超曲面上Cauchy-Riemann函数的全纯扩充

本文讨论复空间中实超曲面上CR函数的全纯扩充中,关于极小凸点的判定及刚性超曲面的整体扩充等问题。     

基于连通度的多跳传输路由算法

针对由各种功能不同的传感器构成的无线传感器网络,提出了一种基于连通度的多跳传输的路由协议(MHTA),该算法根据网络中节点能量分布的不同,引入权重因子作为调节参数进行簇头选举,选举过程中综合考虑了各节点消耗能量,与基站的邻近程度和周围邻节点的数目.为了减少在数据传输过程中消耗的能量,提出了一种簇内多跳和簇间多跳相结合进行数据传输的方法.模拟实验结果证明:该算法能够降低簇头能量消耗,均衡网络负载,从而延长网络生存时间.     

刚性Volterra泛函微分方程Runge-Kutta法的B-理论

为求解非线性刚性Volterra泛函微分方程初值问题的Runge-Kutta方法建立了B-稳定与B-收敛理论. 这项工作为非线性刚性常微分方程、非线性刚性延迟微分方程、非线性刚性积分微分方程以及实际问题中遇到的其他各种类型的刚性泛函微分方程的Runge-Kutta方法研究提供了统一的理论基础.     

复射影空间中极小曲面的整体刚性定理

本文主要研究复射影空间中的紧复曲线以及全实极小曲面的整体刚性问题.定义|A|2为复射影空间中紧复曲线∑的第二基本形式的模长平方.我们证明了如果∫∑|A|2dμ＜1/378π,那么∑是全测地的.对于全实极小曲面,我们也得到了类似的刚性定理.更一般地,我们证明了复射影空间中关于极小曲面的整体刚性定理.     

复杂网络的可控性及算法

复杂网络可控性问题的核心在于解决两个最少问题:最少需要多少输入和最少需要控制多少节点.Liu和Barabasi将现代控制理论应用到线性系统的结构可控性问题上,提出了最少需要多少输入的计算方法,解决了复杂有向网络结构能控性的可计算问题.针对现实网络中存在的无向图或者加权图,文章引入了节点控制能力的概念,利用添加输入或者连边的方法,给出了求系统精确可控的最小驱动点集合和极小被控点集合的算法.     

Banach空间中非线性刚性Volterra泛函微分方程稳定性分析

获得了Banach空间中非线性刚性Volterra泛函微分方程理论解的一系列稳定性、收缩性及渐近稳定性结果,为非线性刚性常微分方程、延迟微分方程、积分微分方程及实际问题中遇到的其他各种类型的泛函微分方程的解的稳定性分析提供了统一的理论基础.     

可靠性数学中的若干问题和进展

本文将综述可靠性数学理论中的一些重要问题和进展,其中包括网络可靠度计算、多状态coherent系统理论以及可修系统理论.由于篇幅限制,文中论题并不概括可靠性数学理论的全貌,文献也是基本的.一、网络可靠度网络系统可靠度的计算,特别是对大型复杂系统寻找有效的算法,以及各类算法优劣的比较,一直是理论和实用上都感兴趣的问题.1.基本问题给定一个网络(图)G,其中节点(顶点)集合V={v_i,…,v_n},弧(边)的集合E={e_l,…,e_b}。假定节点与弧只有正常和失效两种状态,并进一步设失效之间是互相独立的.(a)有源问题记S、t为两个特定的节点,称作“发点”和“收点”,求     

有向循环图寻径控制

有向循环图 G(N ;1 ,s)作为有向双环网的图论模型备受关注 .本文将图的点集分划为几个不交子集 ,找到任意节点对之间路径沿跳长为 1和跳长为 s的边数的上确界 .找到了判断节点对间最短路径的充要条件 ,利用点集的分布特征设计了一个最优寻径算法 .对双环网络的容错路径进行了深入研究 ,给出了容错直径公式 ,提出了一个最优容错路径算法 .     

求解变系数半线性刚性问题的Rosenbrock方法的定量误差分析

本文研究了Rosenbrock方法关于带变系数线性部分的半线性刚性问题的定量误差性态,获得了局部和整体误差分析结果.这是对Strehmel等人于1991年所获的Rosenbrock方法关于带常系数线性部分的半线性刚性问题相应结果的推广和发展.     

分数阶复杂网络的同步分析

本文主要研究了节点动力学为Caputo型的分数阶微分方程的复杂网络的同步,建立了判定分数阶网络的同步定理.数值例子验证了理论结果的有效性.     

Global Rigidity: The Effect of Coning

Recent results have confirmed that the global rigidity of bar-and-joint frameworks on a graph G is a generic property in Euclidean spaces of all dimensions. Although it is not known if there is a deterministic algorithm that runs in polynomial time and space, to decide if a graph is generically globally rigid, there is an algorithm (Gortler et al. in Characterizing generic global rigidity, arXiv:, 2007) running in polynomial time and space that will decide with no false positives and only has false negatives with low probability. When there is a framework that is infinitesimally rigid with a stress matrix of maximal rank, we describe it as a certificate which guarantees that the graph is generically globally rigid, although this framework, itself, may not be globally rigid. We present a set of examples which clarify a number of aspects of global rigidity.     

