New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bendin...New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bending stresses of circular plates with movable and immovable edges under uniform pressures or a central point load.The shortcomings existing in the earlier analysis by the DQ method have been overcome by a new approach in applying the boundary conditions. The accuracy and the efficiency of the newly developed method for solving nonlinear problems are demonstrated.展开更多
Wet etching characteristics of cubic GaN (c GaN) thin films grown on GaAs(001) by metalorganic vapor phase epitaxy (MOVPE) are investigated.The samples are etched in HCl,H 3PO 4,KOH aqueous solutions,and molten KOH...Wet etching characteristics of cubic GaN (c GaN) thin films grown on GaAs(001) by metalorganic vapor phase epitaxy (MOVPE) are investigated.The samples are etched in HCl,H 3PO 4,KOH aqueous solutions,and molten KOH at temperatures in the range of 90～300℃.It is found that different solution produces different etch figure on the surfaces of a sample.KOH based solutions produce rectangular pits rather than square pits.The etch pits elongate in 1 0] direction,indicating asymmetric etching behavior in the two orthogonal <110> directions.An explanation based on relative reactivity of the various crystallographic planes is employed to interpret qualitatively the asymmetric etching behavior.In addition,it is found that KOH aqueous solution would be more suitable than molten KOH and the two acids for the evaluation of stacking faults in c GaN epilayers. direction,indicating asymmetric etching behavior in the two orthogonal <110> directions.An explanation based on relative reactivity of the various crystallographic planes is employed to interpret qualitatively the asymmetric etching behavior.In addition,it is found that KOH aqueous solution would be more suitable than molten KOH and the two acids for the evaluation of stacking faults in c GaN epilayers.展开更多
With the rural concealed communication cable as the study object, the shielding effectiveness of different slot shapes was analyzed by using LBEM （linear boundary element method）. The engineering example results sho...With the rural concealed communication cable as the study object, the shielding effectiveness of different slot shapes was analyzed by using LBEM （linear boundary element method）. The engineering example results showed that for twocore shielded cable, the coupling capacitance of trapezoid slots （asymmetric and symmetric） changed the most, followed by rectangular slots （asymmetric and symmetric）, and the changes of wedge slots were the smallest, but the change tenden- cies were consistent. In addition, with the increase of slot width of different slots, the coupling capacitance of tow-cored shielded cable showed small change.展开更多
Two types of symmetry of a generalized Zakharov-Kuznetsov equation are obtained via a direct symmetry method. By selecting suitable parameters occurring in the symmetries, we also find some symmetry reductions and new...Two types of symmetry of a generalized Zakharov-Kuznetsov equation are obtained via a direct symmetry method. By selecting suitable parameters occurring in the symmetries, we also find some symmetry reductions and new explicit solutions of the generalized Zakharov-Kuznetsov equation.展开更多
Applying the classical Lie symmetry method to the （29-1）-dimensional resonant Davey-Stewartson system introduced by Tang IX. Y. Tang et al., Chaos, Solitons and Practals 42 （2007） 2707], a more general infinite di...Applying the classical Lie symmetry method to the （29-1）-dimensional resonant Davey-Stewartson system introduced by Tang IX. Y. Tang et al., Chaos, Solitons and Practals 42 （2007） 2707], a more general infinite dimensional Lie symmetry with Kac-Moody-Virasoro type Lie algebra is obtained, which involves four arbitrary functions of t. Alternatively, by a simple direct method, the full symmetry groups including Lie symmetry group and non-Lie symmetry group are gained straightly. In this way, the related Lie algebra can be easily found by a more simple limiting procedure. Lastly, via solving the characteristic equations, three types of the general similar reductions are derived.展开更多
A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known （2＋1）-dimensional asymmetric Nizhnik-Novikov-Ves...A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only speciai cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches.展开更多
In this paper, we investigate symmetries of the new （4＋1）-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symm...In this paper, we investigate symmetries of the new （4＋1）-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symmetries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries wave solutions and other solutions of the Fokas equation. and some constructive methods to get some doubly periodic In particular, some solitary wave solutions are also given.展开更多
In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov- Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal sys...In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov- Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases.展开更多
In this paper, the problem of determining the largest possible set of symmetries for an important nonlinear dynamical system： the two-dimensional damped Kuramoto-Sivashinsky （（21）） DKS ） equation is studied. By ...In this paper, the problem of determining the largest possible set of symmetries for an important nonlinear dynamical system： the two-dimensional damped Kuramoto-Sivashinsky （（21）） DKS ） equation is studied. By applying the basic Lie symmetry method for the （217）） DKS equation, the classical Lie point symmetry operators are obtained. Also, the optimal system of one-dimensional subalgebras of the equation is constructed. The Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries are obtained. The nonclassicaJ symmetries of the （2D） DKS equation are also investigated.展开更多
文摘New developments have been made on the applications of the differential quadrature(DQ)method to analysis of structural problems recently.The method is used to obtain solutions of large deflections, membrane and bending stresses of circular plates with movable and immovable edges under uniform pressures or a central point load.The shortcomings existing in the earlier analysis by the DQ method have been overcome by a new approach in applying the boundary conditions. The accuracy and the efficiency of the newly developed method for solving nonlinear problems are demonstrated.
