查询词典 differential and integral calculus

With the publication of the Dai Wei Ji Shi Ji, a translation of Loomis' textbook Elements of Analytical Geometry and of the Differential and Integral Calculus (1851), in 1859, the differential and integral calculus was introduced into China.

19世纪后期是中国数学由传统向近现代转化的一个重要时期，微积分是近代数学乃至大部分自然科学的最基础的理论，这个理论是从1859年出版的译著《代微积拾级》中介绍到中国来的。

Its primary coverage includes: Function and limit, derivative and differential, theorem of mean and derivative application, indefinite integral, definite integral and application, space analytic geometry and vector algebra, function of many variables differential method and application, multiple integral and curvilinear integral, infinite series, differential equation and so on.

其主要内容有：函数与极限，导数与微分，中值定理与导数应用，不定积分，定积分及其应用，空间解析几何与矢量代数，多元函数的微分法及其应用，重积分与曲线积分，无穷级数，微分方程等。

In SPVT (security protocol verifying tool), the specification language is the π-like calculus extended with three appendixes, the Dolev-Yao model is described with Horn logic rules, the π-like calculus model of security protocol is transformed into the logic program model by abstract rules, the security properties are verified based on the calculus of the logic program's fixpoint, and the counter-examples on security properties are constructed from the process of the fixpoint calculus and the process of the property verification.

在SPVT中，以扩展附加项的类演算作为安全协议描述语言，以扩展附加项的Horn逻辑规则描述协议攻击者的Dolev-Yao模型，通过一组抽象规则将安全协议的类(演算模型转换为逻辑程序模型，基于安全协议逻辑程序的不动点计算验证安全性质，从安全协议逻辑程序的不动点计算和安全性质的验证过程中构造不满足安全性质的安全协议反例。

Prolonged markedly the time of sleep in mice with the hypnotic effect induced by phenobarbital sodium, while SWNH (50 mg/kg), the natural calculus bovis (100 mg/kg), and the artificial calculus bovis (100 mg/kg) did not. SWNH (500, 1,000, 2,000 mg/kg), the natural calculus bovis (1,000 mg/kg), and the artificial calculus bovis (1,000 mg/kg) i.g.

生物牛黄中间体100mg/kg体重、150mg/kg体重腹腔注射给药，可使苯巴比妥钠引起的小鼠睡眠时间明显延长；生物牛黄中间体50mg/kg体重、天然牛黄100mg/kg体重和人工牛黄100mg/kg体重对睡眠时间的延长无明显影响。

During the study of incidence calculus theory, we firstly clarified original incidence calculus and the probabilistic reasoning mechanism on it. We then introduced the improvement of generalized incidence calculus theory proposed by Liu~[18], which establishes incidence calculus theory on Lukasiewiczs three valued logic.

本文首先阐述了原始的发生率计算理论及其上的概率推理机制，然后引入Liu对该理论的改进，以Lukasiewicz三值逻辑为基础，并提出了这个扩展的理论与证据理论之间的等价关系。

Remove row and column' and 'put a big number' have been used for the first boundary;a continuous Regional Identification Function is used on the basis of non-variant nodal virtual flux method for the free surface boundary;Gauss formula is used to make the curved surface integral of the free surface boundary transformed as the difference between volumn integral and other curved surface integral to calculate the integral item on boundaries, which avoiding finding the position of free surface, while the continuous Regional Identification Function is applied to calculate volumn integral and surface integral;Crout and PCG method is used for solusion.

对于已知水头边界，采用"去行去列法"和"置大数法"进行处理；对于自由面穿过的单元，在固定网格节点虚流量法的基础上，引入连续的区域识别函数；对于非稳定渗流中自由面边界积分项，采用高斯公式将求自由面的面积分转化为求体积分与其他面积分之差，避免了求自由面的具体位置，同时在计算体积分和面积分时采用连续的区域识别函数；在解法上，采用直接解法和PCG法。

Remove row and column' and 'put a big number' have been used for the first boundary;a continuous Regional Identification Function is used on the basis of non-variant nodal virtual flux method for the free surface boundary;Gauss formula is used to make the curved surface integral of the free surface boundary transformed as the difference between volumn integral and other curved surface integral to calculate the integral item on boundaries, which avoiding finding the position of free surface, while the continuous Regional Identification Function is applied to calculate volumn integral and surface integral;Crout and PCG method is used for solusion.

对于已知水头边界，采用&去行去列法&和&置大数法&进行处理；对于自由面穿过的单元，在固定网格节点虚流量法的基础上，引入连续的区域识别函数；对于非稳定渗流中自由面边界积分项，采用高斯公式将求自由面的面积分转化为求体积分与其他面积分之差，避免了求自由面的具体位置，同时在计算体积分和面积分时采用连续的区域识别函数；在解法上，采用直接解法和PCG法。

The results show that mechanical heterogeneity has great influence on the J-integral of welded joint containing transverse crack. The J-integral on the path cross the interface between welded joint and base metal is higher than the J-integral on the paths in the weld metal for undermatched joint,while the J-integral on the path cross the interface between weld metal and base metal is lower than the J-integral on the paths in the weld metal for overmatched joint. Moreover,the difference of J-integral values increases with the increasing of the load and strength mismatching difference and the path-enclosed length of interface between weld metal and base metal.

计算结果表明：力学不均匀性对含横向裂纹焊接接头的J积分有重要影响，低匹配焊接接头中积分路径穿越焊缝与母材界面的J积分值高于积分路径在焊缝内的J积分值，高匹配焊接接头中积分路径穿越焊缝与母材界面的J积分值低于积分路径在焊缝内的J积分值；载荷越大，焊缝与母材的强度差别越大；积分路径中包含的焊缝与母材界面长度越大，J积分的差值越大。

Calculus deals with the fundamental theories of calculus, including function, limit, continuation, derivative and differential, mean value theorem, the application of indefinite integral and definite integral, infinite series, as well as the practical instances applied in economic management.

微积分讲述微积分的基本知识，包括函数、极限、连续、导数与微分、中值定理、不定积分与定积分的应用、无穷级数等。以及这些知识在经济管理中的应用的实例与练习。

Indefinite integral concept,, indefinite integral nature of the basic integral formula, the indefinite integral proofs, indefinite integral substitution integration, integration by parts, the indefinite integral rational functions.

不定积分概念，，不定积分性质，基本积分公式，不定积分证明方法，不定积分换元积分法，分部积分法，不定积分有理函数积分。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。