形式导数

This result is a higher-dimentional analogue of the Fundamental Theorem of Calculus: it expresses the integral over D of some kind of derivative of P and Q in terms of an integral of P and Q over the boundary of.

格林公式建立了曲线积分和二重积分的关系 O 这是微积分基本定理在高维情形的推广：它将上P、Q某种形式的导数的积分用的边界上 P、 Q 的积分表示出来。

Under the information theory, more applications are provided to those back analysis methods. Based on the Duncan-Chang E-B model, which can simulate earth-rock dam's non-linear mechanics behavior well, the paper introduced the nature coordinate system to the stress space. In this way, hydrostatic stress and stress deviator were decomposed each other.

论文以能较好模拟土石坝非线性力学行为的Duncan-Chang E-B模型为基础，通过引入应力空间下的自然坐标系，分解应力球量与应力偏量，从而导出一个在有限元计算中，位移对参数偏导数的闭合形式公式。

Introduced formal notations of derivative which keep the properties of derivative and their operations are easily realized on computer,A mechanization proving principle of automatic reasoning of transformations between differential equations is built.

引进保持性质的导数的形式记号，建立了微分方程变量间依赖关系的自动推理的机械化证明原理，从而方程间的变换（如Backlund变换等）均可机械地验证。

This paper is the continuance of that of Lewalle (2001). Lewalle has made use of Gaussian wavelet to obtain the N-S equations with flexion as fundamental quantity in the infinite domain. In that work, Lapalace operator has been degraded to one-order operator. Moreover the resulted N-S equations take the form of diffusion equations with local bilinear mutual interaction kernel.

本文是Lewalle工作的继续，Lewalle利用高斯子波，得到了以弯曲度为基本量的无穷域中N-S方程，此时Lapalace算子降低为一阶导数，并且N-S方程变形为具有局部化双线性相互作用的扩散方程的形式。

Additionally, for these non-homogeneous materials, there is a relation between the material energy-momentum tensor and material coefficients under the infinitesimal translation, rotation and dilate of coordinates.

对于此种非均匀材料，物质能量-动量张量在坐标无穷小平移，转动和膨胀条件下与电磁焓中包含材料系数导数的形式有关。

By transforming high - grade gentle lack one type linear differential equation into the linear differential equation of successive integral, the theory and method for the general solutions of this kind of equation are determined.

方程'+=f是高阶线性微分方程，(约定尹0)=刃，是两项和的形式，其特征是含有相同的底，导数的次数相差一阶，因此不妨定义该方程为：高阶和式次数差一型线性微分方程。

Based on the maximum principle,we construct the blowing-up lower solution by the relations of parameters and solution of the ordinary differential equation and then the blow-up properties are studied.We use the maximal principle to analyse the derivative profiles of the solution and get the lower bounds and upper bounds of blow-up rate through the complicated analysis technology and the inequality theory.

基于最大值原理的比较理论，通过一些特定的参数关系，利用相关常微分方程的解构造合适的爆破形式的下解，由此得到退化反应系统初边值问题的爆破解；然后，对爆破解的性质进行进一步的研究，利用极大值原理对解的导数特性进行了分析，给出了解的爆破速率的上、下界估计。

In the last part of this dissertation, we discuss how to model an image is discussed and how to segment an image by EDEK.Zero-Cross principle is a classical concept in signal processing. We generalize the concept to be zero normal curvature after the geometry frame built. Furthermore, we present the explanation to choose the dual parameters in SPMVIF. And we research why the Laplacian gradient superior to edge gradient.

梯度方向二阶导数过零原理是信号处理中的经典结论，在运用微分几何的知识建立SPMVIF的几何框架的同时，将这个结论推广到零-法曲率的形式；另外我们对SPMVIF的双参数选取规则进行了讨论并给出它们的几何意义，并且对SPMVIF中法向矢量选取时拉普拉斯梯度优于边缘图像梯度的结论给予统计信息熵的解释。

Three different numerical iterative algorithms are developed and the accuracy and stabilities of them are compared. Tension and compression instabilities are studied and effects of Conservative Smoothing Approach and artificial viscosity on stabilities are discussed. Based on Taylor series expansion, Modified SPH method is proposed. The discrete forms of the function and its first derivative estimations of the kernel function are deduced in both one and two dimensional space.

讨论了三种不同的数值迭代算法对计算精度和稳定性的影响；分析了不稳定性产生的根源，包括拉伸不稳定和压缩不稳定，探讨了保守光滑算法和人为粘性对稳定性的影响；在Taylor展开的基础上提出了一种修正的SPH方法，并推导一维和二维情形下函数的核估计和函数的一阶导数核估计的离散形式，结果表明，二维情形下MSPH方法可以很好的改善边界粒子的计算精度。

Nextly, the definition of Perron integral and Denjoy integral for fuzzy-number-valued functions in the plane are given, and by using them, we discuss the characterization theorems of the primitive functions for fuzzy Henstock integral in the sense of the special derivate bases.

其次，定义了平面上的模糊Perron积分及模糊Denjoy积分，并利用这两种积分对平面上两种特殊形式的导数基意义下的模糊Henstock积分原函数进行了刻划。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。