Table of Content

  

24 March 2009
Volume 44 Issue 2

Articles

Gorenstein projective modules

ZHANG Pu

J4. 2009, 44(2):  1-13. 

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The aim of this lecture note is to outline some basic concept, results, typical proofs and some recent progress on Gorenstein homological algebras.

Positive periodic solutions of nonlinear thirdorder boundary value problems

YAO Qingliu

J4. 2009, 44(2):  14-18. 

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Positive solutions were studied for the nonlinear thirdorder periodic boundary value problem　u(t)+ρ3u(t)=f(t,u(t)), 0<t<2π, u(i)(0)=u(i)(2π), i=0,1,2, where the nonlinear term f(t,u) is allowed to be singular at t=0,t=2π and u=0. By considering the integrations of height functions of nonlinear term on some bounded sets and applying the GuoKrasnosel′skii fixed point theorem, the existence of n positive solutions was proved.

Asymptotic behavior of  nonoscillatory solutions of second  order nonlinear differential equation with perturbation

J4. 2009, 44(2):  19-23. 

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The asymptotic behavior of nonoscillatory solutions of a class of second order nonlinear differential equation with perturbation was studied, three new asymptotic theorems were established, and some known results were extended and improved.

The solution of the fractional reactiondiffusion equation with a fractional oscillator in a finite fractal medium

J4. 2009, 44(2):  24-27. 

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he fractional reactiondiffusion differential equation with  a fractional oscillator in  a finite fractal medium was  established. By applying Laplace transformation, the finite Hankel transformation and their inverse transform, the exact solution of the model were obtained. The expression  in the form of the generalized MittagLeffler function was  given. Finally, the solutions of twodimensional space, threedimensional space and the integral diffusion equation as some particular cases of this paper were discussed.

Estimates on the extremal weighted SobolevHardy functions

J4. 2009, 44(2):  28-32. 

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The finite element method for  controlledrelease and spread of solute coupling with fluid velocity in a porous medium

J4. 2009, 44(2):  33-38. 

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The process of controlledrelease and spread of a solute in porous media contains three physical processes: the process of release of the solute into the porous media through the border of the film, the flow of fluid and the process of the  spread of the solute in porous media. The process of controlledrelease was governed by a boundary integralordinary differential equation, while the process of spread was characterized by a convectiondiffusion (with mechanical dispersion)equation with a boundary condition of the third type in the unknown velocity field, which follows Darcy′s law. A mixed finite elementGalerkin finite element scheme was proposed for solving the coupled nonlinear systems.Convergence was analyzed by a priori estimate method.

A highorder parallel difference scheme for a parabolic equation

J4. 2009, 44(2):  39-44. 

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A high order parallel finite difference algorithm of a parabolic equation was presented. First,  the values of the previous three levels at the interface points were combined with the compact scheme to solve the values of subdomains in parallel, then the values at the interface points were computed by the compact scheme. The stability bound of the procedure was derived to be at least 23+16, and the convergence rate was proved to be of order four. Numerical examples show that this method has much better accuracy than  other  methods.

A high accuracy finite volume element method based on cubic spline interpolation for twopoint boundary value problems

J4. 2009, 44(2):  45-51. 

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A high accuracy finite volume element method was given based on cubic spline interpolation for linear and nonlinear twopoint boundary value problems of ordinary differential equations. The computational scheme(FVCS) was derived and the property of positive type was discussed. Further we presented the convergence analysis and the scheme was proved having fourth order error estimate in discrete energy norm. Finally, numerical examples including linear and nonlinear problems, and source term with singularity problem were given to illustrate the high efficiency and wide adaptation of the method.

An endogenous economic growth model with the restraints of environment and energy

J4. 2009, 44(2):  52-55. 

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By considering the two factors affecting the economic growth, environment and energy, the relationship between economic growth, environmental quality and energy intensity was setup. The health index of people was introduced to measure environmental quality. Meanwhile, the health index was taken as a variable of the utility function. Finally, the conditions that the sustainable development of economy needed to satisfy were shown, which can maximize the utility function including two variables, consumption and health index.

Application of the combination prediction model in forecasting the GDP of China

J4. 2009, 44(2):  56-59. 

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On  basis of the ARIMA model, mixedtime series model and GM(1,1) model,  a combination forecast model was established by using the Chinese economic development data, and the forecasted GDP of China was applied. The resulted show that the error of this combination prediction model is smaller than the other three models, and denoted that the combination prediction model in forecasting  the timeseries data is more advantageous.

The differential price coordination of the closedloop supply chain under asymmetric information

J4. 2009, 44(2):  60-64. 

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Based on  game theory, the differential price coordination mechanism of the  closedloop supply chain composed of one manufacturer and one retailer was studied. The results showed, that  coordination can be achieved under symmetric product cost information by setting a profit sharing coordination policy. Under asymmetric product cost information, if exogenous parameters satisfy some certain condition, only the abovementioned coordination policy can achieve the supply chain coordination. Otherwise, the retailer can set profit sharing proportion as the function of the manufacturers announced cost. This strategy can make the closedloop supply chain coordinative.

On Ringel duality of dual extension algebras of posets

J4. 2009, 44(2):  65-72. 

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Study on impulsive synchronization based on the  T S fuzzy model of preypredator systems

J4. 2009, 44(2):  73-78. 

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There are the characteristics of randomicity, fuzziness and impulsive phenomenon in the ecological system. Taking a three species selected preypredator system and preypredator with Holling functional response as an example, the TS fuzzy dynamical model and impulsive synchronization of the systems were proposed. The fuzzy impulsive synchronization controllers were designed based on Lyapunov theory. The problems of the impulsive synchronization and the stability were obtained. The scheme makes the species arrive at a new state, in which they can coexist and develop. The effectiveness of this scheme was tested by simulation.

A Kolmogorov’s inequality for gexpectation

J4. 2009, 44(2):  79-83. 

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The Coifman condition and the  balancing of a multiwavelet

J4. 2009, 44(2):  84-90. 

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Vertex distinguishing IEtotal chromatic numbers of  complete bipartite graph K5,n

J4. 2009, 44(2):  91-96. 

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Let G be a simple graph. An IEtotal coloring f of G refers to a coloring of the vertices and edges of G so that no two adjacent vertices receive the same color. Let C(u) be the set of colors of vertex u and edges incident to u under f. For an IEtotal coloring f of G using k colors, if C(u)≠C(v) for any two different vertices u and v of V(G), then f is called a kvertexdistinguishing IEtotalcoloring of G, or a kVDIET coloring of G for short. The minimum number of colors required for a VDIET coloring of G is denoted by χievt (G), and it is called the VDIET chromatic number of G. VDIET chromatic numbers for the complete bipartite graph K5,n (n≥6) were given.