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Moreover, we present a lattice path interpretation of the isobaric divided difference operators, and derive an expression for the flagged Schur function in terms of isobaric operators acting on a monomial.

并且，我们提供了齐次差分算子的一个格路径解释，从而证明了每一个带标志的Schur函数可以通过作用齐次算子序列在某个单项式上得到。

We explicitly derive a domain of attraction for the positive equilibrium of system by using Liapunov method. We also investigate Hopf bifurcation by using Hassard method. Finally, some numerical simulations are made for system.Our paper are separated into seven chapters.

本文对一类具时滞和比率依赖的HollingⅢ型捕食-食饵系统进行了研究，利用Liapunov方法精确估计了正平衡点的吸引域，并利用Hassard方法研究了系统的Hopf分支，最后本文对一个具体模型进行了数值模拟。

The first part presents develops of predator-prey systems and gives the model that is investigated in our paper; Chapter 2 presents the results on boundedness of solutions and permanence of system; In chapter 3, we explicitly derive a domain of attraction for the positive equilibrium of system by using Liapunov method; The local stability and the conditions that Hopf bifurcation occurs are obtained in chapter 4; In chapter 5, some explicit fomulae of the direction of Hopf bifurcation and the stability of bifurcating periodic solutions on the center manifold are determined,using normal form and center manifold introduced by Hassard et al; In chapter 6, some numerical simulations are performed to illustrate the analytical results found; Our paper ends with a brief conclusion.

全文共分七章，第1章对捕食-食饵系统的发展背景做了介绍并给出了本文研究的模型；第2章讨论了系统的保持性和解的有界性；第3章研究正平衡点的全局性质，对正平衡点的吸引域进行了精确估计；第4章研究了系统的正平衡点的局部稳定性和Hopf分支存在的条件；第5章利用规范型和中心流形定理得到了一个决定Hopf分支方向、分支周期解的稳定性及其他性质的精确公式；第6章对一个具体模型进行了数值模拟；第7章对全文进行了总结。

Therefore, the author studied speculative activities and government countermeasures under the double-track price system in two periods, and at the same time put forward the core viewpoint of this article: China's M2/GDP changes derive from speculation and control arranged by the double-track price system.

如同麦金农在提出了自己的宏观模型之后转入关于金融深化的政策讨论一样，我们在新模型的基础上也进行了类似的研究，将着眼点集中在中国市场化改革过程中一项极具特色的体制安排——价格双轨制上。

Having derived the fundamental drag force formula, one can derive a number of important parameters.

在导出阻力的基本公式后，就可以得出一系列重要的参数。

We also derive some properties of the transfer function which can reduce the number of dual codewords stored.

我们也推导一些转换函的性质，这些性质可以用以减少对偶码字的储存。

Chapter 1 gives the background,current research process of relatedproblems and summarizes this thesis\'s work.In chapter 2,we study the Brownian motion with holding and jumping on the boundary.We use the resolvent method to obtain the infinitesimal generator because the domain of the infinitesimal generator is essentially the same as the range of the resolvent.Knowledge of this range and of the differential operator determines uniquely the infinitesimal generator.Since the semigroup generated by the DHJ is not strongly continuous,to use the nice property of strongly continuous semigroup in analytic theory,in chapter 3 we show that the dual is strongly continuous and derive ergodicity through spectral radius formulas and finally obtain the ergodic theorem by duality. In chapter 4,we discuss a class of a more general process---one dimensional Feller diffusion proposed by W.Feller in 1954.The Feller diffusion allows the possibility of jumps from boundary to boundary,not only from boundary to the interior.We give the stationary distribution of this process.

具体地，本文的结构如下：第一章给出了问题产生的背景，研究现状及本文的主要工作；第二章研究了在边界上逗留后随机跳的布朗运动，我(来源：3dABC论文网www.abclunwen.com)们用预解算子的方法得到其无穷小生成元，因为无穷小生成元的定义域本质上就是预解算子的值域，知道这个值域和微分算子形式就能唯一地决定无穷小生成元；由于DHJ过程产生的半群不是强连续的，为利用强连续半群的一些漂亮性质，在第三章中我们证明其对偶半群是强连续的，然后由谱半径公式得到遍历性并且最后由对偶得到遍历定理；第四章讨论了Feller在1954年引入的更广的一类过程----一维Feller扩散过程，Feller扩散过程允许有从边界到边界的跳发生，即不仅仅局限于从边界到内部的跳，在这一章中，我们给出了一维Feller扩散过程的平稳分布；在第五章，我们讨论了一些相关的问题，给出了DHJ过程对应的PDE问题及特征值与收敛速度的关系。

Other Italian leaders whose names derive from dux are the Doges of Venice and Genoa, and the title of nobility duca.

这个后来一人说，有的地方是总督威尼斯）有的地方公爵的简单答复，这个我小有异议

Although Einstein did "derive" the perihelion of Mercury, Gullstrand [10] pointed out in his report to the Nobel Committee that Einstein's field equation may not be able to produce a solution for a two-body problem.

虽然爱氏"推导"了水星近日点的移动，Gullstrand在给诺贝尔委员会的报告中指出，爱氏的场方程可能没有二体问题的解。

We derive the ellipticity and position angle of Abell 2199, and our result coincides remarkably with those in previous studies which are based on the data from a very small core region (～30) to a very large area (～5.5°).

将我们的结果与Rines等人研究的Abell 2199的引力内流区域X-ray群的空间分布椭率和方位角进行对比，发现这些星系团基本在同一条直线上，且空间分布方位角基本相同。

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。