In this paper we establish direct local and global approximation theorems for Baskakov type operators and Szasz - Mirakjan type operators, respectively.
This paper is devoted to study direct and converse approximation theorems of the generalized Bemstein operators Cn （f, sn,x） via so-called unified modulus ωφλ^2 （f,t）, 0 ≤ λ ≤1. We obtain main results as fol...This paper is devoted to study direct and converse approximation theorems of the generalized Bemstein operators Cn （f, sn,x） via so-called unified modulus ωφλ^2 （f,t）, 0 ≤ λ ≤1. We obtain main results as followsωφλ^2 （f,t）=O（t^α）←→｜Cn（f,sn,x）-f（x）｜=O（（n^-1/2δn^1-λ（x））^α）,where δn^2（x）=max{φ^2（x）,1/n} and 0〈α〈2.展开更多
The dust distribution law acting at the top of a blast fumace(BF)is of great significance for understanding gas flow distribution and mitigating the negative influence of dust particles on the accuracy and service lif...The dust distribution law acting at the top of a blast fumace(BF)is of great significance for understanding gas flow distribution and mitigating the negative influence of dust particles on the accuracy and service life of detection equipment.The harsh environment inside a BF makes it difficult to describe the dust disthibution.This paper adresses this problem by proposing a dust distribution k-Sε-u_(p)model based on interphase(gas-powder)coupling.The proposed model is coupled with a k-Sεmodel(which describes gas flow movement)and a u_(p)model(which depicts dust movement).First,the kinetic energy equation and turbulent dissipation rate equation in the k-Sεmodel are established based on the modeling theory and single Green-function two scale direct interaction approximation(SGF-TSDIA)theory.Second,a dust particle mnovement u_(p)model is built based on a force analysis of the dust and Newton's laws of motion.Finally,a coupling factor that descibes the interphase interaction is proposed,and the k-Sε-u_(p)model,with clear physical meaning.ligorous mathematical logic,and adequate generality,is dleveloped.Siumulation results and o-site verification show that the k-Sε-u_(p)model not only has high precision,but also reveals the aggregate distribution features of the dust,which are helpful in optimizing the installation position of the detection equipment and imnproving its accuracy and service life.展开更多
This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method. Using both methods it obtains the similarity reduction solutions an...This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method. Using both methods it obtains the similarity reduction solutions and similarity reduction equations of different orders, showing that the approximate homotopy direct method yields more general approximate similarity reductions than the approximate homotopy symmetry method. The homotopy series solutions to the generalized Kawahara equation are consequently derived.展开更多
There are some equivalence theorems on Baskakov Operators. In this paper, we make use of ω 2 φ λ (f;t) to give a new equivalence theorem which includes the existing results as its special cases.
The approximate direct reduction method is applied to the perturbed mKdV equation with weak fourth order dispersion and weak dissipation. The similarity reduction solutions of different orders conform to formal cohere...The approximate direct reduction method is applied to the perturbed mKdV equation with weak fourth order dispersion and weak dissipation. The similarity reduction solutions of different orders conform to formal coherence, accounting for infinite series reduction solutions to the original equation and general formulas of similarity reduction equations. Painleve Ⅱ type equations, hyperbolic secant and Jacobi elliptic function solutions are obtained for zeroorder similarity reduction equations. Higher order similarity reduction equations are linear variable coefficient ordinary differential equations.展开更多
In this paper,a model of a large-scale optimal power flow(OPF)under voltage grading and network partition and its algorithm is presented.Based on the principles of open loop operations,the node injecting current metho...In this paper,a model of a large-scale optimal power flow(OPF)under voltage grading and network partition and its algorithm is presented.Based on the principles of open loop operations,the node injecting current method is used to divide the large-scale power grid into voltage grading and district dividing structures.The power network is further divided into a high-voltage main network and several subnets according to voltage levels of 220 kV.The subnets are connected by means of boundary nodes,and the partition model is solved using the improved approximate Newton direction method,which achieves complete dynamic decoupling simply by exchanging boundary variables between the main network and the subnets.A largescale power grid thus is decomposed into many subnets,making the solution of the problem simpler and faster while helping to protect the information of individual subnets.The system is tested for correctness and effectiveness of the proposed model,and the results obtained are matched in real-time.Finally,the algorithm is seen to have good convergence while improving calculation speed.展开更多
文摘In this paper we establish direct local and global approximation theorems for Baskakov type operators and Szasz - Mirakjan type operators, respectively.
