M序列自相关系数的递推算法

一、前言 伪随机序列是一类有着广泛应用的伪随机码.在数字通讯、测距及跟踪系统中常用其来调制信号,以达到提高可靠性与有效性以及保密等目的.最常用的一类伪随机码则是由移位寄存器产生的序列.对于线性的情形,已有比较完整的结果,而对于非线性情形,则要复杂得多.目前,讨论得最多而用途最广的是所谓最长的序列,即M序列. 在我们的工作中,已经证明了,凡满足下述两条件:     

一类具有分离变量的非线性离散系统的镇定控制器

在控制理论和控制工程中，镇定控制器的设计是一个经典问题。许多有关这个问题的结论一般都是针对线性系统。对于非线性系统，很少见到有构造性结果能用于控制工程中。本针对一类广泛的非线性控制系统，我们构造了一些控制器，这些判据在工程实际问题中将具有一定的指导意义。     

论de Bruijn-Good图

<正> 前言 de Bruijn-Good图(文中简记为D-G图)是非线性移位寄存器的k(≥2)元n级序列的所有可能状态转移的一种图象表示.它在寄存器设计及编码理论中有着广泛的应用.因而对它的研究具有较高的理论与实际价值. 万哲先、刘木兰在[4]中研究了k=22的D-G图的自同构和2—1同态.最近,刘木     

计算机代数系统应用研究

计算机代数是近三十年发展起来的关于数学、计算机及人工智能方面的交叉学科,是数学发展的前沿学科,应用广泛.应用计算机代数系统的强大的符合运算功能以及该系统提供的控制语句,对一类弱非线性系统的有效渐近展开式解进行了研究,不但能使其自动求解,而且自动实现在平衡点附近降低微分方程阶数和实行中心流形方法,并试图解决了G r bner基在图论中关于连通图的最短路径问题.     

浮游生态系统的极限环存在唯一性与Hopf分叉

运用非线性系统理论研究了一类浮游生态系统模型,分析了平衡点的稳定性,给出并证明了系统极限环的存在唯一性条件.同时运用分支理论,对系统hopf分叉问题进行了讨论.最后,通过计算机仿真,对文中论述进行了验证.     

新三维自治混沌系统动力学性质研究

采用动力系统理论分析和计算机数值仿真相结合的方法,研究了一类新三维自治混沌系统的非线性动力学行为,如平衡点及其稳定性、不变集、混沌吸引子、吸引域等,从而展示了该混沌系统的丰富的动力学特性并且用matlab给出了相应的计算机模拟.创新点在于同时考虑了该混沌系统的最终界和全局吸引集,并且对于这个混沌系统的任意正参数,分别得到了该混沌系统最终界的一个参数族数学表达式和全局指数吸引集的一个参数族数学表达式,最后利用交集的思想分别得到了混沌系统最终界和全局吸引集的一个较小的数学表达式.混沌系统有望在实际保密通信中得到应用.     

Dn型非线性反馈移位寄存器

研究了一类Dynkin型非线性反馈移位寄存器,给出了n长码是Dn型反馈函数的周期码的充分必要条件,并得出了所有周期码及其周期。     

含间隙非线性弹性超材料的低频宽带机理北大核心CSCD

揭示了基于非线性混沌理论含间隙的非线性局域共振结构的低频宽带形成机理,提出了一类含间隙非线性局域共振结构设计的新理念.在该间隙非线性局域共振系统中,产生了非线性混沌现象,且这种非线性运动可以成功地改变振动噪声中的频谱结构,当系统运动进入混沌状态时,线性谱能量大大削弱,变成了一个连续的宽频谱,进而有效隔离低频线谱.有限元计算结果表明,正是这个间隙引起的非线性混沌现象导致了低频宽带的产生,且理论分析和有限元分析结果高度一致.因此,这类含间隙非线性局域共振弹性超材料结构的设计新思想为局域共振弹性超材料的发展开辟了新天地,且基于非线性混沌理论的低频带隙的形成机理为减振降噪应用研究奠定了非常重要的理论基础.     

产生 M 序列的一个递推算法

§1.引言M 序列又称 de Bruijn 序列,是一类具有最长周期的非线性移位寄存器序列。本文研究产生 M 序列的算法。早在70年代万哲先等对构造 M 序列的方法已有系统的研究。此后有一系列的文章研究 M 序列的构造问题。最近 Fredricksen 对这方面的工作给出了一个很好的综述。产生 M 序列的一个常用方法是先由一个较简单的移位寄存器产生许多短圈,再用并圈法将这些短圈合并起来构成 M 序列。如在[1,6]中就已给出过一些将 n 级纯轮换移位寄存器(简记为 PCK_n)和 n 级补轮换移位寄存器(简记为 CCR_n)产生的圈合并为 M 序列的方法。与[1—7]不同,Fredricksen 给出一个将 PCR_n 产生的圈合并为 M 序列的递推算法。最近 Etzion 和 Lempe 在 Fredricksen 算法的基础     

批量马尔可夫到达过程概述

批量马尔可夫到达过程(Batch Markovian Arrival Processes,BMAP)对平稳点过程类具有稠密性,能够描述许多到达过程,在计算机、可靠性、通信和库存等领域的随机建模中获得广泛应用,是一类非常重要的随机点过程.通过对BMAP理论主要文献的分析,系统介绍了BMAP的概念和主要性质,回顾了BMAP应用成果和拟合工作的发展,展望了BMAP理论的发展前景.     

