微分方程的积分

To study the taxiing-induced dynamic response of the aircraft with multiple wheels and multiple landing gears due to runway unevenness, base on several reasonable and necessary assumptions, the mathematical model of aircraft in taxiing is established using the d'alembert's principle. It can simulate taxiing inpact properties accurately, it considers in detail the vertical and horizontal motion and pitching about its center of gravity and the significant symmetric elastic modes.

在一些必要合理的假设下，利用达朗贝尔原理，建立了多轮多支柱式及小车式起落架飞机地面滑跑动态响应分析的全机模型，考虑全机沉浮、机体弹性和定常气动力的影响，起落架支柱的弹性变形，小车式起落架的车架的俯仰运动以及弹性变形，对等速滑跑飞机建立了全机运动的微分方程，并以旧金山28-R跑道为地面输入，利用时域积分的方法得到飞机滑跑的各种响应。

In this part, the characteristics of transient responses of flexible rotor systems with arbitrarily distributed mass on isotropic or anisotropic supports passing through several critical speeds seguencially are examined. Here, the current knowledge of rotor dynamics on the eigenproblem of damped free whirling vibration, the generaliged damped mode theary, the transient forced vibration and so on combined with KBM asymptotic method in the nonlinear vibration theory is employed and extended.

作者综合运用并引伸推广转子动力学关于阻尼自由回旋振动的特征问题、广义阻尼模态理论、瞬态强廹振动等現代理论和方法，结合非线性振动理论中的KBM渐近法，提出自己独創見解和覌点，成功地建立起正回旋和逆回旋两种情况下转子通过临界点的瞬态振动一阶微分方程组，可以在临界点的邻域内从事方程的数值积分计算。

Under suit upper and lower solution, iteration sequences were constructed, and existence and unique of solutions of linear boundary value problems on second order nonlinear Hammerstein type integro-differential-difference equation were obtained by means of applying the Arzela-Ascoli theorem Lebesque control convergence theorem and disproof method.

在上下解存在的条件下，构造迭代序列，由Arzea-Ascoli定理和Lebesque控制收敛定理得到了二阶非线性Hammerstein型积分微分差分方程的线性边值问题的解的存在性。再利用反证法获得了解的唯一性。

Chapter 1 we introduce the risk process with positive and negative risk sums,show the background of the risk process. Chapter 2 we show the integral and differential equation of birth probability,give the Lundberg inequation that the ruin probability satisfies with martingale approach,then discuss then ruin probability of the risk process with two dependent positive and negative risk sums,study how the dependence impacts on the ruin probability. Chapter 3 we compare the concrete examples by numbers,and makes further comparison between the two results coming out of independency and dependency,with the purpose of narrating their respective impacts on the probability of ruin probability.

本文第一章引入含正、负风险和的风险模型，介绍风险过程的实际背景；第二章给出生存概率Φ所满足的积分-微分方程，利用典型鞅方法给出破产概率Ψ满足的Lundberg不等式，并且讨论两个相关正、负风险和模型的破产概率，研究相关性对破产概率的影响；第三章对具体实例给出数值比较，进一步把相关性和独立性两种情形的结果进行比较，说明对破产概率的影响。

Chapter 2 discuss firstly the local existence of solutions for a class of abstract functionalintegro-differential equations with unbounded delay by Schauder's fixed point theorem, then byintroducing an inequality condition and applying the continuity property of solutions it obtainsthe global existence of the solutions.

第二章先利用Schauder不动点定理讨论一类具有无限时滞抽象泛函积分微分方程解的局部存在性，然后引入一不等式条件并利用解的延拓性质获得了解的整体存在性

Firstly, the integral-differential equation described the radiation field evolution is derived, and then the instability of its solution is also investigated analytically. By using the perturbation and iteration method, the threshold detuning and threshold linear growth rate of the unstable solution are analyzed and discussed in detail.

首先，建立了一个描述辐射场演化的积分一微分方程，解析分析了系统解的不稳定性，并采用线性方程解的微扰迭代方法进一步对系统不稳定解出现的失谐量阈值和线性增长率阈值等作了详细讨论。

In this paper, we consider a class of integrodifferential equations of mixed type with dripules in abstract spaces the exitence theorem of maximum and minimum solutions and unique solutions are proved.

研究了Banach空间一类脉冲积分微分方程最大解、最小解的存在性及解的存在唯一性。所得结果推广和改进了文[1]的工作

By establishing a new comparison principle,and using method of L-quasi-upper and lower solutions and mixed monotone iterative technique,the results of existence and uniqueness of solutions to Cauchy problem s of first order nonlinear integrodifferential equations in Banach spaces are obtained.

通过建立一个新的比较原理，利用L-拟上下解方法和混合单调迭代法，研究了Banach空间中一阶非线性积分微分方程初值问题解的存在唯一性，并给出了近似解的迭代序列和误差估计式。

Analyzing on the fault of local rubbing caused by compatible misalignment of rotors, a dynamic model for the rotor system with misalignment and rub-impact was established. Then the dynamic behaviors of this system, which varied with the values of parallel misalignment and declination, were investigated by using numerical integral method.

以水轮发电机组转子系统为研究对象，针对刚性联轴器综合不对中引起转子局部碰摩的问题，建立了机组转子不对中–碰摩耦合故障的动力学模型和微分方程，并利用数值积分方法研究该系统随不对中平行量和偏角参数变化的动力学行为。

To solve the velocity potential,we used an integro-differential equation.

采用关于扰动速度势的基本积分微分方程，并采用双曲面形状的面元以消除面元间的缝隙。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。