微分

Matrix differential system; Damped term; Oscillation; Riccati transformation; Integral average

基础科学，数学，数学分析矩阵微分系统；阻尼项；振动性； Riccati变换；积分平均

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。

In particular, we study the properties of the solutions of the DDE with local monotone in the delay term.

阐述了用动力学方法研究神经网络的重要性以及时滞微分方程理论研究的必要性。

This article applies the simplified differential coefficient equation on rising-sinking and swinging movement of high-speed sliding body model in the static water. The paper presents a method of theoretical prediction for the movement of high-speed planning hulls with a constant dead rise angle in regular waves.

应用简化了的高速滑行体模型在静水中滑行的升沉和纵摇运动的微分方程，提供了对不变侧缘角的高速滑行体在规则波浪中运动的动力分析方法。

Some conclusions were summarized as following: wood、 paper、 fabric and kitchen rubbish have the resemble pyrolysis characteristics; it is obvious that plastic"s decalescence happened during it"s pyrolysis process; the range of τ_max from great to small in sequence is plastic、 rubber、 fabric、 paper、 kitchen rubbish and wood.

其次，本文对垃圾典型组分的快速热解特性作了研究，并同程序升温时的热解特性作了比较，得到以下一些结论：木屑，纸屑，织物和厨余，其热解特性具有相似之处，微分转化率曲线均表现为单峰曲线；塑料在反应时存在较明显的吸热现象；τ_max(最大失重率所对应的时间)由大到小依次是塑料，橡胶，织物，纸屑，厨余，木屑。

At many occasions they arise quite natu-rally.For example,they appear in the Iwasawa decomposition of the isometry group ofa non-compact Riemannian symmetric space.Also,every connected homogeneous Rie-mannian manifold of non-positive sectional curvature can be represented as a connectedsolvable Lie group with a left-invariant Riemannian metric.

它们出现在非紧致黎曼对称空间的等距群的Iwasawa分解中；任一非正截面曲率的连通齐性和黎曼流形可以表为带有左不变黎曼度量的连通可解李群等，带有左不变黎曼度量的幂零及可解李群的微分几何，调和分析和谱几何是重要的研究课题。

A dynamic interaction schematic of an end bearing or elastic bearing pile with arbitrary force at pile top is founded. By using Helmholtz resolution and the operator decomposition method, Biots equations governing motions of a porous solid saturated with interstitial fluid are decoupled.

建立饱和土中端承桩和摩擦桩在任意激振力作用下的理论模型，利用位移势函数及微分算子分解方法，得到饱和土层Biot动力固结方程的分离变量解。

The first section is to introduce some corresponding basic definiens and properties on the fractional calculous. The rest of the chapter is to present solving methods for the approximation solutions of the nonlinear fractional differential equations and their application.

首先介绍了本章涉及到的分数微积分的定义及其性质，然后介绍了非线性分数阶微分方程近似求解的方法及其应用。

The linerarized step contains solving differential equation, defining feedback control and new coordinate.

其精确线性化步骤含：求解微分方程、定义反馈控制及反馈线性化后的新坐标。

Based on the Von Karman theory of thin plate with large deflection, the nonlinear dynamic differential equations of elastic elliptical plate are first established.

然后应用Galerkin技术和KBM法求解了此微分方程，并讨论了有关参数对粘弹性椭圆板动力学行为的影响

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。