To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem...To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.展开更多
In this paper,making use of upper and lower solutions,we first prove the existence of the solu tion for integral differential equation of Volterra type.Then applying the theory of differential in equalities obtained,u...In this paper,making use of upper and lower solutions,we first prove the existence of the solu tion for integral differential equation of Volterra type.Then applying the theory of differential in equalities obtained,under the appropriate assumptions,by constructing the special function of upper and lower solutions,we demonstrate the existence of the solution for singularly preturbed integral differential equation of Volterra type,and give the uniformly valid approximate estimation.展开更多
The structure of a microwave radiator used for medical purposes is described. The dyadic Green's function and the method are used to analyze this Kind of multimode rectangular medium-filled cavity. The distributio...The structure of a microwave radiator used for medical purposes is described. The dyadic Green's function and the method are used to analyze this Kind of multimode rectangular medium-filled cavity. The distribution of electromagnetic field intensity and the power density,as well as the temperature effect in the biological sample load are obtained.OPtimization of the size of cavity and the position of the input aperture have been performed with the computer to optimize the uniformity or microwave effect and the input VSWR.Necessary experiments were performed to compare the data obtained with theoretical analysis.展开更多
This paper is concerned with the generalzed global solution and its asymptotic properties for the initial value problem of the partial differential equationu t+u x 3 =F(u).
In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of ...In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of the functions at a given feasible point. The linearized procedure for differentiable nonlinear programming problems can be naturally generalized to the quasi differential case. As in classical case so called constraint qualifications have to be imposed on the constraint functions to guarantee that for a given local minimizer of the original problem the nullvector is an optimal solution of the corresponding 'quasilinearized' problem. In this paper, constraint qualifications for inequality constrained quasi differentiable programming problems of type min {f(x)|g(x)≤0} are considered, where f and g are qusidifferentiable functions in the sense of Demyanov. Various constraint qualifications for this problem are presented and a new one is proposed. The relations among these conditions are investigated. Moreover, a Wolf dual problem for this problem is introduced, and the corresponding dual theorems are given.展开更多
In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solu...In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.展开更多
In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.
Aim To investigate the boundary value problem for second order functional differentiai equations with impulses. Methods The fixed point principle was used to establish our results. Results and Conclusion The results o...Aim To investigate the boundary value problem for second order functional differentiai equations with impulses. Methods The fixed point principle was used to establish our results. Results and Conclusion The results of the esistence, the uniqueness and the continuous dependence on aprameter of soiutions of the boundary value problems for second order functional differential equations with impulses are obtained.展开更多
This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y(4) =f(t,y',y'',y'''),0t1,0ε1 with the nonlinear boundary conditions y(0)=y'(1)=0,p...This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y(4) =f(t,y',y'',y'''),0t1,0ε1 with the nonlinear boundary conditions y(0)=y'(1)=0,p(y''(0),y'''(0))=0,q(y''(1),y'''(1))=0 where f:[0,1]×R3→R is continuous,p,q:R2→R are continuous.Under certain conditions,by introducing an appropriate stretching transformation and constructing boundary layer corrective terms,an asymptotic expansion for the solution of the problem is obtained.And then the uniformly validity of solution is proved by using the differential inequalities.展开更多
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic beh...The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.展开更多
A class of fourth order singularly perturbed boundary value problems are studied. The existence of solution and its uniformly valid asymptotic estimation are obtained.