A Hopf algebra for counting cycles

Cycles, also known as self-avoiding polygons, elementary circuits or simple cycles, are closed walks which are not allowed to visit any vertex more than once. We present an exact formula for enumerating such cycles of any length on any directed graph involving a sum over its induced subgraphs. This result stems from a Hopf algebra, which we construct explicitly, and which provides further means of counting cycles. Finally, we obtain a more general theorem asserting that any Lie idempotent can be used to enumerate cycles.     

On the noncommutative Donaldson-Thomas invariants arising from brane tilings

Given a brane tiling, that is a bipartite graph on a torus, we can associate with it a quiver potential and a quiver potential algebra. Under certain consistency conditions on a brane tiling, we prove a formula for the Donaldson-Thomas type invariants of the moduli space of framed cyclic modules over the corresponding quiver potential algebra. We relate this formula with the counting of perfect matchings of the periodic plane tiling corresponding to the brane tiling. We prove that the same consistency conditions imply that the quiver potential algebra is a 3-Calabi-Yau algebra. We also formulate a rationality conjecture for the generating functions of the Donaldson-Thomas type invariants.     

Applying a combinatorial determinant to count weighted cycle systems in a directed graph

One method for counting weighted cycle systems in a graph entails taking the determinant of the identity matrix minus the adjacency matrix of the graph. The result of this operation is the sum over cycle systems of −1 to the power of the number of disjoint cycles times the weight of the cycle system. We use this fact to reprove that the determinant of a matrix of much smaller order can be computed to calculate the number of cycle systems in a hamburger graph.     

Output feedback stabilization for a class of nonlinear time-evolution systems

A variety of problems in nonlinear time-evolution systems such as communication networks, computer networks, manufacturing, traffic management, etc., can be modelled as min–max-plus systems in which operations of min, max and addition appear simultaneously. Systems with only maximum (or minimum) constraints can be modelled as max-plus system and handled by max-plus algebra which changes the original nonlinear system in the traditional sense into linear system in this framework. Min-max-plus systems are extensions of max-plus systems and nonlinear even in the max-plus algebra view. Output feedback stabilization for min–max-plus systems with min–max-plus inputs and max-plus outputs is considered in this paper. Max-plus projection representation for the closed-loop system with min–max-plus output feedback is introduced and the formula to calculate the cycle time is presented. Stabilization of reachable systems with at least one observable state and a further result for reachable and observable systems are worked out, during which max-plus output feedbacks are used to stabilize the systems. The method based on the max-plus algebra is constructive in nature.     

Computing centre conditions for certain cubic systems

We present necessary and sufficient conditions for a critical point of certain two-dimensional cubic differential systems to be a centre. Extensive use of the computer algebra system REDUCE is involved. The search for necessary and sufficient conditions for a centre has long been of considerable interest in the theory of nonlinear differential equations. It has proved to be a difficult problem, and full conditions are known for very few classes of systems. Such conditions are also required in the investigation of Hilbert's sixteenth problem concerning the number of limit cycles of polynomial systems.     

The Lie algebra structure and controllability of spin systems

In this paper, we study the controllability properties and the Lie algebra structure of networks of particles with spin immersed in an electro-magnetic field. We relate the Lie algebra structure to the properties of a graph whose nodes represent the particles and an edge connects two nodes if and only if the interaction between the two corresponding particles is active. For networks with different gyromagnetic ratios, we provide a necessary and sufficient condition of controllability in terms of the properties of the above-mentioned graph and describe the Lie algebra structure in every case. For these systems all the controllability notions, including the possibility of driving the evolution operator and/or the state, are equivalent. For general networks (with possibly equal gyromagnetic ratios), we give a sufficient condition of controllability. A general form of interaction among the particles is assumed which includes both Ising and Heisenberg models as special cases. Assuming Heisenberg interaction we provide an analysis of low-dimensional cases (number of particles less than or equal to three) which includes necessary and sufficient controllability conditions as well as a study of their Lie algebra structure. This also provides an example of quantum mechanical systems where controllability of the state is verified while controllability of the evolution operator is not.     

Enumeration of weak isomorphism classes of signed graphs

A signed graph is a graph in which each line has a plus or minus sign. Two signed graphs are said to be weakly isomorphic if their underlying graphs are isomorphic through a mapping under which signs of cycles are preserved, the sign of a cycle being the product of the signs of its lines. Some enumeration problems implied by such a definition, including the problem of self-dual configurations, are solved here for complete signed graphs by methods of linear algebra over the two-element field. It is also shown that weak isomorphism classes of complete signed graphs are equal in number to other configurations: unlabeled even graphs, two-graphs and switching classes.     

路或圈的笛卡尔乘积图的支撑树数

设G是路或圈的笛卡尔乘积图，t(G)表示G的支撑树数.该文借助于第二类Chebyshev多项式给出t(G)的公式，并考虑了t(G)的线性递归关系及渐近性态.     

基于一类积分不等式上的中立型时滞微分方程的稳定性

利用一类积分不等式以及参数变易法,Jensen不等式,给出了更为一般的中立型时滞微分系统的Lyapunov稳定性的判别准则,推广和改进了一些文献中有关中立型微分方程的Lyapunov稳定性的结论.