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An improvement on measure methods of the complexity theory and its applications

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Chinese Physics B 2009年第9期18卷 4042-4048页

作者：王福来杨辉煌 department of Mathematics and Statistics Zhejiang University of Finance and Economics

A new method is proposed to transform the time series gained from a dynamic system to a symbolic series which extracts both overall and local information of the time series. Based on the transformation, two measures are defined to characterize the complexity of the symbolic series. The measures reflect the sensitive dependence of chaotic systems on initial conditions and the randomness of a time series, and thus can distinguish periodic or completely random series from chaotic time series even though the lengths of the time series are not long. Finally, the logistic map and the two-parameter Henon map are studied and the results are satisfactory.

关键词： complexity theory complexity dynamic system chaos

A universal algorithm to generate pseudo-random numbers based on uniform mapping as homeomorphism

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Chinese Physics B 2010年第9期19卷 244-249页

作者：王福来 department of Mathematics and Statistics Zhejiang University of Finance and Economics

A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained are topologically equivalent to each other so the map can preserve the most dynamic properties of chaotic systems such as permutation entropy. Based on the uniform map, a universal algorithm to generate pseudo random numbers is proposed and the pseudo random series is tested to follow the standard 0-1 random distribution both theoretically and experimentally. The algorithm is not complex, which does not impose high requirement on computer hard ware and thus computation speed is fast. The method not only extends the parameter spaces but also avoids the drawback of small function space caused by constraints on chaotic maps used to generate pseudo random numbers. The algorithm can be applied to any chaotic system and can produce pseudo random sequence of high quality, thus can be a good universal pseudo random number generator.

关键词： pseudo random numbers uniform map chaos

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Acta Mathematica Sinica,English Series 2019年第11期35卷 1827-1840页

作者： Xun Xiang GUO department of Mathematics Southwestern University of Finance and Economics

In this paper, we give an operator parameterization for the set of dilations of a given pair of dual g-frames and the set of dilations of pairs of dual g-frames of a given g-frame. In particular,for the dilations of a given pair of dual g-frames, we introduce the concept of joint complementary g-frames and prove that the joint complementary g-frames of a pair of dual g-frames are unique in the sense of joint similarity, which then helps to obtain a sufficient condition such that the complementary g-frames of a g-frame are unique in the sense of similarity and show that the set of dilations of a given dual g-frame pair are parameterized by a set of invertible diagonal operators. For the dilations of pairs of dual g-frames, we prove that the set of dilations of pairs of dual g-frames are parameterized by a set of invertible upper triangular operators.

关键词： g-frame dual g-frame pair dilation g-Riesz basis joint similarity

Homological Dimensions of the Extension Algebras of Monomial Algebras

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Acta Mathematica Sinica,English Series 2015年第4期31卷 675-694页

作者： Hong Bo SHI department of Mathematics Nanjing University of Finance and Economics

The main objective of this paper is to study the dimension trees and further the homological dimensions of the extension algebras -- dual and trivially twisted extensions -- with a unified combinatorial approach using the two combinatorial algorithms -- Topdown and Bottomup. We first present a more complete and clearer picture of a dimension tree, with which we are then able, on the one hand, to sharpen some results obtained before and furthermore reveal a few more hidden subtle homological phenomenons of or connections between the involved algebras; on the other hand, to provide two more efficient combinatorial algorithms for computing dimension trees, and consequently the homological dimensions as an application. We believe that the more refined complete structural information on dimension trees will be useful to study other homological properties of this class of extension algebras.

关键词： Topdown bottomup dimension tree syzygy finitistic dimensions

Scanner color management model based on improved back-propagation neural network

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Chinese Optics Letters 2008年第3期6卷 231-234页

作者：黎新伍 Electronic Business department of Jiangxi University of finance and economics

Scanner color management is one of the key techniques for color reproduction in information optics. A new scanner color management model is presented based on analyzing rendering principle of scanning objects. In this model, a standard color target is taken as experimental sample. Color blocks in color shade area are used to substitute complete color space to solve the difficulties in selecting experimental color blocks. Immune genetic algorithm is used to correct back-propagation neural network （BPNN） to speed up the convergence of the model. Experimental results show that the model can improve the accuracy of scanner color management.

关键词： Backpropagation algorithms Genetic algorithms Neural networks Scanning

Triple Positive Periodic Solutions of Nonlinear Singular Second-order Boundary Value Problems

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Acta Mathematica Sinica,English Series 2014年第2期30卷 361-370页

作者： Qing Liu YAO department of Applied Mathematics Nanjing University of Finance and Economics

This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″（t）＋ λ（t）u（t） = f（t,u（t））,a.e.t ∈ [0,2π],u（0） = u（2π）,u′（0） = u′（2π）,where f（t,u） is a local Carath′eodory *** shows that the problem is singular with respect to both the time variable t and space variable *** applying the Leggett-Williams and Krasnosel＇skii fixed point theorems on cones,an existence theorem of triple positive solutions is *** order to use these theorems,the exact a priori estimations for the bound of solution are given,and some proper height functions are introduced by the estimations.

关键词： Periodic boundary value problem singular nonlinearity triple positive solutions fixedpoint theorem

Application of Homotopy Analysis Method to Solve Relativistic Toda Lattice System

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Communications in Theoretical Physics 2010年第6期53卷 1111-1116页

作者：王琪 department of Applied Mathematics Shanghai University of Finance and Economics

In this letter, the homotopy analysis method is successfully applied to solve the Relativistic Toda lattice system. Comparisons are made between the results of the proposed method and exact solutions. Analysis results show that homotopy analysis method is a powerful and easy-to-use analytic tool to solve systems of differential-difference equations.

关键词： Jhomotopy analysis method relativistic Toda lattice system

Application of Rational Expansion Method for Differential-Difference Equation

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Communications in Theoretical Physics 2011年第12期56卷 981-986页

作者：王琪 department of Applied Mathematics Shanghai University of Finance and Economics

In this paper, we applied the rational formal expansion method to construct a series of sofiton-like and period-form solutions for nonlinear differential-difference equations. Compared with most existing methods, the proposed method not only recovers some known solutions, but also finds some new and more general solutions. The efficiency of the method can be demonstrated on Toda Lattice and Ablowitz-Ladik Lattice.

关键词： rational expansion method Toda lattice Ablowitz-Ladik lattice

Improved modal truncation method for eigensensitivity analysis of asymmetric matrix with repeated eigenvalues

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Applied Mathematics and Mechanics(English Edition) 2014年第4期35卷 437-452页

作者：张振宇 department of Applied Mathematics Shanghai University of Finance and Economics

An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an asymmetric and non-defective matrix with repeated eigenvalues. If the different eigenvalues λ1, λ2,……, λs of the matrix satisfy ｜λ1｜ ≤... ≤｜λr｜ and ｜λs｜〈｜〈s＋1｜（s ≤r-l）, then associated with any eigenvalue λi （i≤ s）, the errors of the eigenvalue and eigenvector derivatives obtained by the qth-order approximate method are proportional to ｜λi｜/λs＋1｜q＋l, where the approximate method only uses the eigenpairs corresponding to λ1, λ2,……,λs A numerical example shows the validity of the approximate method. The numerical example also shows that in order to get the approximate solutions with the same order accuracy, a higher order method should be used for higher order eigenvalue and eigenvector derivatives.

关键词： modal truncation method eigenvector derivative asymmetric matrix,repeated eigenvalue