微分

The author then introduces the differential relationship between vectors as well as tensors in a curve coordinate system and curve coordinates, and the transformation relationship between coordinate systems and their matrix expressions.

简要介绍了卫星重力测量中所涉及到的曲线坐标系下矢量、张量与曲线坐标之间的微分关系、坐标系之间的变换关系以及它们的矩阵表示。

A curve coordinate system is established in which the original problem may be reduced to a fixed boundary problem over a rectangular region and thus may be solved by difference methods .

给出了一种用曲线坐标求解椭圆型偏微分方程自由边值问题的数值解法；该方法通过引入两个辅助问题，它们构成一个曲线坐标系。

This paper puts forward a united Laplacian transform which is based on the differential geometry curve coordinate system,the practical numerical experiment results show that this method has a strong edge detection ability and produces the better effect compared with old method.

该文采用基于微分几何曲线坐标系下普遍的Laplacian算子进行边缘检测，从结果可以看到处理效果明显优于普通的方法。

As the foundation of algebra, this course also offers indispensable preparation for subsequent core curriculum and sample curriculum such as differential equations, numerical calculation, functional analysis, probability theory and multivariate analysis, etc.

它不仅是代数学的基础，而且为微分方程，数值计算，泛函分析，概率论，多元分析等后继的基础课及选修课程提供了必要的

The inertia force and coriolis force are calculated to draw deviation for opposite balance, fall and plane motions close to the earth, based on the particle motion differential equation to no-inertial frame of reference.

在质点对非惯性参考系的运动微分方程的基础上，计算惯性离心力和科里奥利力对地球表面附近物体的相对平衡，落体运动和平面运动引起的偏差。

The bending of rectangular plate is divided into the generalized statically determinate bending and the generalized statically indeterminate bending based on the analysis of the completeness of calculating condition at the corner point. The former can be solved directly by the equilibrium differential equation and the boundary conditions of four edges of the plate.

在分析角点求解条件完备性的基础上将矩形板弯曲划分为广义静定问题和广义超静定问题，广义静定弯曲可以由板的平衡微分方程及四边边界条件直接求解，广义超静定弯曲可以由叠加法求解。

The definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented. Some properties of the directional derivative and gradient are proved by using tangent and cotangent mapping. The minimization necessary condition of nonsmooth Lipschitz functions is given. Moreover, Fritz John necessary optimality condition in mathematical programming is provided on Riemannian manifold.

在黎曼流形上给出了Lipschitz函数的广义方向导数和广义梯度的概念，利用黎曼流形局部上与欧氏空间开集微分同胚的性质以及切映射和余切映射导出了广义梯度的性质和运算法则，证明了定义在黎曼流形上的函数取得极小值的必要条件是广义梯度包含零元素，并利用这些性质给出了黎曼流形上数学规划问题的Fritz John型最优性条件。

Based on detailed mathematical model of the heat and mass transfer processes in packed-type counterflow liquid desiccant systems, a set of linear ordinary differential equations describing the transfer processes is obtained by some appropriate simplications.

在建立逆流填料式液体除湿系统传热传质过程的数学模型基础上，通过合理的简化处理，导出了描述这一热质传递过程的常微分方程组，得到了相应的解析解；并与精确数学模型的数值解进行了对比，二者具有良好的吻合性；利用解析解分析了各参数对除湿性能的影响；所得解析解具有较好的理论及应用价

Based on detailed mathematical model of the heat and mass transfer processes in packed type counterflow liquid desiccant systems,a set of linear ordinary differential equations describing the tramsfer processes is obtained by some appropriate simplications.

通过对逆流填料式液体除湿系统传热传质过程数学模型的合理简化，推导出描述这一热质传递过程的常微分方程组的分析解，并与未简化数学模型的数值解作对比，二者具有良好的吻合性。

Based on the dynamics fundamental equation, the rigid ships rolling coupled oscillation model was established, then the definite condition of the coupled oscillation equation under the regular transverse wave and first-order ordinary differential equations were presented. The ship vibration rule under the regular transverse wave was analyzed by examples, simultaneously the influence of damping coefficient on the vibration type was discussed.

基于动力学基本方程，首先建立了刚性船舶横摇的耦合振动方程，然后给出了在规则横浪激励下的耦合振动方程的定解条件和一阶常微分方程组，最后通过算例计算了在规则横浪作用下船舶的振动规律，同时研究了阻尼系数等参数对其振动规律的影响情况。

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。