随机哈密尔顿系统的周期变差解和近不变环面解

本文研究具有随机扰动的哈密顿系统的重现现象,尤其是轨道随机周期变差解和近不变环面解.具体来说,对线性薛定谔方程,我们完整阐述了随机周期变差解何时存在;对随机扰动的近可积哈密顿系统,我们证明了近不变环面的存在性与驱动噪声对应的哈密顿函数的对合性相关.     

Timing matters in foreign exchange markets

We show using nonlinear time series analysis that the timing of trades in foreign exchange markets has significant information. We apply a set of methods for analyzing point process data developed in neuroscience and nonlinear science. Our results imply that foreign exchange markets might be chaotic and have short-term predictability.     

Multi-scale analysis of flow structures in fluidized beds with immersed tubes

Multi-scale analysis and non-linear analysis were combined to investigate the hydrodynamics of fluidized beds with and without horizontal tubes. Pressure fluctuations were measured and analyzed employing discrete wavelet analysis, recurrence plot analysis, and recurrence quantification analysis. A systematic procedure was followed to determine wavelet parameters. At low gas velocities, the energy of macro-structures reduces with the addition of the first tube and then increases with the addition of a second tube. However, there is no notable difference at high gas velocities. Determinism is high for the bed without tubes, which can be attributed to the periodic behavior of bubbles. Determinism decreases with the addition of tubes because the breakage of bubbles results in less periodic behavior. The three methods of analysis used in this study captured the effects of immersed tubes on the hydrodynamics of fluidized beds. Recurrence quantitative analysis was found to be a powerful and easy-to-use method that can capture the nonlinear characteristics of fluidized beds much more quickly than conventional methods of nonlinear analysis. This method can thus be effectively used for the online monitoring of hydrodynamic changes in fluidized beds.     

Semilocal Convergence of Steffensen-Type Algorithms for Solving Nonlinear Equations

In this article, we provide a semilocal analysis for the Steffensen-type method (STTM) for solving nonlinear equations in a Banach space setting using recurrence relations. Numerical examples to validate our main results are also provided in this study to show that STTM is faster than other methods ([7 I. K. Argyros , J. Ezquerro , J. M. Gutiérrez , M. Hernández , and S. Hilout ( 2011 ). On the semilocal convergence of efficient Chebyshev-Secant-type methods . J. Comput. Appl. Math. 235 : 3195 – 3206 .[Crossref], [Web of Science ®] , [Google Scholar], 13 J. A. Ezquerro and M. A. Hernández ( 2009 ). An optimization of Chebyshev's method . J. Complexity 25 : 343 – 361 .[Crossref], [Web of Science ®] , [Google Scholar]]) using similar convergence conditions.     

On the conditional increments of degradation processes

Recently, Wang and Xu (2010) developed an efficient EM algorithm for the semiparametric inference of the inverse Gaussian (IG) process. In the presence of missing degradation data, the algorithm needs to compute the mean of the IG increment during some time interval [_s1,_s2]$[s_1,s_2]$ conditional on that the process is tied down on two points before _s1$s_1$ and after _s2$s_2$, respectively. This study derives the conditional distribution of this increment and gives the expectation of the increment and of the reciprocal of the increment. The results simplify the implementation of the EM algorithm for the IG process. In a similar vein, we further derive distributions for the conditional increments of the Wiener process and the Gamma process, respectively.     

Universal Upper Bound for the Growth of Artin Monoids

In this paper we study the growth rates of Artin monoids, and we show that 4 is a universal upper bound. We also show that the generating functions of the associated right-angled Artin monoids are given by families of Chebyshev polynomials. Applications to Artin groups and positive braids are given.     

Combinatorial methods and recurrence relations with two indices

In this paper, we solve several recurrence relations with two indices by using combinatorial methods. Moreover, we present several recurrence relations with two indices related to Dyck paths and Schröder paths.     

Recurrence relations for discrete hypergeometric functions

We present a general procedure for finding linear recurrence relations for the solutions of the second order difference equation of hypergeometric type. Applications to wave functions of certain discrete system are also given.