Computer Algebra and Solutions to the Karamoto-Sivashinsky Equation

The method of Riccati equation is extended for constructing travelling wave solutions of nonlinear partial differential equations. It is applied to solve the Karamoto-Sivashinsky equation and then its more new explicit solutions have been obtained. From the results given in this paper, one can see the computer algebra plays an important role in this procedure.

Using Symbolic Computation to Exactly Solve the Integrable Broer-Kaup Equations in （2＋1）-Dimensional Spaces

The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.

GLOBAL EXISTENCE AND EXPONENTIAL STABILITY OF SMOOTH SOLUTIONS TO A MULTIDIMENSIONAL NONISENTROPIC EULER-POISSON EQUATIONS

The global existence and large time behavior of smooth solutions to multidimensional nonisentropic Euler-Poisson equations are established.

Lienard Equation and Exact Solutions for Some Soliton-Producing NonlinearEquations

In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq,generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.

Axial Anomaly for Eguchi-Hanson Metrics with Nonzero Total Mass

We compute the Dirac indexes for the two spin structures K0 and K1 for Eguchi-Hanson metrics with nonzero total mass. It shows that the Dirac indexes do not vanish in general, and axial anomaly exists. When the metric has zero total mass, the Dirac index vanishes for the spin structure K0, and no axial anomaly exists in this case.

On boundary feedback stabilization of Timoshenko beam with rotor inertia at the tip

The feedback stabilization problem of a nonuniform Timoshenko beam system with rotor inertia at the tip of the beam is studied. First, as a special kind of linear boundary force feedback and moment control is applied to the beam' s tip, the strict mathematical treatment,a suitable state Hilbert space is chosen, and the well-poseness of the corresponding closed loop system is proved by using the semigroup theory of bounded linear operators. Then the energy corresponding to the closed loop system is shown to be exponentially stable. Finally, in the special case of uniform beam,some sufficient and necessary conditions for the corresponding closed loop system to be asymptotically stable are derived.

Singularity of Farhi-Gutmann Analog Quantum Search

We show that the Farhi-Gutmann analog quantum search is a singular algorithm in the following sense:when the original driving Hamiltonian is perturbed slightly such that it is made of projections to the starting state and to the target state with different energies, the maximum fidelity (transition probability) between the searching state and thetarget state is strictly less than 1 over the entire evolution period, and the first time to achieve this maximum fidelity is of order √n/√1+cN, whose behavior depends crucially on whether c = 0 or not (here N is the total number of items, and the original Farhi-Gutmann case corresponds to c = 0). Moreover, when c ≠ 0 and N tends to infinity, the maximum fidelity tends to zero, and the first time to achieve the maximum fidelity tends to a positive constant! The condition for guaranteeing the algorithm's efficiency is determined explicitly.

The Unitary Equivalence of Operators and K_0-Group of Commutant Algebras

We show that two irreducible operators on H are unitari1y equivalentif and only if W*(A B)’≌M2(C), and give an answer to the open question posedby J. B. Conway (Subnormal Operators, πPitman, Advanced Publishing Program,Boston, London, Melbourne, 1981) for irreducible operator. We also show that ifT, T1 and T2 are irreducible operators with T T1≌T T2, then T1≌T2. Finally,weshow that K0 (A(D))≌Z, giving a new result on the K0-group of Banach algebras.

CRUDE OIL PRICE FORECASTING WITH TEI@I METHODOLOGY

The difficulty in crude oil price forecasting, due to inherent complexity, has attracted much attention of academic researchers and business practitioners. Various methods have been tried to solve the problem of forecasting crude oil prices. However, all of the existing models of prediction can not meet practical needs. Very recently, Wang and Yu proposed a new methodology for handling complex systems-TEI@I methodology by means of a systematic integration of text mining, econometrics and intelligent techniques.Within the framework of TEI@I methodology, econometrical models are used to model the linear components of crude oil price time series (i.e., main trends) while nonlinear components of crude oil price time series (i.e., error terms) are modelled by using artificial neural network (ANN) models. In addition, the impact of irregular and infrequent future events on crude oil price is explored using web-based text mining (WTM) and rule-based expert systems (RES) techniques. Thus, a fully novel nonlinear integrated forecasting approach with error correction and judgmental adjustment is formulated to improve prediction performance within the framework of the TEI@I methodology. The proposed methodology and the novel forecasting approach are illustrated via an example.

OPTIMAL HARVESTING POLICY AND STABILITY FOR SINGLE-SPECIES GROWTH MODEL WITH STAGE STRUCTURE

Abstract. In this paper, we consider a stage structure population model with two lifestages, immature and mature, with harvesting mature population and stocking immaturepopulation. It is shown that under suitable hypotheses there exists a globally asymptoti-cally stable positive equilibrium. The effect of the delay on the populations at equilibriumand the optimal harvesting policy for mature population are also considered.

