The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the...The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The （2＋1）-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples i11ustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries.展开更多
In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified...In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona- Mahoney （mBBM） equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions： amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional deriva- tives are described in the modified Riemann-Liouville sense.展开更多
Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some prop...Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some properties of meromorphic solutions, and we ob- tain some results, which are the improvements and extensions of some results in references. Examples show that our results are precise.展开更多
A new boundary extension technique based on the Lagrange interpolat- ing polynomial is proposed and used to solve the function approximation defined on an interval by a series of scaling Coiflet functions, where the c...A new boundary extension technique based on the Lagrange interpolat- ing polynomial is proposed and used to solve the function approximation defined on an interval by a series of scaling Coiflet functions, where the coefficients are used as the single-point samplings. The obtained approximation formula can exactly represent any polynomials defined on the interval with the order up to one third of the length of the compact support of the adopted Coiflet function. Based on the Galerkin method, a Coifiet-based solution procedure is established for general two-dimensional p^Laplacian equations, following which the equations can be discretized into a concise matrix form. As examples of applications, the proposed modified wavelet Galerkin method is applied to three typical p-Laplacian equations with strong nonlinearity. The numerical results justify the efficiency and accuracy of the method.展开更多
In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitar...In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitarywave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions,are obtained.展开更多
The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF me...The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.展开更多
In this paper, a new approach was introduced to estimate surface soil moisture using alternating polarization （AP） data of ad- vanced synthetic aperture radar （ASAR）. First, synthetic aperture radar （SAR） backsc...In this paper, a new approach was introduced to estimate surface soil moisture using alternating polarization （AP） data of ad- vanced synthetic aperture radar （ASAR）. First, synthetic aperture radar （SAR） backscattering characteristic of bare surface at C band was simulated using advanced integrated equation model （AIEM）, and four bare surface backscattering models with different polarization were established. In addition, with simultaneous equations of the for- mer four formulas, the surface roughness was eliminated, and models used to estimate soil moisture on bare surface were derived from simulated multipolarization and multiangle ASAR-AP data. Based on these, the best combination of polarization and incident angle was determined. Finally, soil moisture in the middle stream of the Heihe River Basin was estimated. The field measured data demonstrated that the proposed method was capable of retrieving surface soil moisture for both sparse grassland and homogeneous farmland area.展开更多
A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some resul...A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach.展开更多
Vessels with semi-closed tanks(i.e.,well docks)are widely applied in the military operation and maritime engineer-ing.The water is bound by the semi-closed floating tank and forced by both the incident waves and ship...Vessels with semi-closed tanks(i.e.,well docks)are widely applied in the military operation and maritime engineer-ing.The water is bound by the semi-closed floating tank and forced by both the incident waves and ship’s motions.The free surface oscillations inside the flooded well dock is thus distinctive and very complicated.So far,the natural modes of semi-closed floating tanks have not yet been studied.This paper investigates the characteristics of natural modes of a floating semi-closed tank by combining a mode-resolving model based on mild-slope equations and a hydrodynamic model based on computational fluid dynamics.Results show that the first three natural periods(i.e.,74,23.6,and 14 s)of the tank fall into the band of swell and infragravity waves and they could be triggered under certain circumstance.Multi-period free surface oscillations are observed inside the tank,including the longest natural period(i.e.,74 s),though the incident waves are monochromatic.A possible generation mechanism for the long-period mode is explained on the basis of liquid sloshing and harbor oscillations.Moreover,a long-period component with a period close to the natural mode of well dock is observed in the ship motions,which is generated by the interaction between the waves and ship.展开更多
The duality properties of string cosmology model with negative energy matter are investigated by means of renormalization group equation,the cosmological solutions with exotic matter coupling are obtained in D=d+1 dim...The duality properties of string cosmology model with negative energy matter are investigated by means of renormalization group equation,the cosmological solutions with exotic matter coupling are obtained in D=d+1 dimensional space-time.These inflation-power solutions can describe accelerated and decelerated process in the early universe,and the duality solutions can be generated through O(d,d) transformations.展开更多
