导出方程

By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the measure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed.

通过讨论一般函数的分维导数的位置假设及幂函数的分维导数的形式假设，进一步明晰了幂函数的分维导数、分维微分及分维积分的具体方程形式，给出分维导数与分数阶导数的区别，随后讨论了基于一般分形测度的分维微积分形式定义导出的自相似分形的测度计算方程具体形式，给出了其与目前 Hausdorff 测度方法的区别，并对包括三分 Cantor 集合、 Koch 曲线、 Sierpinski 垫片及正交十字星形等自相似分形在内的测度进行了计算分析。

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。

First, we derive the Slant operational matrix of integration and set up Slant conversion table, then we could solve the differential equation and the partial differential equation easily.

首先，推导出 Slant 转换的积分运算矩阵，然后建 Slant 转换表，之后我们就能轻地求解微分方程和偏微分方程的问题。

In the present paper,we first investigate the following initial-boundary valueproblem of parabolic Monge-Ampere equation〓 in 〓(1)〓 on 〓(2)where Ω is a bounded convex domain in 〓 denotes the parabolic boundaryof Q,and second give a preliminary probe into the initial value problem of aspecial kind of parabolic Monge-Ampere equation which comes from the theoryof optimal investment in mathematical finance.

本文首先讨论如下抛物型Mongc-Ampère方程的第一初边值问题〓（1）〓（2）其中〓为〓中的有界凸区域，〓为Q的抛物边界，然后针对一种在数学金融学的最优投资理论中导出的特殊形式的抛物型Monge-Ampère方程的初值问题进行了初步的探讨。

The PSE in the curve coordinate systems are solved by the numerical techniques developed efficiently in this paper. A normal transform is introduced, and there are enough much grids in the region between the critical layer and the wall, where the variation of the disturbance is the quickest. The finite-difference of governing equations with fourth-order accuracy in the normal direction is utilized in full regions including points close the wall, and is very important for accurately discreting equations.

对于曲线坐标系下的抛物化稳定性方程，文中发展了求解的高效数值方法：引进法向变换，使得在临界层与壁面之间的扰动量变化最快的区域有更多的法向网格点；导出包含边界邻域在内的完全四阶精度的法向有限差分格式，这对方程精确离散至关重要；采用全局法和局部法相结合的方法及其新的迭代公式，大大加速收敛并得到更精确的特征值。

In this thesis, we express one dimension wave equation by arithmetic theory and prove D'Alembert Solution in the light of method on one stage linear partial differential equations.

本文从另一角度即算子的方法，将弦振动方程写成算子的形式，再根据一阶线性偏微分方程的求解方法，最终推导出D'Alembert公式。

Here the deriver' self-equilibrium velocity denotes the deriver' desired equilibrium velocity accompanying that the traffic flow is in the equilibrium state. Consequently the adaptive flux model like Navier-stokes traffic equation is derived from the extended Paveri-Fontana equation. Characteristics and the linear stability are analyzed. Numerical solution of the macroscopic traffic equations verifies rationality of our model.

把适应性公式和约化Paveri-Fontana等式结合得到扩展的Paveri-Fontana方程，通过使用Chapman – Enskog方法导出类Naveri-Stokes 方程的适应性交通流模型；通过线性稳定性分析，得到了适应性交通流模型的稳定条件；通过对算例的数值分析与其它连续性模型和交通实测数据的对比，验证了我们模型的合理性。

At first, we introduce in detail relativistic mean-field theory, where a common Lagrangian density is presented. Starting with this Lagrangian density, we can obtain the Dirac equation and Klein-Gordon equations for nucleon and meson field by using Euler-Lagrangian equation.

本文首先详细介绍了相对论平均场理论的一些公式推导，给出了常用的一般的相对论平均场的拉格朗日量，从这个拉氏量出发，利用Euler-Lagrange方程就可导出核子与介子场的运动方程。

In this paper, the modeling theory of multi-rigid-body dynamics was thoroughly investigated in order to make up the shortcoming in the above modeling method. The major research achievements are as follows:①Based on the matrix of direction cosine between the body-fixed base and the reference base, and Poisson equation of a rigid body rotating, the coordinate transformation method for the modeling of treelike multi-rigid-body dynamics is derived. The method is very routinization and easy to use the computer to carry on the symbol derivation.

本文针对上述建模方法存在的不足，深入地研究了多刚体系统动力学的建模方法，并将所研究的新方法应用于惯性振动设备的建模，取得的主要研究成果如下：①基于刚体连体基关于参考基的方向余弦矩阵和刚体转动的Poisson方程，导出了建立树形多刚体系统动力学方程的坐标变换法，其过程极其程式化，便于利用计算机进行符号推导。

" "Experimentally established...the conception of localized light-quanta out of which Einstein got his equation must still be regarded as far from being established.

然而，很难在他已发表的实验文章中找到任何支持自己期望的内容，所以密立根内心的这种冲突发生了细微的变化，他勉强承认爱因斯坦的光电方程在"实验上是成立的"，但是他依然认为"导出光电方程的光量子理论远远没有建立起来

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。