查询词典 summation formula

Furthermore, the general formula is illustrated as the weighted summation of historical position states, so as to prove that in terms of cumulative iterations, parameters of PSO have an inherent forgetting characteristic in probability, moreover the searching mechanisms of canonical PSO and Barebones particle swarm are almost the same.

通过将粒子运动的一般性描述图解为历史状态加权和的形式，进一步证明了PSO参数随迭代周期的积累，在概率意义上的遗忘特性。分析表明在经过一定周期的搜索后，标准PSO方法同Barebones粒子群方法(Barebones particle swarm， BBPS)具有近似的搜索机制。

Gauss is a farmer's son, childhood, his math on the show extraordinary talent. Three-year-old father to correct an error in calculation; They found 10-year-old independent series of arithmetic summation of the formula; 11-year-old found the binomial theorem.

高斯是一个农民的儿子，幼年时，他在数学方面就显示出了非凡的才华。3岁能纠正父亲计算中的错误；10岁便独立发现了算术级数的求和公式；11岁发现了二项式定理。

I am in the teaching and problem-solving process, some of their predecessors encountered a better summation of the series method is summarized and collated in order to review the future of teaching and better transport specific as follows:①direct sum of the Law;②reverse the sum of the Law;③dislocation of subtraction;④Sub-group transformation;⑤Cancellation of law crack;⑥Sum formula.

本人在教学和解题过程中，对遇到的前人的一些较好的有关数列的求和方法进行了归纳和整理，以便在以后的教学和复习中更好地运具体叙述如下

A transformation formula containing four independent bases is found and applied to derive a few summation formulas for basic hypergeometric series.

由此说明我们又找到了一个新的证明和发现Rogers-Ramanujan型恒等式的有效方法。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容，包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵，同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

On the other hand, this paper introduces the idea of making the use of general formula or recurrence formula to resolve the summation problem and debugging the program on the blackboard.

另外，本文提出了利用通项公式或递推公式求和及在黑板上调试程序的思想。

The primary studying works and characteristics:1 To summarize reinforcing theory of cement mixing pile composite foundation2 To analyze the primary mechanics characters and changing rules of cement mixing pile, based on analysis of test data both indoor and outdoor.3 To discuss siding frictional resistance, ending resistance, ultimate bearing capacity of simple mixing pile and effectiveness factor of grouped piles, loading ratio of soil between piles under cushion cap of grouped piles and stress ratio of pile and soil and so on, and use many computation method and experimentation method to ensure bearing capacity of mixing piles composite foundation.4 To point out and analyze eight sides flaws and problems of the bearing capacity calculation method of mixing pile compositefoundation which ensured by national and normative method/ formula.5 To apply test results of loading tests and a few settlement observation data, use gray theory to predicate ultimate bearing capacity of deep mixing piles, actual example demonstrate engaging between theoretical predicted value and actual value.6 To apply groovy layerwise summation method to discuss entity piles method, double foundation method, equivalent layerwise summation method and consolidation theoretical method and so on, especially by combination of engineering example, use FEM to calculate or discuss the settlement and changing rules of composite foundation.7 To discuss problems of critical length of composite foundation by combination of engineering example and numerical analysis method, and analyze the contrast of critical length between simple pile load and most area load of composite foundation, not only critical length of composite foundation is relative to modulus ratio between piles and soil, but also upside load distribution area of composite foundation.

主要的研究工作与特色为：(1)总结了水泥搅拌桩复合地基的加固原理；(2)在对室内外试验资料进行统计分析的基础上，系统分析了搅拌桩水泥土的主要力学特性及其变化规律；(3)探讨了搅拌单桩的侧摩阻力、端阻力、极限承载力及群桩效率系数、群桩承台下桩间土荷载分担比及桩土应力比等，提出用多种计算方法并结合试验方法来综合确定搅拌桩复合地基的承载力；(4)明确指出和分析了按国家有关规范的方法确定搅拌桩复合地基承载力所存在的八个方面的缺陷与问题；(5)利用过去没有加载至破坏阶段的载荷试验成果和较少的沉降观测数据，尝试了用灰色理论预测深层搅拌桩的极限承载力，实例表明理论预测值与实测值吻合较好；(6)在常规分层总和法的基础上，探讨了复合地基沉降计算的实体墩基法、双层地基法、等效作用分层总和法、固结理论法等，特别是结合工程实例，用有限元数值计算等方法计算和讨论了搅拌桩复合地基的沉降及其变化规律；(7)结合工程实例，用数值分析方法探讨了复合地基临界桩长的问题，指出和分析了单桩荷载下的临界桩长与复合地基大面积荷载下的临界桩长存在很大的差别，复合地基的临界桩长不仅与桩土模量比有关，而且与复合地基上部荷载分布面积有关。

In other words, we are going to have to use the formulas given in the summation notation review to eliminate the actual summation and get a formula for this for a general n.

换句话说，我们要用求和符号来代替实际的求和，从而就能得出对于一般的n都适用的公式。

Test results show that the equivalent strain method exhibits a higher life assessment precision as compared to that by linear damage summation. The critical damage formula for equivalent strain can quite well predict the actual damage incurred and the equivalent strain-life curve with hardness modification fundamentally conforms with the pure fatigue strain-life curve.

试验结果表明，在预测寿命时等效应变法比线性累计损伤法具有更高的精度，等效应变的应力下临界损伤公式能够很好地预测实际损伤，考虑硬度修正的等效应变-寿命曲线和纯疲劳应变-寿命曲线基本一致。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。