FAREY SEQUENCE OF NONLINEAR DIFFERENTIAL DYNAMIC SYSTEM IN TWO DIMENSIONS

In this paper , through the discrim ination of Farey sequence in the forced Brusselator withweak coupling , it is proved that there is a topological translation fro m a nonlinear differen tial system ( limit cycle) to the circle m ap .

Non-linear dynamic behaviours and chaos of environ-economic system

This paper applied the theory and method of non linear dynamic to study the integrated environ economic system( EES ). The results of the numerical computational experiment and theoretical inductions showed that the system behaviour pattern of the EES will be changed with the variation of the force power level. When the force DP become higher, the system loss its stability gradually, until the chaos occurs. Based on these results, this paper presented an explanation for the long wave economic fluctuation, and proposed in order to guarantee the sustainable development of the specific EES, the DP value of the system should be limited within a reasonable range.

Dynamics Response and Non⁃linear Characteristics Analysis of Complex Planar 2⁃DOF Mechanism with Revolute Clearances

There are clearances in mechanism because of manufacture and assembly error,which reduces operation life and working accuracy of mechanism and has a great impact on dynamical responses.At the moment,research in this area mainly focuses on single degree⁃of⁃freedom mechanism considering one clearance,while research of multi⁃DOF mechanism considering multi⁃clearance is less.With the purpose of studying the dynamical characteristics of complex multi⁃DOF mechanism with multi⁃clearances,a dynamic model was developed.The dynamic responses of 2⁃DOF mechanism with two clearances under different positions,values,and numbers of clearance were analyzed.The displacement,velocity,acceleration,collision force,and the axis trajectory at clearance were then given.In addition,there is a limited amount of literature on chaotic phenomena,which mainly focuses on the chaotic phenomena of end⁃effector of mechanism.But in this paper,the non⁃linear characteristics were analyzed by chaotic phenomenon of clearance joint,then chaotic phenomenon was identified by Poincarémappings and phase diagrams.Bifurcation diagrams were given.The results will offer a reliable technical support for the study of dynamical responses of planar mechanisms and the analysis of chaotic phenomena.

SOLUTIONS FOR A SYSTEM OF NONLINEAR RANDOM INTEGRAL AND DIFFERENTIAL EQUATIONS

In this paper we first prove a Darbao type fixed point theorem for a system of continuous random operators with random domains. Thenb, by using the theorem. wegive the existence criteria of solutions for a systems of nonlinear random Volterraintegral equations and for the Cauchy problem of a system of nonlinear random differential equations. The existence of extremal random solutions and random comparison results for these systems of random equations are also obtained Our theorems improve and generalize the corresponding results of Vaughn Lakshmikantham Lakshmidantham-Leela De blasi-Myjak and Ding

The inversion of 3-D crustal structure and hypocenter location in the Beijing-Tianjin-Tangshan-Zhangjiakou area by genetic algorithm

This paper discusses the inversion of velocity structure and hypocenters location in the Beijing Tianjin Tangshan Zhangjiakou area by genetic algorithm. The hypocenters location of selected earthquakes and crustal structure of this area are obtained using the travel time data of local earthquakes acquired by the Telemetered Seismic Network of Northern China. The mean and standard residuals of hypocenter location acquired by this method are much less than those provided by the report of respective earthquakes. The crustal structure of the first and the second layers obtained interpret the outline of the plain and mountain area in the region successfully and the crustal structure of the third layer nearly coincides with the Moho discontinuity obtained by artificial seismic sounding. These show the genetic algorithm is effective to the inversion of hypocenter location and three dimensional velocity structure.

FUZZY IDENTIFICATION METHOD BASED ON A NEW OBJECTIVE FUNCTION

A method of fuzzy identification based on a new objective function is proposed. The method could deal with the issue that input variables of a system have an effect on the input space while output variables of the system do not exert an influence on the input space in the proposed objective functions of fuzzy clustering. The method could simultaneously solve the problems about structure identification and parameter estimation; thus it makes the fuzzy model become optimal. Simulation example demonstrates that the method could identify non linear systems and obviously improve modeling accuracy.

A study on frequency domain mathematics model of arc welding reverse converter

Arc welding converter (AWC) power source is a nonlinear and discrete abnormal system. It is difficult to get the accurate analytic solution in theory. In this paper, an average state equation of the system is established by means of state space analysis method. The mathematics model of the reverse converter is gotten after the average equation of the system is linearized. The model is a two ranks oscillation link. With the parameters of the AWC, when the condition of (1/RC) 2 >>4/LC is available, the mathematics model may be simplified to a serial structure which includes a integral link and a one rank inertia link. On the basis of this, it can be analyzed and rectified in frequency domain, then some groups of reality rectification parameters are gotten around the theory rectification parameters. These groups of parameters are taken to do the resistance load experiment and welding technology experiment. The result of experiment accords with the theory analysis result. This paper also provides some practical analysis of the model under the large signal process such as the sudden opening of the load, short circuit, turning on and turning off the machine. The result of the research shows that the power source system of AWC can be analyzed and rectified by the frequency domain analysis method in the engineering. The deduced mathematics model of small signal average frequency domain shows the basic characteristics of the system, and the structure parameters of the system is formed by R, L, C and switching ratio D. The model is very simple and clear, and it can be used to analyze and design the power source system of AWC and it can also be used to direct the regulation for dynamic characteristics of the system.

