定义方程

For the second order inclusion, using the transformation of variable, the existence of nonoscillatory solutions can be reduced to the existence of solutions for a first order inclusion.

在引进了微分包含解的振动性和非振动性的定义之后，通过分析解的单调性给出了一类二阶包含解的渐近性和振动性的判别准则；对于一阶微分包含，首先证明了时滞微分方程的振动性定理，在此基础上给出微分包含的结果。

In this paper we have studied the Upper bound for the time derivative of information entropy for a dynamical system driven by colored cross-correlated colored noises. The Fokker-Planck equation was obtained by using the unified colored noise approximation. The upper bound for the rate of entropy change can be calculated explicitly based on the definition of Shannon's information entropy and the Schwartz inequality principle.

" T！ z2 r" j0 S0 F5 J* T 摘要：本文研究了一种由色关联乘性和加性色噪声驱动的随机耗散动力学系统随时间演化的熵变化率上界，通过统一色噪声近似方法给出了该系统的近似Fokker-Planck方程，然后结合Shannon信息熵的定义及Schwartz不等式原理给出了该系统经近似后熵变化率上界随时间演化的精确表达式。

In the first chapter, we introduce the definition of value sharing and some former results of value distribution theory in complex differential equations, and describe the main results of this thesis.

第一章介绍了公共值的定义及以前的值分布论在复微分方程中的研究成果，并叙述了本文的主要结果。

The obtained results indicate that in the case of Riemann-Liouville definition, theequivalence between FDEs and weak formulation does not require any initial conditions.

上述研究结果表明在Riemann-Liouville分数阶导数定义的情况下，分数阶扩散方程与弱形式的等价性证明不需要添加初值条件。

By studying the known concepts and methods, this paper quotes a new concept of weak solution of the above equation. This concept contains some important information, which had been lost in the old definitions.

基于已有的研究基础上，本文对上述方程提出了一个新的弱解概念，该概念隐含了原来所定义的弱解所丢弃的一些有用的信息。

As the basis of inversion, we have summarized the overall expressions for Thomsen's parameters and their physical meanings, deduced the expressions of azimuthally varying NMO velocity that usually specifies an ellipse in the horizontal plane for any arbitrary anisotropy, and derived the expressions for the NMO ellipses described by Thomsen's parameters.

作为反演理论的基础，归纳总结了各类各向异性介质中Thomsen参数定义的形式及其相应的物理意义，推导了水平层状各向异性介质中方位NMO速度的椭圆属性方程及其Thomsen参数表示形式，并根据具体的介质参数，分别计算了HTI介质、正交介质和单斜介质中，在干裂隙和饱和流体填充裂隙的情况下的方位NMO速度。

InSection 2,we give several sufficient conditions for the existence of one solution,multiplesolutions and infinitely many solutions of the Sturm-Liouville bvps via the generalizedpolar coordinates.Then in Section 3,the existence of positive solutions are proved undersuperlinearity,sublinearity and many other conditions by a fixed point theorem in cones.Our results have generalized those in many articles.A detailed discussion of periodic solu-tions of a kind of functional differential equations with high-order Laplacian-like operatorcan be found in Section 4 and this subject has not been studied before.

在第二节，我们定义了一种新的坐标变换-广义极坐标，并利用它讨论了p-Laplacian算子和Laplacian-型算子的Sturm-Liouville边值问题，分别得到了存在一个解、多个解、无穷多个解的多个充分条件；第三节研究p-Laplacian算子的Sturm-Liouville边值问题正解的存在性与多重性，采用的是锥上的不动点定理，全面推广了这一方面已有的结果；对目前研究较少的高维Laplacian-型算子及带有Laplacian-型算子的泛函微分方程的周期解问题，我们在第四节做了一些研究，这也是拓扑方法的一个应用。

According to the character of condensate gas and the injected dry gas inside the UGS based on condensate gas reservoirs, the paper puts forward a mathematical model of multicycle working inventory for constant volume and weak waterbearing condensate gas reservoir by the mixed fluid density calculation method with molar volume balance and the gas equation of state.

为此，针对凝析气藏型地下储气库库内凝析气与注入干气混气的特点，从库存量的定义入手，利用摩尔体积权衡混合流体密度计算方法和气体状态方程，提出了定容和弱边底水凝析气藏型地下储气库多周期运行系列盘库计算的数学模型。

The aim of the watershed transform is to search for regions of high intensity gradients that divide neighbored local minima .

能量函数定义如下：〓clique主要是一些集合点，这些集合依赖于属于clique集合C的象素正如第四章中方程4.26。

Using the Green function theory, the integral equation of perturbational parameters was obtained.

基于非均匀介质中波函数的局部理论和射线理论，引入了全波场的广义射线近似形式，通过定义介质参数函数，把反演目标归结为其第一类Fredholm积分方程。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。