Enumeration of perfect matchings of a type of Cartesian products of graphs

Let G be a graph and let Pm(G) denote the number of perfect matchings of G.We denote the path with m vertices by P_m and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [W. Yan, F. Zhang, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math. 32 (2004) 175-188], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results:1. Let T be a tree and let C_n denote the cycle with n vertices. Then Pm(C₄×T)=∏(2+α²), where the product ranges over all eigenvalues α of T. Moreover, we prove that Pm(C₄×T) is always a square or double a square.2. Let T be a tree. Then Pm(P₄×T)=∏(1+3α²+α⁴), where the product ranges over all non-negative eigenvalues α of T.3. Let T be a tree with a perfect matching. Then Pm(P₃×T)=∏(2+α²), where the product ranges over all positive eigenvalues α of T. Moreover, we prove that Pm(C₄×T)=[Pm(P₃×T)]².     

Dubrovin赋值斜群环

本文中对一个斜群环为Dubrovin赋值环给出了一系列等价刻画,并且刻画了一个Dubrovin赋值斜群环的所有素理想.     

Skew Models II

If g and G are the pdf and the cdf of a distribution symmetric around 0 then the pdf 2g(u)G(λ u) is said to define a skew distribution. In this paper, we provide a mathematical treatment of the skew distributions when g and G are taken to come from one of Pearson type II, Pearson type VII or the generalized t distribution.      

A family of skew Hadamard difference sets

In 1933 a family of skew Hadamard difference sets was described by Paley using matrix language and was called the Paley-Hadamard difference sets in the literature. During the last 70 years, no new skew Hadamard difference sets were found. It was conjectured that there are no further examples of skew Hadamard difference sets. This conjecture was proved to be true for the cyclic case in 1954, and further progress in favor of this conjecture was made in the past 50 years. However, the conjecture remains open until today. In this paper, we present a family of new perfect nonlinear (also called planar) functions, and construct a family of skew Hadamard difference sets using these perfect nonlinear functions. We show that some of the skew Hadamard difference sets presented in this paper are inequivalent to the Paley-Hadamard difference sets. These new examples of skew Hadamard difference sets discovered 70 years after the Paley construction disprove the longstanding conjecture on skew Hadamard difference sets. The class of new perfect nonlinear functions has applications in cryptography, coding theory, and combinatorics.     

计算器时钟切换及自动关断电路的分析与改进

时钟切换和自动关断是新一代计算器集成电路档器芯片快慢时钟切换电路,详细分析了计算器的两种关断途径,在此基础上设计了一种新的关断电路.给出了这两种电路的仿真结果,证明了改进电路的正确性和高效性.     

高速系统PCB设计中的几个关键问题

随着微电子技术的飞速发展，高速大规模集成电路的广泛应用，高速系统的设计也越来越受到重视，高速系统与低速系统的PCB设计有很大不同。本文从实际设计的角度介绍了高速系统中电源、接地、时钟电路、过孔等的设计和需要注意的问题。     

Bayesian robustness under a skew-normal class of prior distribution

We develop a global sensitivity analysis to measure the robustness of the Bayesian estimators with respect to a class of prior distributions. This class arises when we consider multiplicative contamination of a base prior distribution. A similar structure was presented by van der Linde [12]. Some particular specifications for this multiplicative contamination class coincide with well known families of skewed distributions. In this paper, we explore the skew-normal multiplicative contamination class for the prior distribution of the location parameter of a normal model. Results of a Bayesian conjugation and expressions for some measures of distance between posterior means and posterior variance are obtained. We also elaborate on the behavior of the posterior means and of the posterior variances through a simulation study.     

一种实现时序快速有效收敛的时钟树综合方案

针对低频下数字集成电路实现时序收敛需要插入大量缓冲器而导致芯片布线困难、运行时间较长等问题,提出了一种降低时钟树级数与增加保持时间余量相结合的时钟树综合方案。基于CSMC 0.35 μm CMOS工艺,采用提出的方案,使用IC Compiler和Prime Time工具,分别完成了应用于高精度隔离型Σ-Δ ADC芯片的低速数字滤波器的物理设计以及静态时序分析。结果表明,与传统方案相比,保持时间负松弛总值降低了95.62%,时序收敛所需缓冲器个数减少了约98.13%,运行时间缩短了97.25%,有效地降低了布线拥塞程度,快速有效地实现了时序收敛。     

基于EPL的分布式时钟同步方法

工业以太网协议Ethernet POWERLINK(EPL)分布式站点的时钟同步方法并不能在实时运行过程中保持很高的同步精度,无法满足特定环境下的控制要求。研究了工业以太网协议EPL的两种时钟同步机制,通过数理计算分析了时钟同步误差产生的原因,针对误差较大的缺点,提出了减小误差的方法。通过迭代计算消除了主从站同步报文往返的路径延迟,并设计基于现场可编程门阵列(FPGA)的集线器(Hub)用于EPL菊花链网络拓扑结构,有效地克服了时钟同步报文往返传输延时不一致的缺点,测试结果表明新方法明显优于协议自身的时钟同步方法,对于实现基于EPL的高精度分布式时钟同步网络具有重要意义。