大族长度为pq的伪随机k元序列

Mauduit与Sárkzy在一系列论文中研究了κ元序列的伪随机性.本文通过对模pq剩余类环Z_(pq)进行分割,进而结合离散对数的方法,构造了一大族长度为pq的伪随机κ元序列,并证明其具有很好的伪随机性.     

三项指数和四次均值的精确计算公式(2)

本文进一步深入研究了三项指数和四次均值的计算问题.运用指数和的相关性质并结合求解同余方程组的方法与技巧,利用两种不同的方法获得了两个精确的均值计算公式,揭示了三项指数和的计算与同余方程组解的个数之间的本质联系,推广了已有的结果.     

二项指数和四次混合均值的计算

本文研究了二项指数和四次均值的计算问题.利用初等数论及代数数论的方法获得了一个精确的计算公式以及一个转换公式,推广了已有的结果,揭示了均值计算与同余方程组的本质联系.     

可修复人机系统的指数稳定性

研究了两相同部件温储备可修的人机系统,运用C_0半群的相关理论,对系统主算子的谱界进行估值.估算系统的算子产生的半群的增长界,然后运用了共尾的概念及相关的理论,得到了系统算子A+B的谱界与系统算子产生的半群的增长界相同.进而运用相关代数知识证得,0为系统算子的简单本征值,并分析了系统算子的谱分布,得到系统的指数稳定性.并研究了系统算子预解式的特性.对任意给定的δ0,γ=a+bi,-μ+δa_1≤a≤a_2,得到lim|b|→∞‖R(γ;A+B)‖=0.进而得到在~sRγ≥a_1的右半平面内相应于系统算子A+B的谱点由有限个本征值组成.     

股票市场的长记忆及其动态结构

本文提出了结合平均小波系数法和自回归原始自助法的稳健长记忆检验,蒙特卡罗模拟显示该方法对于短期记忆过程具有稳定性。基于该方法对2005年4月8日至2015年6月30日的中国、美国、香港和德国股市进行了实证分析。全局检验结果表明仅中国的股票市场存在显著的长记忆,并且风险因素无法对长记忆解释,而美国、德国和香港的股市不存在长记忆。基于递增窗口的动态Hurst指数分析显示,金融危机时期4个股市都存在显著的长记忆。2010年后,除中国股市外,其余三个股市几乎不存在长记忆现象。     

MOLSIM: A modular molecular simulation software

The modular software MOLSIM for all‐atom molecular and coarse‐grained simulations is presented with focus on the underlying concepts used. The software possesses four unique features: (1) it is an integrated software for molecular dynamic, Monte Carlo, and Brownian dynamics simulations; (2) simulated objects are constructed in a hierarchical fashion representing atoms, rigid molecules and colloids, flexible chains, hierarchical polymers, and cross‐linked networks; (3) long‐range interactions involving charges, dipoles and/or anisotropic dipole polarizabilities are handled either with the standard Ewald sum, the smooth particle mesh Ewald sum, or the reaction‐field technique; (4) statistical uncertainties are provided for all calculated observables. In addition, MOLSIM supports various statistical ensembles, and several types of simulation cells and boundary conditions are available. Intermolecular interactions comprise tabulated pairwise potentials for speed and uniformity and many‐body interactions involve anisotropic polarizabilities. Intramolecular interactions include bond, angle, and crosslink potentials. A very large set of analyses of static and dynamic properties is provided. The capability of MOLSIM can be extended by user‐providing routines controlling, for example, start conditions, intermolecular potentials, and analyses. An extensive set of case studies in the field of soft matter is presented covering colloids, polymers, and crosslinked networks. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

非均匀圆柱型正交各向异性圆板的弯曲

研究了非均匀圆柱型正交各向异性圆板在均布横向载荷作用下的弯曲问题，求得了折算刚度随半径按指数规律变化的非均匀圆柱型正交各向异性圆板弯曲问题的渐近解，给出了周边固支和简支条件下的渐近解．通过算例可以看出，这种非均匀性对圆板中心挠度的影响是显著的     

EXPONENTIAL STABILITY OF INTERVAL DYNAMICAL SYSTEM WITH MULTIDELAY

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔａｂｉｌｉｔｙｏｆｔｈｅｉｎｔｅｒｖａｌｍａｔｒｉｘａｎｄｕｎｃｅｒｔａｉｎｓｙｓｔｅｍｗｉｔｈｔｉｍｅｄｅｌａｙｈａｖｅｂｅｅｎｃｏｎｓｉｄｅｒｅｄｂｙｒｅｓｅａｒｃｈｅｒｓｉｎｔｈｅｐａｐｅｒｓ [1 -1 3 ] .Ｔｈｅｓｔａｂｉｌｉｔｙａｎｄαｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙｏｆｔｈｅｆｏｌｌｏｗｉｎｇｉｎｔｅｒｖａｌｄｙｎａｍｉｃａｌｓｙｓｔｅｍｗｉｔｈｓｉｎｇｌｅｔｉｍｅｄｅｌａｙ ｘ(ｔ) =Ｎ[Ｐ ,Ｑ]ｘ(ｔ) +Ｎ[Ｃ ,Ｄ]ｘ(ｔ-τ)ｈａｖｅｂｅｅｎｃｏｎｓｉ…     

On exponential stability of nonlinear Volterra difference equations in phase spaces

Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear Volterra difference equations in phase spaces. In particular, this gives a solution to an open problem posed very recently by E. Braverman and I. M. Karabash in Journal of Difference Equations and Applications 18 , 909–939 (2012). As an application, we apply the obtained results to study asymptotic behavior of equilibriums of discrete time neural networks.