In this article, we propose an alternative approach of the generalized and improved （G＇/G）-expansion method and build some new exact traveling wave solutions of three nonlinear evolution equations, namely the Boiti...In this article, we propose an alternative approach of the generalized and improved （G＇/G）-expansion method and build some new exact traveling wave solutions of three nonlinear evolution equations, namely the Boiti- Leon-Pempinelle equation, the Pochhammer-Chree equations and the Painleve integrable Burgers equation with free parameters. When the free parameters receive particular values, solitary wave solutions are constructed from the traveling waves. We use the Jacob/elliptic equation as an auxiliary equation in place of the second order linear equation. It is established that the proposed algorithm offers a further influential mathematical tool for constructing exact solutions of nonlinear evolution equations.展开更多
The object of this paper is to investigate the three-dimensional electro- magnetic scattering problems in a two-layered background medium. These problems have an important application in today＇s technology, such as t...The object of this paper is to investigate the three-dimensional electro- magnetic scattering problems in a two-layered background medium. These problems have an important application in today＇s technology, such as to detect objects that are buried in soil. Here, we model both the exterior impedance problem and the inhomogeneous medium problem in R3. We establish uniqueness and existence for the solution of the two scattering problems, respectively.展开更多
By using the continuation theorem of coincidence degree theory due to Mawhin and the new analytical method, we study the T-periodic solutions to a class of third order p-Laplacian equations with distributed delays as ...By using the continuation theorem of coincidence degree theory due to Mawhin and the new analytical method, we study the T-periodic solutions to a class of third order p-Laplacian equations with distributed delays as follows . Some new results for existence of T-periodic solutions to such equations are obtained.展开更多
This paper introduced characteristics of refractories and step of simulation. During simulation,firstly analyzed mechanism of technology; secondly described the mechanism as quadratic equation; thirdly designed and ex...This paper introduced characteristics of refractories and step of simulation. During simulation,firstly analyzed mechanism of technology; secondly described the mechanism as quadratic equation; thirdly designed and executed experiment; later made regression equation and optimization; then found technical conflict; finally analyzed and resolved the conflict. Doing repeatedly like this,resolved difficult problems.展开更多
Efficient optimization strategy of multibody systems is developed in this paper. Aug- mented Lagrange method is used to transform constrained optimal problem into unconstrained form firstly. Then methods based on seco...Efficient optimization strategy of multibody systems is developed in this paper. Aug- mented Lagrange method is used to transform constrained optimal problem into unconstrained form firstly. Then methods based on second order sensitivity are used to solve the unconstrained problem, where the sensitivity is solved by hybrid method. Generalized-α method and generalized-α projection method for the differential-algebraic equation, which shows more efficient properties with the lager time step, are presented to get state variables and adjoint variables during the optimization procedure. Numerical results validate the accuracy and efficiency of the methods is presented.展开更多
The authors analyze continuity equations with Stratonovich stochasticity,■ρ+divh[ρo(u(t,x)+∑_(i=1)^(N)a_(i)(x)w_(i)(t))]=0defined on a smooth closed Riemannian manifold M with metric h.The velocity field u is pert...The authors analyze continuity equations with Stratonovich stochasticity,■ρ+divh[ρo(u(t,x)+∑_(i=1)^(N)a_(i)(x)w_(i)(t))]=0defined on a smooth closed Riemannian manifold M with metric h.The velocity field u is perturbed by Gaussian noise terms Wi(t),:WN(t)driven by smooth spatially dependent vector fields a1(x),...,aN(x)on M.The velocity u belongs to L_(t)^(1)W_(x)^(1,2)with divh u bounded in Lf,for p>d+2,where d is the dimension of M(they do not assume div_(h) u∈L_(t,x)^(∞)).For carefully chosen noise vector fields ai(and the number N of them),they show that the initial-value problem is well-posed in the class of weak L^(2) solutions,although the problem can be ill-posed in the deterministic case because of concentration effects.The proof of this“regularization by noise”result is based on a L^(2) estimate,which is obtained by a duality method,and a weak compactness argument.展开更多
Based on the method deriving dissipative compact linear schemes ( DCS), novel high-order dissipative weighted compact nonlinear schemes (DWCNS) are developed. By Fourier analysis, the dissipative and dispersive featur...Based on the method deriving dissipative compact linear schemes ( DCS), novel high-order dissipative weighted compact nonlinear schemes (DWCNS) are developed. By Fourier analysis, the dissipative and dispersive features of DWCNS are discussed. In view of the modified wave number, the DWCNS are equivalent to the fifth-order upwind biased explicit schemes in smooth regions and the interpolations at cell-edges dominate the accuracy of DWCNS. Boundary and near boundary schemes are developed and the asymptotic stabilities of DWCNS on both uniform and stretching grids are analyzed. The multi-dimensional implementations for Euler and Navier-Stokes equations are discussed. Several numerical inviscid and viscous results are given which show the good performances of the DWCNS for discontinuities capturing, high accuracy for boundary layer resolutions, good convergent rates (the root-mean-square of residuals approaching machine zero for solutions with strong shocks) and especially the damping effect on the spurious oscillations which were found in the solutions obtained by TVD and ENO schemes.展开更多