Increasing production and disposal of coal fly ash (CFA) is a matter of serious environment concern. However, CFA contains various beneficial metals and mineral matters whose demand is increasing in the industrializ...Increasing production and disposal of coal fly ash (CFA) is a matter of serious environment concern. However, CFA contains various beneficial metals and mineral matters whose demand is increasing in the industrialized world, while natural supplies are diminishing. Therefore, recovery of these potential resources from CFA can be an alternative way to save mineral resources, as well as to reduce the environmental burden of CFA disposal. There are numerous methods developed for the recovery of beneficial products from CFA. Based on the US patents and journal literatures, the present review describes the recovery status and technologies of major elements such as Al, Si, Fe and Ti, and trace elements such as V, Ga, Ge, Se, Li, Mo, U, Au, Ag, Pt groups and rare earth elements (REEs) and other beneficial products such as magnetic materials, cenospheres, and unburned carbon from CFA. It also highlights the recovery efficiency and drawbacks for their extraction, and suggests future research to develop satisfactory results in terms of selective recovery and purification.展开更多
Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a ...Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a Cauchyproblem for a system of ordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry.Complete classification theorems are obtained and some examples are taken to show the main reduction procedure.展开更多
Filtration is one of the most effective methods to remove suspended fine particles from air. In filtration processes,pressure drop of compact dust cake causes problems in efficiency and economy, which has received inc...Filtration is one of the most effective methods to remove suspended fine particles from air. In filtration processes,pressure drop of compact dust cake causes problems in efficiency and economy, which has received increasing attention and still remains challenging. In this study, we developed a novel technique to intensify the filtration of fine particles with efficient humidification. Two strategies for humidification, including ultrasonic atomization and steam humidification(controlling of ambient humidity), were employed and proved to be both effective. The regeneration frequency of the filter could be reduced by 55% with ultrasonic atomization, while steam humidification could lead to a 78% reduction in regeneration frequency. The effect of operating conditions on pressure drop and the mass loading during filtration were investigated. The dust cake showed a loose and porous structure with an optimized droplet-to-particle ratio. With the ratio of 1.53 and 0.0282, the maximum mass loading was 552 g·m-2upon the ultrasonic atomization and 720 g·m-2upon the steam humidification. The results show that humidification could slow down the increase of pressure drop during filtration and improve the efficiency of process.展开更多
We study the existence of solutions to the second order three-point boundary value problem:{x″(t)+f(t,x(t),x′(t))=0,t≠ti,△x(ti)=Ii(x(ti),x′(ti)),i=1,2,…,k,△x′(ti)=Ji(x(ti),x′(t)),i=1...We study the existence of solutions to the second order three-point boundary value problem:{x″(t)+f(t,x(t),x′(t))=0,t≠ti,△x(ti)=Ii(x(ti),x′(ti)),i=1,2,…,k,△x′(ti)=Ji(x(ti),x′(t)),i=1,2,…,k,x(0)=0=x(1)-αx(η),where 0〈η〈1,α∈R,and f:[0,1]×R×R→R,Ii:R×R→R,Ji:R×R→R(i=1,2,…,k)are continuous. Our results is new and different from previous results. In particular, we obtain the Green function of the problem, which makes the problem simpler.展开更多
文摘To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.
文摘In this paper,making use of upper and lower solutions,we first prove the existence of the solu tion for integral differential equation of Volterra type.Then applying the theory of differential in equalities obtained,under the appropriate assumptions,by constructing the special function of upper and lower solutions,we demonstrate the existence of the solution for singularly preturbed integral differential equation of Volterra type,and give the uniformly valid approximate estimation.
文摘The structure of a microwave radiator used for medical purposes is described. The dyadic Green's function and the method are used to analyze this Kind of multimode rectangular medium-filled cavity. The distribution of electromagnetic field intensity and the power density,as well as the temperature effect in the biological sample load are obtained.OPtimization of the size of cavity and the position of the input aperture have been performed with the computer to optimize the uniformity or microwave effect and the input VSWR.Necessary experiments were performed to compare the data obtained with theoretical analysis.
文摘This paper is concerned with the generalzed global solution and its asymptotic properties for the initial value problem of the partial differential equationu t+u x 3 =F(u).
文摘In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of the functions at a given feasible point. The linearized procedure for differentiable nonlinear programming problems can be naturally generalized to the quasi differential case. As in classical case so called constraint qualifications have to be imposed on the constraint functions to guarantee that for a given local minimizer of the original problem the nullvector is an optimal solution of the corresponding 'quasilinearized' problem. In this paper, constraint qualifications for inequality constrained quasi differentiable programming problems of type min {f(x)|g(x)≤0} are considered, where f and g are qusidifferentiable functions in the sense of Demyanov. Various constraint qualifications for this problem are presented and a new one is proposed. The relations among these conditions are investigated. Moreover, a Wolf dual problem for this problem is introduced, and the corresponding dual theorems are given.
