基于单电子晶体管 - 金属氧化物场效应晶体管电路的离散混沌系统实现

提出了一种利用单电子晶体管与金属氧化物半导体的混合结构(SET-MOS)实现离散混沌系统的方法.研究了两个并联结构的单电子晶体管在电流源偏置下的传输特性,并建立其相应的S形分段线性函数模型.基于该模型实现了一维离散映射系统,分析了它的动力学特性,包括一维映射过程、分岔图和Lyapunov指数等.最后利用SET-MOS混合电路设计出该离散混沌系统的电子电路,验证了理论分析和实现方法的正确性.研究结果表明,该方法不仅可行,而且物理实现结构简单,利于集成. 关键词： 离散映射 Lyapunov指数 分岔 电路实现     

一种新的三维自治混沌系统

通过对蔡氏电路的研究,提出了一种新的混沌系统,并对该系统的基本动力学特性进行了深入研究,得到该系统的Lyapunov指数和Lyapunov维数,给出了相图、Lyapunov指数谱、分岔图、Poincaré映射以及功率谱等.利用OrCAD-PSpice软件设计了该新混沌系统的振荡电路并进行了仿真实验.研究结果表明,该系统与蔡氏电路产生的混沌吸引子并不拓扑等价,且该系统的参数变化范围较大,最大Lyapunov指数接近1,数值仿真和电路系统实验仿真具有很好的一致性,证实了该系统的存在性和物理上可实现性. 关键词： 混沌系统 Lyapunov指数谱 分岔图 电路实现     

The plane‐width of graphs

Map the vertices of a graph to (not necessarily distinct) points of the plane so that two adjacent vertices are mapped at least unit distance apart. The plane‐width of a graph is the minimum diameter of the image of its vertex set over all such mappings. We establish a relation between the plane‐width of a graph and its chromatic number. We also connect it to other well‐known areas, including the circular chromatic number and the problem of packing unit discs in the plane. © 2011 Wiley Periodicals, Inc. J Graph Theory 68: 229‐245, 2011     

重尾数据的混合Erlang分布拟合方法

PH分布具有良好的解析性质,重尾数据的PH近似是随机模型分析中的重要课题.混合Erlang分布是一种常见的PH分布,本文利用EM方法给出了重尾数据的混合Erlang分布拟合算法,通过Matlab软件对两类常见重尾数据进行实验,结果令人满意.最后,文章对混合Erlang分布拟合算法的进一步改进做了总结.     

Principal component analysis for multivariate stochastic processes

The problem of characterizing a /c-dimensional statistic contained in the past cj>f a discrete-time stochastic process y, which allows the best linear least-squares prediction of th^ future of y, is considered. The solution is provided in terms of the Schmidt pairs and singular values of an infinite matrix, and of the linear innovations of y. In the stationary case, the spectral characteristic of the optimal statistic, and of the corresponding prediction estimate, is obtained. In the base of a rational spectrum, the results are shown to assume a form particularly attractive from the algorithmic point of view. The results admit a straightforward extension to multivariate stochastic processes.     

Flat wavelet bases adapted to the homogeneous Sobolev spaces

We present a construction of “flat wavelet bases” adapted to the homogeneous Sobolev spaces ?^s (?ⁿ ). They solve the problem of the phenomenon of infrared divergence which appears for usual wavelet expansions in ?^s (?ⁿ ): these bases remove the divergence in the case s – n /2 ? ? since they are also bases of the realization of ?^s (?ⁿ ). In the critical case s – n /2 ∈ ?, they provide a confinement of the divergence in a “small” space. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hermitian Star Products are Completely Positive Deformations

Let M be a Poisson manifold equipped with a Hermitian star product. We show that any positive linear functional on C^∞(M) can be deformed into a positive linear functional with respect to the star product.     

Skew‐selfadjoint Dirac systems with rational rectangular Weyl functions: explicit solutions of direct and inverse problems and integrable wave equations

In this paper we study direct and inverse problems for discrete and continuous skew‐selfadjoint Dirac systems with rectangular (possibly non‐square) pseudo‐exponential potentials. For such a system the Weyl function is a strictly proper rational matrix function and any strictly proper rational matrix function appears in this way. In fact, extending earlier results, given a strictly proper rational matrix function we present an explicit procedure to recover the corresponding potential using techniques from mathematical system and control theory. We also introduce and study a nonlinear generalized discrete Heisenberg magnet model, extending earlier results for the isotropic case. A large part of the paper is devoted to the related discrete systems of which the pseudo‐exponential potential depends on an additional continuous time parameter. Our technique allows us to obtain explicit solutions for the generalized discrete Heisenberg magnet model and evolution of the Weyl functions.     

Aspects of QCD current algebra on a null plane

Consequences of QCD current algebra formulated on a light-like hyperplane are derived for the forward scattering of vector and axial–vector currents on an arbitrary hadronic target. It is shown that current algebra gives rise to a special class of sum rules that are direct consequences of the independent chiral symmetry that exists at every point on the two-dimensional transverse plane orthogonal to the lightlike direction. These sum rules are obtained by exploiting the closed, infinite-dimensional algebra satisfied by the transverse moments of null-plane axial–vector and vector charge distributions. In the special case of a nucleon target, this procedure leads to the Adler–Weisberger, Gerasimov–Drell–Hearn, Cabibbo–Radicati and Fubini–Furlan–Rossetti sum rules. Matching to the dispersion-theoretic language which is usually invoked in deriving these sum rules, the moment sum rules are shown to be equivalent to algebraic constraints on forward S$S$-matrix elements in the Regge limit.