The Korteweg-de Vries equation with a forcing term is established by recent studies as a simple mathematicalmodel of describing the physics of a shallow layer of fluid subject to external forcing.In the present paper,...The Korteweg-de Vries equation with a forcing term is established by recent studies as a simple mathematicalmodel of describing the physics of a shallow layer of fluid subject to external forcing.In the present paper,we study theanalytic solutions to the KdV equation with forcing term by using Hirota's direct method.Several exact solutions aregiven as examples,from which one can see that the same type soliton solutions can be excited by different forced term.展开更多
To obtain a better Vinogradov's bound, assistant function with two or three zeros and all Dirichlet's characters has been evaluated. Assistant function g(X1,X2,X3,X4)with four zeros and all nonprincipal charac...To obtain a better Vinogradov's bound, assistant function with two or three zeros and all Dirichlet's characters has been evaluated. Assistant function g(X1,X2,X3,X4)with four zeros and all nonprincipal characters but X1X2X3X4 is constructed and evaluated in the paper. And the constant obtained is 8.395 511 841 994.展开更多
In this paper, we first consider the position restriction scheduling problems on a single machine. The problems have been solved in certain special cases, especially for those obtained by restricting the processing ti...In this paper, we first consider the position restriction scheduling problems on a single machine. The problems have been solved in certain special cases, especially for those obtained by restricting the processing time pj = 1. We introduce the bipartite matching algorithm to provide some polynomial-time algorithms to solve them. Then we further consider a problem on unrelated processors.展开更多
Efficiency and selectivity of hydrogenating depolymerization of the coal extract benzene-insoluble part over the heterogeneous Co–Mo/Al2O3 catalyst were assessed using a mathematical model. The analytical equations o...Efficiency and selectivity of hydrogenating depolymerization of the coal extract benzene-insoluble part over the heterogeneous Co–Mo/Al2O3 catalyst were assessed using a mathematical model. The analytical equations of the mathematical model were generated based on material balance incorporating the physico-chemical phenomena(reaction and diffusion) both in the autoclave and the catalyst grain. The equations offer the possibility for predicting changes of the reactants in the autoclave during the process and for determining the distribution of reactant concentrations in the grain as a function of its radius. The analytical equations of the model serve as the basis of the algorithm for assessing the influence of restrictive diffusion on the effectiveness and selectivity of the catalyst, and also for defining the optimal radii of the catalyst's pores to enable free transport of reactants in the grain interior.展开更多
In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetso...In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetsov(m ZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie's modified Riemann–Liouville sense.展开更多
The 2D Pauli equation with Hulthen potential for spin-1/2 particle in the presence of Aharonov-Bohm （AB） field is solved analytically, on the assumption that an effective approximation is used for the centrifugal te...The 2D Pauli equation with Hulthen potential for spin-1/2 particle in the presence of Aharonov-Bohm （AB） field is solved analytically, on the assumption that an effective approximation is used for the centrifugal term. Singular and regular solutions of the problem are obtained. It is shown that the AB field lifts the degeneracy of the energy levels. The range of the flux parameter for which singular solutions are allowed is modified compared to the pure AB case. When the screening parameter vanishes, it is shown that the obtained energy spectrum becomes the same as that of the Aharonov-Bohm Coulomb problem.展开更多
基金Supported by the GUCAS President Grant,the National Natural Science Foundation of China under Grant No.10701076
文摘The Korteweg-de Vries equation with a forcing term is established by recent studies as a simple mathematicalmodel of describing the physics of a shallow layer of fluid subject to external forcing.In the present paper,we study theanalytic solutions to the KdV equation with forcing term by using Hirota's direct method.Several exact solutions aregiven as examples,from which one can see that the same type soliton solutions can be excited by different forced term.
基金Supported by the National Natural Science Foundation of China(10171076)Supported by the Scientific and Technical Committee Foundation of Shanghai(03JC14027)
文摘To obtain a better Vinogradov's bound, assistant function with two or three zeros and all Dirichlet's characters has been evaluated. Assistant function g(X1,X2,X3,X4)with four zeros and all nonprincipal characters but X1X2X3X4 is constructed and evaluated in the paper. And the constant obtained is 8.395 511 841 994.
文摘In this paper, we first consider the position restriction scheduling problems on a single machine. The problems have been solved in certain special cases, especially for those obtained by restricting the processing time pj = 1. We introduce the bipartite matching algorithm to provide some polynomial-time algorithms to solve them. Then we further consider a problem on unrelated processors.
文摘Efficiency and selectivity of hydrogenating depolymerization of the coal extract benzene-insoluble part over the heterogeneous Co–Mo/Al2O3 catalyst were assessed using a mathematical model. The analytical equations of the mathematical model were generated based on material balance incorporating the physico-chemical phenomena(reaction and diffusion) both in the autoclave and the catalyst grain. The equations offer the possibility for predicting changes of the reactants in the autoclave during the process and for determining the distribution of reactant concentrations in the grain as a function of its radius. The analytical equations of the model serve as the basis of the algorithm for assessing the influence of restrictive diffusion on the effectiveness and selectivity of the catalyst, and also for defining the optimal radii of the catalyst's pores to enable free transport of reactants in the grain interior.
基金Supported by BRNS of Bhaba Atomic Research Centre,Mumbai under Department of Atomic Energy,Government of India vide under Grant No.2012/37P/54/BRNS/2382
文摘In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetsov(m ZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie's modified Riemann–Liouville sense.
基金Supported by the Algerian Ministry of Higher Education and Scientific Research(MESRS)
文摘The 2D Pauli equation with Hulthen potential for spin-1/2 particle in the presence of Aharonov-Bohm （AB） field is solved analytically, on the assumption that an effective approximation is used for the centrifugal term. Singular and regular solutions of the problem are obtained. It is shown that the AB field lifts the degeneracy of the energy levels. The range of the flux parameter for which singular solutions are allowed is modified compared to the pure AB case. When the screening parameter vanishes, it is shown that the obtained energy spectrum becomes the same as that of the Aharonov-Bohm Coulomb problem.