Dengue fever is caused by the dengue virus and transmitted by Aedes mosquitoes.A promising avenue for eradicating the disease is to infect the wild aedes population with the bacterium Wolbachia driven by cytoplasmic i...Dengue fever is caused by the dengue virus and transmitted by Aedes mosquitoes.A promising avenue for eradicating the disease is to infect the wild aedes population with the bacterium Wolbachia driven by cytoplasmic incompatibility(CI).When releasing Wolbachia infected mosquitoes for population replacement,it is essential to not ignore the spatial inhomogeneity of wild mosquito distribution.In this paper,we develop a model of reaction-diffusion system to investigate the infection dynamics in natural areas,under the assumptions supported by recent experiments such as perfect maternal transmission and complete CI.We prove non-existence of inhomogeneous steady-states when one of the diffusion coefficients is sufficiently large,and classify local stability for constant steady states.It is seen that diffusion does not change the criteria for the local stabilities.Our major concern is to determine the minimum infection frequency above which Wolbachia can spread into the whole population of mosquitoes.We find that diffusion drives the minimum frequency slightly higher in general.However,the minimum remains zero when Wolbachia infection brings overwhelming fitness benefit.In the special case when the infection does not alter the longevity of mosquitoes but reduces the birth rate by half,diffusion has no impact on the minimum frequency.展开更多
In this paper, nonreflecting artificial boundary conditions are considered for an acoustic problem in three dimensions. With the technique of Fourier decomposition under the orthogonal basis of spherical harmonics, th...In this paper, nonreflecting artificial boundary conditions are considered for an acoustic problem in three dimensions. With the technique of Fourier decomposition under the orthogonal basis of spherical harmonics, three kinds of equivalent exact artificial boundary conditions are obtained on a spherical artificial boundary. A numerical test is presented to show the performance of the method.展开更多
This paper discusses the H∞ control problem for a class of linear stochastic systems driven by both Brownian motion and Poisson jumps. The authors give the basic theory about stabilities for such systems, including i...This paper discusses the H∞ control problem for a class of linear stochastic systems driven by both Brownian motion and Poisson jumps. The authors give the basic theory about stabilities for such systems, including internal stability and external stability, which enables to prove the bounded real lemma for the systems. By means of Riccati equations, infinite horizon linear stochastic state-feedback H∞ control design is also extended to such systems.展开更多
文摘The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The （2＋1）-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples i11ustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries.
文摘In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona- Mahoney （mBBM） equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions： amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional deriva- tives are described in the modified Riemann-Liouville sense.
基金supported by the National Natural Science Foundation of China(11171013)supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(16XNH117)
文摘Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some properties of meromorphic solutions, and we ob- tain some results, which are the improvements and extensions of some results in references. Examples show that our results are precise.
基金supported by the National Natural Science Foundation of China(Nos.11472119 and11421062)
文摘A new boundary extension technique based on the Lagrange interpolat- ing polynomial is proposed and used to solve the function approximation defined on an interval by a series of scaling Coiflet functions, where the coefficients are used as the single-point samplings. The obtained approximation formula can exactly represent any polynomials defined on the interval with the order up to one third of the length of the compact support of the adopted Coiflet function. Based on the Galerkin method, a Coifiet-based solution procedure is established for general two-dimensional p^Laplacian equations, following which the equations can be discretized into a concise matrix form. As examples of applications, the proposed modified wavelet Galerkin method is applied to three typical p-Laplacian equations with strong nonlinearity. The numerical results justify the efficiency and accuracy of the method.
基金The project supported by National Natural Science Foundation of China under Grant No. 1007201, the National Key Basic Research Development Project Program under Grant No. G1998030600 and Doctoral Foundation of China under Grant No. 98014119
文摘In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitarywave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions,are obtained.
文摘The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.
基金Supported by the Knowledge Innovation Program of Chinese Academy of Sciences(XMXX280722)Special Fund of China Institute of Water Resources and Hydropower Research(2011)Open Fund of State Key Laboratory of Remote Sensing Science(OFSLRSS201105)
文摘In this paper, a new approach was introduced to estimate surface soil moisture using alternating polarization （AP） data of ad- vanced synthetic aperture radar （ASAR）. First, synthetic aperture radar （SAR） backscattering characteristic of bare surface at C band was simulated using advanced integrated equation model （AIEM）, and four bare surface backscattering models with different polarization were established. In addition, with simultaneous equations of the for- mer four formulas, the surface roughness was eliminated, and models used to estimate soil moisture on bare surface were derived from simulated multipolarization and multiangle ASAR-AP data. Based on these, the best combination of polarization and incident angle was determined. Finally, soil moisture in the middle stream of the Heihe River Basin was estimated. The field measured data demonstrated that the proposed method was capable of retrieving surface soil moisture for both sparse grassland and homogeneous farmland area.
