We propose a new exactly solvable potential which is Formed by modified Kratzer potential plus a new ring-shaped potential η cot^2 θ/r^2 The solutions of the Dirac equation with equal scalar and vector ring-shaped m...We propose a new exactly solvable potential which is Formed by modified Kratzer potential plus a new ring-shaped potential η cot^2 θ/r^2 The solutions of the Dirac equation with equal scalar and vector ring-shaped modified Kratzer potential are found by using the Nikiforov-Uvarov method. The nonrelativistic limit of the energy spectrum has been discussed.展开更多
Under the condition of an equal mixing of vector and scalar potentials, exact solutions of bound states of theKlein-Gordon equation with pseudo-Coulomb potential plus a new ring-shaped potential are presented. Simulta...Under the condition of an equal mixing of vector and scalar potentials, exact solutions of bound states of theKlein-Gordon equation with pseudo-Coulomb potential plus a new ring-shaped potential are presented. Simultaneously,energy spectrum equations are also obtained. It is shown that the radial equation and angular wave functions areexpressed by confluent hypergeogetric and hypergeogetric functions respectively.展开更多
A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman tr...A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal eurvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.展开更多
Many by-products are generated in the process of oxidizing cyclohexene to produce 1,2-epoxycyclohexane by hydrogen peroxide,including cyclohexanol,cyclohexanone,etc.To obtain high-purity 1,2-epoxycyclohexane, the by-p...Many by-products are generated in the process of oxidizing cyclohexene to produce 1,2-epoxycyclohexane by hydrogen peroxide,including cyclohexanol,cyclohexanone,etc.To obtain high-purity 1,2-epoxycyclohexane, the by-products and unreacted cyclohexene must be removed through rectification,in which the vapor-liquid equilibrium(VLE)data of the system are needed.In this study,the VLE data of cyclohexene-cyclohexanol system were studied at 101.3 kPa using an improved EC-2 VLE still.The thermodynamic consistency of the data was examined by Herington's method.The results obtained were exemplary.The VLE data were correlated by the Wilson equation. The difference between the calculated values and the experimental data is minor,indicating that the VLE data are suitable for engineering design.展开更多
In this paper, under the generalized conservation condition of mass flux in a unbounded domain, we are concerned with the global existence and stability of a perturbed subsonic circulatory flow for the two-dimensional...In this paper, under the generalized conservation condition of mass flux in a unbounded domain, we are concerned with the global existence and stability of a perturbed subsonic circulatory flow for the two-dimensional steady Euler equation, which is assumed to be isentropic and irrotational. Such a problem can be reduced into a second order quasi-linear elliptic equation on the stream function in an exterior domain with a Dirichlet boundary value condition on the circular body and a stability condition at infinity. The key ingredient is establishing delicate weighted Hlder estimates to obtain the infinite behaviors of the flow under physical assumption.展开更多
文摘We propose a new exactly solvable potential which is Formed by modified Kratzer potential plus a new ring-shaped potential η cot^2 θ/r^2 The solutions of the Dirac equation with equal scalar and vector ring-shaped modified Kratzer potential are found by using the Nikiforov-Uvarov method. The nonrelativistic limit of the energy spectrum has been discussed.
基金Supported by National Natural Science Foundation of China under Grant No.10865003
文摘Under the condition of an equal mixing of vector and scalar potentials, exact solutions of bound states of theKlein-Gordon equation with pseudo-Coulomb potential plus a new ring-shaped potential are presented. Simultaneously,energy spectrum equations are also obtained. It is shown that the radial equation and angular wave functions areexpressed by confluent hypergeogetric and hypergeogetric functions respectively.
文摘A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal eurvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.
基金Supported by the Outstanding Personality Innovation Funds of Henan Province(0121001900)
文摘Many by-products are generated in the process of oxidizing cyclohexene to produce 1,2-epoxycyclohexane by hydrogen peroxide,including cyclohexanol,cyclohexanone,etc.To obtain high-purity 1,2-epoxycyclohexane, the by-products and unreacted cyclohexene must be removed through rectification,in which the vapor-liquid equilibrium(VLE)data of the system are needed.In this study,the VLE data of cyclohexene-cyclohexanol system were studied at 101.3 kPa using an improved EC-2 VLE still.The thermodynamic consistency of the data was examined by Herington's method.The results obtained were exemplary.The VLE data were correlated by the Wilson equation. The difference between the calculated values and the experimental data is minor,indicating that the VLE data are suitable for engineering design.
基金supported by National Natural Science Foundation of China (Grant Nos.10871096, 11001122)China Postdoctoral Science Foundation (Grant No. 200904501112)Jiangsu Planned Projects for Postdoctoral Research Funds (Grant No. 0901046C)
文摘In this paper, under the generalized conservation condition of mass flux in a unbounded domain, we are concerned with the global existence and stability of a perturbed subsonic circulatory flow for the two-dimensional steady Euler equation, which is assumed to be isentropic and irrotational. Such a problem can be reduced into a second order quasi-linear elliptic equation on the stream function in an exterior domain with a Dirichlet boundary value condition on the circular body and a stability condition at infinity. The key ingredient is establishing delicate weighted Hlder estimates to obtain the infinite behaviors of the flow under physical assumption.