基金Supported by the Natural Science Foundation of China (No. 11271263, 11371258)
文摘This paper is devoted to study direct and converse approximation theorems of the generalized Bemstein operators Cn （f, sn,x） via so-called unified modulus ωφλ^2 （f,t）, 0 ≤ λ ≤1. We obtain main results as followsωφλ^2 （f,t）=O（t^α）←→｜Cn（f,sn,x）-f（x）｜=O（（n^-1/2δn^1-λ（x））^α）,where δn^2（x）=max{φ^2（x）,1/n} and 0〈α〈2.
基金supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(61621062)the National Major Scientific Research Equipment of China(61927803)+1 种基金the National Natural Science Foundation of China(61933015)National Natural Science Foundation for Young Scholars of China(61903325)。
文摘The dust distribution law acting at the top of a blast fumace(BF)is of great significance for understanding gas flow distribution and mitigating the negative influence of dust particles on the accuracy and service life of detection equipment.The harsh environment inside a BF makes it difficult to describe the dust disthibution.This paper adresses this problem by proposing a dust distribution k-Sε-u_(p)model based on interphase(gas-powder)coupling.The proposed model is coupled with a k-Sεmodel(which describes gas flow movement)and a u_(p)model(which depicts dust movement).First,the kinetic energy equation and turbulent dissipation rate equation in the k-Sεmodel are established based on the modeling theory and single Green-function two scale direct interaction approximation(SGF-TSDIA)theory.Second,a dust particle mnovement u_(p)model is built based on a force analysis of the dust and Newton's laws of motion.Finally,a coupling factor that descibes the interphase interaction is proposed,and the k-Sε-u_(p)model,with clear physical meaning.ligorous mathematical logic,and adequate generality,is dleveloped.Siumulation results and o-site verification show that the k-Sε-u_(p)model not only has high precision,but also reveals the aggregate distribution features of the dust,which are helpful in optimizing the installation position of the detection equipment and imnproving its accuracy and service life.
基金Project supported by the National Natural Science Foundations of China(Grant Nos.10735030,10475055,10675065 and 90503006)the National Basic Research Program of China(Grant No.2007CB814800)
文摘This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method. Using both methods it obtains the similarity reduction solutions and similarity reduction equations of different orders, showing that the approximate homotopy direct method yields more general approximate similarity reductions than the approximate homotopy symmetry method. The homotopy series solutions to the generalized Kawahara equation are consequently derived.
文摘There are some equivalence theorems on Baskakov Operators. In this paper, we make use of ω 2 φ λ (f;t) to give a new equivalence theorem which includes the existing results as its special cases.
基金supported by the National Natural Science Foundations of China (Grant Nos 10735030,10475055,10675065 and 90503006)National Basic Research Program of China (Grant No 2007CB814800)+2 种基金PCSIRT (Grant No IRT0734)the Research Fund of Postdoctoral of China (Grant No 20070410727)Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No 20070248120)
文摘The approximate direct reduction method is applied to the perturbed mKdV equation with weak fourth order dispersion and weak dissipation. The similarity reduction solutions of different orders conform to formal coherence, accounting for infinite series reduction solutions to the original equation and general formulas of similarity reduction equations. Painleve Ⅱ type equations, hyperbolic secant and Jacobi elliptic function solutions are obtained for zeroorder similarity reduction equations. Higher order similarity reduction equations are linear variable coefficient ordinary differential equations.
基金supported by National Basic Research Program of China(973 Program)under Grant 2013CB228205National Natural Science Foundation of China under Grant 51541707.
文摘In this paper,a model of a large-scale optimal power flow(OPF)under voltage grading and network partition and its algorithm is presented.Based on the principles of open loop operations,the node injecting current method is used to divide the large-scale power grid into voltage grading and district dividing structures.The power network is further divided into a high-voltage main network and several subnets according to voltage levels of 220 kV.The subnets are connected by means of boundary nodes,and the partition model is solved using the improved approximate Newton direction method,which achieves complete dynamic decoupling simply by exchanging boundary variables between the main network and the subnets.A largescale power grid thus is decomposed into many subnets,making the solution of the problem simpler and faster while helping to protect the information of individual subnets.The system is tested for correctness and effectiveness of the proposed model,and the results obtained are matched in real-time.Finally,the algorithm is seen to have good convergence while improving calculation speed.
