函数的积分

Then by using the Riemann's function of the operator and constructing an auxiliary problem, an integrodifferential equation equivalent to former problem is got.

然后利用该算子的Riemann函数，通过构造辅助问题，得到了一个等价积分微分方程。

Then by using the Riemanns function of the operator and constructing an auxiliary problem, an integrodifferential equation equivalent to former problem is got.

然后利用该算子的Riemann函数，通过构造辅助问题，得到了一个等价积分微分方程。

By taking the energy integral as Lyapunov function, it is proved that nonlinear transverse vibrations of the beam undergoing uniform extension or retrieval are stable when there are not controlling moment in the central rigid body and driving force on the beam, according to the partial stable theorem.

利用能量积分构造Lyapunov函数，根据部分变量稳定性定理，证明等速伸展或收缩梁的横向非线性振动稳定。

In the numerical calculations,the unknown density of dislocation is approximated with the product of fundamental function and Chebyshev polynomials.The calculations show the present method yields rapidly converging and high accurate numerical results.

在数值求解这组奇异积分方程中未知位错分布密度近似为基本密度函数与Chebyshev多项式之积，计算表明，本文方法的数值结果不但收效快而且精度高。

The paper includes:The author calculate the structures inner force and displacement of the free end , analyze the influence of the height and the value of pretress of cable by making use of ANSYS 9.0 soft, pose the concept of critical prestress,conclude the function relation between displacement of the free end, initial strain and the height of cable ,analyze the dynamic properity and point out that Newmark-β method should be adopted when we analyze the dynamic properity of the cable-stayed spatial structure with direct integral test to guarantee the contribution of high mode,finally conclude the functional relation among coefficient of earthquake inner force, initial strain and the height of cable, wish to get some helpful conclusion applied to cable-stayed spatial truss design.

本文系统介绍了斜拉空间桁架竖向地震反应的分析理论与方法、详细分析了斜拉空间桁架结构在静力和竖向地震作用下的受力性能，主要内容包括：利用通用有限元软件ANSYS9.0计算了斜拉空间桁架在静力和竖向地震作用下内力及自由端位移分布规律并得出地震内力系数与节间位置、预应力以及斜拉索高度之间的函数关系；详细分析了斜拉索中施加的预应力以及斜拉索高度的变化对于该种结构内力及自由端位移的影响并提出了斜拉空间桁架的临界预应变概念，进而得到了自由端位移与初始预应变以及斜拉索高度的函数关系，即：△=-(40h+2180)ε+9.8；分析了该种结构的动力性能，并指出：在时域内采用直接积分法计算该种结构的动力响应时，应该考虑采用不引起振幅率减小的Newmark-β法，以保证高阶模态响应的贡献仍然保留在响应中而不致于被忽略。

Through this method for judging the uniform convergence, later, discriminate functions meet function series and parameter improper integral. We uniform convergence problem can be given according to the problems in accordance with the terms of this list, choose the proper, concise method are verified.

通过本文对判别一致收敛方法的总结，以后遇到判别函数列、函数项级数以及含参量反常积分一致收敛的问题时可以根据问题所给的条件再依照本文所罗列的方法，选用适当的、简洁的方法进行证明。

The calcalus learns is a mathematic branch connected closely with scientific application.Infinitesimal is an important componant in the theoretical system and has an outstanding effect on the forming of the basis and conception of the theory. infinitesimal ; calculus ; the calculus learns ; differential calculus ; integral calculus

引 言微积分学是建立在实数、函数和极限理论基础上，研究函数微分、积分以及有关概念与应用的数学分支。17世纪精密科学的飞速发展，天文学、力学、光学、工业技术要求数学彻底革新，导致了无穷小概念的问世，促使费马增量理论开创微分学的先河，同时奠定了柯西的极限理论。

Secondly, point out that meshless method is different from finite element method in handling boundary condition and numerical integral because the approximation function of meshless method is not inserted function, it have itself special methods. Deduces meshless Galerkin essential equation of parabolic partial differential equation with the method ofweighted residuals------Galerkin. Furthermore, discusses the main factors which may effectthe calculation precision and give some suggestion with which can get the best result.

其次，由于无网格法的近似函数不是插值函数，所以无网格Galerkin法在处理边界条件和对区域积分时是不同于有限元的，它有其独特的处理方法，从加权残量法——Galerkin出发，推导出抛物型偏微分方程无网格Galerkin法的基本方程，并对影响无网格Galerkin法的主要因素进行探讨，给出了取得最佳效果的相应建议。

Secondly, based on the different structure characteristics and additional conditions, we study several kinds of inverse problems of pseudoparabolic equations. One is a kind of pseudoparabolic inverse problem of identifying a constant coefficient solved by combining the formal solution of the problem and the additional condition properly. The second is the pseudoparabolic inverse problems of identifying an unknown boundary function and an unknown source term solved by using the Riemann function method to get the formal solution of the problem and then using the additional condition to transform the problem into a Volterra integral equation of the second kind. The third is a kind of backward heat flow problem of nonlinear pseudoparabolic equation solved by combining the Riemann function method and the fixed point theory properly.

其次，根据不同模型的结构特点和附加条件，研究了几类伪抛物型方程的反问题：一是利用问题的形式解并结合附加条件，解决了一类伪抛物型方程常数系数的反问题；二是利用Riemann函数方法获得问题的形式解，利用附加条件将问题转化成求解第二类Volterra积分方程问题，解决了一类伪抛物型方程未知边界值的反问题和未知源项的反问题；三是将Riemann函数方法和不动点定理相结合，解决了一类非线性伪抛物型方程的后向热流问题。

In this paper,it will be shown that by replacing the time integral of the Hamiltonian by another appropriate functional,and by substituting the scalar product by a semi-scalar product,an appropriate function space can be found in which classically non- conservative systems,i.e.,systems which are non-...

本文将指出用另一个适当的泛函代替啥密顿的时间积分以及用一个拟标量积代替标量积，可以建立一个适当的函数空间，在那个函数空间中，传统的非保守系统——即关于能量是非保守的系统具有保守系统的性质。

This paper discusses design and realizable methods of remote test output interface from logical design angle.

本文从逻辑设计的角度讨论遥测输出接口的设计及实现方法。

This also 星体投射plies to buildings, structures and geological features.

这也适用于建筑物和地质特征。