A GENERAL APPROACH BASED ON AUTOCORRELATION TO DETERMINE INPUT VARIABLES OF NEURAL NETWORKS FOR TIME SERIES FORECASTING

Input selection is probably one of the most critical decision issues in neural network designing, because it has a great impact on forecasting performance. Among the many applications of artificial neural networks to finance, time series forecasting is perhaps one of the most challenging issues. Considering the features of neural networks, we propose a general approach called Autocorrelation Criterion (AC) to determine the inputs variables for a neural network. The purpose is to seek optimal lag periods, which are more predictive and less correlated. AC is a data-driven approach in that there is no prior assumptiona bout the models for time series under study. So it has extensive applications and avoids a lengthy experimentation and tinkering in input selection. We apply the approach to the determination of input variables for foreign exchange rate forecasting and conductcomparisons between AC and information-based in-sample model selection criterion. The experiment results show that AC outperforms information-based in-sample model selection criterion.

The Dynamics of a Predator-prey Model with Ivlev's Functional Response Concerning Integrated Pest Management

A mathematical model of a predator-prey model with Ivlev’s functional response concerning integrated pest management (IPM) is proposed and analyzed. We show that there exists a stable pest-eradication periodic solution when the impulsive period is less than some critical values. Further more, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence and stability of a positive periodic solution. These results are quite different from those of the corresponding system without impulses. Numerical simulation shows that the system we consider has more complex dynamical behaviors. Finally, it is proved that IPM stragey is more effective than the classical one.

Analyses of Bifurcations and Stability in a Predator-prey System with Holling Type-Ⅳ Functional Response

In this paper the dynamical behaviors of a predator-prey system with Holling Type-Ⅳ functionalresponse are investigated in detail by using the analyses of qualitative method,bifurcation theory,and numericalsimulation.The qualitative analyses and numerical simulation for the model indicate that it has a unique stablelimit cycle.The bifurcation analyses of the system exhibit static and dynamical bifurcations including saddle-node bifurcation,Hopf bifurcation,homoclinic bifurcation and bifurcation of cusp-type with codimension two(ie,the Bogdanov-Takens bifurcation),and we show the existence of codimension three degenerated equilibriumand the existence of homoclinic orbit by using numerical simulation.

On the Blow-up Criterion of Smooth Solutions to the 3D Ideal MHD Equations

In this paper, we consider the blow-up of smooth solutions to the 3D ideal MHD equations. Let (u, b) be a smooth solution in (0, T). It is proved that the solution (u, b) can be extended after t = T if . This is an improvement of the result given by Caflisch, Klapper, and Steele [3].

ASYMPTOTIC NORMALITY OF SOME ESTIMATORS IN A FIXED-DESIGN SEMIPARAMETRIC REGRESSION MODEL WITH LINEAR TIME SERIES ERRORS

Consider a semiparametric regression model with linear time series errors Yk=x'kβ+g(tk)+εk,1≤k≤n,where Yk's are responses,xk=(xk1，xk2，…,xkp)' and tk∈T包含R are fixed design points,β=(β1,β2,…,βp)'is an unknown parameter vector,g(·)is an unknonwn bounded real-valued function defined on a compact subset T of the real line R,and εk is a linear process given by εk=∑j=0^∞ψjek-j,ψ0=1,where ∑j=0^∞|ψj|<∞,and ej,j=0,±1,±2,…,are i.i.d.random variables.In this paper we establish the asymptotic normality of the least squares estimator of β,a smooth estimator of g(·),and estimators of the autocovariance and autocorrelation functions of the linear process εk.

ON AN SIS EPIDEMIC MODEL WITH STAGE STRUCTURE

A SIS infectious disease model with stage structure consisting of immature and mature stages is proposed using a discrete time delay. The aim of the paper is to investigate under which conditions the disease becomes endemic or not and to find the difference between the model with stage structure and the corresponding model without stage structure. It is shown that either there exists a unique endemic equilibrium point which is globally asymptotically stable or the disease dies out by using an iterative scheme. The effect of the time delay on the populations at equilibria is considered.

UNIFORM PERSISTENCE AND GLOBAL ATTRACTIVITY FOR NONAUTONOMOUS COMPETITIVE SYSTEMS WITH DISPERSION

In this paper,we consider a nonautonomous competitive model with dispersion and a finite number of discrete delays.The system,which consists of two lotka-Volterra patches,has two competitors:one can disperse between the two patches,but the other is confined to one patch and coannot disperse.Our purpose is to demonstrate that the dispersion rates have no effect on the uniform persistence of the solutions of the system.Furthermore,we establish the conditions under which the system admits a positive periodic solution which attracts all solutions.