula also have problems, that is, it has a data expression cannot and Visual feeling of one's eyes, so the match chromatology experts have implemented written by CMC (1 c) CIE94 seeastigmatism seeastigmatism formulas, the formulas as well as the latest CIEDE2000 seeastigmatism formula, where written by CMC (1 c) chromatic aberration formula in the textile industry is listed as a range of international and national standards. X-Rite ′?ˉs 528 integrates CIE LAB color difference equation, written by CMC (1 c) and the color difference formula, the formula CIE94 seeastigmatism seeastigmatism measurement shall be free to choose from.

随着查究的浮浅，忽然发掘该色差公式也有题目，即它的数据外达不克不及够和人眼的触觉感施相成婚，因此色彩教查究大师接踵推出了CMC(1∶c)色差公式、CIE94色差公式以及最新的CIEDE2000色差公式，其洋CMC(1∶c)色差公式在纺织行业被列为不国外和国度尺度。X-Rite 528集不败了CIE 1976 LAB色差公式、CMC(1∶c)色差公式和CIE94色差公式，在色差丈度时可以自由拔取。

This immediately brings us to the next part of this article: creating an output "replace function".

下面进入文章的第二部分：建立一个"缓存处理函数"。

He was elected as an International Ornithological Committee member in 2002 during the 24th IOC held in Beijing.

现为中国鸟类学会理事和WPA 专家组成员。2002年被推选为国际鸟类委员会委员。