文摘A generalized Gauss-type quadrature formula is introduced, which assists in selection of collocation points in pseudospectral method for differential equations with two-point derivative boundary conditions. Some results on the related Jacobi interpolation are established. A pseudospectral scheme is proposed for the Kuramoto-Sivashisky equation. A skew symmetric decomposition is used for dealing with the nonlinear convection term. The stability and convergence of the proposed scheme are proved. The error estimates are obtained. Numerical results show the efficiency of this approach.
基金supported by the National Natural Science Foundation of China(Grant No.51979029)。
文摘Vessels with semi-closed tanks(i.e.,well docks)are widely applied in the military operation and maritime engineer-ing.The water is bound by the semi-closed floating tank and forced by both the incident waves and ship’s motions.The free surface oscillations inside the flooded well dock is thus distinctive and very complicated.So far,the natural modes of semi-closed floating tanks have not yet been studied.This paper investigates the characteristics of natural modes of a floating semi-closed tank by combining a mode-resolving model based on mild-slope equations and a hydrodynamic model based on computational fluid dynamics.Results show that the first three natural periods(i.e.,74,23.6,and 14 s)of the tank fall into the band of swell and infragravity waves and they could be triggered under certain circumstance.Multi-period free surface oscillations are observed inside the tank,including the longest natural period(i.e.,74 s),though the incident waves are monochromatic.A possible generation mechanism for the long-period mode is explained on the basis of liquid sloshing and harbor oscillations.Moreover,a long-period component with a period close to the natural mode of well dock is observed in the ship motions,which is generated by the interaction between the waves and ship.
基金Supported by Natural Science Foundation of Sichuan Education Committee under Grant No. 11ZA100
文摘The duality properties of string cosmology model with negative energy matter are investigated by means of renormalization group equation,the cosmological solutions with exotic matter coupling are obtained in D=d+1 dimensional space-time.These inflation-power solutions can describe accelerated and decelerated process in the early universe,and the duality solutions can be generated through O(d,d) transformations.
文摘In this article, we propose an alternative approach of the generalized and improved （G＇/G）-expansion method and build some new exact traveling wave solutions of three nonlinear evolution equations, namely the Boiti- Leon-Pempinelle equation, the Pochhammer-Chree equations and the Painleve integrable Burgers equation with free parameters. When the free parameters receive particular values, solitary wave solutions are constructed from the traveling waves. We use the Jacob/elliptic equation as an auxiliary equation in place of the second order linear equation. It is established that the proposed algorithm offers a further influential mathematical tool for constructing exact solutions of nonlinear evolution equations.
基金The NSF (10801046) of Chinathe Heilongjiang Education Committee Grant(11551362,11551364)the Heilongjiang University Grant(Hdtd2010-14)
文摘The object of this paper is to investigate the three-dimensional electro- magnetic scattering problems in a two-layered background medium. These problems have an important application in today＇s technology, such as to detect objects that are buried in soil. Here, we model both the exterior impedance problem and the inhomogeneous medium problem in R3. We establish uniqueness and existence for the solution of the two scattering problems, respectively.
基金Foundation item： Supported by the National Natural Science Foundation of China（ll07100t） Supported by the 211 Project of Anhui University（KJTD002B） Supported by the Natural Science Foundation of Anhui Province（t208085MAB）
文摘By using the continuation theorem of coincidence degree theory due to Mawhin and the new analytical method, we study the T-periodic solutions to a class of third order p-Laplacian equations with distributed delays as follows . Some new results for existence of T-periodic solutions to such equations are obtained.
基金funded by the Twelfth Five-year National Science and Technology Support Project(2013BAE03B01-01B)
文摘This paper introduced characteristics of refractories and step of simulation. During simulation,firstly analyzed mechanism of technology; secondly described the mechanism as quadratic equation; thirdly designed and executed experiment; later made regression equation and optimization; then found technical conflict; finally analyzed and resolved the conflict. Doing repeatedly like this,resolved difficult problems.
基金supported by the National Natural Science Foundation of China (11002075 and 10972110)
文摘Efficient optimization strategy of multibody systems is developed in this paper. Aug- mented Lagrange method is used to transform constrained optimal problem into unconstrained form firstly. Then methods based on second order sensitivity are used to solve the unconstrained problem, where the sensitivity is solved by hybrid method. Generalized-α method and generalized-α projection method for the differential-algebraic equation, which shows more efficient properties with the lager time step, are presented to get state variables and adjoint variables during the optimization procedure. Numerical results validate the accuracy and efficiency of the methods is presented.
