Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

On the convergence of the affine-scaling algorithm

The affine-scaling algorithm, first proposed by Dikin, is presently enjoying great popularity as a potentially effective means of solving linear programs. An outstanding question about this algorithm concerns its convergence in the presence of degeneracy. In this paper, we give new convergence results for this algorithm that do not require any non-degeneracy assumption on the problem. In particular, we show that if the stepsize choice of either Dikin or Barnes or Vanderbei, et al. is used, then the algorithm generates iterates that converge at least linearly with a convergence ratio of , wheren is the number of variables and (0,1] is a certain stepsize ratio. For one particular stepsize choice which is an extension of that of Barnes, we show that the cost of the limit point is within O(/(1–)) of the optimal cost and, for sufficiently small (roughly, proportional to how close the cost of the nonoptimal vertices are to the optimal cost), is exactly optimal. We prove the latter result by using an unusual proof technique, that of analyzing the ergodic convergence of the corresponding dual vectors. For the special case of network flow problems with integer data, we show that it suffices to take = 1/(6mC), wherem is the number of constraints andC is the sum of the cost coefficients, to attain exact optimality.This research is partially supported by the U.S. Army Research Office, contract DAAL03-86-K-0171 (Center for Intelligent Control Systems), by the National Science Foundation, grant NSF-ECS-8519058, and by the Science and Engineering Research Board of McMaster University.     

Light traffic for workload in queues

General exact light traffic limit theorems are given for the distribution of steadystate workloadV, in open queueing networks having as input a general stationary ergodic marked point process {(t _n ,K _n )n0 (where t_n denotes the arrival time and K_n the routing and service times of the nth customer). No independence assumptions of any kind are required of the input. As the light traffic regime, it is only required that the Palm distribution for the exogenous interarrival time converges weakly to infinity (while the service mechanism is not allowed to change much). As is already known in the context of a single-server queue, work is much easier to deal with mathematically in light traffic than is customer delayD, and consequently, our results are far more general than existing results forD. We obtain analogous results for multi-channel and infinite-channel queues. In the context of open queueing networks, we handle both the total workload in the network as well as the workload at isolated nodes.Research supported in part by the Japan Society for the Promotion of Science during the author's fellowship in Tokyo, and by NSF Grant DDM 895 7825.     

马尔可夫链及其在经济预测中的应用

研究了马尔可夫链及其在经济预测中的应用，目的在于，在产品销售过程中，如何才能投入最小、收益最大。     

非线性算子半群的遍历收敛定理

在Banach空间中引入一般渐近非扩张型半群的广义殆轨道的概念，证明了渐近非扩张型半群的遍历收敛定理等价于相应的广义殆轨道的遍历收敛定理。     

混沌少体系统不可逆过程中的Jarzynski等式

数值研究了混沌少体系统不可逆过程中的Jarzynski等式，并且比较了功和自由能之间的不等式关系，发现Jarzynski等式不止在传统的统计力学适用范围——多体系统远平衡时成立，在混沌少体系统远平衡时也适用。     

基于EEF准则的认知无线电合作频谱感知

频谱感知是认知无线电的一个重要组成部分.提出了一种基于指数嵌入族(exponentially embedded family,EEF)准则的合作频谱感知算法.与传统方式下所有合作用户皆参加检测的方法不同,提出的算法依靠用户选择机制,并且不需要知晓授权用户信号的任何先验信息.该算法先对参与合作频谱感知的认知用户进行筛选,然后在筛选出的最优用户频谱观测数据的基础上生成全局检测统计量(global decision statistic,GTS),最后对授权用户是否存在做出全局判决.仿真表明,在虚警概率保持不变的情况下,进行最优用户选择(optimal user selection,OUS)的合作频谱感知算法的检测概率优于未进行最优用户选择的算法.     

指数稳定双系统同时近似可观测的充分条件

利用指数稳定半群生成元的谱理论,得到了判断指数稳定双系统在[0,∞)同时近似可观测的充分条件.{z1(t)=A1z1(t),z1(0)=x1,y1(t)=C1z1(t)2(t)=A2z2(t),z2(0)=x2,y2(t)=C2z2(t)     

Perturbation models

A Markov chain (with a discrete state space and a continuous parameter) is perturbed by forcing a chain to return to “permissible” states whenever it happens to enter “forbidden” states, with returns governed by a replacement distribution.The compensation method is employed to obtain the distribution for the modified chain, in terms of the original chain and the perturbation mechanism.Emphasis is placed on ergodic chains, and interpretation of results in terms of perturbation theory of semi-groups and the ergodic potential theory (based on the fundamental matrix of a chain) is mentioned.     

Stationarity and invertibility of simple bilinear models

Necessary and sufficient conditions for strict stationarity and invertibility are found for one-parameter bilinear models. These conditions involve the expectations of the logarithms of the absolute values of the input and output sequences.