微分

Based on the equilibrium equation of an arch element the cubic nonlinear dynamic model with second order is established and the nonlinear differential dynamic system without constant term is obtained through a transfer process of T=U+b. Hence three fixed points and the homoclinic orbits are found. The critical condition of the chaotic vibration of the elastic arch is given by using the method of Melnikov function. The numerical results of the stationary and chaotic motion are given and discussed.

首先利用拱的单元平衡方程建立了拱的二阶三次非线性动力学模型；然后通过变换使方程转化为不含常数项的非线性微分动力系统，并由此得到无扰动系统的3个不动点与同宿轨道；再用Melnikov函数法给出了发生混沌的临界条件；最后给出了该系统出现定常运动和混沌运动的数值结果。

In HSCM, the homotopy arclength continuation method is improved in three aspects.

在同伦－同时校正混合算法中，对同伦弧长微分算法进行了多项改进。1。

At firstly assuming shear modulus is linear along depth, introducing differentiating operator of structure and using the stochastic vibration theory of continuative linear system, this paper studies the dynamic response problem of non-homogenize site soil.

首先假定土层的剪切模量随深度线性变化，引入结构微分算子，利用连续线性系统的随机振动理论，研究了非均匀场地土层地震的动力反应问题。

Derive the equations of continuity by using the method of infinitesimal based on the mass balance equations and the differential equations of gas and oil phase fluid flow.

再根据物质平衡原理，利用微元法分析凝析油气渗流规律，建立连续性方程，从而导出凝析油气渗流微分方程。

Based on the modal superposition method and the exact solution of beam nature vibration, the motion equations of the simply supported and continuo...

基于模态叠加法和梁固有振动的精确解，建立了移动荷载作用下简支梁和连续梁的运动方程；利用样条最小二乘法逼近桥梁应变响应，由样条数值微分求得响应导数；再通过Tikhonov正则化方法结合奇异值分解技术得到了荷载识别的正则解。

The solution of this algebraic system contains the nodal values that collectively represent an approximation to the continuous solution of the initial PDE.

求解结果中整个网格的节点值可视为对原连续偏微分方程的近似解。

Both continuous paraxial approximation formula and two order discrete paraxial approximation formula are developed for one way wave motion transmitting apparently along normal direction based on kinematics model and local polynomial interpolation function.

引言 Clayton和Engquist在1977年和1980年提出的傍轴近似公式[1，2]是迄今为止最具代表性的局部人工边界条件之一。但是上述傍轴近似公式是从特定的波动微分方程出发推导建立的，因此其普适性受到限制。

A numerical simulation to the whole motion differential equation is finished, and a continuous angular displacement curve of micro reflectmirror is obtained.

通过对该模型的完整机电动力学微分方程数值求解所作的运动仿真，得到了微镜基板的连续角位移曲线，表明该装置具有良好的光束稳定特性

In section 2, the integral expression, continuity and twice continuous differentiability and integro-differential equation satisfied by the expected discounted penalty at ruin Ф〓 are derived.

在第二节，我们得到了Ф〓的积分表达，连续性及二次连续可微性和积分-微分方程。

Institute of Statistics and Actuary, Shandong Economic UniversityAbstract We consider the risk process perturbed by diffusion under interest force in this article. The integral expressions, continuities, twice continuous differentiability and integro-differential equations about $F_{\delta}$, the distribution of the surplus immediately before ruin, and $H_{\delta}$, the joint distribution of the surplus immediately before ruin and the deficit at ruin are obtained.

我们考虑既带有随机干扰又带有确定投资回报的风险过程，得到了破产前瞬间盈余的分布$F_{\delta}$及破产前瞬间盈余和破产时赤字的联合分布$H_{\delta}$所满足的积分表达，连续性及二次连续可微性和积分--微分方程。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。