Globally Linked Pairs of Vertices in Equivalent Realizations of Graphs

A two-dimensional framework (G,p) is a graph G = (V,E) together with a map p: V → ℝ². We view (G,p) as a straight line realization of G in ℝ². Two realizations of G are equivalent if the corresponding edges in the two frameworks have the same length. A pair of vertices {u,v} is globally linked in G if %and for all equivalent frameworks (G,q), the distance between the points corresponding to u and v is the same in all pairs of equivalent generic realizations of G. The graph G is globally rigid if all of its pairs of vertices are globally linked. We extend the characterization of globally rigid graphs given by the first two authors [13] by characterizing globally linked pairs in M-connected graphs, an important family of rigid graphs. As a byproduct we simplify the proof of a result of Connelly [6] which is a key step in the characterization of globally rigid graphs. We also determine the number of distinct realizations of an M-connected graph, each of which is equivalent to a given generic realization. Bounds on this number for minimally rigid graphs were obtained by Borcea and Streinu in [3].     

On the motion of rigid bodies in a viscous fluid

We consider the problem of motion of several rigid bodies in a viscous fluid. Both compressible and incompressible fluids are studied. In both cases, the existence of globally defined weak solutions is established regardless possible collisions of two or more rigid objects.     

A sufficient connectivity condition for generic rigidity in the plane

A graph G=(V,E) is said to be 6-mixed-connected if G−U−D is connected for all sets U⊆V and D⊆E which satisfy 2|U|+|D|≤5. In this note we prove that 6-mixed-connected graphs are (redundantly globally) rigid in the plane. This improves on a previous result of Lovász and Yemini.     

Necessary Conditions for the Global Rigidity of Direction–Length Frameworks

It is an intriguing open problem to give a combinatorial characterisation or polynomial algorithm for determining when a graph is globally rigid in ℝ ^d . This means that any generic realisation is uniquely determined up to congruence when each edge represents a fixed length constraint. Hendrickson gave two natural necessary conditions, one involving connectivity and the other redundant rigidity. In general, these are not sufficient, but they do suffice in two dimensions, as shown by Jackson and Jordán. Our main result is an analogue of the redundant rigidity condition for frameworks that have both direction and length constraints. For any generic globally rigid direction-length framework in ℝ ^d with at least 2 length edges, we show that deleting any length edge results in a rigid framework. It seems harder to obtain a corresponding result when a direction edge is deleted: we can do this in two dimensions, under an additional hypothesis that we believe to be unnecessary. Our proofs use a lemma of independent interest, stating that a certain space parameterising equivalent frameworks is a smooth manifold. We prove this lemma using arguments from differential topology and the Tarski–Seidenberg theorem on semi-algebraic sets.     

关于刚体系统的单侧约束运动

本文研究了一大类刚体系统的单侧约束运动的局部和整体性质。主要结论是;局部地,这类系统的运动相当于某带过黎曼流形上的质点的运动;整体地,在能量守恒的假定下。这类系统相当于某带边黎曼流形上的台球系统。     

The 2‐dimensional rigidity of certain families of graphs

Laman's characterization of minimally rigid 2‐dimensional generic frameworks gives a matroid structure on the edge set of the underlying graph, as was first pointed out and exploited by L. Lovász and Y. Yemini. Global rigidity has only recently been characterized by a combination of two results due to T. Jordán and the first named author, and R. Connelly, respectively. We use these characterizations to investigate how graph theoretic properties such as transitivity, connectivity and regularity influence (2‐dimensional generic) rigidity and global rigidity and apply some of these results to reveal rigidity properties of random graphs. In particular, we characterize the globally rigid vertex transitive graphs, and show that a random d‐regular graph is asymptotically almost surely globally rigid for all d ≥ 4. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 154–166, 2007     

Combining globally rigid frameworks

It is shown how to combine two generically globally rigid bar frameworks in d-space to get another generically globally rigid framework. The construction is to identify d+ 1 vertices from each of the frameworks and erase one of the edges that they have in common.     

A rigid graph for every set

A graph G is called rigid if the identical mapping V(G)→V(G) is the only homomorphism G→G. In this note we give a simple construction of a rigid oriented graph on every set. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 108–110, 2002     

Rigid‐plastic hybrid element analyses of the plane strain upsetting

A rigid‐plastic hybrid element method (HEM) for simulation of metal forming is developed. This method is a mixed approach of the rigid‐plastic domain‐BEM and the rigid‐plastic FEM based on the theory of compressible plasticity. Because the compatibilities of not only velocity but also velocity's derivative between the adjoining boundary elements and finite elements can be met, the velocities and the derivatives of the velocity can be calculated with the same precision for the rigid‐plastic HEM. Then, it is considered that the rigid‐plastic HEM is a more precise method in formulation than the conventional rigid‐plastic FEMs for which the compatibilities of velocity's derivative cannot be met. The plane strain upsetting processes with two friction factors are analyzed by the rigid‐plastic HEM in this article. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 726–737, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10031.