A note on static spaces and related problems

In this paper we study static spaces introduced in Hawking and Ellis (1975)  [1], Fischer and Marsden (1975) [3] and Riemannian manifolds possessing solutions to the critical point equation introduced in Besse (1987)  [11], Hwang (2000)  [12]. In both cases, on the manifolds there is a function satisfying a particular Ricci–Hessian type equation (1.6). With an idea similar to that used in Cao et al. (2012)  [15], [16], we have made progress in solving the problem raised in Fischer and Marsden (1975)  [3] of classifying vacuum static spaces and in proving the conjecture proposed in Besse (1987)  [11] concerning manifolds admitting solutions to the critical point equation in general dimensions. We obtain even stronger results in dimension 3.     

Schreier rewriting beyond the classical setting Dedicated to our teacher Alfred Lvovich Shmelkin on his 70th birthday

Using actions of free monoids and free associative algebras, we establish some Schreier-type formulas involving ranks of actions and ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish a generalization of the Schreier formula in the case of subgroups of infinite index. We also study and apply large modules over free associative and free group algebras.     

Polytopal estimate of Mirkovi?–Vilonen polytopes lying in a Demazure crystal

In this paper, we give a polytopal estimate of Mirkovi?–Vilonen polytopes lying in a Demazure crystal in terms of Minkowski sums of extremal Mirkovi?–Vilonen polytopes. As an immediate consequence of this result, we provide a necessary (but not sufficient) polytopal condition for a Mirkovi?–Vilonen polytope to lie in a Demazure crystal.     

von Neumann��s mean ergodic theorem on complete random inner product modules

We first prove two forms of von Neumann’s mean ergodic theorems under the framework of complete random inner product modules. As applications, we obtain two conditional mean ergodic convergence theorems for random isometric operators which are defined on L _ℱ ^p (ℰ, H) and generated by measure-preserving transformations on Ω, where H is a Hilbert space, L ^p (ℰ, H) (1 ⩽ p < ∞) the Banach space of equivalence classes of H-valued p-integrable random variables defined on a probability space (Ω, ℰ, P), F a sub σ-algebra of ℰ, and L _ℱ ^p (ℰ(E,H) the complete random normed module generated by L ^p (ℰ, H).     

CP~n中具有循环调和序列的平坦极小环面

研究具有循环调和序列的平坦极小浸入ψ:T2→CPn。证明了存在T2的一个有限覆盖p:T2→T2和一个全迷向的平坦极小浸入φ:T2→CPn使得ψ。p=A。φ,其中A:CPn→CPn:[v]→[vA]是线性全纯同胚。     

扭曲模及扭曲Hopf模的基本结构定理的推广

扭曲的方法在构造新的代数结构和模的结构中起了重要作用,在不必是双相关Hopf模甚至是余模的模上引入了更一般的扭曲组的概念,得到了扭曲模,与此同时,给出了扭曲模的基本结构定理和直接扭曲与分步扭曲的关系.     

基于中国邮递员问题的可信平台模块测试序列生成优化研究

现今国内外已经有不少对可信平台模块进行测试的研究成果,但是对测试效率分析不足.本文基于自动机理论和中国邮递员问题,提出了可信平台模块改进的有限状态机模型与相应的优化测试方案,通过寻找一条遍历有限状态机模型中每一条转移至少一次的最短路径的方法,从而生成费用优化的测试序列.测试结果表明,测试方案能够简化有限状态机状态的测试.     

基于STM32F407的以太网通信模块设计

物联网的大规模形成和高速发展,使得基于以太网通信的嵌入式系统开发成为物联网应用的一个实际课题。本论文设计了一种以STM32F407作为主处理器的以太网通信模块;利用32位闪存微控制器STM32F407与以太网模块CH395实现串口通信;采用CH395控制芯片内置的TCP/IP协议栈与上位机LabVIEW客户端建立数据通信,并实时发送测试数据进行实验研究。实测结果表明：基于STM32F407的以太网通信嵌入式系统工作稳定,数据传输可靠,能够满足系统设计需求。     

A new construction of rational electromagnetic knots

We set up a correspondence between solutions of the Yang–Mills equations on $\mathbb{R}\times S^3$ and in Minkowski spacetime via de Sitter space. Some known Abelian and non-Abelian exact solutions are rederived. For the Maxwell case we present a straightforward algorithm to generate an infinite number of explicit solutions, with fields and potentials in Minkowski coordinates given by rational functions of increasing complexity. We illustrate our method with a nontrivial example.