基金Supported by the Natural Science Foundation of Zhejiang Provivce (102009)Supported by the Natural Foundation of Huzhou Teacher's College(200302)
文摘In this paper, a class of strongly nonlinear singular perturbed boundary value problems are coasidered by the theory of differential inequalities and the correction of boundary layer, under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.
文摘In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.
文摘Aim To investigate the boundary value problem for second order functional differentiai equations with impulses. Methods The fixed point principle was used to establish our results. Results and Conclusion The results of the esistence, the uniqueness and the continuous dependence on aprameter of soiutions of the boundary value problems for second order functional differential equations with impulses are obtained.
文摘This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y(4) =f(t,y',y'',y'''),0t1,0ε1 with the nonlinear boundary conditions y(0)=y'(1)=0,p(y''(0),y'''(0))=0,q(y''(1),y'''(1))=0 where f:[0,1]×R3→R is continuous,p,q:R2→R are continuous.Under certain conditions,by introducing an appropriate stretching transformation and constructing boundary layer corrective terms,an asymptotic expansion for the solution of the problem is obtained.And then the uniformly validity of solution is proved by using the differential inequalities.
文摘The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
文摘A class of fourth order singularly perturbed boundary value problems are studied. The existence of solution and its uniformly valid asymptotic estimation are obtained.
文摘Increasing production and disposal of coal fly ash (CFA) is a matter of serious environment concern. However, CFA contains various beneficial metals and mineral matters whose demand is increasing in the industrialized world, while natural supplies are diminishing. Therefore, recovery of these potential resources from CFA can be an alternative way to save mineral resources, as well as to reduce the environmental burden of CFA disposal. There are numerous methods developed for the recovery of beneficial products from CFA. Based on the US patents and journal literatures, the present review describes the recovery status and technologies of major elements such as Al, Si, Fe and Ti, and trace elements such as V, Ga, Ge, Se, Li, Mo, U, Au, Ag, Pt groups and rare earth elements (REEs) and other beneficial products such as magnetic materials, cenospheres, and unburned carbon from CFA. It also highlights the recovery efficiency and drawbacks for their extraction, and suggests future research to develop satisfactory results in terms of selective recovery and purification.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a Cauchyproblem for a system of ordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry.Complete classification theorems are obtained and some examples are taken to show the main reduction procedure.
基金Supported by the National High Technology Research and Development Program of China(863 Program)(No.2013AA065003)the National Natural Science Foundation of China(No.21276011)the Ph.D.Programs Foundation of Ministry of Education of China(200800100001)
文摘Filtration is one of the most effective methods to remove suspended fine particles from air. In filtration processes,pressure drop of compact dust cake causes problems in efficiency and economy, which has received increasing attention and still remains challenging. In this study, we developed a novel technique to intensify the filtration of fine particles with efficient humidification. Two strategies for humidification, including ultrasonic atomization and steam humidification(controlling of ambient humidity), were employed and proved to be both effective. The regeneration frequency of the filter could be reduced by 55% with ultrasonic atomization, while steam humidification could lead to a 78% reduction in regeneration frequency. The effect of operating conditions on pressure drop and the mass loading during filtration were investigated. The dust cake showed a loose and porous structure with an optimized droplet-to-particle ratio. With the ratio of 1.53 and 0.0282, the maximum mass loading was 552 g·m-2upon the ultrasonic atomization and 720 g·m-2upon the steam humidification. The results show that humidification could slow down the increase of pressure drop during filtration and improve the efficiency of process.
基金Supported by the National Natural Science Foundation of China(10371006)
文摘We study the existence of solutions to the second order three-point boundary value problem:{x″(t)+f(t,x(t),x′(t))=0,t≠ti,△x(ti)=Ii(x(ti),x′(ti)),i=1,2,…,k,△x′(ti)=Ji(x(ti),x′(t)),i=1,2,…,k,x(0)=0=x(1)-αx(η),where 0〈η〈1,α∈R,and f:[0,1]×R×R→R,Ii:R×R→R,Ji:R×R→R(i=1,2,…,k)are continuous. Our results is new and different from previous results. In particular, we obtain the Green function of the problem, which makes the problem simpler.