基金supported by the Research Council of Norway through the projects Stochastic Conservation Laws (No. 250674)(in part) Waves and Nonlinear Phenomena (No. 250070)
文摘The authors analyze continuity equations with Stratonovich stochasticity,■ρ+divh[ρo(u(t,x)+∑_(i=1)^(N)a_(i)(x)w_(i)(t))]=0defined on a smooth closed Riemannian manifold M with metric h.The velocity field u is perturbed by Gaussian noise terms Wi(t),:WN(t)driven by smooth spatially dependent vector fields a1(x),...,aN(x)on M.The velocity u belongs to L_(t)^(1)W_(x)^(1,2)with divh u bounded in Lf,for p>d+2,where d is the dimension of M(they do not assume div_(h) u∈L_(t,x)^(∞)).For carefully chosen noise vector fields ai(and the number N of them),they show that the initial-value problem is well-posed in the class of weak L^(2) solutions,although the problem can be ill-posed in the deterministic case because of concentration effects.The proof of this“regularization by noise”result is based on a L^(2) estimate,which is obtained by a duality method,and a weak compactness argument.
基金This work was supported by the project of Basic Research on Frontier Problems in Fluid and Aerodynamics China and the National Natural Science Foundation of China (Grant No.19772072) .
文摘Based on the method deriving dissipative compact linear schemes ( DCS), novel high-order dissipative weighted compact nonlinear schemes (DWCNS) are developed. By Fourier analysis, the dissipative and dispersive features of DWCNS are discussed. In view of the modified wave number, the DWCNS are equivalent to the fifth-order upwind biased explicit schemes in smooth regions and the interpolations at cell-edges dominate the accuracy of DWCNS. Boundary and near boundary schemes are developed and the asymptotic stabilities of DWCNS on both uniform and stretching grids are analyzed. The multi-dimensional implementations for Euler and Navier-Stokes equations are discussed. Several numerical inviscid and viscous results are given which show the good performances of the DWCNS for discontinuities capturing, high accuracy for boundary layer resolutions, good convergent rates (the root-mean-square of residuals approaching machine zero for solutions with strong shocks) and especially the damping effect on the spurious oscillations which were found in the solutions obtained by TVD and ENO schemes.
基金supported by National Natural Science Foundation of China(GrantNos.11471085 and 91230104)Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT1226)+1 种基金Program for Yangcheng Scholars in Guangzhou(Grant No.12A003S)Natural Science Foundation of USA(Grant No.0531898)
文摘Dengue fever is caused by the dengue virus and transmitted by Aedes mosquitoes.A promising avenue for eradicating the disease is to infect the wild aedes population with the bacterium Wolbachia driven by cytoplasmic incompatibility(CI).When releasing Wolbachia infected mosquitoes for population replacement,it is essential to not ignore the spatial inhomogeneity of wild mosquito distribution.In this paper,we develop a model of reaction-diffusion system to investigate the infection dynamics in natural areas,under the assumptions supported by recent experiments such as perfect maternal transmission and complete CI.We prove non-existence of inhomogeneous steady-states when one of the diffusion coefficients is sufficiently large,and classify local stability for constant steady states.It is seen that diffusion does not change the criteria for the local stabilities.Our major concern is to determine the minimum infection frequency above which Wolbachia can spread into the whole population of mosquitoes.We find that diffusion drives the minimum frequency slightly higher in general.However,the minimum remains zero when Wolbachia infection brings overwhelming fitness benefit.In the special case when the infection does not alter the longevity of mosquitoes but reduces the birth rate by half,diffusion has no impact on the minimum frequency.
基金This work is supported partly by the Special Funds for Major State Basic Research Projects of China and the National Science Foundation of China.
文摘In this paper, nonreflecting artificial boundary conditions are considered for an acoustic problem in three dimensions. With the technique of Fourier decomposition under the orthogonal basis of spherical harmonics, three kinds of equivalent exact artificial boundary conditions are obtained on a spherical artificial boundary. A numerical test is presented to show the performance of the method.
基金supported by the National Natural Science Foundation of China under Grant Nos.60874032 and 70971079
文摘This paper discusses the H∞ control problem for a class of linear stochastic systems driven by both Brownian motion and Poisson jumps. The authors give the basic theory about stabilities for such systems, including internal stability and external stability, which enables to prove the bounded real lemma for the systems. By means of Riccati equations, infinite horizon linear stochastic state-feedback H∞ control design is also extended to such systems.
