广义de Bruijn有向图及其叠线图的支撑树与欧拉环游的计数

给出了一类特殊的广义 de Bruijn有向图的支撑树与欧拉环游的数目的简洁表示式 .并得到广义 de Bruijn有向叠线图的支撑树与欧拉环游数目的计算公式 .

组织循环运输问题的图论方法

本文对组织循环运输路线问题,提出了一种图论方法。在一辆车作业的情况下,问题归结为求有向 Euler 图的有向 Euler 环游。对于多辆车作业的情况,问题转化为把有向 Euler 图分解为若干个边不重的有向子 Euler 环游的并。与此同时,也解决了车场的处理问题。

无向和有向Euler环游变换图的直径

本文得到了无向和有向Ｅｕｌｅｒ环游交换图的直径的上界．（１）设Ｇ是一个无向Ｅｕｌｅｒ多重图．令Ｑ（Ｇ）＝｛ｖ∈Ｖ（Ｇ）｜ｄｖ的Ｅｕｌｅｒ环游（Ｋ－）变换图Ｅｕ（Ｇ）的直径ｄｉａｍ（Ｅｕ（Ｇ））≤λ（Ｃ）－３．（２）设Ｄ是一个有向Ｅｕｌｅｒ多重图，ｄ（ｖ）＝ｉｄ（ｖ）＝ｏｄ（ｖ），令Ｑ（Ｄ）＝｛ｖ∈Ｖ（Ｄ）｜ｄ（ｖ）≥２｝及。则Ｄ的有向Ｅｕｌｅｒ环游（Ｔ－）变换图Ｅｕ．（Ｄ）的直径我们给出例子说明这两个上界都是最佳可能的．

基于运行距离最短的车队调度问题图解算法

对于一类基于运行距离最短的车队调度问题,构建了问题的数学规划模型。由于模型难以直接求解,构造网络图对车队问题进行表述。通过求解车队调度网路图的最小生成树,去除最小生成树中车辆和车辆之间连接线,从而将问题分解为一个个单车辆调度问题。对于单车辆调度问题的处理,设计了最小权奇点边添加法。该方法通过构造奇点边集合,使单车辆调度网络图成为所有顶点均为偶点的多重图;进而寻找欧拉环,并删除欧拉环中的重复中间点,最终得到问题的求解方案。最后设计了实例,分别采用图解算法和禁忌搜索算法进行求解。对比发现图解算法在求解车辆调度问题方面具有一定的优越性。

基于中国邮递员问题的城区烟草配送线路优化模型与算法

文中利用中国邮递员问题研究城区烟草配送问题,首先分析城区烟草配送的特点,提出多人中国邮递员问题。然后给出最优匹配模型和生成城区烟草配送的欧拉图的方法,设计欧拉环游的有向回路分割算法。最后给出算例,通过计算说明算法的可行性。

一类3度正则有向图网络模型

讨论了一种3度正则网络,这类网络具有较小的网络直径,本文给出了网络直径、网络支撑树和欧拉环游的数目的公式。

对“中国邮递员问题”的数理分析

如果一个非空连通图G是一个欧拉图,则很容易由Fleury算法求出一个欧拉环游,但是若图G不是欧拉图,即存在奇点,则中国邮递员问题的解决要困难得多。本文的主要目标是给出在有奇点的连通图中寻找最小权数的环游的方法.

有根无环欧拉地图的数目

本文首先解决了有根无环欧拉地图依边数的三次计数方程的求解问题,同时提供一种有效的计数方法对先前的一些相关结果及其推导过程进行了必要的改进．

带根无环欧拉平面地图的计数(英文)

自20世纪60年代初Tutte的开创性工作以来,许多学者在带根地图的计数方面作了很多工作,但许多类无环地图的计数仍没有被处理.本文主要研究以根点次、非根点数和内面数为三个参数的带根无环欧拉平面地图的计数问题.

Pseudo-Fluid Simulation of Transient Behaviors in a CFB Riser

The kinetic theory of granular flow (KTGF) is modified to fit the Einstein′s equation for effective viscosity of dilute flow. A pseudo-fluid approach based on this modified KTGF is used to simulate the dynamic formation and dissipation of clusters in a circulating fluidized bed riser. The agglomeration of particles reduces slip velocity within particle clusters, and hence results in two reverse trends: discrete particles are lifted by air while particle clusters fall down along the wall. The dynamic equilibrium of these two types of motion leads to the characteristic sigmoid profile of solid concentration along the longitudinal direction. The predicted solid velocity, lateral and longitudinal profiles of solid volume fraction and annulus thickness are in reasonable agreement with experimental results.

Enumeration of Eulerian Maps on the Torus

In this article we count the number of rooted planar Eulerian trails and present an explicit enufunction for such maps. Based on this result, we count rooted Eulerian maps on the torus in an exact way.

On the existence and stability of 2-D perturbed steady subsonic circulatory flows

In this paper, under the generalized conservation condition of mass flux in a unbounded domain, we are concerned with the global existence and stability of a perturbed subsonic circulatory flow for the two-dimensional steady Euler equation, which is assumed to be isentropic and irrotational. Such a problem can be reduced into a second order quasi-linear elliptic equation on the stream function in an exterior domain with a Dirichlet boundary value condition on the circular body and a stability condition at infinity. The key ingredient is establishing delicate weighted Hlder estimates to obtain the infinite behaviors of the flow under physical assumption.

A PINNED NETWORK OF EULER-BERNOULLI BEAMS UNDER FEEDBACK CONTROLS

In this paper, the authors design boundary feedback controllers at the interior node to stabilize a star-shaped network of Euler-Bernoulli beams. The beams are pinned each other, that is, the displacements of the structure are continuous but the rotations of the beams are not continuous. The weil-posed-ness of the closed loop system is proved by the semigroup theory. The authors show that the system is asymptotically stable if the authors impose a bending moment control on each edge. Finally, the authors derive the exponential stability of the system.