室内环境中脑控轮椅的路径跟踪控制

为了实现室内环境中脑控轮椅的自主导航,提出了一种简单有效的路径跟踪控制方法。给定的路径通常被表示为一系列离散点,根据这一特点,提出了分段直线路径跟踪方法,即依次跟踪由前后两个路径点构成的直线路径到达目标点。基于预瞄点技术并结合模糊算法和传统的PID控制方法设计控制器,完成各分段直线路径的跟踪,并给出了有效的切换条件。实验结果表明,本文提出的路径跟踪控制方法能够使脑控轮椅在室内环境中精确地跟踪给定路径。     

Nonvertex‐Balanced Factors in Random Graphs

We prove part of a conjecture by Johansson, Kahn, and Vu (Factors in random graphs, Random Struct. Algorithms 33 (2008), 1, 1–28.) regarding threshold functions for the existence of an H‐factor in a random graph . We prove that the conjectured threshold function is correct for any graph H which is not covered by its densest subgraphs. We also demonstrate that the main result of Johansson, Kahn, and Vu (Factors in random graphs, Random Struct. Algorithms 33 (2008), 1, 1–28) generalizes to multigraphs, digraphs, and a multipartite model.     

On independent sets in random graphs

The independence number of a sparse random graph G(n,m) of average degree d = 2m/n is well‐known to be with high probability, with in the limit of large d. Moreover, a trivial greedy algorithm w.h.p. finds an independent set of size , i.e., about half the maximum size. Yet in spite of 30 years of extensive research no efficient algorithm has emerged to produce an independent set with size for any fixed (independent of both d and n). In this paper we prove that the combinatorial structure of the independent set problem in random graphs undergoes a phase transition as the size k of the independent sets passes the point . Roughly speaking, we prove that independent sets of size form an intricately rugged landscape, in which local search algorithms seem to get stuck. We illustrate this phenomenon by providing an exponential lower bound for the Metropolis process, a Markov chain for sampling independent sets. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 436–486, 2015     

关于图的同构判定方法的探讨

对于两图的同构的判定方法进行较深入的探讨,给出判定两图同构和判定两图不同构的几种方法,并对其判定方法的优劣进行比较.     

微尺度下壁面粗糙度对面向导热影响研究

随着空间尺度的缩小,界面对导热的影响就会越来越明显。本文采用非平衡分子动力学模拟方法模拟了壁面的粗糙度对面向导热的影响,并给出微尺度下的粗糙度定义。在模拟中构造了不同的壁面粗糙度,得到了面向热导率随着壁面粗糙度增加而减小的结果。分析认为壁面的镜面反射率随着粗糙度增加而减小,而镜面反射率减小将导致热导率下降．     

Fundamental Groups of Graphs of Cyclic Subgroup Separable and Weakly Potent Groups

We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form × D,where h has infinite order and D is finite.     

颗粒材料三维应力路径下的接触组构特性

颗粒材料的宏观应力变形特征与其微观接触力、组构等紧密相关.一般而言,强接触系统属于颗粒内部体系的传力结构,其对应的组构张量是影响宏观应力性质的重要因素.细观数值方法(如离散单元法)能够反映物理试验的基本规律,并且可以方便地提取宏微观数据来研究颗粒体系的应力变形机制.采用离散单元法(discrete element method,DEM)进行一系列等$p$等$b$应力路径下颗粒材料的真三轴试验,在此基础上研究了三维应力路径下颗粒材料的宏微观力学参数的演化过程、三维组构张量与应力张量多重联系以及强接触体系反映的宏观应力特征.研究表明:颗粒体系偏应力峰值状态和临界状态均存在与加载路径无关的宏微观特征;三维应力路径下组构张量与应力张量存在非共轴性,但其联合不变量演化过程表现出加载路径无关的特征;与弱接触系统的组构张量相比,强接触系统的组构张量更能反映宏观应力张量的特征;强弱接触体系的组构张量对颗粒体系宏观响应的贡献不同,其分界点存在一定取值范围,但采用平均接触力较为简单合理.      

Perpetual cutoff method and CDE′(K,N) condition on graphs

By using the perpetual cutoff method, we prove two discrete versions of gradient estimates for bounded Laplacian on locally finite graphs with exception sets under the condition of CD{E}^{\prime }(K,N). This generalizes a main result of F. Münch who considers the case of CD(K, \infty) curvature. Hence, we answer a question raised by Münch. For that purpose, we characterize some basic properties of radical form of the perpetual cutoff semigroup and give a weak commutation relation between bounded Laplacian \text{Δ} and perpetual cutoff semigroup P_t^W in our setting.