文摘Wet etching characteristics of cubic GaN (c GaN) thin films grown on GaAs(001) by metalorganic vapor phase epitaxy (MOVPE) are investigated.The samples are etched in HCl,H 3PO 4,KOH aqueous solutions,and molten KOH at temperatures in the range of 90～300℃.It is found that different solution produces different etch figure on the surfaces of a sample.KOH based solutions produce rectangular pits rather than square pits.The etch pits elongate in 1 0] direction,indicating asymmetric etching behavior in the two orthogonal <110> directions.An explanation based on relative reactivity of the various crystallographic planes is employed to interpret qualitatively the asymmetric etching behavior.In addition,it is found that KOH aqueous solution would be more suitable than molten KOH and the two acids for the evaluation of stacking faults in c GaN epilayers. direction,indicating asymmetric etching behavior in the two orthogonal <110> directions.An explanation based on relative reactivity of the various crystallographic planes is employed to interpret qualitatively the asymmetric etching behavior.In addition,it is found that KOH aqueous solution would be more suitable than molten KOH and the two acids for the evaluation of stacking faults in c GaN epilayers.
基金Supported by the Science and Technology Program of the Education Department of Shaanxi Provincial Government(09JK378)the Key Scientific Research Fund of Shaanxi University of Technology(SLGKY12-02)~~
文摘With the rural concealed communication cable as the study object, the shielding effectiveness of different slot shapes was analyzed by using LBEM （linear boundary element method）. The engineering example results showed that for twocore shielded cable, the coupling capacitance of trapezoid slots （asymmetric and symmetric） changed the most, followed by rectangular slots （asymmetric and symmetric）, and the changes of wedge slots were the smallest, but the change tenden- cies were consistent. In addition, with the increase of slot width of different slots, the coupling capacitance of tow-cored shielded cable showed small change.
基金The project supported by Natural Science Foundation of Shandong Province of China under Grant 2004 zx 16The authors would like to thank professor Bai Cheng-Lin and the referees for their valuable advices.
文摘Two types of symmetry of a generalized Zakharov-Kuznetsov equation are obtained via a direct symmetry method. By selecting suitable parameters occurring in the symmetries, we also find some symmetry reductions and new explicit solutions of the generalized Zakharov-Kuznetsov equation.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10735030 and 11075055Shanghai Leading Academic Discipline Project under Grant No.B412Program for Changjiang Scholars and Innovative Research Team in University(IRT0734)
文摘Applying the classical Lie symmetry method to the （29-1）-dimensional resonant Davey-Stewartson system introduced by Tang IX. Y. Tang et al., Chaos, Solitons and Practals 42 （2007） 2707], a more general infinite dimensional Lie symmetry with Kac-Moody-Virasoro type Lie algebra is obtained, which involves four arbitrary functions of t. Alternatively, by a simple direct method, the full symmetry groups including Lie symmetry group and non-Lie symmetry group are gained straightly. In this way, the related Lie algebra can be easily found by a more simple limiting procedure. Lastly, via solving the characteristic equations, three types of the general similar reductions are derived.
基金The project supported by the National 0utstanding Youth Foundation of China under Grant No. 19925522 and the National Natural Science Foundation of China under Grant Nos. 90203001, 10475055. The authors are in debt to thank helpful discussions with Drs. X.Y. Tang, C.L. Chen, Y. Chen, H.C. Hu, X.M. Qian, B. Tong, and W.R. Cai.
文摘A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only speciai cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches.
基金supported by the National Natural Science Foundation of China under Grant No.60821002the National Key Basic Research Program of China under Grant No.2004CB318000
文摘In this paper, we investigate symmetries of the new （4＋1）-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symmetries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries wave solutions and other solutions of the Fokas equation. and some constructive methods to get some doubly periodic In particular, some solitary wave solutions are also given.
文摘In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov- Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases.
文摘In this paper, the problem of determining the largest possible set of symmetries for an important nonlinear dynamical system： the two-dimensional damped Kuramoto-Sivashinsky （（21）） DKS ） equation is studied. By applying the basic Lie symmetry method for the （217）） DKS equation, the classical Lie point symmetry operators are obtained. Also, the optimal system of one-dimensional subalgebras of the equation is constructed. The Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries are obtained. The nonclassicaJ symmetries of the （2D） DKS equation are also investigated.
