查询词典 integral calculus

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

The paper states the distinctions between Riemann integral and Lebesgue integral from the aspects of the definition of integral,the continuity of integrable function,the additivity of integral,integral limitation theorems and Newton-Leibnitz formula.

从积分的定义，可积函数的连续性，积分的可加性，积分极限定理，牛顿-莱布尼兹公式五个方面阐述了黎曼积分与勒贝格积分的区别。

This course mainly contents real number muster and function, limit of number sequence, limit of function, continuity, derived number and differential, differential mean value theorem and its application, completeness of real number, integral, series(including positive series and Fourier series), multiple- differential, double integral, integral with parameter, curve integral, camber integral and so on.

理解和掌握《数学分析》的概念、理论和方法，对于学生加深理解数学的基本思想和方法，培养抽象思维能力和逻辑思维能力，提高数学素养具有重要的意义。主要内容包括：实数集和函数，数列极限，函数极限，连续性，导数和微分，微分中值定理及其应用，实数完备性，积分、级数(包括幂级数、Fourier级数)、多元微分学、重积分、含参变量积分、曲线积分、曲面积分等。

In the computation of aerodynamic forces, the present work is based on the work of Morino et al., but the following aspects are improved:(1) In computing the steady transonic aerodynamic load, the steady transonic nonlinear integral equation is solved by relaxation-iteration method in this thesis, instead of solving the time dependent transonic nonlinear integral equation, so that the computing time is saved greatly;(2) The influence coeifficients represented by volume integral are transformed to surface integral by using the Gaussian Theorem, so the analytical form of these coeifficients can be obtained and this leads to be more convenient to analyse and compile computer program;(3) The shock capturing method is used in every time step in present work, no shock moving term is added in the integral equation, so that it is more convenient and simpler to treat.

在气动力计算方面，本文基于Morino等人的工作，作了如下几方面的改进：（1）在计算定常跨音速流场（作为非定常绕流计算的初场）时，本文采用松驰迭代法直接求解跨音速定常非线性积分方程，而不是采用时间相关法求解非定常非线性积分方程，这样大大节省了计算机时；（2）将以体积分形式出现的影响系数化为面积分，并获得解析公式，这样便于分析和编写程序；（3）对运动的激波，本文通过在每一个时间步长上采用激波捕捉法而得到，而不是在积分方程中附加激波运动项，因而处理起来简单方便得多。

Based on the analysis of existed fuzzy integral theories, the notions of the Choquet upper and lower fuzzy integral and rough interval numbers' integral form were proposed; the rough properties of Choquet fuzzy integral and an information fusion method based on rough Choquet fuzzy integral were given.

在分析现有模糊积分理论的基础上，提出了Choquet上、下模糊积分的概念和粗糙区间数的积分形式，给出了Choquet模糊积分的粗糙特性，建立了基于粗糙Choquet模糊积分形式和信息融合方法。

Triple integral and surface integral are first simplified through the alternation of integral variable and integral extent and then calculated in other ways so that the two kinds of integral calculation can be made simple.

探讨了轮换对称性在积分计算中的应用，利用积分变量与积分区域的轮换对称性先简化重积分及面积分，然后再采用其它方法来计算，使这两类复杂的积分计算变得简单。

In modern physics research, the calculus of variations has a broad application of law. As a solid mechanics, structural mechanics and computational mechanics of the theoretical foundation, it has important value in theory and practice on the mechanics; Variation method ruled out the perturbation of the restrictions can be widely used in many state-level and the state function in the calculation in the optical; Calculus of variations can be calculated with the parameters, we can guarantee the reliability of the results, can effectively reduce the workload of calculation, It can be said that the applications of calculus of variations are very broad.

在现代的物理学研究中，变分法有着广泛的应用：在力学上，变分法作为固体力学、结构力学及计算力学的理论基础，在理论上和实践上都有重要的价值；在光学上，变分法排除了微扰法的限制，可以广泛应用于诸多定态能级和态函数的计算中；在量子力学的应用中，具有可算出系统的参数，既可以保证计算结果的可靠性，又能有效地减少计算的工作量等的优点，可以说变分法的应用领域十分广阔。

ELNF calculus is a functional/logic calculus system which based on LNF calculus by extending it to include logic programming ability.

ELNF演算的解释技术金海，李智勇，张运桢，阳富民，银海（华中理工大学计算机系，武汉430074）摘要ELNF演算是我们在LNF演算的基础上扩充逻辑程序设计能力而得到的一种函数／逻辑演算系统，它构成了作者设计的函数／逻辑语言RFUNLOG的基础。

These descriptions are brief, but based on them it is indeterminable and has disadvantage in system design and direct implementation. On the other hand, these works mostly focus on describing variants behaviors of Ambient calculus in one level, which makes it complicated to understand clearly how these variants behaviors work and how they work together. As a result, based on the unit ambient of Ambient calculus, a three-level semantics description framework is given for Ambient calculus.

这种描述方式尽管简洁，一方面却具有不确定性，不利于实际的网络计算系统的设计和直接实现；另一方面，这种语义描述方式均在一个层次上描述Ambient演算系统中的各种行为语义，使得Ambient演算中各种计算行为纠缠在一起，复杂而难以理解。

Results: The grinding rate of calculus after one lithotrity was 83.5%, of 9 cases calculus run in kidney, other 8 cases were subject to surgery due to renal duct severe twist under calculus.

结果：123例输尿管结石患者一次手术取尽率为86.2%（106例），有9例结石完整进入肾内，8例因结石之下输尿管严重扭曲改其他术式。

These rules reflect some inherent feature of self and nonself, and they are the basic detection criterion of GECISM.

这些规则反映了"自我"和"非我"的内在特征，是GECISM进行"非我"检测的判据。

Until today, the media from China and the outside world still uses the term "Post 89". Regardless to whether it is for commercial gimmick or convenience, everybody still remember "Post 89", a term which carries a strong Cantonese accent.

时至今日，国内外艺术媒体还是在沿用&后八九&这个称谓，不管当初是为了商业噱头还是容易上口好记，反正大家现在是记住了&后八九&这个广东口音很重的词。