Addendum to “Variations of selective separability” [Topology Appl. 156 (7) (2009) 1241-1252]

Two proofs omitted in the paper mentioned in the title are presented.     

基于MC9S08DZ60的CAN总线振动传感器设计

基于单片机MC9S08DZ60和收发器TJA1040,遵循CAN总线协议,设计一款振动传感器。详细介绍整个系统的设计方案及各个模块的硬件电路和软件实现。采集到的数据由CAN总线上传至主控机存储,便于进行分析整理。测试表明,该设备响应快、传输精度高,具有CAN总线实时、可靠、灵活的特点。为生产提供了安全保障。     

MT-ZigBee硬件平台的设计

ZigBee无线传感器网络应用最为广泛的技术,在设计开发ZigBee协议之前必须要有相应硬件平台的支撑.硬件平台是整个通信网络的基础,主要负责ZigBee协议所规定频率的射频信道的物理发送与接收、数据采集、控制部分的相关物理接口.在深入研究IEEE 802.15.4和ZigBee协议规范的基础上,给出MT-ZigBee硬件平台的整体框架,同时阐述芯片选型、电源电路、MC9S08GB60与MC13192接口电路和MC13192射频模块的详细设计,通过自主研发,设计了ZigBee硬件平台,并对平台各个硬件模块进行了测试.此平台有所简化地实现了物理层、MAC层和网络层协议栈,在硬件设计上为实现低功耗提供了电路基础.     

基于CM300和SM79164的基站监控系统

介绍了一种采用高性能8位单片机SM79164作为主要控制芯片的通信基站环境和动力监控系统的设计,该系统使用各种高性能传感器采集基站里的环境和动力参数,利用串口摄像头获取基站里的图像,在初步分析和处理数据后,通过CDMA2000-1X模块CM300与中心机房建立TCP/IP连接,把所有数据传送回主机,主机将信息进一步处理后通知相关维护人员,从而实现了对基站的实时监控,提高了基站动力设备和通信设备运行的可靠性.     

基于MC9S08QG8低端微控制器的无线控制器设计

为改变ZigBee无线控制器节点设计中通常需要使用高端微控制器的现状,引入Freescale低端微控制器MC9S08QG8配合MC13192无线收发器再加上少量外围元器件,实现了一种ZigBee无线控制器的精简硬件设计电路.同时描述了器件选择、总体构建思路与硬件设计细节,最后介绍了该无线控制器的一个实例应用.基于低端微控制器的设计也能够完成无线网络要求的一些基本任务,并且满足无线控制应用中的低功耗、低成本、高性能、多功能等要求.     

Best approximation properties in spaces of measurable functions

We research proximinality of μ‐sequentially compact sets and μ‐compact sets in measurable function spaces. Next we show a correspondence between the Kadec–Klee property for convergence in measure and μ‐compactness of the sets in Banach function spaces. Also the property S is investigated in Fréchet spaces and employed to provide the Kadec–Klee property for local convergence in measure. We discuss complete criteria for continuity of metric projection in Fréchet spaces with respect to the Hausdorff distance. Finally, we present the necessary and sufficient condition for continuous metric selection onto a one‐dimensional subspace in sequence Lorentz spaces .     

Explicit sparse almost‐universal graphs for ${\bf {{\cal G}(n, {k \over n})}}$

For any integer n, let be a probability distribution on the family of graphs on n vertices (where every such graph has nonzero probability associated with it). A graph Γ is ‐almost‐universal if Γ satisifies the following: If G is chosen according to the probability distribution , then G is isomorphic to a subgraph of Γ with probability 1 ‐ . For any p ∈ [0,1], let (n,p) denote the probability distribution on the family of graphs on n vertices, where two vertices u and v form an edge with probability p, and the events {u and v form an edge}; u,v ∈ V (G) are mutually independent. For k ≥ 4 and n sufficiently large we construct a ‐almost‐universal‐graph on n vertices and with O(n)polylog(n) edges, where q = ? ? for such k ≤ 6, and where q = ? ? for k ≥ 7. The number of edges is close to the lower bound of Ω( ) for the number of edges in a universal graph for the family of graphs with n vertices and maximum degree k. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Clifford analysis versus its quaternionic counterparts

For a positive integer n let Cl_0,n be the universal Clifford algebra with the signature (0,n). The name Clifford analysis is usually referred to the function theories for functions in the kernels of the two operators: the (Cliffordian) Cauchy–Riemann operator and the Dirac operator. For n=2, Cl_0,2 becomes the skew‐field of Hamilton's quaternions for which the two operators are widely known: the Moisil–Théodoresco and the Fueter operators. We establish the precise relations between the Moisil–Théodoresco operator and the Dirac operator for Cl_0,3. It turns out that the case of the Cauchy–Riemann operator for Cl_0,3 and the Fueter operator is more sophisticated, and we describe the peculiarities emerging here. Copyright © 2009 John Wiley & Sons, Ltd.     

Generic Morse–Smale property for the parabolic equation on the circle

In this paper, we show that, for scalar reaction–diffusion equations ut=u_xx+f(x,u,ux)$u_t=u_{xx}+f(x,u,u_x)$ on the circle S¹$S^1$, the Morse–Smale property is generic with respect to the non-linearity f. In Czaja and Rocha (2008) [13], Czaja and Rocha have proved that any connecting orbit, which connects two hyperbolic periodic orbits, is transverse and that there does not exist any homoclinic orbit, connecting a hyperbolic periodic orbit to itself. In Joly and Raugel (2010) [31], we have shown that, generically with respect to the non-linearity f, all the equilibria and periodic orbits are hyperbolic. Here we complete these results by showing that any connecting orbit between two hyperbolic equilibria with distinct Morse indices or between a hyperbolic equilibrium and a hyperbolic periodic orbit is automatically transverse. We also show that, generically with respect to f, there does not exist any connection between equilibria with the same Morse index. The above properties, together with the existence of a compact global attractor and the Poincaré–Bendixson property, allow us to deduce that, generically with respect to f, the non-wandering set consists in a finite number of hyperbolic equilibria and periodic orbits. The main tools in the proofs include the lap number property, exponential dichotomies and the Sard–Smale theorem. The proofs also require a careful analysis of the asymptotic behavior of solutions of the linearized equations along the connecting orbits.