On Distributary Model of Public Transportation in Metropolis

The expansion of population and the worsening of the city development pattern brought serious effects on public transportation in the metropolis. The traditional method is not suitable for the analysis of city public transportation. This paper presents the model of “frog jumping and permeation” of passage flow in city public transportation. In this model, the passages between the first class gradient centers are transported by the fastest ways, and transferred in the mode of permeation between the second class gradient centers. this model will improvc the situation in the metropolitan communications.

Synthesis and characterization of multifunctional copolyimide incorporating triarylamine and NLO chromophore in backbone

Presents the synthesis of Copolyimide containing triarylamine and NLO chromophore in backbone by azo coupling of 4 nitrobenzenediazonium tetrafloroborate to copoly(amic acid) in organic solvent and characterized by IR and UV Vis spectra, which had high glass transition temperatrue and big second order nonlinear optical coefficient  x (2) .

Approximate Analytical Expressions for the Concentrations of Acetate and Methane in the Microbial Electrochemical Cell

Mathematical modeling of microbial electrochemical cells (MXCs) for both microbial fuel cell and microbial electrolysis cell is discussed. The model is based on the system of reaction diffusion of reaction-diffusion equation containing a non-linear term related to substrate consumption rates by electrogeneic and methanogenic microorganism in the bioflim. This paper presents the approximate analytical method to solve the non-linear differential equation that describes the diffusion coupled with acetate (substrate) consumption rates. Simple analytical expressions for the concentrations of acetate and methane have been derived for all experimental values of bulk concentration, distributions of microbial volume fraction, local potential in the biofilm and biofilm thickness. In addition, sensitivity of the parameters on concentrations is also discussed. Our analytical results are also validated with the numerical results and limiting cases results. Further, a graphical procedure for estimating the kinetic parameters is also suggested.

FLOW FIELD ANALYSIS AND GRAPHIC CAD DURING 3─ROLL REDUCING OF THE HOLLOW TUBE

The 3─roll reducing processes are simulated and predicted by using 3─D elastic─plastic large strain FEM on the PC / 386 computer.The displacement field and flow field of workpiece deformation are given. The internal angle defects of the seamless tube are studied in detail during 3─roll reducing.the predictions of the forming product quality and technology parameter are realized by means of PC / 386 computer.

Hydrothermal Syntheses, Supramolecular Structures and the Third-order Non-linear Optical Properties of Three Copper(I) Halide Amine Complexes Connected via Secondary Bonding Interactions

The hydrothermal reactions of CuI, KI and bidentate amines [ 1,10 phenanthroline (phen) or ethylenediamine (en)] gave the three copper(I) halide compounds, Cu3I3(phen)2 (1), CuI(phen)2 (2) and 2 (3), which were structurally characterized via singlecrystal Xray diffraction studies. Hydrogen bonds and ππ interactions are the most remarkable structural features of the title compounds. All can be described as higherdimensional supramolecular compounds connected via these secondary bondings. Moreover, the title compounds were characterized by elemental analyses, IR spectra and TGA analyses. The thirdorder nonlinear optical properties of the title compounds were also investigated and all exhibit nicer nonlinear absorption and selffocusing performance.Keywords copper(I) halide, hydrothermal synthesis, the thirdorder nonlinear optical property, supramolecular structure

Forecasting China′s Stock Market Volatility Using Non-Linear GARCH Models

This paper studies the performance of the GARCH model and two of its non linear modifications to forecast China′s weekly stock market volatility. The models are the Quadratic GARCH and the Glosten, Jagannathan and Runkle models which have proposed to describe the often observed negative skewness in stock market indices. We find that the QGARCH model is best when the estimation sample does not contain extreme observations and that the GJR model cannot be recommended for forecasting.

Depth-averaged Nonlinear k-ε Model and Technique for Its Program Development

Without the ‘rigid lid’ assumption, the depth averaged linear k-ε model can describe the change of water depth. However, it is incapable of accurately simulating turbulent flows, where the normal Reynolds stresses play an important role. A depth averaged nonlinear k-ε model is developed taking into account the stress relations described by Speziale. The depth averaged linear and nonlinear k-ε models can both be used to calculate the flow field near a side discharge into open channel flow, but the results of the nonlinear model are in much closer agreement with experimental results. Furthermore, the technique of changing the 2D linear k-ε program into a depth averaged, nonlinear program is presented.

Superlinear/Quadratic One-step Smoothing Newton Method for P_0-NCP

We propose a one–step smoothing Newton method for solving the non-linearcomplementarity problem with P 0–function (P_0–NCP) based on the smoothing symmetric perturbedFisher function (for short, denoted as the SSPF–function). The proposed algorithm has to solve onlyone linear system of equations and performs only one line search per iteration. Without requiringany strict complementarity assumption at the P_0–NCP solution, we show that the proposed algorithmconverges globally and superlinearly under mild conditions. Furthermore, the algorithm has localquadratic convergence under suitable conditions. The main feature of our global convergence resultsis that we do not assume a priori the existence of an accumulation point. Compared to the previousliteratures, our algorithm has stronger convergence results under weaker conditions.

Linearized model for optimization of coupled electricity and natural gas systems

In this paper,a combined optimization of a coupled electricity and gas system is presented.For the electricity network a unit commitment problem with optimization of energy and reserves under a power pool,considering all system operational and unit technical constraints is solved.The gas network subproblem is a medium-scale mixed-integer nonconvex and nonlinear programming problem.The coupling constraints between the two networks are nonlinear as well.The resulting mixed-integer nonlinear program is linearized with the extended incremental method and an outer approximation technique.The resulting model is evaluated using the Greek power and gas system comprising fourteen gas-fired units under four different approximation accuracy levels.The results indicate the efficiency of the proposed mixed-integer linear program model and the interplay between computational requirements and accuracy.