查询词典 summation formula

The contents of the abstract of the short Communication is:"The paper gives a complete differential partition to a Euclidean straight line with a fixed frame, and three axioms for the integral of infinitesimals indexed by real numbers; proves in standard mathematics there are positive infinitesimals outside of real number set; Gives cosmic, macro and micro counterexamples to two axioms in Jordan, Carathéodory, and Lebesgue measure theory; transforms Weierstrass limit into Huang limit, Cantor continuum into Huang continuum, and Newton-Leibniz formula into Huang formula."

这个短的发言的摘要的内容如下："此文对一条确定了固定标架的欧几里德直线给出了完整的微分分拆，并对以实数为标号的无穷小的积分给出了三条公理；在标准数学中证明了在实数集合之外存在正的无穷小；对若当，卡拉特欧多里和勒贝格测度论中的两条公理给出了宇观的，宏观的和微观的反例；将外尔斯特拉斯极限改进为黄氏极限，将康托连续统改进为黄氏连续统，和将牛顿－莱布尼茨公式改进为黄氏公式。"

So, the approximate calculating formula of parabola and the length of ellipse arc is developed by the method of finding experience formula from point of view of simplifying the calculating process and getting certain accura...

本文从既能简化计算又能达到一定精度的设想，通过找经验公式的方法给出了计算机抛物线及椭圆弧长的近似公式，并给出了常用区间上计算抛物线和椭圆弧长的一次式和二次式。

In the paper, on the basis of aggregation of previous studies, the development of optical technology and development trends at home and abroad are introduced, the principle of Fresnel lens is summarized. In accordance with its principle, circle equidistant steps Fresnel lens design is described. And on this basis, based on Fresnel design, also based on a continuous upward spiral of the plane curve concept, incidence surface and the backlight is set up to greet Archimedes - Fresnel lens design formula and the Second parabolic type Fresnel lens design formula, and on this basis, the advantages and disadvantages of the three designs is discussed.

本文在充分了解非球面光学技术在国内外的发展状况和趋势的基础上，同时从菲涅尔透镜的光学原理出发，并根据它的工作原理推导了圆环等距菲涅尔透镜的设计步骤，并在此基础上依据菲涅尔的设计思想，同时依据平面曲线的连续又呈螺旋的构思，推导出了迎光面和背光面阿基米德型菲涅尔透镜的设计公式和二次抛物面型菲涅尔透镜的设计公式，并在此基础上讨论了这三种设计各自的优缺点。

Based on the traits of the aspherical lens, the sunlight was focused on a very small spot, and then it was transferred into a plastic fiber by an aspherical lens and a selfoc lens. A formula for calculating the optimal length of selfoc lens is presented. The optimal assembly of the aspherical lens and selfoc lens was implemented by the aid of this formula. Therefore, sunlight is coupled into a plastic fiber efficiently.

根据非球面透镜垂轴球差小的特点把太阳光会聚到很小的光点，再利用长度约为1/4节距的自聚焦透镜改变光线的数值孔径使其满足光纤的数值孔径，通过一个计算公式来计算最佳的自聚焦透镜长度，实现非球面透镜和自聚焦透镜的最佳组合，把太阳光以较高的耦合效率耦合进塑料光纤。

Systemic studies environment temperature how to influence construction control, finds out linear regularity and function formula of the arch rib, selects optimal closure time, then fully meets requirements of closure precision and linear. By testing a lot of data on temperature and strain and adopting least squares collocation, this dissertation deduces the strain calculate formula that is amended by joining temperature factor, then improves accuracy of stresses testing data.

系统地研究外界温度变化对施工监控的影响，找出了拱肋变化的线性规律和函数式，选择出最佳合龙时机，保证了拱肋的合龙精度和线形要求；测试了大量温度与应力对应关系的实验数据，采用最小二乘拟合推估法，推导出温度修正后的应变计算公式，从而提高了应力测试数据的准确性。

In Chapter 4, using the formula A_k(2) given by Wei, we propose a new A_k(2)-SQP method, which develepments the using of the quasi-Newton formula BFGS, and combines with SQP method to solve constrained optimization problems, the corresponding algorithm possesses global convergence and supei linear convergence property.

第四章，利用韦提出的A_κ(2)公式，我们给出了一种A_κ(2)-SQP方法，该方法把拟牛顿修正公式BFGS进行了推广，并结合SQP方法去解约束优化问题，相应的算法具有全局收敛性和超线性收敛性。

The new form of Lorentz Force Formula,that will be suitable for the charge at any speed,has been derived,and it can be transformed into the general Lorentz Force Formula in any case at lower speed.

并在此基础上导出了适用于任意速度的新的洛伦兹力公式，它在低速情况下转化为通常的洛伦兹力公式。

Experimental Verification : Theory formula is the average value of the random variable mathematical expectation formula.

实验验证：理论平均值公式就是随机变量取值的数学期望计算公式。

However, each factor has its marked feature, it is difficult to use an accurate mathematical formula or statistical formula to ...

但各相关因素具有非显著性的特点，很难用一个准确的数学公式或统计公式来描述相互间的关系。

Lastly, the formula that can calculate the stack space which is maximal was presented based on tree structure and the stack space of a real system was calculated by the formula.

分析了任务栈空间结构，定义了能够表示栈空间最坏使用情况的树结构，提出了用树结构计算最坏情况下栈空间的计算公式，并计算了一个实际系统的栈空间。

Nowadays, most of research are to build a transmutative Petri Nets through adding controlling place sets, controlling arc sets and controlling policy to the basic Petri Nets, while the Controlled Petri Nets could be used to argue many controlling theory problems conveniently and to induce many logically and physically supervisory and solve the Event Feedback Controlling Problems and State Feedback Controlling Problem in DEDS supervisory theory.

目前大多数的研究表现为在变形后的受控Petri网基础上，利用各种方法求得各种逻辑型、结构型控制器，解决DEDS监控理论中的事件反馈控制问题与状态反馈控制问题。

On one hand, there are discussions with the works council and union about extension of short time working up to the end of September.

一方面，有讨论，工程理事会和联盟关于延长工作时间短至9月底。